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Investigations into the use of continuous shear wave measurements in geotechnical engineering Styler, Mark Anthony 2014

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Investigations into the use of continuous shearwave measurements in geotechnical engineeringbyMark Anthony StylerB.Sc. Computer Engineering, Purdue University, 2003M.A.Sc. Civil Engineering, University of Florida, 2006a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoralstudies(Civil Engineering)The University Of British Columbia(Vancouver)October 2014c© Mark Anthony Styler, 2014AbstractThe research presented within this thesis covers the development of a meansto continuously monitor shear waves in a laboratory triaxial apparatus anddown-hole during seismic cone penetration. This work resulted from aninvestigation of ageing of Fraser River Sand using a bender element triaxialapparatus.Shear wave propagation times from bender elements were interpretedusing published time domain and frequency domain techniques. These tech-niques provided similar results, but the variability exceeded the effect ofageing. The frequency domain and time domain techniques had differentshortcomings. The two techniques could be combined to converge on asingle frequency-dependent propagation time that was independent of thetrigger signal waveform. This contribution was capable of resolving the smallincrease in shear wave velocity with age duration.The frequency domain component of the combined bender element tech-nique could run continuously during an experiment. With this further con-tribution, it was possible to track the change in shear wave propagation timethroughout an experiment. The continuous bender element testing was notobserved to influence the effect of ageing.It was found that in Fraser River Sand ageing had a small effect on theshear wave velocity, no effect on the ultimate strength, and a significant effecton the shear stiffness over the intermediate small-strain range (observed from0.01 to 1%). The normalized shear stiffness curve shifts to larger strains andbecomes more brittle with ageing.The concepts of the developed continuous bender element method areiinot restricted to this equipment or even to just bender element testing.The continuous bender element method was adapted to down-hole seismictesting in the field. This contribution resulted in a continuous profile of theshear wave velocity during seismic cone penetration testing that is obtainedwithout stopping the cone penetration.The developments in this thesis provide a continuous measure of theshear wave velocity through a laboratory experiment and a continuous profilewith down-hole penetration depth, i.e. the shear wave velocity is measuredevery time the other parameters are taken.iiiPrefaceThis dissertation is based mostly on original work by the author M.A. Styler.My contributions included re-developing the laboratory equipment, per-forming the laboratory experiments, developing and investigating new tech-niques in the laboratory, and analysis of the results. The bender elementequipment was constructed and installed by Scott Jackson. The workedpresented in Chapter 6 combined my laboratory program with selected ex-perimental results from T.A. Shozen and K. Lam, two previous graduatestudents at the University of British Columbia. For the work in Chapter 7,I specified the requirements for the perpetual source testing, but the equip-ment was constructed by ConeTec Investigations. I was responsible for thein-situ testing program and analysis of the results.Chapter 4 was adapted for publication in the ASTM Geotechnical Test-ing Journal [Styler, M.A., and Howie, J.A., 2013, “Measuring the phasevelocity with bender elements by combining time and frequency domain ap-proaches,” ASTM Geotechnical Testing Journal, Vol. 36, No. 5]. Chapter 5was adapted for publication in the ASTM Geotechnical Testing Journal[Styler, M.A., and Howie, J.A., 2014, “Continuous monitoring of BenderElement shear wave velocities in triaxial specimens of Fraser River Sand,”ASTM Geotechnical Testing Journal, Vol. 37, No. 2, pp. 218-229]. The re-sults presented in Chapter 7 have also been used in three conference papers:at GeoManitoba [Styler, M.A., Howie, J.A., Woeller, D., 2012, “PerpetualSource Seismic Piezocone Penetration Testing: A new method for down-holeshear wave velocity profiling,” GeoManitoba, Winnipeg, Manitoba, Septem-ber 2012], at GeoMontreal [Styler, M.A., Howie, J.A., Woeller, D., 2013,iv“Measuring down-hole shear waves from a vibrating perpetual source dur-ing Cone Penetration Testing,” GeoMontreal, Montreal, Quebec, Septem-ber 2013], and at CPT’14 [Styler, M.A., Howie, J.A., Sharp, J.T., 2014,“Perpetual source SCPTu: Signal stacking shear waves during continuouspenetration,” CPT 14, Las Vegas, NV.].vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . .xxxiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . 52 Measurement of soil stiffness . . . . . . . . . . . . . . . . . . 72.1 Triaxial testing . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.1 Local versus external sensors . . . . . . . . . . . . . . 92.1.2 Systematic error corrections for external sensor mea-surements . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.3 Previous UBC triaxial testing research on ageing ofFraser River Sand . . . . . . . . . . . . . . . . . . . . 112.2 Laboratory measurement of VS by bender element testing . . 122.2.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 Series and Parallel type bender elements . . . . . . . . 17vi2.2.3 Signal conditioning . . . . . . . . . . . . . . . . . . . . 192.2.4 Near field effect . . . . . . . . . . . . . . . . . . . . . . 202.2.5 Sample size effects . . . . . . . . . . . . . . . . . . . . 222.2.6 Classification of observed bender element response sig-nals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2.7 Interpreting VS in the time domain . . . . . . . . . . . 272.2.8 Interpreting VS in the frequency domain . . . . . . . . 332.2.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 392.3 Factors influencing shear wave propagation in soil . . . . . . . 402.3.1 Saturation . . . . . . . . . . . . . . . . . . . . . . . . . 412.3.2 Micro-mechanical G0 characterization . . . . . . . . . 422.3.3 Anisotropic effective stress state . . . . . . . . . . . . 452.3.4 Age and Stiffness . . . . . . . . . . . . . . . . . . . . . 462.3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . 502.4 Stiffness degradation with strain . . . . . . . . . . . . . . . . 502.5 Proposed research . . . . . . . . . . . . . . . . . . . . . . . . 543 Equipment, materials, and initial results . . . . . . . . . . . 563.1 Test programme . . . . . . . . . . . . . . . . . . . . . . . . . 573.2 Material tested . . . . . . . . . . . . . . . . . . . . . . . . . . 593.2.1 Fraser River Sand sample properties . . . . . . . . . . 593.2.2 Specimen reconstitution . . . . . . . . . . . . . . . . . 613.3 Improved triaxial apparatus . . . . . . . . . . . . . . . . . . . 623.3.1 Improved stress path control . . . . . . . . . . . . . . 643.3.2 Addition of bender elements . . . . . . . . . . . . . . . 653.4 Confirmation testing . . . . . . . . . . . . . . . . . . . . . . . 693.4.1 Comparing to previous triaxial results . . . . . . . . . 693.4.2 Evaluation of measurement uncertainty . . . . . . . . 733.4.3 Initial bender element testing and interpretation . . . 773.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834 Development of a combined time and frequency domainbender element interpretation method . . . . . . . . . . . . 84vii4.1 Proposed method . . . . . . . . . . . . . . . . . . . . . . . . . 854.2 Validation using simulated bender element signals . . . . . . 864.3 Experimental demonstration . . . . . . . . . . . . . . . . . . . 924.4 Observing the effect of ageing on VS . . . . . . . . . . . . . . 994.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015 Development of a continuous bender element phase veloc-ity monitoring method . . . . . . . . . . . . . . . . . . . . . . 1045.1 Continuous monitoring method . . . . . . . . . . . . . . . . . 1055.2 Experimental demonstration . . . . . . . . . . . . . . . . . . . 1065.3 Interpretation challenges . . . . . . . . . . . . . . . . . . . . . 1165.4 Evaluation of bender element induced disturbance . . . . . . 1225.5 G0 during ageing of Fraser River Sand . . . . . . . . . . . . . 1255.6 Calibration of G0 equation for Fraser River Sand . . . . . . . 1275.6.1 Evaluation of calibrated equation . . . . . . . . . . . . 1295.6.2 Comparing to other empirical G0 equations for FraserRiver Sand . . . . . . . . . . . . . . . . . . . . . . . . 1315.6.3 Comparing effect of age on G0 to calibrated G0 equation1335.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336 Characterizing normalized stiffness degradation curves inthe laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.1 Consolidation of Fraser River Sand specimens . . . . . . . . . 1386.2 Developed creep strains during ageing . . . . . . . . . . . . . 1396.3 Secant stiffness during shearing . . . . . . . . . . . . . . . . . 1406.4 Normalizing Gsec degradation curves with G0 . . . . . . . . . 1466.5 Factors influencing Gsec/G0 degradation curves . . . . . . . . 1506.5.1 Effect of shear stress path . . . . . . . . . . . . . . . . 1506.5.2 Effect of initial stress ratio . . . . . . . . . . . . . . . 1516.5.3 Effect of reconstituted specimen age . . . . . . . . . . 1546.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1576.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157viii7 Development of Perpetual Source SCPTu . . . . . . . . . . 1607.1 Existing down-hole in-situ VS measurements . . . . . . . . . . 1637.1.1 Conventional SCPTu . . . . . . . . . . . . . . . . . . . 1637.1.2 Continuous SCPTu . . . . . . . . . . . . . . . . . . . . 1647.2 Perpetual source method . . . . . . . . . . . . . . . . . . . . . 1657.2.1 Perpetual source . . . . . . . . . . . . . . . . . . . . . 1657.2.2 True interval cone . . . . . . . . . . . . . . . . . . . . 1667.2.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 1687.2.4 Interpretation of collected signals for VS . . . . . . . . 1687.3 Field testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1697.3.1 PS-SCPTu-01: Feasibility test . . . . . . . . . . . . . . 1707.3.2 PS-SCPTu-02: Concurrent hammer testing . . . . . . 1757.3.3 PS-SCPTu-03: Pseudo Interval . . . . . . . . . . . . . 1817.3.4 Comparing to conventional pseudo-interval VS . . . . 1887.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1897.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1908 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198A Triaxial apparatus preparation . . . . . . . . . . . . . . . . . 211A.1 Sensor calibrations . . . . . . . . . . . . . . . . . . . . . . . . 212A.2 Apparatus constants . . . . . . . . . . . . . . . . . . . . . . . 214A.3 Systematic error corrections . . . . . . . . . . . . . . . . . . . 217B Triaxial testing procedure . . . . . . . . . . . . . . . . . . . . 223B.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . 223B.2 Specimen reconstitution procedure . . . . . . . . . . . . . . . 224B.3 Triaxial testing procedure . . . . . . . . . . . . . . . . . . . . 228C Triaxial data reduction . . . . . . . . . . . . . . . . . . . . . . 231ixD Triaxial Results . . . . . . . . . . . . . . . . . . . . . . . . . . 236D.1 Results from this study . . . . . . . . . . . . . . . . . . . . . 236D.1.1 Summarized creep strains . . . . . . . . . . . . . . . . 236D.1.2 Triaxial results . . . . . . . . . . . . . . . . . . . . . . 239D.2 Results from Lam (2003) . . . . . . . . . . . . . . . . . . . . . 298D.3 Results from Shozen (2001) . . . . . . . . . . . . . . . . . . . 339xList of TablesTable 2.1 Type 1: clear first major pulse, first arrival is easy toselect, simplest to interpret, least common to encounter(Brignoli et al., 1996) . . . . . . . . . . . . . . . . . . . 26Table 2.2 Type 2: apparent near field distortion, the arrival is thefirst strong pulse with correct polarity (Brignoli et al.,1996) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Table 2.3 Type 3: a small amplitude cycle prior to the main shearpulse (Brignoli et al., 1996), selected arrival times areinconsistent . . . . . . . . . . . . . . . . . . . . . . . . . 28Table 2.4 Experimental investigations into factors influencing theageing effect on G0 . . . . . . . . . . . . . . . . . . . . . 49Table 3.1 Experimental details . . . . . . . . . . . . . . . . . . . . 59Table 3.2 Intrinsic properties of Fraser River Sand sample, val-ues reported by Shozen (2001) and Lam (2003) are inparentheses . . . . . . . . . . . . . . . . . . . . . . . . . 60Table 3.3 Reproducing triaxial results from previous investiga-tions from specimens aged for 100 minutes and shearedalong a conventional stress path . . . . . . . . . . . . . 69Table 3.4 Calibration summary table . . . . . . . . . . . . . . . . 74Table 3.5 Sources of error in the measured secant shear modulusfrom 100,000 Monte Carlo simulations for Specimen 245 77xiTable 4.1 Measured phase offsets at four different frequencies forsaturated Fraser River Sand Specimen 016 at 159.6 kPa,79.2 kPa, note that the phase offset, θo, is approxi-mately constant and independent of the input frequency 96Table 4.2 Ten different bender element results at similar stressand void conditions for saturated Fraser River Sand . . 96Table 5.1 Measured absolute phase shifts, phase offsets, and phasevelocities for a loose saturated drained specimens ofFraser River Sand Specimen 040 . . . . . . . . . . . . . 113Table 5.2 Experimental program and specimen properties . . . . . 122Table 5.3 Calculated NG factors(Equation 2.10) for continuouslymonitored bender element tests . . . . . . . . . . . . . 128Table 5.4 Comparing empirical and measured G0 (at 7.15 kHz)during ageing of Specimen 040 . . . . . . . . . . . . . . 134Table 6.1 Specimen variables for Figure 6.7, void ratios and G0measured at end of ageing . . . . . . . . . . . . . . . . . 149Table 6.2 Effect of stress path on curvature(a) and reference strain(εqr)for a hyperbolic model of the normalized secant stiffnesscurve Equation 2.11 from loose specimens consolidatedat a stress ratio of 2.0 up to σ′r=100 kPa and aged for100 minutes . . . . . . . . . . . . . . . . . . . . . . . . . 151Table 6.3 Effect of stress ratio on curvature(a) and reference strain(εqr)for a hyperbolic model of the normalized secant stiffnesscurve Equation 2.11 from loose specimens consolidatedand aged for 100 minutes and sheared along conven-tional stress paths . . . . . . . . . . . . . . . . . . . . . 153Table 6.4 Effect of age on curvature(a) and reference strain(εqr)for a hyperbolic model of the normalized secant stiffnesscurve Equation 2.11 from loose specimens sheared alonga conventional stress path from a stress ratio of 2.0 . . . 155Table A.1 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 221xiiTable D.1 Developed axial creep strains (%) for loose specimenswith σ′r = 100 kPa . . . . . . . . . . . . . . . . . . . . . 238Table D.2 Developed volumetric (%) creep strains for loose speci-mens with σ′r = 100 kPa . . . . . . . . . . . . . . . . . . 238Table D.3 Developed creep strains (%) per log-cycle of age timefor loose specimens with σ′r = 100 kPa . . . . . . . . . . 238xiiiList of FiguresFigure 1.1 Definition of secant and tangent shear stiffness on astress-strain curve . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Conceptual non-linear equivalent elastic shear stiffnessbehaviour for soils, underlying curve adapted from Atkin-son (2000) with referenced annotations . . . . . . . . . 3Figure 1.3 Scatter of G0 = ρV 2S in specimens of Toyoura sand un-der hydrostatic consolidation in an international paral-lel bender element test (Yamashita et al., 2009). Usedwith permission from Satoshi Yamashita. This materialmay be downloaded for personal use only. . . . . . . . . 4Figure 2.1 Photographs of a a bender element . . . . . . . . . . . 13Figure 2.2 Published bender element installation details. Reprinted,with permission, from Geotechnical Testing Journal,copyright ASTM International, 100 Barr Harbor Drive,West Conshohocken, PA 19428. . . . . . . . . . . . . . . 16Figure 2.3 Piezoceramic parallel type bender trigger element . . . 18Figure 2.4 Observed near field distortion in a 3D numerical modelusing linear elastic constitutive elements with absorbinglateral boundaries, adapted from Arroyo et al. (2006) . 21xivFigure 2.5 Experimentally observed near field distortion in a spec-imen of compacted residual soil (λ=31 mm, Ltt=95.57mm), adapted from Leong et al. (2009). Adapted, withpermission, from Canadian Geotechnical Journal, copy-right NRC Research Press, Engineering Institute of Canada 21Figure 2.6 Modelled bender element signals with different slen-derness ratios and boundary conditions (adapted fromArroyo et al. (2006)). Adapted with permission fromGeotechnique, copyright Thomas Telford. This mate-rial may be downloaded for personal use only. Any otheruse requires prior permission of Thomas Telford. . . . 25Figure 2.7 Characteristic received points from a square wave trig-ger: top adapted from Viggiani and Atkinson (1995),bottom adapted from Jovicic et al. (1996). Both sub-figures adapted with permission from Geotechnique, copy-right Thomas Telford. This material may be down-loaded for personal use only. Any other use requiresprior permission of Thomas Telford. . . . . . . . . . . . 29Figure 2.8 Example signals depicting the response following thetrigger signal in the time domain (−∆t) and frequencydomain (−∆θ) . . . . . . . . . . . . . . . . . . . . . . . 34Figure 2.9 Dependence of VS on anisotropic stresses with σ′v equalto the stress in the wave propagation direction, σ′h thestress in the particle motion direction, and σ′s the stressorthogonal to both the wave direction and particle mo-tion, adapted from Roesler (1979). Adapted with per-mission from the American Society of Civil Engineers.This material may be downloaded for personal use only.Any other use requires prior permission of the AmericanSociety of Civil Engineers. . . . . . . . . . . . . . . . . . 47Figure 2.10 Effect of parameters on modelled normalized secant shearstiffness (Equation 2.11) . . . . . . . . . . . . . . . . . . 53xvFigure 3.1 Experimental variables include consolidation stress ra-tio (1.0, 2.0, 2.8), age duration (10 minutes, 100 min-utes, 1000 minutes), and shear path to failure (conven-tional, constant p, slope -1, and slope 0) . . . . . . . . . 57Figure 3.2 Particle size distribution for Fraser River Sand samplefrom the current study and from the sample used byShozen (2001) . . . . . . . . . . . . . . . . . . . . . . . 61Figure 3.3 Triaxial diagram . . . . . . . . . . . . . . . . . . . . . . 63Figure 3.4 Comparing stress path control for new triaxial controlsystem (blue) against previous results from Shozen (2001)(red) and Lam (2003) (green) for Slope 0 and ConstantP shear paths . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 3.5 Bender element installation details . . . . . . . . . . . . 67Figure 3.6 Bender element response (a) in contact; and (b) throughair and water . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 3.7 Comparing stress path control to previous experimentsdetailed in Table 3.3 . . . . . . . . . . . . . . . . . . . . 70Figure 3.8 Comparing developed strains to previous experimentsdetailed in Table 3.3, where the circle points are the endof consolidation and the triangle points are the start ofconventional shear . . . . . . . . . . . . . . . . . . . . . 71Figure 3.9 Comparing stress-strain plot during conventional shearto previous experiments detailed in Table 3.3 . . . . . . 72Figure 3.10 Comparing strains during conventional shear to previ-ous experiments detailed in Table 3.3 . . . . . . . . . . 73Figure 3.11 Comparing stress-strain plot at low strains during con-ventional shear to previous experiments detailed in Ta-ble 3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 3.12 Comparing low strains during conventional shear to pre-vious experiments detailed in Table 3.3 . . . . . . . . . 75xviFigure 3.13 Time-domain results for specimen 261 from a 9 kHzsine pulse (green trigger, red response) at 10 minutesof ageing depicting a first arrival velocity of 190.0 m/sand a peak to peak velocity of 163.6 m/s . . . . . . . . 79Figure 3.14 Time-domain cross-correlation result for specimen 261from a 9 kHz sine pulse at 10 minutes of ageing depictinga velocity of 165.4 m/s . . . . . . . . . . . . . . . . . . . 80Figure 3.15 Time-domain bender element test results for Specimen261 during ageing where FA is First Arrival, PP is peakto peak, and CC is cross correlation . . . . . . . . . . . 81Figure 3.16 Frequency domain interpretation following Viana da Fon-seca et al. (2009) with 1 minute (blue), 10 minutes (red),and 100 minutes (green) bender element tests on Spec-imen 261 . . . . . . . . . . . . . . . . . . . . . . . . . . 82Figure 4.1 Synthetic bender element trigger and response signals:(a) 5 kHz sine pulse trigger; (b) 5 kHz continuous sinepulse trigger; (c) sine pulse response; (d) continuoussine response; (e) cross correlation of sine pulse triggerand response; and (f) cross correlation of continuoussine with circle point marking the peak cross correlationof the sine pulse . . . . . . . . . . . . . . . . . . . . . . 88Figure 4.2 Synthetic bender element results: (a) linear sweepingsine wave trigger; (b) response; and (c) magnitude ofthe trigger and response signals in the frequency domain 89Figure 4.3 Interpreted synthetic frequency domain results: (a) co-herence function; (b) calculated phase shift; (c) un-wrapped and corrected phase shift; and (d) phase andgroup velocities . . . . . . . . . . . . . . . . . . . . . . . 91xviiFigure 4.4 Experimental bender element signals for saturated FraserRiver Sand Specimen 016, σa = 159.6 kPa, σr = 79.2kPa, void = 0.977, ltt = 120.0 mm, slenderness ltt/d =1.90: (a) 9 kHz sine pulse trigger; (b) 9 kHz continuoussine pulse trigger; (c) sine pulse response; (d) contin-uous sine response; (e) cross correlation of sine pulsetrigger and response; and (f) cross correlation of con-tinuous sine with circle point marking the peak crosscorrelation of the sine pulse . . . . . . . . . . . . . . . . 93Figure 4.5 Sweeping sine was trigger and response over saturatedFraser River Sand Specimen 016: (a) linear sweepingsine wave trigger; (b) response; and (c) magnitude ofthe signals in the frequency domain . . . . . . . . . . . 95Figure 4.6 Interpreted results for specimen 016: (a) coherence func-tion; (b) calculated phase shift; (c) unwrapped and cor-rected phase shift; and (d) phase and group velocities . 97Figure 4.7 Interpreted phase and group velocities for all ten ex-periments of saturated Fraser River Sand specimens atstress and volume states indicated in Table 4.2 . . . . . 98Figure 4.8 TD-FD technique on bender elements tests during age-ing of Specimen 261 (σ′a/σ′r = 2.0, e=0.964-0.962) withannotated stable frequency range . . . . . . . . . . . . . 100Figure 5.1 Measured 6.25 kHz sine pulse response and cross corre-lation of 6.25 kHz continuous sine wave during drainedconsolidation of loose saturated Fraser River Sand Spec-imen 040 to acquire absolute phase shift of a 6.25 kHzwave at multiple points during the experiment . . . . . 109xviiiFigure 5.2 Perpetual trigger and response signals in the time do-main (a,b) and frequency domain (c,d) applied to andmeasured over drained saturated Fraser River Sand Spec-imen 040 at σa = 181.1 kPa, σr = 90.2 kPa to monitorthe relative phase shift (∆θr) at four frequencies, 6.15,7.15, 8.35, and 10 kHz . . . . . . . . . . . . . . . . . . . 110Figure 5.3 Measured relative phase shift from 6.25 kHz componentof perpetual trigger and response signals over consoli-dation, ageing, and shearing of saturated Fraser RiverSand specimen 040 . . . . . . . . . . . . . . . . . . . . . 111Figure 5.4 Unwrapped relative phase shift during drained consol-idation of loose saturated Fraser River Sand Specimen040 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure 5.5 Perpetual source measured phase VS for saturated drainedFraser River Sand Triaxial Specimen 040 with consol-idation at a stress ratio of σa/σr = 2.0, aged for 100minutes, and sheared along a conventional shear path . 115Figure 5.6 Correcting a discontinuity in the 0.835 kHz phase shiftin Specimen 048 to result in a continuous measuredphase velocity . . . . . . . . . . . . . . . . . . . . . . . 117Figure 5.7 Monitored 10.0 kHz shear wave velocities during con-solidation of loose saturated Fraser River Sand are notwithin the bender element frequency operating range atlow stresses . . . . . . . . . . . . . . . . . . . . . . . . . 118Figure 5.8 7.15 kHz shear wave phase velocity during ageing offour loose saturated Fraser River Sand specimens at σa= 200, σr = 100 kPa . . . . . . . . . . . . . . . . . . . . 119Figure 5.9 Bender element test results from Saturated Fraser RiverSand specimen 040; (a) Migration of multiple resonancepeaks with increasing stress, (b) Phase velocity againstfrequency . . . . . . . . . . . . . . . . . . . . . . . . . . 120xixFigure 5.10 Measured volumetric strains during constant stress ra-tio ( σa/σr = 2.0) consolidation of loose saturated FraserRiver Sand . . . . . . . . . . . . . . . . . . . . . . . . . 123Figure 5.11 Volumetric strains during ageing of seven loose satu-rated Fraser River Sand specimens at σa = 200, σr =100 kPa . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 5.12 Example of stable ageing for Specimen 040 at 8.35 kHz 126Figure 5.13 Example of unstable ageing for Specimen 015 at 9 kHz . 127Figure 5.14 Comparing empirically estimatedG0 to the entire datasetof measured ρV 2S . . . . . . . . . . . . . . . . . . . . . . 130Figure 5.15 Empirical G0 estimates during consolidation of Speci-men 040 (σ′a/σ′r = 2) using Equation 5.4(blue), Equa-tion 5.6(red), Equation 5.7(green), Equation 5.8(grey),and measured from Specimen 040 (yellow) . . . . . . . . 132Figure 5.16 Empirical G0 estimates during ageing for Specimen 040compared to measured values . . . . . . . . . . . . . . . 134Figure 6.1 Primary compression strains for nine specimens at sixdifferent stress ratios from this study (MS), Shozen (TS),and Lam (KL) . . . . . . . . . . . . . . . . . . . . . . . 140Figure 6.2 Secondary compression strains for nine specimens atsix different stress ratios from this study (MS), Shozen(TS), and Lam (KL) . . . . . . . . . . . . . . . . . . . . 141Figure 6.3 Comparing the strain ratio during consolidation to age . 142Figure 6.4 Effect of stress path for specimens 012 (e=0.960, con-ventional, see Figure D.36), 015 (e=0.959, constant-p,see Figure D.39), and 016 (e=0.971, slope-0, see Fig-ure D.40); all prepared loose, consolidated at a SR 2.0to σ′a =200 kPa and σ′r = 100 kPa, and aged 100 minutes143xxFigure 6.5 Effect of stress ratio for specimens 013 (e=0.969, SR=1.0,see Figure D.37), 012 (e=0.960, SR=2.0, see Figure D.36),and 014 (e=0.934, SR=2.8, see Figure D.38); consoli-dated to σ′r = 100 kPa, aged 100 minutes, and shearedalong a conventional stress path . . . . . . . . . . . . . 145Figure 6.6 Effect of age for specimens 090 (e=0.871 at end of age-ing, 10 minutes, see Figure D.8), 261 (e=0.962 at end ofageing, 100 minutes, see Figure D.28), and 108 (e=0.918at end of ageing, 1000 minutes, see Figure D.14); all pre-pared loose, consolidated at a SR 2.0 to σ′a =200 kPaand σ′r = 100 kPa, and sheared along a conventionalstress path . . . . . . . . . . . . . . . . . . . . . . . . . 146Figure 6.7 Measured and predicted normalized stiffness degrada-tion curves for loose specimens of saturated Fraser RiverSand consolidated at SR 2.0 up to σ′a = 200 kPa andσ′r = 100 kPa, aged for 100 minutes, and sheared con-ventionally where G0 ranged from 58 to 62 MPa withspecimen details in Table 6.1 . . . . . . . . . . . . . . . 148Figure 6.8 Effect of stress path on measured and hyperbolic stiff-ness degradation curves for loose specimens consolidatedat SR 2.0 and aged for 100 minutes . . . . . . . . . . . 152Figure 6.9 Effect of stress ratio on measured and hyperbolic stiff-ness degradation curves for loose specimens, aged for100 minutes, and sheared along a conventional stress path154Figure 6.10 Effect of specimen age duration on measured and hy-perbolic stiffness degradation curves for loose specimensconsolidated at SR 2.0 and sheared along a conventionalstress path . . . . . . . . . . . . . . . . . . . . . . . . . 156Figure 6.11 Extrapolation of normalized secant stiffness curve pa-rameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 157xxiFigure 6.12 Effect of age on secant stiffness curve for σ′a=200 kPa,σ′r=100 kPa, G0 according to Equation 5.4, NG = 1.9%, where solid lines are interpolated and dashed linesare extrapolated, the solid black points correspond toSpecimen 040 (see Figure D.52) aged for 100 minutes . 158Figure 7.1 Three different shear wave sources for down-hole seismictesting during cone penetration . . . . . . . . . . . . . . 162Figure 7.2 Photos of PS equipment taken at Kidd 2 in Richmond,BC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Figure 7.3 Collected signals at a cone tip depth of 6m . . . . . . . 172Figure 7.4 Cross correlation of measured signals shown in Figure 7.3:T-M = 4.00 ms, M-B = 4.50 ms, T-B = 8.75 ms . . . . 173Figure 7.5 First PS-SCPTu profile collected in Richmond, BC wherethe green trace in the fourth column represents the per-petual source results and the black step trace is fromadjacent conventional hammer beam strike tests . . . . 174Figure 7.6 Second PS-SCPTu profile collected in Richmond, BC . . 178Figure 7.7 True interval discrepancy . . . . . . . . . . . . . . . . . 179Figure 7.8 Measured pseudo-interval shear wave velocities for con-current hammer strikes at Kidd 2: blue T, green: B,orange: M . . . . . . . . . . . . . . . . . . . . . . . . . . 180Figure 7.9 Comparing measured True Interval to Pseudo-Intervalshear wave velocities for hammer-test data from a 3-geophone true interval cone . . . . . . . . . . . . . . . . 180Figure 7.10 Measured PI signals with perpetual source proximitysensor: blue T, green: B, orange: M . . . . . . . . . . . 182Figure 7.11 Measured bottom geophone signal and proximity sensorsignal at 6 m and 7 m, where time 0 corresponds to adepth wheel data acquisition trigger . . . . . . . . . . . 183Figure 7.12 Interpreting a pseudo-interval propagation time using asingle geophone with a perpetual source . . . . . . . . . 185xxiiFigure 7.13 Perpetual source PI and conventional PI overlappingwaterfall plots . . . . . . . . . . . . . . . . . . . . . . . 186Figure 7.14 PS-SCPTu profile for pseudo-interval testing (red) withadjacent conventional SCPTu (black) . . . . . . . . . . 187Figure A.1 Apparatus configuration to measure average internal ex-panded membrane diameter . . . . . . . . . . . . . . . . 216Figure A.2 Measuring the rod friction of -0.0624 kg . . . . . . . . . 218Figure A.3 Measured and calculated volumetric strains during hy-drostatic unloading . . . . . . . . . . . . . . . . . . . . . 221Figure A.4 Measured unit membrane penetration against effectiveconfining pressure . . . . . . . . . . . . . . . . . . . . . 222Figure B.1 Specimen pluviation . . . . . . . . . . . . . . . . . . . . 225Figure B.2 Specimen siphon . . . . . . . . . . . . . . . . . . . . . . 226Figure B.3 Specimen preparation . . . . . . . . . . . . . . . . . . . 227Figure D.1 Styler-052.lvm: σa = 200.9 kPa, σr = 99.8 kPa, age=1000.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 240Figure D.2 Styler-059.lvm: σa = 200.9 kPa, σr = 100.0 kPa, age=1000.2min, Stress path=P . . . . . . . . . . . . . . . . . . . . 241Figure D.3 Styler-060.lvm: σa = 201.6 kPa, σr = 100.1 kPa, age=1000.0min, Stress path=? . . . . . . . . . . . . . . . . . . . . . 242Figure D.4 Styler-061.lvm: σa = 200.8 kPa, σr = 100.0 kPa, age=1000.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 243Figure D.5 Styler-067.lvm: σa = 200.9 kPa, σr = 100.1 kPa, age=1000.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 244Figure D.6 Styler-070.lvm: σa = 200.8 kPa, σr = 100.2 kPa, age=1000.2min, Stress path=P . . . . . . . . . . . . . . . . . . . . 245Figure D.7 Styler-073.lvm: σa = 281.0 kPa, σr = 100.0 kPa, age=1000.3min, Stress path=P . . . . . . . . . . . . . . . . . . . . 246Figure D.8 Styler-090.lvm: σa = 200.6 kPa, σr = 100.3 kPa, age=10.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 247xxiiiFigure D.9 Styler-091.lvm: σa = 200.8 kPa, σr = 100.1 kPa, age=10.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 248Figure D.10 Styler-093.lvm: σa = 200.7 kPa, σr = 100.3 kPa, age=10.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 249Figure D.11 Styler-097.lvm: σa = 200.7 kPa, σr = 100.3 kPa, age=10.1min, Stress path=-0.5 . . . . . . . . . . . . . . . . . . . 250Figure D.12 Styler-100.lvm: σa = 200.8 kPa, σr = 99.9 kPa, age=1000.0min, Stress path=-0.5 . . . . . . . . . . . . . . . . . . . 251Figure D.13 Styler-103.lvm: σa = 200.8 kPa, σr = 100.0 kPa, age=1000.3min, Stress path=P . . . . . . . . . . . . . . . . . . . . 252Figure D.14 Styler-108.lvm: σa = 200.7 kPa, σr = 99.9 kPa, age=1000.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 253Figure D.15 Styler-112.lvm: σa = 200.9 kPa, σr = 100.0 kPa, age=100.3min, Stress path=P . . . . . . . . . . . . . . . . . . . . 254Figure D.16 Styler-116.lvm: σa = 200.6 kPa, σr = 99.9 kPa, age=1000.3min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 255Figure D.17 Styler-120.lvm: σa = 280.2 kPa, σr = 100.0 kPa, age=1000.0min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 256Figure D.18 Styler-122.lvm: σa = 280.4 kPa, σr = 100.0 kPa, age=1000.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 257Figure D.19 Styler-123.lvm: σa = 279.6 kPa, σr = 99.8 kPa, age=1000.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 258Figure D.20 Styler-124.lvm: σa = 280.2 kPa, σr = 100.0 kPa, age=1000.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 259Figure D.21 Styler-125.lvm: σa = 279.0 kPa, σr = 99.6 kPa, age=100.0min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 260Figure D.22 Styler-126.lvm: σa = 280.0 kPa, σr = 99.9 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 261Figure D.23 Styler-129.lvm: σa = 200.7 kPa, σr = 99.9 kPa, age=999.9min, Stress path=P . . . . . . . . . . . . . . . . . . . . 262Figure D.24 Styler-245: σa = 199.7 kPa, σr = 100.3 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 263xxivFigure D.25 Styler-246: σa = 199.2 kPa, σr = 100.2 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 264Figure D.26 Styler-247: σa = 198.3 kPa, σr = 99.9 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 265Figure D.27 Styler-248: σa = 195.9 kPa, σr = 100.3 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 266Figure D.28 Styler-261: σa = 198.4 kPa, σr = 100.0 kPa, age=102.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 267Figure D.29 Styler-262: σa = 199.1 kPa, σr = 100.1 kPa, age=102.5min, Stress path=C . . . . . . . . . . . . . . . . . . . . 268Figure D.30 Styler-275: σa = 199.3 kPa, σr = 100.3 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 269Figure D.31 Styler-277: σa = 100.2 kPa, σr = 100.2 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 270Figure D.32 Styler-290: σa = 198.3 kPa, σr = 100.0 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 271Figure D.33 Styler-002: σa = 199.5 kPa, σr = 100.2 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 272Figure D.34 Styler-004: σa = 199.0 kPa, σr = 99.9 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 273Figure D.35 Styler-008: σa = 200.1 kPa, σr = 100.1 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 274Figure D.36 Styler-012: σa = 199.9 kPa, σr = 99.9 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 275Figure D.37 Styler-013: σa = 100.0 kPa, σr = 100.0 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 276Figure D.38 Styler-014: σa = 280.3 kPa, σr = 100.2 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 277Figure D.39 Styler-015: σa = 199.9 kPa, σr = 100.2 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 278Figure D.40 Styler-016: σa = 199.6 kPa, σr = 99.7 kPa, age=100.4min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 279xxvFigure D.41 Styler-018: σa = 199.6 kPa, σr = 99.6 kPa, age=100.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 280Figure D.42 Styler-019: σa = 198.6 kPa, σr = 99.1 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 281Figure D.43 Styler-020: σa = 200.0 kPa, σr = 99.9 kPa, age=10.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 282Figure D.44 Styler-021: σa = 199.5 kPa, σr = 99.8 kPa, age=71.5min, Stress path=C . . . . . . . . . . . . . . . . . . . . 283Figure D.45 Styler-023: σa = 200.3 kPa, σr = 100.0 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 284Figure D.46 Styler-024: σa = 200.7 kPa, σr = 100.2 kPa, age=100.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 285Figure D.47 Styler-026: σa = 99.9 kPa, σr = 99.9 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 286Figure D.48 Styler-033: σa = 200.2 kPa, σr = 100.1 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 287Figure D.49 Styler-034: σa = 200.1 kPa, σr = 100.0 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 288Figure D.50 Styler-036: σa = 200.4 kPa, σr = 100.0 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 289Figure D.51 Styler-037: σa = 200.5 kPa, σr = 99.9 kPa, age=100.0min, Stress path=P . . . . . . . . . . . . . . . . . . . . 290Figure D.52 Styler-040: σa = 200.9 kPa, σr = 100.3 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 291Figure D.53 Styler-042: σa = 201.0 kPa, σr = 100.2 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 292Figure D.54 Styler-043: σa = 194.0 kPa, σr = 100.8 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 293Figure D.55 Styler-044: σa = 200.5 kPa, σr = 100.0 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 294Figure D.56 Styler-047: σa = 200.4 kPa, σr = 100.1 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 295xxviFigure D.57 Styler-048: σa = 200.8 kPa, σr = 100.1 kPa, age=100.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 296Figure D.58 Styler-049: σa = 200.3 kPa, σr = 100.1 kPa, age=100.1min, Stress path=C . . . . . . . . . . . . . . . . . . . . 297Figure D.59 Lam-64020731: σa = 103.4 kPa, σr = 49.5 kPa, age=97.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 299Figure D.60 Lam-53020715: σa = 104.8 kPa, σr = 49.6 kPa, age=97.3min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 300Figure D.61 Lam-66020809: σa = 106.5 kPa, σr = 49.8 kPa, age=995.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 301Figure D.62 Lam-56020717: σa = 103.4 kPa, σr = 49.3 kPa, age=995.2min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 302Figure D.63 Lam-58020719: σa = 99.6 kPa, σr = 99.4 kPa, age=97.3min, Stress path=P . . . . . . . . . . . . . . . . . . . . 303Figure D.64 Lam-57020718: σa = 100.2 kPa, σr = 100.1 kPa, age=97.3min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 304Figure D.65 Lam-60020722: σa = 100.2 kPa, σr = 100.0 kPa, age=97.3min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 305Figure D.66 Lam-51020712: σa = 100.1 kPa, σr = 99.9 kPa, age=995.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 306Figure D.67 Lam-50020711: σa = 99.6 kPa, σr = 99.2 kPa, age=995.1min, Stress path=P . . . . . . . . . . . . . . . . . . . . 307Figure D.68 Lam-49020709: σa = 99.3 kPa, σr = 99.0 kPa, age=995.1min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 308Figure D.69 Lam-52020713: σa = 99.3 kPa, σr = 99.1 kPa, age=995.1min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 309Figure D.70 Lam-72020911: σa = 163.7 kPa, σr = 99.5 kPa, age=97.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 310Figure D.71 Lam-71020911: σa = 163.6 kPa, σr = 99.2 kPa, age=97.3min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 311Figure D.72 Lam-73020913: σa = 164.1 kPa, σr = 100.4 kPa, age=97.3min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 312xxviiFigure D.73 Lam-25020517: σa = 209.9 kPa, σr = 99.8 kPa, age=98.1min, Stress path=C . . . . . . . . . . . . . . . . . . . . 313Figure D.74 Lam-27020521: σa = 209.7 kPa, σr = 99.7 kPa, age=98.1min, Stress path=P . . . . . . . . . . . . . . . . . . . . 314Figure D.75 Lam-24020516: σa = 208.9 kPa, σr = 99.8 kPa, age=98.1min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 315Figure D.76 Lam-31020529: σa = 209.7 kPa, σr = 100.1 kPa, age=995.7min, Stress path=C . . . . . . . . . . . . . . . . . . . . 316Figure D.77 Lam-48020704: σa = 98.8 kPa, σr = 98.8 kPa, age=97.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 317Figure D.78 Lam-26020517: σa = 210.0 kPa, σr = 99.9 kPa, age=98.1min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 318Figure D.79 Lam-24020516: σa = 208.9 kPa, σr = 99.8 kPa, age=98.1min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 319Figure D.80 Lam-32020530: σa = 211.0 kPa, σr = 100.0 kPa, age=995.4min, Stress path=P . . . . . . . . . . . . . . . . . . . . 320Figure D.81 Lam-28020523: σa = 208.4 kPa, σr = 100.1 kPa, age=998.5min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 321Figure D.82 Lam-30020528: σa = 207.4 kPa, σr = 98.8 kPa, age=995.3min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 322Figure D.83 Lam-61020723: σa = 208.6 kPa, σr = 99.7 kPa, age=9996.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 323Figure D.84 Lam-34020603: σa = 206.5 kPa, σr = 98.8 kPa, age=9992.0min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 324Figure D.85 Lam-70020815: σa = 207.1 kPa, σr = 99.3 kPa, age=9996.3min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 325Figure D.86 Lam-69020815: σa = 208.3 kPa, σr = 99.0 kPa, age=97.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 326Figure D.87 Lam-39020614: σa = 252.1 kPa, σr = 99.4 kPa, age=97.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 327Figure D.88 Lam-38020614: σa = 255.0 kPa, σr = 100.0 kPa, age=97.3min, Stress path=P . . . . . . . . . . . . . . . . . . . . 328xxviiiFigure D.89 Lam-35020612: σa = 252.3 kPa, σr = 99.6 kPa, age=97.3min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 329Figure D.90 Lam-37020614: σa = 254.5 kPa, σr = 100.0 kPa, age=97.3min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 330Figure D.91 Lam-44020621: σa = 254.4 kPa, σr = 99.4 kPa, age=990.1min, Stress path=C . . . . . . . . . . . . . . . . . . . . 331Figure D.92 Lam-67020812: σa = 254.3 kPa, σr = 99.7 kPa, age=995.2min, Stress path=P . . . . . . . . . . . . . . . . . . . . 332Figure D.93 Lam-41020619: σa = 254.4 kPa, σr = 99.5 kPa, age=990.0min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 333Figure D.94 Lam-43020620: σa = 251.6 kPa, σr = 99.6 kPa, age=990.0min, Stress path=0 . . . . . . . . . . . . . . . . . . . . . 334Figure D.95 Lam-62020730: σa = 313.8 kPa, σr = 149.6 kPa, age=97.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 335Figure D.96 Lam-54020716: σa = 311.4 kPa, σr = 149.2 kPa, age=97.3min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 336Figure D.97 Lam-65020808: σa = 313.5 kPa, σr = 149.1 kPa, age=995.2min, Stress path=C . . . . . . . . . . . . . . . . . . . . 337Figure D.98 Lam-55020716: σa = 310.4 kPa, σr = 149.0 kPa, age=995.2min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 338Figure D.99 Shozen-rw0824-2: σa = 99.8 kPa, σr = 99.8 kPa, age=98.1min, Stress path=C . . . . . . . . . . . . . . . . . . . . 340Figure D.100 Shozen-rw0416-1: σa = 280.0 kPa, σr = 100.0 kPa,age=98.0 min, Stress path=C . . . . . . . . . . . . . . . 341Figure D.101 Shozen-rw0611-1: σa = 199.3 kPa, σr = 99.7 kPa,age=98.0 min, Stress path=C . . . . . . . . . . . . . . . 342Figure D.102 Shozen-rw0616-2: σa = 200.0 kPa, σr = 99.9 kPa,age=98.0 min, Stress path=C . . . . . . . . . . . . . . . 343Figure D.103 Shozen-rw0415-2: σa = 279.3 kPa, σr = 99.5 kPa,age=1.0 min, Stress path=C . . . . . . . . . . . . . . . 344Figure D.104 Shozen-rw0908-1: σa = 55.8 kPa, σr = 19.9 kPa, age=9.5min, Stress path=C . . . . . . . . . . . . . . . . . . . . 345xxixFigure D.105 Shozen-rw0415-1: σa = 279.8 kPa, σr = 99.8 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 346Figure D.106 Shozen-rw0615-2: σa = 279.7 kPa, σr = 99.7 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 347Figure D.107 Shozen-rw0630-1: σa = 280.0 kPa, σr = 99.9 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 348Figure D.108 Shozen-rw0630-2: σa = 280.0 kPa, σr = 100.0 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 349Figure D.109 Shozen-rw0921-1: σa = 55.1 kPa, σr = 19.7 kPa, age=18.3min, Stress path=C . . . . . . . . . . . . . . . . . . . . 350Figure D.110 Shozen-rw0519-1: σa = 279.9 kPa, σr = 99.9 kPa,age=1023.8 min, Stress path=C . . . . . . . . . . . . . 351Figure D.111 Shozen-rw0420-2: σa = 279.8 kPa, σr = 99.9 kPa,age=1.0 min, Stress path=P . . . . . . . . . . . . . . . 352Figure D.112 Shozen-rw0415-3: σa = 280.2 kPa, σr = 100.0 kPa,age=9.9 min, Stress path=P . . . . . . . . . . . . . . . 353Figure D.113 Shozen-rw0413-2: σa = 279.5 kPa, σr = 99.7 kPa,age=1.0 min, Stress path=-1 . . . . . . . . . . . . . . . 354Figure D.114 Shozen-rw0413-1: σa = 280.0 kPa, σr = 99.9 kPa,age=9.9 min, Stress path=-1 . . . . . . . . . . . . . . . 355Figure D.115 Shozen-rw0420-1: σa = 280.0 kPa, σr = 100.0 kPa,age=1.0 min, Stress path=0 . . . . . . . . . . . . . . . . 356Figure D.116 Shozen-rw0603-2: σa = 280.0 kPa, σr = 99.9 kPa,age=1.0 min, Stress path=0 . . . . . . . . . . . . . . . . 357Figure D.117 Shozen-rw0419-1: σa = 279.8 kPa, σr = 99.9 kPa,age=9.9 min, Stress path=0 . . . . . . . . . . . . . . . . 358Figure D.118 Shozen-rw0603-1: σa = 280.1 kPa, σr = 100.0 kPa,age=9.9 min, Stress path=0 . . . . . . . . . . . . . . . . 359Figure D.119 Shozen-rw0521-1: σa = 279.9 kPa, σr = 100.0 kPa,age=98.1 min, Stress path=0 . . . . . . . . . . . . . . . 360Figure D.120 Shozen-rw0602-1: σa = 279.9 kPa, σr = 99.9 kPa,age=98.1 min, Stress path=0 . . . . . . . . . . . . . . . 361xxxFigure D.121 Shozen-rw0520-1: σa = 279.7 kPa, σr = 99.8 kPa,age=980.1 min, Stress path=0 . . . . . . . . . . . . . . 362Figure D.122 Shozen-rw0426-2: σa = 200.0 kPa, σr = 99.8 kPa,age=1.0 min, Stress path=C . . . . . . . . . . . . . . . 363Figure D.123 Shozen-rw0705-1: σa = 199.9 kPa, σr = 100.0 kPa,age=1.0 min, Stress path=C . . . . . . . . . . . . . . . 364Figure D.124 Shozen-rw0423-1: σa = 198.0 kPa, σr = 98.9 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 365Figure D.125 Shozen-rw0702-1: σa = 200.0 kPa, σr = 100.0 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 366Figure D.126 Shozen-rw0829-1: σa = 200.1 kPa, σr = 99.9 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 367Figure D.127 Shozen-rw0525-1: σa = 199.9 kPa, σr = 99.8 kPa,age=980.0 min, Stress path=C . . . . . . . . . . . . . . 368Figure D.128 Shozen-rw0830-3: σa = 199.7 kPa, σr = 99.8 kPa,age=980.1 min, Stress path=C . . . . . . . . . . . . . . 369Figure D.129 Shozen-rw0831-1: σa = 199.3 kPa, σr = 99.5 kPa,age=9800.1 min, Stress path=C . . . . . . . . . . . . . 370Figure D.130 Shozen-rw0908-2: σa = 200.1 kPa, σr = 100.0 kPa,age=9800.1 min, Stress path=C . . . . . . . . . . . . . 371Figure D.131 Shozen-rw0423-2: σa = 199.9 kPa, σr = 99.8 kPa,age=1.0 min, Stress path=P . . . . . . . . . . . . . . . 372Figure D.132 Shozen-rw0422-2: σa = 199.9 kPa, σr = 99.9 kPa,age=9.9 min, Stress path=P . . . . . . . . . . . . . . . 373Figure D.133 Shozen-rw0423-3: σa = 200.0 kPa, σr = 99.9 kPa,age=1.0 min, Stress path=-1 . . . . . . . . . . . . . . . 374Figure D.134 Shozen-rw0422-3: σa = 200.1 kPa, σr = 99.9 kPa,age=9.9 min, Stress path=-1 . . . . . . . . . . . . . . . 375Figure D.135 Shozen-rw0830-2: σa = 200.1 kPa, σr = 100.0 kPa,age=9.9 min, Stress path=-1 . . . . . . . . . . . . . . . 376Figure D.136 Shozen-rw0426-1: σa = 200.0 kPa, σr = 100.0 kPa,age=1.0 min, Stress path=0 . . . . . . . . . . . . . . . . 377xxxiFigure D.137 Shozen-rw0422-1: σa = 200.0 kPa, σr = 99.9 kPa,age=9.9 min, Stress path=0 . . . . . . . . . . . . . . . . 378Figure D.138 Shozen-rw0608-1: σa = 199.8 kPa, σr = 99.9 kPa,age=98.1 min, Stress path=0 . . . . . . . . . . . . . . . 379Figure D.139 Shozen-rw0829-2: σa = 199.8 kPa, σr = 99.8 kPa,age=980.0 min, Stress path=0 . . . . . . . . . . . . . . 380Figure D.140 Shozen-rw0826-2: σa = 99.7 kPa, σr = 99.8 kPa, age=1.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 381Figure D.141 Shozen-rw0825-2: σa = 99.9 kPa, σr = 99.9 kPa, age=9.9min, Stress path=C . . . . . . . . . . . . . . . . . . . . 382Figure D.142 Shozen-rw0824-1: σa = 99.6 kPa, σr = 99.7 kPa, age=9.8min, Stress path=C . . . . . . . . . . . . . . . . . . . . 383Figure D.143 Shozen-rw0826-3: σa = 99.7 kPa, σr = 99.9 kPa, age=980.0min, Stress path=C . . . . . . . . . . . . . . . . . . . . 384Figure D.144 Shozen-rw0915-2: σa = 99.9 kPa, σr = 99.9 kPa, age=9.9min, Stress path=-1 . . . . . . . . . . . . . . . . . . . . 385Figure D.145 Shozen-rw0618-2: σa = 419.7 kPa, σr = 149.9 kPa,age=1.0 min, Stress path=C . . . . . . . . . . . . . . . 386Figure D.146 Shozen-rw0915-1: σa = 420.0 kPa, σr = 149.9 kPa,age=1.0 min, Stress path=C . . . . . . . . . . . . . . . 387Figure D.147 Shozen-rw0617-2: σa = 420.1 kPa, σr = 149.9 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 388Figure D.148 Shozen-rw0629-1: σa = 419.9 kPa, σr = 150.0 kPa,age=98.1 min, Stress path=C . . . . . . . . . . . . . . . 389Figure D.149 Shozen-rw0618-1: σa = 420.1 kPa, σr = 149.9 kPa,age=9.8 min, Stress path=P . . . . . . . . . . . . . . . 390Figure D.150 Shozen-rw0625-2: σa = 139.6 kPa, σr = 49.8 kPa,age=1.0 min, Stress path=C . . . . . . . . . . . . . . . 391Figure D.151 Shozen-rw0624-2: σa = 139.8 kPa, σr = 49.9 kPa,age=9.9 min, Stress path=C . . . . . . . . . . . . . . . 392Figure D.152 Shozen-rw0629-2: σa = 140.1 kPa, σr = 50.1 kPa,age=98.1 min, Stress path=C . . . . . . . . . . . . . . . 393xxxiiAcknowledgementsI’d like to first thank my research supervisor, Dr. John A. Howie, for hisenthusiasm, breadth of geotechnical knowledge, and support. He helpeddrive my work by linking the small details to the larger picture. He has beeninstrumental in developing my ability to get my ideas on to paper throughnumerous collaborations on journal and conference papers. His commentson practice runs through my presentations were also incredibly valuable. I’dalso like to thank my committee members in alphabetical order: Dr. AlexSy, Dr. Mahdi Taiebat, and Dr. Dharma Wijewickreme. It was very usefulto obtain a different perspective on my work. My thesis is improved throughtheir contributions.I am grateful to have been a part of the Geotechnical Research Groupat the University of British Columbia during my studies. They have beenboth my colleagues and friends throughout my years at UBC. We haveworked through courses together, commiserated over marking assignments,and celebrated each other’s graduations. I am grateful to have had theopportunity to share ideas during seminars and informally in the lab andfield.My work in the geotechnical laboratory would not have succeeded with-out the technical support provided from Scott Jackson, Harold Schrempp,and Bill Leung. If you knew what you wanted, they were very helpful. Ad-ditionally, meeting with Dr. Yogi Vaid in the lab was instrumental to mysuccessful research program. He quickly identified many improvements forthe equipment and in my procedure.I’d like to thank ConeTec Investigations, Ltd. for their financial supportxxxiiiof my research. I’d also like to thank them for supporting the PerpetualSource testing and equipment. Specifically, I’d like to thank David Woeller,Ron Dolling, Jamie Sharp, and James Greig. We have collaborated onvarious conference papers and they have provided constructive feedback onpractice runs of my presentation.I’d like to thank my parents for their continued support through my timeat the University of British Columbia. They always believed me when I toldthem that I was almost finished.I’d also like to thank Dr. Kaley Crawford-Flett. She showed me what ittakes to finish a PhD and how great it is to be done.xxxivChapter 1IntroductionThis thesis covers continuous shear wave velocity measurements in labora-tory triaxial tests and during seismic cone penetration. Continuous mea-surements are an alternative to the conventional discrete measurements. Adiscrete bender element test uses a finite length trigger signal, obtains a re-sponse wave, and determines the shear wave velocity at a single point in theexperiment. The continuous technique was developed during this research.It uses a perpetual bender element trigger signal and tracks the changein propagation time through-out the experiment. This technique was thenadapted to down-hole seismic testing during a cone penetration test.These developments occurred during an investigation of the effect ofageing on the small-strain stiffness of Fraser River Sand. Ageing is poorlyunderstood despite significant observed effects in the field. The deformationand performance of non-failing geotechnical structures is dependent on thesoil stiffness, not soil strength. The stiffness over small strains less than1 % governs the behaviour for most applied stresses in actual geotechnicaldesigns (Atkinson, 2000; Burland, 1989). Clayton (2011) recently reviewedresearch and practice for small strain stiffness applications. His motivationwas the increasing importance of consideration of deformation for design ofsubstructures. This is a pressing concern for inner city redevelopment inorder to evaluate the effects on buried infrastructure and adjacent buildingsand roads.1Stiffness is the ratio of the change in stress against strain. The stiffnesscan be quantified as either the secant stiffness or the tangent stiffness. Thesetwo related values are depicted in Figure 1.1. The secant shear stiffness,Gsec, is the slope of a line from the origin to a point on the shear-stressshear-strain curve. The tangent shear stiffness, Gtan, is the local slope ofthe shear-stress shear-strain curve at a point. The secant shear stiffness isnon-linear and usually decreases with increasing shear strain.τ (kPa)γ (%)Gsec=τ/γGtan=dτ/dγFigure 1.1: Definition of secant and tangent shear stiffness on a stress-strain curveAs implied by Figure 1.1, a single stiffness value does not describe soilbehaviour. Figure 1.2 shows a conceptual illustration of non-linear shearstiffness for soil. Atkinson (2000) divided the non-linear stiffness degradationcurve into three regions. The “very small strain” region has a constant high2stiffness plateau up to a threshold shear strain. The “small strain” regioncovers the stiffness from this threshold strain up to 0.1 %. The “large strain”region is shear strain greater than 0.1 %.(a) Bender element testing < 0.0001%(Jovicic and Coop 1997, Kuwanoand Jardine 2002)(b) Non-linear beyond 0.001% (Afifi and Richart 1973, Kuwano andJardine 2002, Muir Wood 2007)(c) Mean elastic threshold strain in sand 0.0007% (Oztoprak and Bolton 2013)Typical strain ranges:Retaining wallsFoundationsTunnelsShear strain, s (%)Shear stiffness, G0.0001 0.001 0.01 0.1 1 10(a)(b)(c)Figure 1.2: Conceptual non-linear equivalent elastic shear stiffnessbehaviour for soils, underlying curve adapted from Atkinson(2000) with referenced annotationsThe stress-strain curve and soil stiffness are very sensitive to the soilstate. In-situ sands cannot be routinely sampled undisturbed for carefullaboratory testing. Therefore, stiffness characterization in sands is challeng-ing. This problem has led to the empirical characterization of the influenceof various factors affecting the stiffness of sands.Previous research at the University of British Columbia (UBC) investi-gated the effect of ageing, initial stress ratio, and stress path on the secantstiffness of reconstituted specimens of Fraser River Sand (Lam, 2003; Shozen,2001). These previous investigations observed a large effect of age on the se-cant shear stiffness at strains from 0.03 % up to failure, with the effect beingmuch more significant at low strains. These research projects were unableto resolve the secant shear stiffness below 0.03%. The trends suggested thatthe effect of ageing should be even more pronounced at smaller strains.Both of these investigations recommended the addition of bender ele-ments to link the effect of ageing from the small strain range to the very-small strain range. Bender elements are used to measure shear waves anddetermine the shear wave velocity, VS . The shear wave velocity can be used3to calculate the very small strain stiffness, G0. The first objective of thecurrent research project is to install bender elements into the UBC triaxialapparatus.There is no standard for bender element installation, operation, or in-terpretation. Figure 1.3 depicts the scatter in interpreted G0 stiffness fromparallel bender element tests on Toyoura sand from different labs underthe same stress state. Different bender element installation details, triggerwaveforms, signal processing, and interpretation methods result in a widerange of VS for a given soil at a given density and stress state. Robertsonet al. (1995b) also observed that an additional source of variation may havebeen due to differences in specimen preparation. The second objective ofthis research project is to investigate the application of bender elements forstudying ageing of Fraser River Sand.Figure 1.3: Scatter of G0 = ρV 2S in specimens of Toyoura sand underhydrostatic consolidation in an international parallel bender el-ement test (Yamashita et al., 2009). Used with permission fromSatoshi Yamashita. This material may be downloaded for per-sonal use only.Normalizing the laboratory Gsec stiffness curves by G0 permits the re-4sults to be compared to recent published stiffness degradation curves fromWichtmann and Triantafyllidis (2013) and Oztoprak and Bolton (2013).These published stiffness degradation curves do not account for the effect ofageing, despite the huge effect observed by previous investigations at UBC.The third objective of this research is to integrate the bender element char-acterized G0 values into a small strain stiffness investigation of Fraser RiverSand.1.1 Research objectivesTo reiterate, the following research objectives have been identified:1. Install bender elements into the UBC triaxial apparatus,2. Investigate the use of bender elements for an investigation of ageingof Fraser River Sand,3. Integrate the bender element determined G0 into a laboratory studyof Fraser River Sand stiffness,1.2 Thesis organizationChapter 2 reviews the background for this research work, including triax-ial testing(Section 2.1), bender element equipment and signal interpretation(Section 2.2), factors affecting VS and G0(Section 2.3), and empirically mod-elling normalized shear stiffness degradation curves (Section 2.4).Chapter 3 describes the improvements in UBC’s triaxial equipment, com-pares preliminary triaxial results to previous studies, and illustrates thechallenge of using prevalent and state of the art bender element techniquesto observe the effect of ageing of Fraser River Sand on G0. The results ofChapter 3 met the first research objective and demonstrated that the secondobjective cannot be achieved with the interpretation techniques describedin Section 2.2.Chapter 4 and Chapter 5 investigate the use of bender elements. InChapter 4 a technique that combined a suite of signals in the time and5frequency domains was developed. This technique converged on a single fre-quency dependent phase velocity solution. In Chapter 5 this technique wasfurther developed to provide continuous bender element signal monitoringduring a triaxial test. The results from these two chapters achieved thesecond research objective.Chapter 6 presents the integration of bender element determined G0values into a laboratory investigation of the stiffness of Fraser River Sand.Normalized Gsec/G0 stiffness degradation curves were characterized. Thisachieved the third objective of this research.Chapter 7 switches from the laboratory setting to the field. It was real-ized that the continuous bender element technique developed and describedin Chapter 5 could be adapted to in-situ measurements. This adaptation ofthe continuous VS technique to down-hole seismic testing during cone pen-etration, and preliminary results, are presented. A continuous depth-profileof VS was successfully obtained. This technique has the potential to increasethe depth resolution of in-situ VS measurements. Measuring VS in-situ andcalculating G0 could permit the laboratory characterized normalized stiff-ness curves to be scaled to in-situ conditions.Chapter 8 contains a summary of the implications, conclusions, contri-butions, unresolved issues, and identifies future research topics.The appendices contain details necessary for reproducing the triaxialresults and data from each laboratory test. Appendix A contains the equip-ment sensor and systematic error calibrations. Appendix B details the tri-axial testing procedure using the UBC triaxial apparatus - including samplepreparation, specimen preparation, and testing. Appendix C contains theequations used to reduce the raw sensor measurements to soil state proper-ties. Appendix D contains the reduced laboratory results.6Chapter 2Measurement of soil stiffnessThis work continues from previous research performed at UBC (Howie et al.,2002; Lam, 2003; Shozen, 2001). The previous work used triaxial testing tointerpret the secant shear stiffness above 0.03 % shear strain. The tests wereperformed on Fraser River Sand, a major foundation soil unit and buildingmaterial in the lower mainland of British Columbia. The previous work didnot include bender elements. Shear waves were not measured. The previousresearchers were unable to normalize the secant shear stiffness degradationcurves with a very small strain G0 value. This made it difficult to comparethe effect of the testing variables on the shape of the stiffness degradationcurve. The previous research projects recommended the addition of benderelements to be able to measure shear waves and obtain normalized secantstiffness, Gsec/G0, degradation curves. Normalized curves are useful as theycan be scaled to in-situ measured VS and G0 values.Bender element applications can be a challenge. There are no standardsfor manufacture, installation, operation, or data reduction. The reportedresults from various researchers are highly variable (Yamashita et al., 2009).This chapter contains a literature review covering the use of bender elementsand interpretation of the shear wave velocity.Bender elements are used in order to obtain G0 from VS . The simplestand most widely used model for shear wave propagation is through an infinitehomogeneous isotropic linear elastic continuum. Under these assumptions,7Equation 2.1 can be derived from Cauchy’s momentum transport equation.A derivation can be found in most text books covering elasticity or wavepropagation, including Slawinski (2003).G0 = ρV2S (2.1)In this equation ρ is the bulk density of the medium and G0 is the verysmall strain shear stiffness. The first application of this equation to inves-tigate laboratory sand specimens was by Iida (1938). His justification wasthat elastic waves propagated through sand, and therefore that sand shouldpossess elastic constants. He acknowledged that the assumption that elas-tic theory can be applied to sand behaviour required further experimentalsupport.A bender element equipped triaxial apparatus should be able to obtainboth Gsec and G0 in order to obtain normalized secant stiffness degradationcurves. This can be used to investigate the influence of soil variables on theshape of the curve. Wichtmann and Triantafyllidis (2013) and Oztoprakand Bolton (2013) empirically characterized the effect of the uniformity co-efficient, mean stress, and density on the shape of the normalized stiffnessdegradation curves. The significance of their work, for this thesis, is thetechnique by which this empirical characterization was carried out. They fithyperbolic functions to the normalized stiffness degradation curves. Thesehyperbolic functions reduced the entire curve to two (Wichtmann and Tri-antafyllidis, 2013) or three (Oztoprak and Bolton, 2013) parameters. Theythen fit equations between the soil properties of interest to these hyperboliccoefficients. This is relevant to this thesis as the previous work by Shozen(2001) and Lam (2003) investigated various factors affecting Gsec degrada-tion. With this empirical characterization procedure, the influence of thesefactors can be quantified.The normalized curves have additional value due to the use of G0. Shearwaves can be measured both in-situ and in laboratory soil specimens. In-situshear waves are measured during seismic cone penetration testing (SCPTu),down-hole seismic testing, from cross-hole testing with multiple bore holes,8and inferred from the frequency dispersion of non-invasive surface Rayleighwave velocities (SASW, MASW). The laboratory or empirical characterizednormalized curves may be applicable in field applications.The purpose of this chapter is to cover the background for the mea-surement of soil stiffness in a laboratory using a bender element equippedtriaxial apparatus.2.1 Triaxial testingTriaxial testing is used to investigate fundamental soil behaviour (Bishopand Henkel, 1957; Saada and Townsend, 1981), including small strain be-haviour (Atkinson, 2000; Kuwano and Jardine, 2002a; Negussey, 1984; Shozen,2001). The laboratory work in this thesis acquired small strain measure-ments using triaxial testing due to previous experience in the UBC labo-ratory for similar research programs (Lam, 2003; Negussey, 1984; Shozen,2001), availability of equipment, and intent to complement past studies withbender element results. Small strain measurements challenge the limitationsof the sensors.2.1.1 Local versus external sensorsThe triaxial test is an element test and to be considered an element test, thestresses and strains should be uniformly distributed in the specimen (Saadaand Townsend, 1981). Test procedures should be designed to achieve asclose to uniform conditions as possible. Local sensor measurements over themiddle third of the specimen have shown that conventional triaxial testingdevices do not achieve uniformity (Scholey et al., 1995). It has even beensuggested that the difference between laboratory and in-situ measurementsis not sample disturbance, but non-uniform strain distributions (Scholeyet al., 1995).Local measurements are made on the specimen. The advantage of localmeasurements is that they eliminate a number of systematic correctionsnecessary for external measurements. The disadvantages are that they addcomplexities to the apparatus and experimental procedure and may limit9the radial deformations and stress paths that can be explored. Scholeyet al. (1995) provide an overview of common local measurement sensorsand applications for triaxial specimens. An alternative to local sensors areexternal sensors.External measurements are not made on the specimen. The externalsensors respond to the displacement of the top cap, the load applied to thedownward ram, the pressure due to a volume of water expelled or drawn intothe specimen. The advantages of external sensors are simplicity, reliability,and easier reproducibility of measurements. The disadvantages are thatthey assume uniform stress and strain distributions and the measurementscontain a set of systematic errors that must be corrected to characterizethe soil behaviour. Each of these corrections adds to the uncertainty in thecalculated specimen state.The UBC triaxial apparatus uses external sensors. Uniformity of thestress and strain within the specimen is assumed.Enlarged frictionless end platens have been recommended to promotestrain uniformity. Negussey (1984) attempted to use enlarged frictionlessend platens in his research on the small strain. He found that they onlypromoted uniform stresses and strains in the bottom half of the specimen.Furthermore, he found that at a height to diameter ratio of 2 the effectof end restraint is insignificant for small strain investigations. The UBCtriaxial specimens are prepared at a height to diameter ratio of 2 and donot use enlarged end platens.The UBC triaxial apparatus uses polished metal end platens and con-centrates on the early part of the stress-strain curve. The early part of thestress-strain curve is less influenced by barrelling of the sample.2.1.2 Systematic error corrections for external sensormeasurementsThe stress state needs to be evaluated at the centre of the specimen. Sincemeasurements are not made at the centre of the specimen, the measuredvalues need to be corrected.The systematic corrections for the axial stress include the weight of the10top cap, half the weight of the soil, ram friction, uplift from cell pressure onunequal end areas, and membrane elasticity. The uplift from unequal endarea is due to the pore water pressure acting on the cross-sectional area ofthe specimen and the chamber pressure acting on the specimen cross-sectionarea minus the driving ram area. Kuerbis and Vaid (1990) presented thecorrections necessary to adjust for the systematic errors due to membraneelasticity on the axial and radial stresses.A systematic error in the volume measurement results from the elasticmembrane penetrating into the pore space on the surface of the specimen.This changes the volume of the water within the membrane enclosed speci-men without a corresponding change in the soil skeleton volume. A simpleprocedure to approximately characterize this correction was presented byVaid and Negussey (1984). This procedure compares the volumetric strainsdeveloped during hydrostatic unloading to an assumed isotropic strain re-sponse. The difference between these volumetric strains is approximatelythe membrane penetration into the cylindrical soil surface.2.1.3 Previous UBC triaxial testing research on ageing ofFraser River SandShozen (2001) investigated the effect of age on the small strain secant shearstiffness, Gsec, of drained triaxial specimens of Fraser River Sand. Themotivation for his research came from the published significant effect ofage in-situ (Mitchell and Solymar, 1984; Schmertmann, 1991) on the CPTresponse in man-made hydraulic deposits, the focus of laboratory resonantcolumn investigations on the very small strain (Anderson and Stokoe, 1978),and the working strains of less than 0.5 % imposed by typical geotechnicaldesigns (Burland, 1989). The desired knowledge was the effect of age onsecant shear stiffness over the small strain range from 0.001 % to 1 %. Tri-axial tests that accounted for the small-strain measurement considerationsdeveloped by previous UBC research (Kuerbis and Vaid, 1990; Negussey,1984; Vaid and Negussey, 1984) were performed on reproducible and ho-mogeneous water pluviated specimens (Vaid and Negussey, 1988). Shozen(2001) investigated the effect of ageing under different stress-ratios on the11subsequent shearing along various stress paths to failure. The stress ratiois the ratio of axial to radial effective stress during ageing. The shear stresspaths are the stress paths followed to failure after the ageing phase. Heobserved that the increase in the secant shear stiffness with age was signifi-cantly greater at shear strains of 0.03 % than at 0.15 %. He was unable toconfidently measure Gsec at strains below 0.03 %. He noted that the per-centage increase in Gsec with age increased with the imposed axial to radialstress ratio. He confirmed published observations that ageing has no effecton the ultimate strength of the soil. His work, and subsequent work at UBC,showed the importance of uniform ageing to get reproducible small-strainsoil behaviour. He pointed out that empirical relationships derived fromcalibration chamber tests may not work very well on geological aged in-situsoil. He concluded with a recommendation to add the measurement of thevery small strain stiffness using bender elements to allow the investigationof the effect of ageing from the very small strain through the small strainrange.Lam (2003) complemented the work of Shozen (2001) with tests at ad-ditional stress ratios and stress paths. Lam (2003) also recommended theinclusion of bender elements to measure the stiffness at very small strainsto investigate Gsec/G0 attenuation.2.2 Laboratory measurement of VS by benderelement testingAdding bender elements to a triaxial apparatus adds the capability of mea-suring shear waves. Measured shear waves can be interpreted to obtain VSand calculate G0. This section covers background for the bender elementinstrumentation, data acquisition, and interpretation.Piezoceramic bender elements are used to both generate and measureshear waves through soil specimens. They comprise a conductive centreshim sandwiched between two piezoceramic plates, as shown in Figure 2.1a.Figure 2.1b shows a bender element cantilever beam. It is installed into arecess, as shown in Figure 2.1c, such that only a few millimetres of the free12end penetrates into the soil specimen. These cantilever beams will benddue to an applied voltage or generate a small voltage due to an appliedmechanical disturbance. To exploit this behaviour, bender elements areinstalled on opposite ends of a specimen to both trigger and receive a shearwave through the soil.(a) Pizeoceramic plates sandwichingconductive centre shim(b) Bender element(c) Bender element installed in triax-ial end platenFigure 2.1: Photographs of a a bender elementPiezoceramics have a long history of use for measuring shear waves in soilspecimens. The first published application using piezoceramics to acquireVS in soil specimens was by Lawrence Jr (1965). Shirley (1978) introducedmodern cantilever beam bender elements that penetrate into the soil speci-13men. Since then, a significant body of research has been created to addressthe various encountered difficulties and applications.Alternatively, the shear stiffness, G0, can be obtained using a laboratoryresonant column (Drnevich et al., 1978) or torsional shear device (Woods,1994). These techniques are briefly described here as they were used inmany of the investigations covered later in Section 2.3. This subsequentsection covers some of the soil properties that influence G0 and the shearwave velocity.Resonant column testing identifies the first resonant frequency due to anoscillating torsional driving force. The system is comprised of a cylindricalsoil specimen capped with an active end platen and passive end platen.The active end platen is driven with an adjustable frequency sinusoidaltorsional force. This results in a set of peak resonant frequencies. The peakresonant frequency corresponding to the cylindrical soil specimen dependson the conditions of the passive end platen. The passive end platen canbe fixed or free with an associated mass. In resonant column testing, theshear modulus is found by solving an equation for an idealized system withthe same resonant frequency. This system includes the mass and inertia ofthe end platens and a cylindrical, uniform, linear elastic material with thesame mass and dimensions as the soil specimen. Additional information onresonant column testing can be found in the ASTM Standard (D4105-07)and in Drnevich et al. (1978).A torsional shear test is a result of instrumenting the resonant columndevice to measure the applied torque and resulting rotation of the activeplaten. Similar to resonant column testing, this information is interpretedassuming an idealized elastic cylindrical specimen (Isenhower et al., 1987).The shear modulus is calculated for the measured rotation angle and appliedtorque. d’Onofrio et al. (1999) designed a torsional shear apparatus thatcould perform dynamic testing over a frequency range from 0.1 to 100 Hz.Compared to resonant column testing, bender element testing has thefollowing disadvantages: it is unable to measure the degradation of the shearmodulus at higher strains (Thomann and Hryciw, 1990), VS is measured atfrequencies above 1000 Hz, while in-situ measurements are typically made14below 100 Hz; and VS interpretation methods are inconsistent (Yamashitaet al., 2009). It has the following advantages: bender elements are small,versatile, economical; the test is fast (Thomann and Hryciw, 1990); and it isless destructive than resonant column testing (Thomann and Hryciw, 1990).Another disadvantage of bender elements stated by Thomann and Hryciw(1990) was that they cannot be used to measure soil damping. However,Brocanelli and Rinaldi (1998) subsequently developed a method to measuredamping using bender elements.Bender elements have become the prevalent means to characterize theshear wave velocity in laboratory soil specimens. Bender elements are mostcommonly installed in conventional geotechnical laboratory equipment suchas triaxial cells (i.e. Kuwano and Jardine (2002b)) and oedometers (i.e. Leeet al. (2008), Thomann and Hryciw (1990)). The versatility of bender ele-ments has also permitted their inclusion in more unconventional laboratoryequipment (Comina et al., 2008), and even in-situ tools (Jang et al., 2010).2.2.1 InstallationThe research covered in this thesis used a triaxial apparatus that was mod-ified to include bender elements. There is no standard for the manufactureor installation of bender elements. This makes bender element testing bothversatile and potentially variable.The bender elements themselves are a cantilever beam. This beam isas thick as the piezoceramic plates, but has a variable length and width.A fraction of the cantilever beam penetrates into the soil specimen. In acomparison of 23 different bender element systems (Yamashita et al., 2009),the cantilever length was 12-20 mm, the width was 10-12 mm, and theaverage specimen penetration length was 4.7 mm. For comparison, eventhough it is out of place in this literature review chapter, the installed UBCbender elements were 14 mm long, 10 mm wide, and penetrated 4.5 mmand 4.6 mm into the specimen. More installation details are provided inSection 3.3.2.Figure 2.2 depicts three published examples of installed bender elements.15This figure shows some common features to all bender element installations.They are installed in a recess such that only a fraction of the length pene-trates into the soil specimen. If this recess is a thin slot the bender elementcan be glued in place, as illustrated in Figure 2.2a and Figure 2.2b. Benderelements have also been mounted onto the surface of latex membranes asdepicted in Figure 2.2c. Figure 2.2a also shows how two bender elementsare mounted opposite to each other in an apparatus.(a) Pedestal mounted bender element(Leong et al., 2005) (b) Pedestal mounted bender element(Cha and Cho, 2007)(c) Membrane mounted bender element(Kuwano et al., 2000)Figure 2.2: Published bender element installation details. Reprinted,with permission, from Geotechnical Testing Journal, copy-right ASTM International, 100 Barr Harbor Drive, West Con-shohocken, PA 19428.16There are no standard design details for bender element installations.However, there are a lot of common features. They all have similar dimen-sions. They are all installed in a recess. They are all coated to be waterproof. They all require electrical cables and wiring. Following a similar de-sign to what has been done in the past makes a significant body of benderelement research relevant.2.2.2 Series and Parallel type bender elementsThere are two different types of bender elements, series or parallel, withdifferent wiring configurations. Different results are obtained based on thetype of bender element used.A series type element has opposing piezoceramic plate polarization direc-tions. A series type bender element is wired by completing a circuit acrossthe outside faces of the entire bender element. The outside edge of one plateis wired to ground, and the outside edge of the opposite plate is wired tothe trigger voltage source. The electrical potential drop is in the same direc-tion across both plates. Since the polarization is in opposite directions, thiscauses one plate to extend and one to contract. The result is the bendingof the cantilever beam.The polarization directions for the piezoceramic plates in a polar elementare aligned. A parallel type bender element has three connecting wires. Twooutside face wires are connected to ground and the centre shim is wired to thetrigger voltage signal. A parallel type bender element with wiring is shownin Figure 2.3. Parallel type wiring results in the same voltage potentialacross both piezoceramic plates. On one of the plates, this voltage potentialis aligned with the polarization direction. On the other plate, it opposes thepolarization direction. This causes one plate to extend, one to contract, andthe bender element to bend when a voltage is applied.If the series or parallel bender elements are wired incorrectly they will notbend. An applied voltage would cause both piezocermaic plates to extendor contract. A shear wave will not be generated.Parallel type elements generate more deformation than series type for17+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -+ -Piezoceramic platesBrass reinforcing shimVoltage triggersignalVoltage ground reference(a) Trigger bender element wired in par-allelExtendContract(b) Piezoceramic plates extend and con-tract causing the cantilever beam to bendFigure 2.3: Piezoceramic parallel type bender trigger elementan applied trigger voltage amplitude. Conversely, series type elements gen-erate more voltage than parallel type for a received mechanical wave. Seriestype elements are easier to manufacture and install. However, parallel-typeelements are self-shielding.Lee and Santamarina (2005) present measured signals from series-seriesunshielded, series-series with installed shielding, parallel-series, and parallel-parallel combinations of bender element triggers and receivers. Series typebender elements can be shielded with a coating of conductive paint that iswired to ground. Parallel type elements are self shielding when the outerplate is wired to ground. The least distorted signals were provided byshielded series-series and parallel-parallel bender element systems. Shield-ing reduces the environmental electrical noise and cross-talk in the receivedsignals. Cross-talk results in a systematic distortion of the received signal.A distorted version of the applied trigger signal is almost instantaneouslyobserved in the received channel. With unshielded bender elements the18electrical signals propagate through the specimen pore fluid.2.2.3 Signal conditioningThe signal to noise ratio (SNR) is the ratio of the amplitude of the in-formative signal to the amplitude of the random noise. The SNR may beincreased through signal conditioning. Signal conditioning includes filtering,amplification, and signal stacking.Amplification uses an external power source to increase the amplitude ofa signal. The trigger signal can be amplified to induce stronger shear waves.The response signal can be amplified prior to analogue to digital conversionto increase the resolution of the signal.Filtering alters features in the measured signals. A low-pass filter reduceshigh frequency content, a high pass filter reduces low frequency content, anda band-pass filter reduces both low and high frequency contents. Filteringmay be used to reduce frequency contents outside of the bender elementoperating range. Filtering may increase the clarity of the measured shearwave for visual interpretation. Improper filtering can adversely affect theinterpretation of the propagation time. It can distort the informative shearwave component of the received signal. Filtering cannot be used when thenoise is over the same frequencies as the signal.Signal stacking sums up the results of a series of identical tests performedback to back. Signal stacking is very useful when the frequency of the noisecoincides with the frequency of the signal. In signal-stacking, random noisecancels itself out and systematic signal components are amplified. The signalto noise ratio increases with the square root of the number of stacked signals.A two-fold increase is realized by stacking only 4 signals. A 10-fold increaseis realized with 100 stacked signals. Lee and Santamarina (2006) recommendsignal stacking over filtering.To use signal stacking, a period of time must elapse between repeatedtests to permit any reflected waves in the specimen to dissipate. Branden-berg et al. (2008) developed a fast stacking procedure by randomizing thepause time between subsequent trigger signals. With these random wait19times, the residual signal components become random and only the mainshear wave is systematic and amplified. SNR does not increase with thesquare root of the number of stacked signals using this fast-stacking ap-proach.Signal stacking only reduces random noise. There are systematic benderelement distortions that are amplified through signal stacking. These includethe near field effect (Section 2.2.4) and wave reflections (Section 2.2.5).2.2.4 Near field effectThe near field effect is a phenomenon that can distort measured benderelement shear waves. The near field effect is a shear-motion distortion thatprecedes the arrival of the main shear wave. This effect is systematic, andnot random. It cannot be reduced through signal stacking. It is at a similarfrequency as the shear wave. It cannot be eliminated through filtering.The near field effect is not compression wave interference. It is interfer-ence from transverse motion at the speed of a compression wave. Cruse andRizzo (1968) derived an equation for particle motion due to elastic wavesin linear, isotropic, homogeneous, elastic materials. Sa´nchez-Salinero et al.(1986) applied the solution from Cruse and Rizzo (1968) to investigate an-alytically the response of a material to excitation from single cycles of sinepulse waves. Sa´nchez-Salinero et al. (1986) includes both 2D and 3D ana-lytical solutions. The calculations for transverse motion predicted two wavearrivals. The first was an arrival of transverse motion at the speed of thecompression wave. The second was the arrival of transverse motion at thespeed of the shear wave.The amplitude of the shear motion propagating at a compression wavevelocity attenuates over shorter distances than the shear wave velocity com-ponent. At a large enough propagation distance, the shear motion propa-gating at a shear wave velocity dominates the response. This is why it istermed a near field effect, it is only observed close to the source.The near field effect was observed in 3D numerical finite element mod-elling of bender element tests (Arroyo et al., 2006). Figure 2.4 depicts the20received wave after propagation through a linear elastic constitutive model.The near field effect is observed between the arrival of waves travelling atspeeds of VP and VS .Figure 2.4: Observed near field distortion in a 3D numerical modelusing linear elastic constitutive elements with absorbing lateralboundaries, adapted from Arroyo et al. (2006)Figure 2.5 shows an experimental observation of the near-field effect.This specimen had a propagation length to wavelength ratio (Ltt : λ) of 3.1.The near field effect was observed to be marginal above a Ltt : λ ratio of3.33 for dry sand and unsaturated residual soil (Leong et al., 2009, 2005).Figure 2.5: Experimentally observed near field distortion in a spec-imen of compacted residual soil (λ=31 mm, Ltt=95.57 mm),adapted from Leong et al. (2009). Adapted, with permission,from Canadian Geotechnical Journal, copyright NRC ResearchPress, Engineering Institute of CanadaFor a fixed propagation length, the magnitude of the near field effect21decreases as the frequency of the shear wave increases. It is therefore desir-able to perform bender element testing at high frequencies. However, thereis an upper frequency limit for bender element testing. If the frequenciesare too high the shear wave will attenuate before arriving at the receivingbender element. This frequency limit depends on the bender elements, soilcoupling, soil state, and soil damping. It will change during an experiment.Rio (2006) stated that sine pulse trigger waveforms cannot be used tocontrol the frequency component of the shear wave. Sine pulse triggerscontain a wide band of frequency contents. A single wavelength to use toevaluate the Ltt/λ near field criteria cannot be calculated.The near field effect has been supported theoretically, analytically, nu-merically, and observed experimentally. More distortion occurs over shortpropagation lengths and at low frequencies. The common sine-pulse benderelement trigger does not define or limit the frequencies of the generated orpropagated shear wave.2.2.5 Sample size effectsThe elastic waves induced by the bender elements reflect off the end platensof the apparatus and the constrained sides of the specimen. The receivedmechanical wave is the direct transmitted wave with a superposition of thesereflections. The dimensions of the specimen can result in a distorted shearwave signal. These distortions are systematic. They cannot be reducedthrough signal stacking. They are at the same frequency as the direct shearwave. They cannot be reduced through filtering.Arulnathan et al. (1998) investigated the effects of end platen reflectionsfor shear waves propagated in the axial direction using a 2D finite elementmodel. They modelled the received wave as the summation of four wavepaths: unreflected trigger-receiver, once reflected behind the trigger ele-ment, once reflected behind the receiver element, and twice reflected behindboth the trigger and receiver elements. This model resulted in a distor-tion that was dependent on the bender element penetration length into thesoil. These simulations resulted in signals that were qualitatively similar to22typical measurements.Arroyo et al. (2006) investigated the effects of side reflections on benderelement tests using three dimensional finite element numerical models. Thecylindrical soil specimens were represented by a linear elastic constitutivemodel. The shear waves propagated along the cylindrical axis. The dimen-sions of these cylinders can be normalized by the ratio of the length to diam-eter - the slenderness ratio. These models explored absorbing and reflectiveside-wall boundary conditions with different slenderness ratios. Figure 2.6ashows the results for a shear wave propagating through a specimen with aslenderness ratio of 4.0 and absorbing side walls. The shear wave arrival cor-responded to the first main pulse in the received trace. Figure 2.6b depictsthe results for the same slenderness ratio, but with reflective side walls. Thissignal is highly distorted and the shear wave does not correspond to the firstcomplete pulse or the first major pulse. Figures 2.6c and 2.6d show that theside wall boundary conditions have little influence when the propagationdistance is short.Marjanovic and Germaine (2013) recommend that slenderness ratios beless than 1.0 to avoid reflection interference. Rio (2006) went into more de-tail and recommended that the H2/D ratio be less than 15 mm (oedometerspecimens) or greater than 45 mm (triaxial specimens). These recommen-dations were based on a parametric investigation of sample size effects usingsynthetic rubber samples and FLAC3D numerical models. The behaviourwas observed to depend on the H2/D ratio, rather than H/D. Betweenthese two dimension ratios was a transition geometry with unpredictablebehaviour.Oedometers have low slenderness ratios, so the side wall reflections arenot a source of error. However, the errors due to reflected wave interferencefrom the end caps would have increased significance (Arulnathan et al.,1998). Furthermore, Rio (2006) found some uncertainty in the actual wavepropagation length. He found that it may be longer than the assumed bendertip-tip length. Such uncertainty in the propagation length will have a moresignificant impact on VS determinations over short distances.Triaxial specimens typically have slenderness ratios around two and are23bounded by an elastic latex membrane. Arroyo et al. (2006) suggested thatthe triaxial membrane would represent behaviour somewhere between the re-flective and absorbing side wall models. Results from triaxial specimens areexpected to include some reflection interference. However, the uncertaintyin the propagation length is reduced.24(a) Slenderness 4, absorbing side walls(b) Slenderness 4, reflective side walls(c) Slenderness 0.25, absorbing side walls(d) Slenderness 0.25, reflective side wallsFigure 2.6: Modelled bender element signals with different slender-ness ratios and boundary conditions (adapted from Arroyo et al.(2006)). Adapted with permission from Geotechnique, copy-right Thomas Telford. This material may be downloaded forpersonal use only. Any other use requires prior permission ofThomas Telford.252.2.6 Classification of observed bender element responsesignalsThe distortions due to the near field effect and specimen reflections arecommon in bender element testing. It is possible to characterize the signalsbased on the type of observed distortion. Received bender element signalsfrom sine pulse triggers can be classified into one of three waveform types(Brignoli et al., 1996). Type 1 has no pre-arrival distortion. The first pulsehas the largest amplitude and the first arrival point is easy to select. Type1 signals are rarely observed. Type 2 signals have an observed near fielddistortion obscuring the first arrival pick (see Figure 2.5). Type 3 signalshave a small amplitude cycle prior to a major shear pulse (see Figure 2.6b).They appear to be a result of reflected wave interference. Type 3 signalshave the most inconsistent propagation time interpretations.Published bender element signals encountered during the literature re-view for this thesis were classified with the waveform characteristics iden-tified by Brignoli et al. (1996). Table 2.1, Table 2.2, and Table 2.3 detailpublished bender element tests that depicted Type 1, 2, and 3 waves. Notethat only two of the encountered signals could be classified as Type 1. Thesesignals have a high propagation length to wavelength ratio. The specimensdescribed in Table 2.2 generally have low propagation length to wavelengthratios. In Table 2.3, the specimens have a higher slenderness ratio - theratio of the propagation length to specimen diameter. It is important tonote that these observations of common features between the signal typesare fairly weak.Table 2.1: Type 1: clear first major pulse, first arrival is easy to select,simplest to interpret, least common to encounter (Brignoli et al.,1996)Soil Equip. Ltt/dia. Ltt/λCompacted Residual, Sat=90 %(Leong et al., 2009)Trx. 2 6.1Clay (Jovicic et al., 1996) Trx. – 8.126Table 2.2: Type 2: apparent near field distortion, the arrival is thefirst strong pulse with correct polarity (Brignoli et al., 1996)Soil Equip. Ltt/dia. Ltt/λCompacted Residual, Sat=90 %(Leong et al., 2009)Trx. 2 0.8-3.1Sand, dry (Leong et al., 2009) Trx. 2.4 1.2Linear-elastic (Arroyo et al., 2006) F.E. 0.25 3.3Clay, Saturated (Brignoli et al.,1996)Trx. 2.0 2.7Clay (Bonal et al., 2012) Ltt=91 mm 1.4-4.1Clay (Chan et al., 2010) Trx. 2.0 4.8Sand, dry (Kumar and Madhusud-han, 2010)RC 2.0 0.8-1.9Sand, P.sat. (Ghayoomi and Mc-Cartney, 2011)N/A 2-4Clay (Jung et al., 2007) Trx. 2.1-2.3 1.8Silt (Karl et al., 2008) Trx. 1.7 1.1-2.2It will be described in Section 2.2.7 and Section 2.2.8 how the typeof observed bender element signal should be considered when selecting anappropriate interpretation technique.2.2.7 Interpreting VS in the time domainBender elements trigger and receive shear wave signals. These signals mustbe interpreted to obtain a shear wave velocity. As previously covered, thereare significant distorting factors that can affect the measured signals. Thismakes the interpretation of the shear wave velocity challenging.Historically, bender element testing was performed using a square wavetrigger signal. A square wave trigger signal is a sharp step in voltage appliedto the trigger bender element. For square wave trigger signals, three char-acteristic points in the received wave have been used to identify the arrival:the first marked deflection, the first reversal, and the first polarity cross(Viggiani and Atkinson, 1995). Of the three points, Viggiani and Atkin-son (1995) and Jovicic et al. (1996) recommend the first reversal. These27Table 2.3: Type 3: a small amplitude cycle prior to the main shearpulse (Brignoli et al., 1996), selected arrival times are inconsistentSoil Equip. Ltt/dia. Ltt/λPeat, wc = 200% (Arul-nathan et al., 1998)Trx. 2.1 7.3Linear-elastic (Arul-nathan et al., 1998)F.E. 2.0 2.0Linear-elastic (Arroyoet al., 2006)F.E. 2 3.3Linear-elastic (Arroyoet al., 2006)F.E. 4 6.7Sand (Brandenberget al., 2008)Chamber – 1.3-5.4Clay, saturated (Lan-don et al., 2004)Block sample – 3.9Sand, saturated (Brig-noli et al., 1996)Trx. 2.0 2, 4Sand, dry (Kumar andMadhusudhan, 2010)RC 2.0 3.3Sand (Brocanelli andRinaldi, 1998)Trx. 0.3 N/A (Square trigger)points are depicted in Figure 2.7 with the first reversal labelled “1”. Squarewaveforms are now used infrequently due to added uncertainty in the deter-mination of the arrival time (Yamashita et al., 2009).A sine pulse trigger is a single period of a sine pulse waveform. Sinepulse triggers have replaced square wave triggers as the prevalent bender el-ement trigger waveform. Sine pulse bender element tests can be interpretedby selecting the first arrival, measuring the time difference between charac-teristic points, or finding the peak cross correlation time. The rest of thistime-domain section concerns the interpretation of sine pulse trigger signals.Sine pulse triggers require the selection of the sine pulse frequency. Aspreviously covered, high sine pulse frequencies have been suggested to re-duce the near field effect. Leong et al. (2009) suggested a propagation lengthto wavelength ratio greater than 3.33 (see Section 2.2.4). The wavelength28Figure 2.7: Characteristic received points from a square wave trig-ger: top adapted from Viggiani and Atkinson (1995), bottomadapted from Jovicic et al. (1996). Both sub-figures adaptedwith permission from Geotechnique, copyright Thomas Telford.This material may be downloaded for personal use only. Anyother use requires prior permission of Thomas Telford.(λ) is calculated from the selected trigger sine pulse frequency (f) and theinterpreted shear wave velocity VS using VS = λf . Camacho-Tauta et al.(2011) selected a sine pulse frequency that had the largest amplitude re-sponse and a propagation length to wave length ratio greater than 2.0. Theselected sine pulse frequency alters the measured response wave and can29change the VS interpretations. However, as previously stated, Rio (2006)correctly stressed that sine pulse signals should not be used to address anyfrequency dependent effects - including the near field. Sine pulse testingdoes not restrict the frequencies of the shear wave.First arrivalThe first arrival method entails picking the arrival time from a visual in-spection of the received signal. This method is applicable to Type 1 signals(Table 2.1). These are the rarest signals, yet first arrival is the simplestand most common interpretation method. In Type 2 and especially Type 3signals, the distortion will mask the first arrival. In an international parallelbender element test on Toyoura Sand, Yamashita et al. (2009) found thatdifferent laboratories measured similar waveforms but used different pointsas the first arrival. Type 2 signals may be incorrectly interpreted by select-ing a point in the near field as the arrival or by overcompensating for anobserved near field effect. On Type 3 signals, it is not clear if the first lowamplitude pulse is the arrival or the first major pulse is the arrival.Characteristic pointsThe response to sine pulse triggers can be interpreted by measuring the timedifferences between characteristic points on both signals. For example, thepeak-peak points compare the peak in the trigger signal to the first peak inthe response signal. The trough-trough points compare the first minimumpoints. Compared to the first arrival method, this is less subjective. Thismethod can be used to interpret Type 1 or Type 2 signals. On Type 3signals it is not clear if the first low amplitude cycle or subsequent majoramplitude cycle should be used to find the characteristic points.Arulnathan et al. (1998) found that the characteristic points differencerequired a wavelength to bender element penetration length ratio (λ/lb) lessthan 8 for peak-peak, and less than 4 for cross correlation. If λ/lb exceededthese limits, travel times were underestimated and VS was overestimated.Another problem with the characteristic points interpretation is that30the input sine pulse frequency is often different than the response pulsefrequency. This systematically alters the time difference between the peak-peak and trough-trough points based on the selected trigger frequency. Forexample, if a 4 kHz and 6 kHz sine pulse both resulted in an equivalent 5kHz sine pulse response, then the characteristic points on the 6 kHz test willresult in a slower VS then the 4 kHz sine pulse trigger.Cross correlationViggiani and Atkinson (1995) regarded the cross correlation results as moreaccurate than the first arrival or time difference between characteristic points.The cross-correlation function compares the entire trigger signal to the re-sponse signal. The maximum cross correlation value occurs at the time offsetfor the trigger signal which results in the best overlap of the response signal.Equation 2.2 is used to calculate the cross-correlation between two signals(Bendat and Piersol, 2010). In this equation, cxy is the cross correlation, ris an index from 0 to N-1, ∆t is the sampling interval, N is the number ofsamples, x is the discrete input signal and y is the discrete output signal.cxy(r∆t) =1N − rN−r∑n=1xnyn+r (2.2)The maximum cross correlation value occurs at the time offset which re-sults in the strongest overlap between the two signals. For sine pulse tests,the cross correlation function results in a series of peaks. Cross correlationresults can be misleading when constructive and destructive interferencechanges the amplitudes of peaks in the received signal. The cross correla-tion peak corresponding to the arrival may be less than the amplitude of asubsequent peak. This was observed in a numerical model by Arroyo et al.(2006). Cross-correlation methods suffer from the same problem as charac-teristic points for Type 3 signals. The trigger signal and response signals aredifferent waveforms due to the frequency dependence of the bender elements(Lee and Santamarina, 2006).31Auto-correlationAuto-correlation is the same as cross correlation, only the response signalis compared to itself. Lee and Santamarina (2005) showed that this tech-nique can isolate the effect of the soil from the bender elements. A benderelement system is comprised of a series of components including periph-eral electronics, the bender element trigger, the soil, the bender elementresponse, and signal amplifiers. Each component of the bender elementsystem contributes to the distortion and translation from the input triggersignal to the measured response signal. Auto-correlation requires receivedsignals that include the arrival of the first shear wave and a subsequent ar-rival of the twice reflected shear wave. The time difference between thesetwo arrivals is calculated using the auto-correlation function. The advantageof this is that both arriving shear waves have experienced the same time lagdue to the bender elements and peripheral electronics. The disadvantageof this method is that it requires an observed twice reflected wave. Thiscan be challenging in longer propagation lengths or in slender specimens.Arulnathan et al. (1998) also noted that comparing reflected signals doesnot account for non-1D wave travel.Matching simulated signalsLee and Santamarina (2005) presented a method to estimate the arrival timeby matching the response to simulated received bender element signals. Thebender element cantilever beams were modelled as single degree of freedomsystems with a resonant frequency and damping. The soil was modelledusing the analytical results from Sa´nchez-Salinero et al. (1986). The modelparameters were adjusted until the simulated signal agreed with the responsesignal. This may be applicable when significant near field effects obscure thearrival of the shear wave.Time domain summaryIn summary, square wave trigger signals are no longer used in bender elementresearch. Type 1 signals may be easily interpreted with the simplest time32domain method - the selection of the first arrival point. Type 2 signals canbe interpreted with the characteristic points or cross correlation method ifthe measured response signal is similar to the selected trigger signal, or bymatching simulated signals. Type 3 signals are challenging. They can givemisleading results using the time domain methods. Type 3 signals have aleading low amplitude pulse. In a numerical model (Arroyo et al., 2006)found that no characteristic of the received signal corresponded to the shearwave arrival. Type 3 signals cannot be confidently interpreted with timedomain techniques.2.2.8 Interpreting VS in the frequency domainVarious techniques to obtain a shear wave velocity have been developed inthe frequency domain. The frequency domain may be more applicable toType 3 signals. The frequency domain representation of a time domain sig-nal is a summation of continuous sinusoids. Each sinusoid can be representedby g(t) = A × sin(2pift + θ). This function is defined by three parameters:the amplitude (A), the frequency (f), and the phase angle (θ). The changein the phase angle between the trigger signal and response signal is used tocalculate the shear wave propagation time.Frequency domain methods used the Discrete Fourier Transform to con-vert the finite length time-based signals into a finite array of complex num-bers. Each complex number corresponds to a single frequency and can beused to calculate the sinusoid magnitude and phase angle. The Fast FourierTransform (FFT) uses the Cooley-Turkey algorithm (or variation) to per-form Discrete Fourier Transforms on finite sized datasets. The FFT is notan approximation - the exact time domain signal can be recovered from theinverse Fourier Transform. No information is lost on the conversion betweenthe time domain and frequency domain.The change in the phase angle between the trigger and response signals iscalled the phase shift. For a given function of time, g(t), a positive shift alongthe time axis results in g(t − ∆t). By substituting this into the sinusoidalfunction, this results in a phase shift of: ∆θ = −2pif∆t. From the variation33in phase shift and frequency the propagation time can be calculated.Figure 2.8 shows the relationship between an example trigger signal andresponse signal in both the time domain and frequency domain. This signalis a single sinusoid with a frequency of 5 kHz. In the time domain theresponse follows the trigger. Since the signal is periodic, there is no wayto know how many cycles have occurred between the trigger and responsesignal. More information is needed. The frequency domain is plotted ina polar plot. The phase angle for the response is behind the trigger. Thesignal is periodic and there is no way to know how many complete cyclesbehind the trigger is the response.0.511.5302106024090270120300150330180 0Frequency domainTriggerResponse0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 221.510.500.511.52time (ms)amplitudetriggerresponseFigure 2.8: Example signals depicting the response following the trig-ger signal in the time domain (−∆t) and frequency domain(−∆θ)There are two general approaches to adding the missing informationrequired to interpret periodic signals in the frequency domain. The prop-agation time can be assumed constant and additional frequencies can betested. A small change in the frequency will necessarily change the phaseangle if δt is constant and independent of frequency. This results in a groupvelocity - the velocity of a band of frequencies. The second approach is tofigure out how many cycles have occurred and quantify the integer n. Thenthe total phase shift can be calculated and used to find the propagationtime for a single frequency. This results in the phase velocity. These two34velocities are further described in Section 2.2.8.Equation 2.3 is used to calculate the phase shift between the triggersignal, x(t), and response signal, y(t). In this equation FFT is the FastFourier Transform. The imag() function returns the imaginary componentof the complex number and the real() function returns the real component.This equation is used to calculate the phase shift between all of the sinusoidcomponents in the trigger and response signals.∆θ = tan−1(imag (FFT (y(t))/FFT (x(t)))real (FFT (y(t))/FFT (x(t))))(2.3)Frequency domain approaches use signals with a wide band of frequencycontents. Early work used sine pulses (Sachse and Pao, 1978; Viggiani andAtkinson, 1995). Modern work employs linear swept sine waves (Greeningand Nash, 2004; Viana da Fonseca et al., 2009). A linear swept sine signalincreases the frequency with time over the duration of the trigger signal. Atypical signal would increase the frequency from 0 to 10 kHz over 20 ms,g(t) = sin(2pi(500000t)t), where f(t) = 500000t (Hz) and t is in seconds.An advantage of frequency domain interpretations is the quantificationof the bender element operating frequency range. It can be characterizedby the coherence between the trigger and response signals. The coherenceis a function of frequency that ranges between 0 and 1 depending on thelinearity of the relationship between the trigger and response. Coherencevalues less than 1.0 are due to noise, a non-linear relationship between thetrigger and response, and/or the response being a function of additional in-put signals (Bendat and Piersol, 2010). Greening and Nash (2004) found thecoherence between bender element trigger and response waves dropped offrapidly below 0.5 kHz. Viana da Fonseca et al. (2009) calculated coherencefunctions where the low frequency drop off depended on the applied stressand ranged from 1 kHz for a mean stress of 100 kPa to 8 kHz under a meanstress of 800 kPa. Bender elements cannot measure low-frequency shearwaves. Only a small fraction of the mechanical signal is linearly convertedto a voltage and it is obscured by noise. The additional information pro-vided by the coherence function is not typically obtained with time-domain35interpretations.The challenge in all frequency domain approaches is due to uncertaintyin the phase degeneracy. Only the relative phase shift is calculated withEquation 2.3. The absolute phase shift, the total shift in the phase anglebetween the trigger and response signals, is not known.Phase degeneracyThe phase angle in a sinusoidal signal can only be calculated between −piand +pi. For bender element applications this range is too small to directlycalculate the propagation time. For example, a hypothetical specimen witha shear wave velocity of 200m/s and a propagation length of 120 mm has apropagation time of 0.6 ms. This propagation time would result in a 5 kHzsinusoid having an absolute phase shift of -18.85 radians (∆θ = −2pif∆t).However, the measured relative phase shift would be 0 radians. The unob-tainable phase degeneracy is −3× 2pi.The phase shift calculated with Equation 2.3 results in discontinuitiesat frequencies where the the phase shift changes from −pi to +pi and viceversa. An unwrapping algorithm is used to remove these discontinuities.This is possible because the phase-shift against frequency is a continuouscurve. Any observed discontinuities are always equal to 2pi. They are easilycorrected by incrementing or decrementing the remainder of the signal by2pi.The unwrapping procedure may not correct all of the phase degeneracybetween the trigger and response signals. Bender elements do not operateat low frequencies. An integer (non-fraction) number of phase degeneracydiscontinuities may occur over frequencies below the bender element oper-ating range. Therefore, the unwrapped phase shift is still a relative phaseshift between the trigger and response frequency components. It cannot beused directly to calculate the propagation time. The difference between theunwrapped relative phase shift and the unknown absolute phase shift is thephase offset or phase degeneracy.The way the phase degeneracy is addressed leads to two possible fre-36quency domain velocities: the group velocity or the phase velocity.Group versus phase velocityThe group velocity refers to the propagation speed of a band of frequencies.The phase velocity is the speed of a single frequency component. In a non-dispersive linear elastic continuum, these two velocities must be equal. Indispersive media the velocity is a function of frequency and the group andphase velocities will be different.The cross spectrum technique solves for the propagation time using theslope of the phase shift against frequency, ∆t = (−1/(2pi))(∆θ/∆f). Thisslope is calculated from the unwrapped relative phase shift using linear re-gression over the frequency range observed to have high coherence. Cross-spectrum techniques have been found to result in slower velocities than TimeDomain results (Greening and Nash, 2004; Viana da Fonseca et al., 2009;Yamashita et al., 2009). The cross-spectrum technique and the time domainmethods determine the group velocity.Viana da Fonseca et al. (2009) found that the best fit lines over therange of frequencies corresponding to high coherence values gave inconsistentresults over different frequency windows. They calculated the best fit line fora moving frequency window over the unwrapped phase shift. Each best fitline has a corresponding squared correlation coefficient (r2) indicating howlinear the phase shift is within the moving frequency window. They foundthat for frequency windows of 4 and 6 kHz, the arrival time correspondingto the slope (∆θ/∆f) with the maximum r2 appeared to agree with theselected first arrival from time domain results.Greening and Nash (2004) presented a different variation on the cross-spectrum technique for calculating the phase offset. They solved for thephase offset that resulted in the minimum variance in the resulting velocityover the coherent frequency range. This method does not use a best fitline over the phase shift. Using the calculated phase offset to correct theunwrapped phase shift, they were then able to estimate a phase velocityover the bender element frequency operating range. However, it is not clear37if they are actually calculating the absolute relative phase shift using thistechnique.Boonyatee et al. (2009) presented a variable path length method whichmeasured the phase velocity using a continuous sine wave. This methodcalculated the change in phase shift between the trigger and receiver as thereceiver element is penetrated from 5 to 11 mm into the specimen. Thisresulted in a plot of the change in propagation time against the change inpropagation length, which led to a determination of the phase velocity atthe selected continuous sine wave frequency. An advantage of this system isthat any time lag due to the receiver element transfer function or peripheralelectronics is absolute and does not change the measured phase velocity. Thedisadvantages are the requirement of a bender element that can penetrateinto the specimen during an experiment, it is a destructive measure of thephase velocity. It also results in a single measured phase velocity instead ofmeasurements over the bender element frequency range.Blewett et al. (1999) measured the phase velocity by comparing theresponse due to a square wave trigger to the response due to a continuous sinetrigger. This also resulted in a measured phase velocity at a single frequency,instead of over the operating range of the bender elements. The square wavetrigger response was used to figure out which cycle in the response was dueto the absolute phase shift from the trigger.In dispersive systems, the response signal experiences additional distor-tion. In dispersive systems, the velocity is a function of frequency and thegroup and phase velocities are different. Sachse and Pao (1978) identifieddifferent origins of dispersion as geometric, material, scattering, dissipative,and non-linear. Geometric dispersion has been demonstrated by Arroyoet al. (2006) in a numerical solution for a propagating pulse wave under var-ious sample sizes and boundary conditions. Material dispersion includes thefrequency dependence described by the Biot theory for shear wave propaga-tion in saturated soils (Biot, 1956a,b). Scattering dispersion is due to inho-mogeneities in the specimen. It can occur when the wavelength approachesthe size of the particles or specimen features. Dissipative dispersion is thefrequency dependent attenuation of the waves. Non-linear dispersion is the38possible dependence of the shear wave on the amplitude. All of these dis-persion effects add to the distortion of the trigger signal as it propagatesthrough real soils. Additionally, the conversion between electrical and me-chanical signals and vice-versa by the bender elements is not linear. Thebender elements themselves contribute to the frequency dispersion of themeasuring system.In non-dispersive systems the group and phase velocities are identical.This means that the phase shift against frequency is a perfect straight linethat intercepts the origin. In the time domain, the response signal is atime shifted and amplitude scaled version of the trigger signal. In a non-dispersive system, the response signal waveform is identical to the triggersignal waveform.Frequency domain summaryFrequency Domain methods provide an alternative to Time Domain meth-ods. The Frequency Domain methods interpret the shear wave velocity fromthe phase shift of the frequency components. The challenge in FrequencyDomain methods is accounting for the phase degeneracy, also known as thephase offset, between the absolute phase shift and the measured relativephase shift. Cross-spectrum techniques address this challenge by calculat-ing the slope of the phase-shift. This slope is independent of the phaseoffset. However, cross-spectrum techniques result in a group velocity thatis sensitive to dispersion. Therefore, the measured VS will vary depend-ing on the method of interpretation and the frequency window used in thecross-spectrum technique.2.2.9 SummaryInterpreting the shear wave propagation time with bender elements can bechallenging due to numerous factors that contribute to the measured re-sponse signal. The bender elements should be shielded to avoid electroniccross-talk interference from the trigger element. Series type elements can beshielded with a coating of electrically grounded conductive paint. Parallel39type elements are inherently shielded if the outer plates are wired to ground.Signal stacking is a simple procedure to amplify the systematic features inthe collected signals. The systematic features include the shear wave andinterference from the near field and reflections. Bender element signals canbe classified according to the observed interference.Bender element testing can be interpreted in the time domain and fre-quency domain. The selection of the first-arrival point is subjective andvariable between labs with qualitatively similar signals (Yamashita et al.,2009). The difference between characteristic points is affected by the fre-quency contents in the trigger and response signals. The problem with thecross-correlation method is that the peak corresponding to the arrival isnot clear. The applicable interpretation method depends on type of ob-served signal. Type 3 signals have reflected wave interference and includean apparent low amplitude pre-arrival cycle. No characteristic point in areceived Type 3 signal corresponds to the shear wave arrival (Arroyo et al.,2006). Frequency domain interpretations may be more applicable to Type3 signals. However, existing Frequency Domain methods are sensitive todispersion and bender element transform functions are dispersive (Alvaradoand Coop, 2012).Significant differences in shear wave velocity measurements can occurdue to variations in the installation of the bender elements, types of signaldistortion, and interpretation technique. Bender element testing to confi-dently acquire VS is not a simple exercise.2.3 Factors influencing shear wave propagation insoilThe shear wave velocity is affected by many soil factors, some of these includethe fabric, effective stress state, void ratio, and even ageing. Some of thelater work reported in this thesis involves the development of an empiricalrelationship for G0. The functional form of this empirical relationship hasa theoretical underpinning established from micro-mechanical derivations.This section covers the factors that influence G0 and hence, VS .40Soil behaviour is governed by the physical interaction of many particles ofmany different shapes, sizes, orientations, and contacts. To understand thepropagation of elastic waves, the soil can be idealized, such as a linear elasticcontinuum or a particulate material where the particle contact interaction isassumed to follow Hertz-Mindlin contact behaviour between perfect mono-sized elastic spheres. These models can be used to predict the effect ofchanges in the medium stiffness, density, effective stress, void ratio, andparticle contact behaviour. The factors that govern shear wave propagationvelocity through soil have both theoretical and empirical support.2.3.1 SaturationThe shear wave velocity is faster in dry soil than saturated soil. However,the change in VS between dry and saturated can be calculated assumingthat G0 is constant. At a lower bulk density in dry soil, VS must increase tomaintain a constant G0. Youn et al. (2008) published shear wave velocitiesmeasured from dry and saturated specimens of Toyoura and Silica Sandfrom bender elements and resonant column testing. At the same effectivestress and similar void ratios, the dry soil had a significantly higher G0than the saturated soil. A similar observation was make by Hardin andRichart Jr (1963). They observed a 15 % reduction in G0 with as little as1.4 % moisture content compared to the dry specimen. A similar observationon Ottawa Sand was made by Velea et al. (2000). The source of this dropin G0 with small initial moisture changes was attributed to matrix suctionand surface tension by Cho and Santamarina (2001). After this drasticreduction, Hardin and Richart Jr (1963) observed little additional decreasein G0 with saturation; the change in VS with bulk density could be predictedwith Equation 2.1.Therefore, saturation does not affect G0 except when suction increasesthe effective stress. Saturation does affect VS by changing the bulk density.412.3.2 Micro-mechanical G0 characterizationThe functional form of successful empirical relationships for G0 follows theo-retical micro-mechanical derivations. An underlying theory is an importantaspect for empirical relationships (Wroth, 1984). The additional significanceof this is that it provides a theoretical meaning for the characterized empir-ical coefficients.G0 depends on the soil particle interactions. A micro-mechanical ap-proach to soil behaviour estimates macro-scale soil properties by averagingmicro-scale particle interactions. Closed-form solutions for the macro-scaleG0 have been published (Chang et al., 1991; Petrakis and Dobry, 1989; Yim-siri and Soga, 2000) that account for the applied macro-scale effective stress,the soil particle fabric, and the soil particle interaction behaviour.Petrakis and Dobry (1989) presented solutions for G0 for symmetric ide-alized fabrics under hydrostatic stress with Hertz-Mindlin contact behaviour.These idealized fabrics included Simple Cubic Array, Body Centered CubicArray, and Face Centered Cubic Array. Hertz-Mindlin theory is a com-plete contact model that describes the response between two deformableperfectly linear-elastic uniform spheres. It only requires two elastic con-stants for the soil particles. Petrakis and Dobry (1989) observed that thetheoretical micro-mechanical G0 was dependent on the number of contactsper particle, CN , and that CN can change significantly with the void ratioremaining essentially constant.Chang et al. (1991) presented a closed form solution for G0 for isotropicfabric, hydrostatic stress, and with Hertz-Mindlin particle contact behaviour.Their equation has been reformulated into three terms in Equation 2.4.G0 =5− 4νp10− 5νp(Gp√3√2pi(1− νp))2/3(CN1 + e)2/3 (σ′0)1/3(2.4)The first term, 5−4νp10−5νp(Gp√3√2pi(1−νp))2/3, is constant and is defined by thelinear elastic properties of the material forming the soil particles: Gp andνp (elastic shear modulus and Poisson’s ratio). The second term,(CN1+e)2/3,42represents the fabric. The last term contains the dependence of the Hertz-Mindlin inter-particle contact behaviour on the hydrostatic effective stress.Emeriault and Chang (1997) observed that this equation over predictsthe stiffness measured for quartz and attributes it to the averaging processto convert micro to macro behaviour. For a sample of spherical quartz par-ticles with a void ratio of 0.8 under 100 kPa of effective hydrostatic stress,Equation 2.4 results in an unrealistically large estimated shear stiffness of579 MPa. This value was calculated using the elastic properties of naturalquartz: Gp = 46.91 GPa and νp = 0.0600 (Heyliger et al., 2003). Thisstiffness calculation used an estimated CN of 6.88 from a relationship pre-sented by Chang et al. (1991), CN = 13.28 − 8e. Assuming the soil is dryand Quartz has a specific gravity of 2.647, this void ratio results in a bulkdensity of 1470 kg/m3. The shear wave velocity for this material usingEquation 2.1 is then 627 m/s. This stiffness and velocity exceed the rangeof values typically measured in soil.Therefore, Equation 2.4 is not directly applicable to real soil measure-ments. If the particle properties and fabric were measured, it would not beable to predict the shear wave velocity or G0. However, it does provide aninformative analogue for soil behaviour. A stiffer G0 would be expected insoils comprised of stiffer particles, in closely packed soils with higher coor-dination numbers, and in solids under higher effective stresses.Much of the early development of empirical G0 relationships involvedB.O. Hardin and his colleagues performing resonant column testing. Theform of the early empirical relationship for G0 is Equation 2.5:G0 = Af(e)σ′n0 (2.5)This equation includes two empirical coefficients (A and n) and a func-tion of the void ratio, f(e). The comparison of this equation and Equation 2.4suggests that the leading A coefficient depends on the particle properties,f(e) is a function of the fabric, and the n exponent is 1/3 for Hertz-Mindlincontact behaviour.Fam et al. (2002) presented an experimental study that changed the co-43ordination number without changing the effective stress. They prepared dryspecimens of sand with salt grains. These dry specimens were consolidatedand then saturated. The saturation caused the salt particles to dissolve.This increased the void ratio and transferred more load to the soil particleforce chains. They observed a 25 % drop in the shear wave velocity once thesalt was removed. By accounting for the effect of the change in mass andvoid ratio, they concluded that 10 % of this VS drop was due to a change insoil fabric. Therefore, a reduction in the coordination number has a largereffect on VS than an increase in the strength of the force chains. This wasconfirmed in a DEM model by Somfai et al. (2005). They observed that thestrength of the force chains affected the amplitude of the propagating shearwave, but did not affect the velocity.Hardin and Richart Jr (1963) demonstrated that VS was not related tothe relative density, just the void ratio. For a single soil, there will be arelationship between VS and the relative density. However, this relationshipwill not be applicable to other soils. Relative density relationships are notapplicable beyond the immediate context over which it was developed. VScannot be used directly to estimate the relative density of a soil.Hardin and Black (1966) proposed three equations for f(e). The first twof(e) equations were for round grained Ottawa sand at low stresses, Equa-tion 2.6, and high stresses, Equation 2.7. The high-stress f(e) equation isvery similar to Equation 2.6 and was never used again. The third equation,Equation 2.8, was for angular crushed quartz silt. These equations implythat VS and CN are more sensitive to void ratio changes in angular soilsthan in round grained soil. These equations did not work with high voidratio soils. Hardin and Blandford (1989) proposed Equation 2.9, which didnot have this shortcoming.f(e) =(2.17− e)21 + e(2.6)f(e) =(2.12− e)21 + e(2.7)44f(e) =(2.97− e)21 + e(2.8)f(e) =10.3 + 0.7e2(2.9)Hardin and Black (1968) investigated the application of forms of Equa-tion 2.5 in normally consolidated clays. They found that Equation 2.8 wasapplicable for clays if the void ratio did not approach 2.97. They furthervalidated this f(e) application with more clay soils in a discussion of thisarticle (Hardin and Black, 1969).Using the proposed f(e) equations, this early empirical relationship (Equa-tion 2.5) was found to be broadly applicable from clays through sands(Hardin and Drnevich, 1972). The form of this empirical equation is similarto the micro-mechanical solution. One drawback is that this relationshipis in terms of hydrostatic effective stress, i.e. K0 = 1.0, which is rarelyencountered in-situ.2.3.3 Anisotropic effective stress stateThe anisotropic stress state can be completely described by three princi-pal stresses and an orientation. Principal stress directions are normal toplanes with zero shear stress. Principal stresses are given the symbols σ1,σ2, and σ3. A shear wave propagates in one direction with particle motionin the perpendicular direction. It has been found that the shear wave prop-agation velocity only depends on the effective stresses in the directions ofwave propagation and particle motion (Bellotti et al., 1996; Hardin, 1980;Roesler, 1979; Wang and Mok, 2008). It is independent of the out-of-planeeffective stress. Therefore, it is incorrect to use the mean effective stress, p,in empirical G0 and VS equations.Roesler (1979) developed the experimental programme and results todemonstrate this independence on the intermediate stresses. It was exper-imentally demonstrated on a 30cm3 specimen of dry sand. This specimenhad one internal excitation source and two internal transducers to measure45the shear wave velocity propagating in one direction. A vacuum pressurewas used to apply an average effective stress to the soil. The top of the cubicspecimen was loaded to increase one principal effective stress. The specimenwas rotated to align the shear wave propagation direction and particle mo-tion with each of the three principal stresses. Figure 2.9a shows the effectof increasing the stress aligned with the shear wave propagation direction.Figure 2.9b shows the effect of increasing the stress in the direction of shearwave particle motion. Figure 2.9c shows the effect of increasing the out-of-plane effective stress. In Figure 2.9c the mean effective stress (σ1+σ2+σ3)/3is increasing and the shear wave velocity is constant. Therefore, any empir-ical formulation for VS or G0 in terms of the mean stress is fundamentallyflawed, even though it would work if two of the principal stresses are thesame.The results by Roesler (1979) depicted in Figure 2.9c are conclusive.They were immediately supported by Hardin (1980) and further confirma-tion was provided in a later study by Bellotti et al. (1996) and then by Wangand Mok (2008). All of these investigations confirmed the independence ofVS on the out-of-plane effective stress.Hardin and Blandford (1989) reformulated their empirical equation forG0 to account for the observations by Roesler (1979).2.3.4 Age and StiffnessAgeing affects G0. Ageing is observed in reconstituted laboratory speci-mens over a short time frame. Natural deposits continue to age for muchlonger geological-scale durations. G0 increases with time have been mea-sured with resonant column testing (Afifi and Richart, 1973; Anderson andStokoe, 1978; Hardin and Richart Jr, 1963) and bender elements (Baxterand Mitchell, 2004) in the laboratory.Hardin and Richart Jr (1963) observed a strong time-dependence in VSfor crushed quartz silt. Once they recognized that age duration was a vari-able, they kept it constant between experiments. They were able to developan empirical relationship for G0 in terms of stress and void ratio by perform-460 20 40 60 80 100 120 140 160 180200220240260280300320σ’v (kPa)V S (m/s)  σ’h=σ’s=48 kPaσ’v=σ’h=90 kPaσ’v=σ’h=90 kPa(a) VS dependence on σ′v0 20 40 60 80 100 120 140 160 180200220240260280300320σ’h (kPa)V S (m/s)  σ’v=σ’s=48 kPaσ’v=σ’h=55 kPaσ’v=σ’h=90 kPaσ’v=σ’h=95 kPa(b) VS dependence on σ′h0 20 40 60 80 100 120 140 160 180200220240260280300320σ’s (kPa)V S (m/s)  σ’v=σ’h=48 kPaσ’v=σ’h=55 kPaσ’v=σ’h=95 kPaσ’v=σ’h=95 kPa(c) VS dependence on σ′sFigure 2.9: Dependence of VS on anisotropic stresses with σ′v equalto the stress in the wave propagation direction, σ′h the stressin the particle motion direction, and σ′s the stress orthogonalto both the wave direction and particle motion, adapted fromRoesler (1979). Adapted with permission from the AmericanSociety of Civil Engineers. This material may be downloadedfor personal use only. Any other use requires prior permissionof the American Society of Civil Engineers.ing resonant column testing after a constant amount of elapsed time at eachstress state. They observed that age has less of an influence in Ottawa Sandthan in quartz silt. Hardin and Black (1968) found that the increase in den-sity from small volumetric creep changes did not account for the observed47effect of age on G0. Hardin and Black (1969) stated that the stiffness thatbuilt up during ageing was sensitive to disturbance and could be partially ortotal destroyed by changes in effective stress. However, little evidence wasprovided for this conclusion.Afifi and Richart (1973) further investigated the effect of time on G0.The effect was quantified using Equation 2.10. This quantification was firstused by Afifi and Richart (1973) and later termed NG by Anderson andStokoe (1978).NG =∆G0G1000 (log10 (∆t))(2.10)Afifi and Richart (1973) and Anderson and Stokoe (1978) plotted G0against log-time. In kaolinite, Afifi and Richart (1973) observed a steepen-ing of G0 against log-time when it became log-linear. Conversely, Andersonand Stokoe (1978) observed a flattening of the rate of increase inG0 measure-ments when it became log-linear. The conflict between these observationshas not been resolved. The increase in G0 with time is normalized to G0measured at 1000 minutes(G1000) to avoid these initial G0 effects. Andersonand Stokoe (1978) observed that in sands the behaviour was log-linear bythe time they were able to acquire their first measurement. They speculatedthat it may not be log-linear at very short age durations due to visco-elasticeffects.Table 2.4 details the results of various experimental investigations intofactors that influence NG. The expected NG factor for clean sands is lessthan 3 % (Afifi and Richart, 1973; Anderson and Stokoe, 1978). VS mea-surements against time require careful interpretation to observe this smallincrease. The current state of bender element practice may be unable toconfidently resolve the increase in VS due to ageing.Mitchell (2008) reviews the hypothesized mechanisms for the sourceof the effect of ageing on G0. He concludes that a chemical solution-precipitation-cementation hypothesis is unlikely to account for the observedstiffness increase in many experiments. First, Baxter and Mitchell (2004) didnot observe a dependence on temperature. Second, it can not account for the48Table 2.4: Experimental investigations into factors influencing theageing effect on G0Property EffectParticle size Fine grained: NC clay NG=5-20 %, clean sands:NG=1-3 % (Afifi and Richart, 1973; Andersonand Stokoe, 1978)Saturation Saturated kaolinite: NG=11 %, dry kaolinite:NG=6% (Afifi and Richart, 1973)OCR-Clays NC clay NG=5-20 %, OC clay NG=3-10 % (Afifiand Richart, 1973; Anderson and Stokoe, 1978)OCR-Sands NG is higher for NC sands. However there isa measurable increase in G0 after unloading orreloading (Jovicic and Coop, 1997)Plasticity index NG increases with PI (Mitchell, 2008)Undrained shear strength NG decreases with increasing su (Anderson andStokoe, 1978)Void ratio NG has been observed to both increase (Ander-son and Stokoe, 1978) and decrease (Baxter andMitchell, 2004) with increased void ratioFines content NG increases with fines content (Anderson andStokoe, 1978)Confining stress NG increases (Anderson and Stokoe, 1978)Temperature No conclusive effect in Evanston beach sand andDensity sand (Baxter and Mitchell, 2004)Pore fluid NG in water was higher than in ethylene glycol(Baxter and Mitchell, 2004)Stress ratio NG increases with R = σ′v/σ′h (Mitchell, 2008)observed stiffness increase in dry sands. Additionally, Clayton (2011) notedthat cementation has a huge effect on G0 and the observed effect of ageingis small. A microbiological hypothesis may influence ageing under specialenvironmental circumstances, but not globally as observed in almost everyageing investigation. After an examination of the observed effects of age-ing, Mitchell (2008) concludes the the physical rearrangement and a stressredistribution process plays the dominant role in the ageing phenomenon.He views this process as a secondary compression for sands where the soil49skeleton adjusts to the boundary conditions. Petrakis and Dobry (1989)and Santamarina and Cascante (1996) both noted that significant changesin CN can occur with negligible changes on the void ratio. The physicalrearrangement mechanism can account for the observed ageing increase inG0.2.3.5 SummarySoil models are simplifications of a complex medium. Linear elastic andHertz-Mindlin assumptions have been used to gain theoretical insight intofactors affecting small strain wave propagation. The behaviour of thesesimple models have empirical support. The shear wave velocity and smallstrain stiffness depend on in-plane effective stress state, void ratio, fabric,coordination number, and age. The shear wave velocity is a soil measurethat can be obtained in-situ through seismic techniques and in the laboratorythrough bender element and resonant column testing.2.4 Stiffness degradation with strainAs introduced in Chapter 1, the shear stiffness of a soil decreases as addi-tional shear stress is applied. In soils, beyond a very small linear elasticregion, the tangent stiffness and secant stiffness both depend on the shearstrain. The tangent stiffness is the local slope of the shear stress againstshear strain. The secant stiffness is the total change in shear stress dividedby the total shear strain since the start of a shear path. The tangent stiffnessis a derivative. It is very sensitive to noise and is difficult to quantify exper-imentally. The secant stiffness is easy to quantify once the strains exceedthe measurement uncertainty. Furthermore, the secant stiffness can be usedto directly convert total applied shear stress to shear strain and vice versa.Many soil variables govern the secant stiffness curves. To investigate theeffect of these variables it is useful to normalize the curves. Shozen (2001)normalized the secant stiffness degradation curves to compare different testconditions. He normalized Gsec using the measured secant stiffness at 0.03 %shear strain and 10 minutes of ageing along a conventional stress path, if the50comparison was between experiments at the same stress ratio. Otherwise,he normalized the secant stiffness with the mean effective stress or the meaneffective stress to the power of 0.6. Lam (2003) compared different testconditions by normalizing the secant stiffness with the mean stress raised toa power of 0.7.Measuring the shear wave velocity permits the normalization of Gsecwith G0. This is useful for comparing different experimental conditions andto other published observations. More importantly, VS can be measured in-situ to acquire G0. This can be combined with published normalized curvesto estimate the in-situ deformation properties of soils. This is particularlyuseful in soils that cannot be routinely sampled undisturbed - such as sandsand gravels.Ageing results in a very small increase in G0 in sands, significant increaseon the secant modulus over the small strain range (Howie et al., 2002; Lam,2003; Shozen, 2001), and large strain strength measurements are unaffected(Howie et al., 2002; Lam, 2003; Mitchell, 2008; Shozen, 2001). This suggeststhat the shape of the Gsec/G0 versus shear strain will change with age.Darendeli (2001) proposed a hyperbolic model describing the shape ofthe normalized Gsec/G0 curves. His model had two parameters: a refer-ence shear strain to 50% modulus degradation and a curvature parameter.Empirical formulas for these parameters were developed by Wichtmann andTriantafyllidis (2013) and Oztoprak and Bolton (2013). This same approachcan be used to quantify the effect of ageing on the change in shape of theGsec/G0 curves.Fitting Gsec/G0 curves with hyperbolic relationships reduces the entirenormalized stiffness curve to two or three variables depending on the hyper-bolic model. Seed et al. (1984) and Seed et al. (1986) presented results forgranular soils in terms of relative density, mean particle size, and mean effec-tive stress. Wichtmann and Triantafyllidis (2013) characterized the effect ofthe uniformity coefficient and mean grain size on the degradation of Gsec/G0curves. This was accomplished using resonant column testing on a set ofspecimens with different particle size distributions. The specimens were cre-ated by mixing sieve-separated constituents of a natural quartz-sand. The51amplitude of the resonant column cycles was increased to measure the degra-dation from G0 to 0.05 % shear strain. They fitted a hyperbolic curve to thecalculated normalized stiffness degradation curves. They then empiricallyrelated the soil indices Cu and d50 to the hyperbolic curve coefficients. Theyfound that the non-linear stiffness degradation was mostly independent ofthe mean grain size. Oztoprak and Bolton (2013) characterized the effectof mean effective stress, uniformity coefficient, relative density, and void ra-tio on the normalized shear stiffness curves for sands. They characterizedthese effects by fitting hyperbolic curves to a dataset of laboratory measure-ments. This dataset was developed by compiling and digitizing publishedstress-strain curves for sands. They then developed empirical relationshipsfor the hyperbolic model coefficients based on these soil parameters. Theproperties required are frequently estimated (mean effective stress, relativedensity, void ratio) or measured (uniformity coefficient, mean particle size).Equation 2.11 is the hyperbolic-strain stiffness model proposed by Ozto-prak and Bolton (2013). Note that their equation was in terms of γ = εa−εrfor shear strain. The triaxial shear strain is εq = 2/3γ. This 2/3 scaler can-cels out by taking the ratio of the shear strains and does not affect theequation or the coefficients.GsecG0=11 +(εq−εqeεqr)a (2.11)This hyperbolic model has three coefficients: εqe, εqr, and a. The εqeparameter is the elastic threshold strain. At strains below εqe, the secantstiffness equals the very small strain stiffness: Gsec = G0. The εqr parameteris a reference strain that corresponds to Gsec/G0=0.5. The a parameter isthe curvature of the normalized secant stiffness curve. As this parameterincreases, the behaviour becomes more brittle and the stiffness degradationbecomes steeper. It becomes stiffer before the reference strain and softerbeyond the reference strain. Figure 2.10 depicts the effect of these threevariables using typical values.Oztoprak and Bolton (2013) characterized the effect of the mean effec-tive stress (p′), uniformity coefficient (Cu), relative density (Dr), and void520.001 0.01 0.1 1 1000.10.20.30.40.50.60.70.80.91εq (%)G sec/G0  a=0.7εqe=0.007%εqr=0.01εqr=0.05εqr=0.1(a) Effect of reference strain0.001 0.01 0.1 1 1000.10.20.30.40.50.60.70.80.91εq (%)G sec/G0  εqr=0.1%εqe=0.007%a=0.5a=0.7a=0.9(b) Effect of curvature parameter0.001 0.01 0.1 1 1000.10.20.30.40.50.60.70.80.91εq (%)G sec/G0  a=0.7εqr=0.1%εqe=0.0%εqe=0.0007%εqe=0.003%(c) Effect of elastic strain threshold pa-rameterFigure 2.10: Effect of parameters on modelled normalized secantshear stiffness (Equation 2.11)ratio (e) on the hyperbolic-strain model coefficients. The threshold straintrended linearly with the reference strain, Equation 2.12. The referencestrain, Equation 2.13, decreased with the uniformity coefficient, increasedwith mean stress, and increased with the multiple of the void ratio and rel-ative density. They found that the curvature parameter was best estimatedusing only the uniformity coefficient. The Cu is an intrinsic soil propertydefined by the particle size distribution; it is independent of the state of thesoil. Alternatively, Wichtmann and Triantafyllidis (2013) found that the53curvature was independent of the uniformity coefficient and recommended aconstant value of 1.03. Wichtmann and Triantafyllidis (2013) also calibratedEquation 2.15 for the reference strain in terms of Cu and mean effective stressp. The hyperbolic model used by Wichtmann and Triantafyllidis (2013) didnot include a threshold strain.The following are from Oztoprak and Bolton (2013):εqe = 0.002 + 0.012εqr (2.12)εqr = 0.01C−0.3up′pa+ 0.08eDr (2.13)a = C−0.075u (2.14)The following are from Wichtmann and Triantafyllidis (2013):εqr = 0.000652exp (−0.59ln (Cu))(p′pa)0.4(2.15)a = 1.03 (2.16)Neither of these empirical formulations include the effect of ageing, initialstress ratio, or stress path. As confirmed in the current work and previouspublished research (Afifi and Richart, 1973; Anderson and Stokoe, 1978;Baxter and Mitchell, 2004) ageing results in a small increase in G0, a largeincrease in Gsec (Howie et al., 2002), and has no effect on the large strainstrength (Mitchell, 2008). These three observations can all occur if ageingincreases both the curvature and the reference strain of the model normalizedsecant stiffness curve.2.5 Proposed researchThis research began as a continuation of the laboratory studies in FraserRiver Sand that were performed by Shozen (2001) and Lam (2003). These54investigations did not have shear wave measurements, which precluded thenormalization of the measured non-linear shear stiffness curves with G0.The first objective of this research program was to add bender elementsto the UBC triaxial apparatus in order to obtain the capability of acquiringVS and G0.Based on the preceding background section, it is clear that particularattention must be paid to the interpretation of the bender element signalsin order to make consistent estimates of VS and resolve the anticipated smallincrease in VS with age expected for a clean sand.The second objective of this research program was to investigate theapplication of bender elements to observe very small changes in VS duringageing and confidently characterize both G0 and an NG factor.The previous UBC research (Lam, 2003; Shozen, 2001) observed thatthe specimen age had a significant impact on the secant stiffness curve.Conversely, this literature review established that ageing has a small effecton the very small strain G0. Once the first two objectives are met, thebender element equipped triaxial apparatus will be used to investigate theeffect of ageing on the shape of the normalized secant stiffness degradationcurves.The third objective of this research was the integration of G0 from benderelement VS interpretations with triaxial measurements to study the effect ofage on the stiffness of Fraser River Sand.55Chapter 3Equipment, materials, andinitial resultsThe first objective of this research was to add bender elements to the UBCtriaxial equipment. Bender elements were fabricated and installed in thetriaxial apparatus used by Shozen (2001) and Lam (2003). The data acqui-sition system and control needed to be replaced to allow sufficient samplingrates for bender element testing.Initial testing was performed to evaluate the installed bender elements.This was done to see if the new equipment had the capability to allowconfidence in acquired G0 and could be used to investigate the effect ofageing on Fraser River Sand stiffness.This chapter includes these initial triaxial results. The past experimentsby Shozen (2001) and Lam (2003) were replicated in order to check if theredeveloped equipment provides similar results. The purpose was to confirmthat the new equipment and data reduction procedures perform as expectedand that data from the previous investigations could be considered withthe current one. The current study investigated Fraser River Sand. Thiswas the same material that was tested in previous investigations. However,the tested material was from a different bulk sample with slightly differentintrinsic properties. It is necessary to compare the results to past studies tocheck that the updated equipment provides similar results and to observe56the consequence of testing specimens from different bulk samples.3.1 Test programmeThis research project was instigated to complement and continue the pre-vious investigations by Shozen (2001) and Lam (2003) with bender elementshear wave velocity measurements. The experimental variables in this inves-tigation include the consolidation stress ratio, age duration, and shear pathto failure. Figure 3.1 depicts these variables on a p-q stress path plot.0 50 100 150 200 250050100150200250300 SR=1.0, Ageingp’ (kPa)q (kPa)  SR=2.0, Ageing SR=2.8, AgeingConsolidationConventional shearConstant p’Slope −1 shearSlope 0 shearFailureFigure 3.1: Experimental variables include consolidation stress ratio(1.0, 2.0, 2.8), age duration (10 minutes, 100 minutes, 1000minutes), and shear path to failure (conventional, constant p,slope -1, and slope 0)Shozen and Lam carried out tests over a range of stress paths and con-solidation stress ratios. This investigation followed the same general testingprocedure. The consolidation phase of testing occurs over two stages. InFigure 3.1, consolidation begins near the point (p, q) = (20kPa, 0kPa). Thefirst stage of consolidation is an increase in the axial stress until the desired57stress ratio is achieved. This occurs over the blue line segment in the lowerleft corner of Figure 3.1. The second stage of consolidation involves increas-ing the radial and axial stresses simultaneously up to a radial effective stressof 100 kPa. A constant stress ratio (1.0, 2.0, 2.8) is maintained during thesecond stage of consolidation.The next phase of testing involves ageing the specimen at a constantstress state for a set amount of time. In Figure 3.1, this is depicted as a bluepoint for each of the three stress ratios. The second experimental variable isthe age duration. In this investigation, age durations were 10 minutes, 100minutes, or 1000 minutes.The last phase of testing is the stress path to failure. Figure 3.1 depictsfour shear stress paths from each ageing point to the failure surface. The“Conventional” stress path is an increase in axial stress with no changein radial stress. The “Constant P” stress path is an increase in the axialstress and decrease in the radial stress to maintain a constant mean stress.The “Slope -1” shear path is an increase in the axial stress and decrease inthe radial stress by the same amount. This maintains a constant in-planeeffective stress (σ′a+σ′r) during shear. The “Slope 0” shear path is a decreasein the radial stress while maintaining a constant axial stress.The completed test programme included significant amounts of workon testing and evaluating equipment and bender element techniques. Manyexperiments were repeated at the same test conditions. The test programmeincluded two specimens at a stress ratio of 1.0, 46 specimens at a stressratio of 2.0, and eight specimens at a stress ratio of 2.8. It included 6specimens aged for 10 minutes, 33 specimens aged for 100 minutes, and 17specimens aged for 1000 minutes. It included 32 specimens sheared along aconventional stress path, 17 sheared along a constant “p” stress path, fiveshear along a slope 0 stress path, and two sheared along a “-0.5” stress path.These experimental details are summarized in Table 3.1.58Table 3.1: Experimental detailsCount Stress ratio Age (min) Shear path21 2.0 100 C6 2.0 100 P6 2.0 1000 P4 2.0 10 C3 2.0 1000 C3 2.8 1000 P2 1.0 100 C2 2.0 1000 01 2.0 10 -0.51 2.0 100 01 2.0 10 P1 2.0 1000 -0.51 2.8 100 C1 2.8 100 01 2.8 1000 C1 2.8 100 P1 2.8 1000 03.2 Material tested3.2.1 Fraser River Sand sample propertiesA large sample of Fraser River Sand was sourced from Mathers E BulldozingCo. Ltd. on October 6, 2010. Table 3.2 summarizes measured intrinsicproperties from this sample. Tests were repeated multiple times to estimatethe standard deviation of the mean of the intrinsic properties. Figure 3.2depicts the measured particle size distribution. The grain shape is semi-angular. It is a finer bulk sample than what was tested previously. Thissample classifies as a poorly graded sand (SP) by the USCS classification.The mineralogy of this sample was not tested. A published mineralogicalresult for Fraser River Sand contained 40 % quartz, 11 % feldspar, 45 %unstable rock fragments, and 4 % miscellaneous detritus (Garrison et al.,1969).59Table 3.2 presents the classification properties of the sand tested andalso presents those obtained by Shozen and Lam. The characteristic particlesizes were interpolated from adjacent sieve results (as shown in Figure 3.2).In this sand the ASTM method for maximum relative density results in alower than expected void ratio. To avoid this conflict with expectations,Shozen estimated emax as the maximum void ratio achieved during waterpluviation. The same technique for emax is used in this thesis so that waterpluviated relative densities agree with values previously measured at UBC.It is recognized that this means that the relative density calculations in thisthesis are not transferable to other investigations or other sands. However,the relative density is not a good property to use to compare different sands(Hamidi et al., 2013) and the shear wave velocity depends on the void rationot the relative density (Hardin and Richart Jr, 1963). The results for bothof these techniques for estimating the maximum void ratio are included inTable 3.2. This table also shows that the current specimen D50 is slightlyfiner than the previous sample tested by Shozen.Table 3.2: Intrinsic properties of Fraser River Sand sample, valuesreported by Shozen (2001) and Lam (2003) are in parenthesesProperty Average RangeFines content ASTMD1140-000.5 % 0.47 to 0.54 %D10 ASTM D422-63 0.140 mm (0.161, 0.150mm)0.136 to 0.143 mmD50 ASTM D422-63 0.214 mm (0.271, 0.270mm)0.207 to 0.218 mmD60 ASTM D422-63 0.232 mm (NA, 0.280mm)0.228 to 0.238 mmUniformity CoefficientASTM D422-631.66 (1.88, 1.87) 1.61 to 1.72Specific Gravity ASTMD854-102.730 (2.719, 2.719) 2.723 to 2.736emin ASTM D4254-00 0.659 (0.627, 0.627) 0.650 to 0.679emax ASTM D4253-00 0.994 (0.955, NA) 0.977 to 1.006emax Water pluviated 1.05 (0.989, 0.989)600.01 0.1 1 100102030405060708090100Percent finer (%)Particle size (mm)   d50:0.21 mm d60:0.23 mm d10:0.14 mm d30:0.18 mm Cu:1.66 Cc:1.01 Silt Sand  Gravel ShozenCurrent studyFigure 3.2: Particle size distribution for Fraser River Sand samplefrom the current study and from the sample used by Shozen(2001)Smaller sub-samples were prepared from the large bulk sample prior tospecimen preparation. The complete details are described in Appendix B.The sample preparation screened out the large particles, washed out thefines, and saturated the sand in boiling water to remove the air.3.2.2 Specimen reconstitutionVaid and Negussey (1988) demonstrated that clean sand specimens reconsti-tuted by water pluviation were almost full saturated. Saturated specimensare necessary in order to allow the change in the specimen volume to be de-termined from the quantity of water expelled or admitted to the specimenvoids. The water pluviation technique also produces specimens are repeat-able with a homogeneous void ratio distribution. Repeatable specimens arenecessary for reproducible results. Homogeneous specimens are assumedwhen interpreting the triaxial test as an element test. Further details for61the water pluviation procedure can be found in Appendix B.It was noted that the void ratio at the end of water pluviation was con-sistently greater than the maximum void ratio determined following ASTMprocedures. As previously stated, a similar observation was made by Shozen.The average void ratio obtained during loose specimen preparation is in-cluded in Table 3.2.3.3 Improved triaxial apparatusFigure 3.3 is a diagram of the triaxial apparatus used in this research pro-gram. This apparatus includes five external sensors. The load cell is usedto measure the axial load applied through the loading ram. The LVDT re-sponds to the displacement of the top cap. The two pressure transducersare used to measure the pore water and chamber pressure. The differentialpressure transducer monitors the elevation head in a reservoir of water thatchanges as the specimen expels or admits water into its void volume.A new data acquisition system was developed using a National Instru-ments board. This system was controlled with a custom developed programmade with National Instrument’s LabView software. Routines for auto-mated back pressure saturation, stress ratio consolidation, performing suitesof high sampling rate bender element tests, and testing various stress pathswere developed.Additional details for this apparatus can be found in Appendix A. Theprocedures for sample preparation, specimen preparation, and triaxial test-ing are in Appendix B. Appendix C covers the triaxial data reduction.62SpecimenTop CapLoad CellLVDT 2LVDT 1Chamber pressuretransducerChamber pressure electro-pneumatic regulatorPore pressuretransducerDPWPTBack pressuresupply700 kPaRPATMAxial pressure electro-pneumatic regulator700 kPaRMotor for strain controlled testsThis pressure gauge and valve can beused to check for leaks in the system.  This is done by applying pressure to the system, closing this valve, and observing if the pressure reading on the gauge drops.This reservoir serves to supplywater vapor pressure and inhibitevaporation in the volume changemeasuring system.These swage tube coilsincrease the path dissolvedair must travel to de-saturatethe pressure transducers.Both pressure transducers are zeroed atthe same ATMand elevation pressureThis manual regulator is usedto lift the driving piston.  Prior to testing a small downward pressureis applied by the axial EP andcountered with this regulator to causethe driving piston to float.On a stress controlled test the motor portionof the driving ram would be raised to avoidcontact.Doubleactingpiston1234 567891011100 mmThe DPWPT measures the elevation pressurein the one or both of the glass cylinders wherethe specimen can drain to or draw from.  Theback pressure is applied to both sides of theDPWPT.Figure 3.3: Triaxial diagram633.3.1 Improved stress path controlThe stress path for consolidation and shearing imposed during the triax-ial test is computer controlled. The triaxial equipment has two electricalpressure regulators to control the downward load on the axial ram and thechamber pressure (see Figure 3.3). These devices provide indirect control ofthe axial and radial effective stress on the specimen. The computer controlof these two regulators is based upon real-time data reduction of the triaxialsensor measurements (load cell, pressure transducers, differential pressuretransducer, axial displacement). The data recorded from these sensors areused to calculate the specimen cross section area, current axial stress, andcurrent radial stress. Software routines calculate the voltage increment toapply to each electrical pressure regulator based on the current stress state,the desired future stress state, and the past applied voltages and stresses.The change in the applied voltage increment is based on a feedback loopduring back pressure saturation and consolidation. During non-conventionalstress path testing, it is based on linear regression results to hit the desiredstress state on the next iteration of the triaxial control program.The stress control system includes fixed limits on the incremental changein applied voltage. These limits reduce the chance that a noise spike in thesensor measurements will result in a sudden and drastic change in the appliedvoltage to the electrical regulators.Figure 3.4 compares computer controlled stress paths for the present tri-axial equipment to previous experimental results. In this figure the resultsby Shozen (2001) and this investigation were from specimens consolidated ata stress ratio of 2.0. The results from Lam (2003) were from specimens con-solidated at a stress ratio of 2.1. This figure demonstrates that the improvedtriaxial system has better stress control than was previously achieved. Lin-ear shear stress paths from the start of shearing to failure are achieved. Theconstant “p” stress path is significantly improved.64100 105 110 115 120 125 130 135 140100120140160180200220p’ (kPa)q (kPa)  StylerShozenLamFigure 3.4: Comparing stress path control for new triaxial control sys-tem (blue) against previous results from Shozen (2001) (red) andLam (2003) (green) for Slope 0 and Constant P shear paths3.3.2 Addition of bender elementsThe triaxial apparatus shown in Figure 3.3 was modified to include benderelements. Bender sockets have been cut into the triaxial base pedestal andtop cap. The bender elements were mounted as cantilevers within thesesockets.The UBC triaxial apparatus was initially modified with two X-poled se-ries bender elements for triggering and receiving shear waves. This systemexperienced significant cross talk between the elements. An attempt wasmade to shield these series bender elements with conductive paint. Thisshielding was attached to a building ground reference, but created groundloops that ruined the other triaxial sensor measurements. The bender el-ement system was reconfigured using two Y-poled parallel type bender el-ements to take advantage of the inherent shielding (Lee and Santamarina,2005).65Figure 3.5 shows details of the installed bender elements. The benderelements were fabricated from a Y-poled parallel piezoceramic sheet. Thispiezoceramic sheet was sourced from Piezosystems, Inc., part number T226-H4-503Y. The composition of the piezoceramic in the bender elements usedin this study is lead titanate zirconate. The bender elements are approx-imately 14 mm long and 10 mm wide. They were mounted on a piece ofprinted circuit board. A lower corner of the bender element was milledoff to expose the centre shim for wiring in parallel. To avoid shorting theelectrical potential difference across the piezoceramic plates, five coats ofpolyurethane were applied for waterproofing the bender element prior toscrewing the printed circuit board base into the apparatus. To protect thiscoating, the top cap and base pedestal must only be cleaned with flow-ing water. Cleaning the apparatus with pressurized air will damage thepolyurethane coating and electrically short the bender elements. The recesswas filled with RTV silicone. The final bender element penetration lengthinto the sample was 4.5 mm for the base pedestal and 4.6 mm for the topcap.The apparatus includes a signal amplifier on the bender element re-sponse. This is a battery powered 1000-fold amplifier which is applied tothe signal prior to analogue to digital conversion and recording. For eachbender test, the data acquisition system sampled the applied trigger signaland amplified response signal at a rate of 500 kHz for 20 ms. For discretebender element testing, each response signal was a result of 10 stacked sig-nals. A minimum 100 ms pause was included between stacked signals toallow reflected waves to dissipate. No filtering of the response signals wasperformed.For repeatable bender element signals, the polarity of the trigger andreceiver bender elements must be aligned when the top cap is placed on thesoil specimen. To verify the alignment, the bender elements were placed incontact in the same plane and a trigger sine pulse was applied. Figure 3.6adepicts the measured response of in-contact bender elements. The triggersine pulse is not inverted in the responding bender element. The resonanceand damping of the receiver bender element are apparent. The resonant66ABACDEFA: POROUS RINGB: TRIAXIAL BASE PEDESTALC: POTTED IN RTV SILICONED: PRINTED CIRCUIT BOARD BASEE: SCREWSF: PARALLEL BENDER ELEMENT    BRASS CENTER SHIM    5 COATS POLYURETHENE  Figure 3.5: Bender element installation detailsfrequency is near 3.4 kHz and the system is under-damped with ζ=0.5 to0.6. It appears that the bender elements are only in contact for the initialrise of the trigger pulse.Figure 3.6b depicts the measured bender element response for a 100 kHzsine pulse through air and through water. Through air, the response isnegligible. Through water, a clear long duration response is measured. Itis believed that this is a result of the RTV silicone potting (see Figure 3.5)generating compression waves when the bender element cantilever beambends. This same effect on the receiving end is transferring the arrivingcompression waves into the bender element and generating a response. Thiscompression wave feature may be present in the measured signals.A bender element test begins with applying a trigger signal waveform toone of the bender elements. The received signal and applied trigger signal arerecorded. The test is repeated ten times and signal stacking is performedto increase the signal to noise ratio. The applied trigger signal depends670 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.8−0.6−0.4−0.200.20.40.60.8Time (ms)Amplitude  TriggerReceiver(a) Aligned polarity of the bender elements initially in contact0In Air  TriggerReceiver0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20Time (ms)In Water(b) Bender element response through triaxial chamber filled withair and waterFigure 3.6: Bender element response (a) in contact; and (b) throughair and wateron the desired interpretation method. Sine pulses of selected frequenciesare performed for time domain interpretations. Sweeping sine waves areperformed for frequency domain interpretations. The height of the specimenat the time of the test is recorded with the bender element signals to calculatethe bender element tip-tip separation to obtain the shear wave velocity.Due to signal stacking, bender element testing takes a finite amount of68time. The triaxial test is paused during bender element testing. This meansthat the computer controlled changes in the applied stresses are suspended.Apart from suspending computer controlled changes in applied stress, thebender element system operates independently from the triaxial system.3.4 Confirmation testing3.4.1 Comparing to previous triaxial resultsComparing to past results is necessary to demonstrate and confirm that theequipment, procedures, and data reduction give similar results. A subsetof the triaxial dataset with similar experimental parameters was compiledas detailed in Table 3.3. This subset of experiments included two from thepresent study (248, 262), one from Lam (25020517), and two from Shozen(rw0611-1, rw0616-2). These specimens were all prepared loose, consoli-dated near a stress ratio of 2.0, aged for 100 minutes, and sheared alonga conventional stress path. The void ratio in Table 3.3 is from the end ofconsolidation. For completeness, the relative density was calculated usingthe e-min and e-max values for the respective soil sample. The e-max val-ues used were estimated from the end of water pluviation soil state not theASTM standard.Table 3.3: Reproducing triaxial results from previous investigationsfrom specimens aged for 100 minutes and sheared along a con-ventional stress pathInvestigation Specimen Void ratio Dr Stress ratioStyler 248 0.975 19 % 1.95Styler 002 0.955 24 % 1.99Lam 25020517 0.898 25 % 2.10Shozen rw0611-1 0.921 18 % 2.00Shozen rw0616-2 0.924 18 % 2.00The experiment by Lam (2003) was the only one he performed undersimilar conditions to Specimens 248, 002, rw0611-1, and rw0616-2. Between69experimental datasets, the differences in void ratio may be due to the dif-ferent intrinsic properties of the Fraser River Sand sample (Section 3.2.1).Figure 3.7 compares the applied stress paths for each experiment inTable 3.3. The first linear segment is from the state of the specimen at theend of back pressure saturation up to a stress ratio (σ′a/σ′r) of 2.0, or 2.1for Lam. The second line segment is consolidation up to a radial stress of100 kPa, while maintaining a constant stress ratio. The third line segmentis the conventional shear path to failure.0 50 100 150 200 250050100150200250300350p’ (kPa)q (kPa)  StylerLamShozenFigure 3.7: Comparing stress path control to previous experimentsdetailed in Table 3.3Figure 3.8 shows the axial and volumetric strains developed during theseexperiments. One of the experiments by Shozen (2001) appears to have hada compliance issue at the start of the experiment. The consolidation phase isfrom the origin (0,0) to the circle point. As shown in Figure 3.7, this involvesa change in stress path direction once a stress ratio of 2.0 is achieved. Creepstrains are developed over 100 minutes of ageing between the circle andtriangle points. Beyond the triangle point are strains developed during theconventional shear path. The two tests in the current study (blue lines)70appear very reproducible.−0.5 0 0.5 1 1.5 200.511.5εa (%)ε v (%)  StylerLamShozenFigure 3.8: Comparing developed strains to previous experiments de-tailed in Table 3.3, where the circle points are the end of con-solidation and the triangle points are the start of conventionalshearFigure 3.9 shows the shear stress against axial strain during shearing inthe large strain region. The experiment by Lam (2003) appears to be stifferand reaches a higher deviatoric stress at failure. The low strain details aredifficult to observe on this scale.Figure 3.10 shows the corresponding developed volumetric strains. Thespecimens in the current investigation experienced different amounts of con-tractive volumetric strain. The slightly denser specimen, 002, experiencedless contractive volumetric strain than specimen 248. Another feature inthis plot is a kink immediately after the transition from contractive to dila-tive behaviour. This kink is believed to be a result of a meniscus change inthe measurement system for volumetric changes. It is observed in the twocurrent tests and the one performed by Lam (2003). It was not observed inthe two experiments by Shozen (2001) as these were terminated immediately71after the end of contraction.Figure 3.9 and Figure 3.10 are repeated in Figure 3.11 and Figure 3.12over the small strain region of interest to this investigation. The two exper-iments in the current study and the two by Shozen (2001) are very similarover the small strain range. The experiment by Lam (2003) is both stifferand more contractive. This may be a result of his specimen being a higherdensity and consolidated and aged at a higher stress ratio.0 1 2 3 4 5 6 7 8 9050100150200250εa (%)∆ q (kPa)  StylerLamShozenFigure 3.9: Comparing stress-strain plot during conventional shear toprevious experiments detailed in Table 3.3The improved triaxial apparatus, testing procedure, and data reductionappear to give results that are generally similar to those obtained by Shozenand Lam. The results shown by Figure 3.8 show that the current testing isvery reproducible through consolidation. Furthermore, Figure 3.9 throughFigure 3.12 show very good agreement over the small strain range betweenthe current study and Shozen (2001). Despite slightly different particle sizedistributions, the results are very similar.720 1 2 3 4 5 6 7 8 900.10.20.30.40.50.60.70.80.91εa (%)ε v (%)  StylerLamShozenFigure 3.10: Comparing strains during conventional shear to previousexperiments detailed in Table 3.33.4.2 Evaluation of measurement uncertaintyThe evaluation of measurement uncertainty is more than just quantifyingsensor resolution. It also includes the entire measurement model reduc-ing the raw sensor voltages to the calculated small strain shear stiffness.The uncertainty for the calculated small strain shear stiffness was evalu-ated following the recommendations from the Joint Committee for Guidesin Metrology (JCGM) in the “Guide to the expression of Uncertainty inMeasurement document (GUM)” (JCGM et al., 2008a). Specifically, theapproach covering the propagation of uncertainty distributions using theMonte Carlo method (JCGM et al., 2008b) was followed.All of the sensors were calibrated using the triaxial data acquisition sys-tem. This inherently captures the contribution of signal conditioning andenvironmental electrical noise in the uncertainty of the calibration factor.Appendix A contains the sensor calibration factors and conditional standarddeviation for each calibration. The resolution of each sensor can be taken asthe conditional standard deviation value. These values are reported in Ta-730 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.205101520253035404550εa (%)∆ q (kPa)  StylerLamShozenFigure 3.11: Comparing stress-strain plot at low strains during con-ventional shear to previous experiments detailed in Table 3.3ble 3.4. This is in engineering units and conditional on a measured voltage.Table 3.4: Calibration summary tableSensor n Calibration factor Conditional stdev r2xyLoad cell 24 -13.424 kg/V 0.0566 kg 0.999987LVDT 1 28 -3.721 mm/V 0.00386 mm 0.999999LVDT 2 27 0.8046 mm/V 0.0166 mm 0.999075PWPT 22 -86.0205 kPa/V 0.136 kPa 0.999999Cell 22 -136.7504 kPa/V 0.164 kPa 0.999998DPWPT 11 -2.833 cm3/V 0.00735 cm3 0.999985DPWPT 10 -2.831 cm3/V 0.00872 cm3 0.999971DPWPT* 21 -2.832 cm3/V 0.00562 cm3 NADPWPT 14 -87.3715 mm/V 1.37 mm 0.999318A small amount of time-averaging is used to reduce the signal noise. Thedata acquisition system records the average of 200 voltages measured over atenth of a second. It was found to be undesirable to decrease this averagingwindow time. A measurable source of electrical noise was observed at the740 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.200.020.040.060.080.10.120.140.160.180.2εa (%)ε v (%)  StylerLamShozenFigure 3.12: Comparing low strains during conventional shear to pre-vious experiments detailed in Table 3.3power supply frequency of 60 Hz (0.0167 seconds). If the averaging timewindow was less than 0.0167 seconds then this electrical environmental noisewould contribute a noticeable amount of noise on the recorded voltages. Theerror in the calibration factors account for the 200-point time averaging inthe conditional standard deviations for each calibration.The sensor calibrations and apparatus measurements detailed in Ap-pendix A were used with the data reduction equations in Appendix C tocreate a measurement model to propagate the uncertainties for Specimen245. Log-normal random variables were assumed if the variable must bepositive. Otherwise normal random variable distributions were used. TheMonte Carlo simulation generated 100,000 sets of possible input variables foreach row of triaxial sensor measurements. This is sufficient for estimatingthe dispersion of the results, but not the probabilities of the extreme tailsof the distributions.In this measurement model the secant shear modulus, Gsec, has 18sources of error. Gsec is a result of all five triaxial sensors: the linear dis-75placement (LVDT), cell pressure (CELL), pore water pressure (PWP), dif-ferential pore water pressure (DPWPT), and load cell (LOAD). It includesmost of the specimen preparation variables: dial gauge (DIAL), dummyspecimen height (DATUM), calibrated graduated cylinder (GC), and theexpanded membrane diameter (XPN DIA). It includes contributions due tothe membrane penetration volume (MEM-P), elasticity of the membrane,including the initial membrane strain (MEM i), Young’s modulus (Emem),the unstretched membrane thickness (Tmem), and the unstretched membranediameter (DIAmem). It includes contributions to the axial stress from thetop cap mass (CAP MASS), ram friction (RAM), soil weight (SOIL), andan uplift pressure correction due to the driving rod diameter (ROD DIA).The contribution to the uncertainty in Gsec from these variables de-pended on the magnitude of the developed shear strain. Table 3.5 detailsthe sources of error at three different magnitudes of shear strain. In the smallstrain secant shear modulus at 0.02 % shear strain, 82 % of the uncertaintyis due to the LVDT. It is clear that improvements in the LVDT have themost potential for reducing the uncertainty in the small strain secant shearmodulus. However, it is unlikely that this sensor can be further improvedthrough re-calibration. The calibration procedure is not complicated andvery good results were achieved (see Table 3.4).The value in performing this measurement uncertainty quantification isthat resources in money, time, and effort can be focused on the specificarea that will yield the most beneficial results. The first time the sourcesof measurement uncertainty were evaluated it led to two recalibrations. Asignificant source of error was observed due to the measurement of the ex-panded membrane diameter and the differential pore water pressure sensor.Both of these calibrations were repeated.The current investigation has an improved signal resolution compared topast studies (Lam, 2003; Shozen, 2001), despite using the same sensors andsignal amplifier. The main difference is the new computer and developeddata acquisition and stress control program. The resolution of the sensorsis slightly improved due to a reduction in random noise through more time-averaging of the recorded data. The current system also records data more76Table 3.5: Sources of error in the measured secant shear modulus from100,000 Monte Carlo simulations for Specimen 245q=0.02 % q=0.6 % q=2.5 %Gsec = 20 ± 5 MPa 3.84 ± 0.03 MPa 1.797 ± 0.005 MPaSource Contribution to errorLVDT 82.0 % 42.8 % 20.2 %CELL 0.2 % 1.3 % 2.4 %PWP 0.0 % 1.3 % 2.4 %DPWPT 10.0 % 7.0 % 4.1 %LOAD 6.5 % 22.1 % 21.4 %DIAL 0.1 % 1.3 % 2.4 %DATUM 0.0 % 0.4 % 0.8 %GC 0.1 % 1.3 % 2.4 %XPN DIA 0.5 % 10.4 % 18.6 %MEM-P 0.1 % 1.5 % 2.8 %MEM-i 0.1 % 1.3 % 2.4 %Emem 0.1 % 1.7 % 5.0 %Tmem 0.1 % 1.3 % 2.8 %DIAmem 0.1 % 1.3 % 2.5 %CAP MASS 0.1 % 1.3 % 2.4 %RAM 0.1 % 1.3 % 2.4 %SOIL 0.1 % 1.2 % 2.4 %ROD DIA 0.1 % 1.3 % 2.4 %frequently than what was previously performed. This increases the time-resolution of the collected signals.The triaxial system is capable of obtaining Gsec degradation curves. Theerror in Gsec increases at lower strains.3.4.3 Initial bender element testing and interpretationThe developed triaxial equipment and data acquisition system were able toreproduce past experimental results and enabled the VS and hence G0 to beobtained. As one objective of the research was to obtain G0 and to studythe effect of ageing on stiffness, initial testing was carried out to assess thecapability of the bender element system.77A set of signals collected during ageing of Specimen 261 have been inter-preted using existing techniques. A suite of 12 different trigger signals weretested at 1 minute, 10 minutes, and 100 minutes of age duration.Figure 3.13 depicts a 9 kHz sine pulse trigger (green) and response signal(red) at 10 minutes of ageing. As previously discussed (and shown in Fig-ure 3.6b), a higher frequency compression wave signal is observed prior to thearrival of the shear wave. The first arrival characteristic points were selectedwhere the signal first deviates under the lower shear wave frequencies. Thisoccurred at 0.6200 ms resulting in an estimated shear wave velocity of 190.0m/s. The peak to peak propagation time was selected using the maximumpeak in the response signal. This resulted in a propagation time of 0.7200ms and a much slower shear wave velocity of 163.6 m/s. Figure 3.14 presentsthe cross correlation function for this 9 kHz sine pulse test. The peak cross-correlation results in a propagation time of 0.7125 ms and velocity of 165.4m/s.This bender element test exhibited Type 3 signals (Table 2.3). Therewas an early, low amplitude, first pulse in the response. Consequently, adecision must be made on which feature in the response signal correspondsto the arriving shear wave. If the first deviation is selected, then the mainshear pulse is travelling at a slower velocity or over a longer distance. Ifthe main shear pulse is selected, then there is a pre-arrival distortion. Thecross-correlation results do not provide an answer to this problem. As shownin Arroyo et al. (2006), constructive and destructive interference can changewhich cross-correlation peak has the maximum amplitude. The maximumpeak may not be the peak that corresponds to the arrival. A peak prior to0.7125 ms at 0.6050 ms can be selected that is close to the chosen first-arrivalpoint. Figure 3.14 shows such a peak.Another problem not depicted in Figure 3.13 or Figure 3.14, is thatdifferent sine pulse frequencies systematically change the measured velocity.This can be observed in Figure 3.15. This figure presents the results forall 12 tested frequencies at three times during specimen ageing. There is arange of possible velocities for each method at each suite of bender elementsine pulses. There is no scientific justification for taking the average of these780 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−6−4−2024680.0275 ms0.6200 ms0.7475 msLtt = 117.82 mm9 KHz sine pulseTime (ms)AmplitudeFigure 3.13: Time-domain results for specimen 261 from a 9 kHz sinepulse (green trigger, red response) at 10 minutes of ageingdepicting a first arrival velocity of 190.0 m/s and a peak topeak velocity of 163.6 m/sresults. The difference in velocities is systematic, not random.Figure 3.15 does show a general slightly increasing effect of age on VS .An NG factor might be estimated from this figure. However, this figurealso demonstrates another problem. G0 would vary significantly based onthe technique used to select the propagation time. It is not clear if theshear wave arrival corresponds to the first distortion or to the subsequentlarger amplitude cycle. This is seen in Figure 3.14. The arrival could be thepreceding peak which would agree with the first-arrival results.One of the trigger signals included in the suite of bender element testswas a sweeping sine wave. This was used to calculate the propagation timeand shear wave velocity in the Frequency domain. Figure 3.16 presents thecross-spectrum method results using the approach from Viana da Fonseca790 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1−0.8−0.6−0.4−0.200.20.40.60.810.7125 msLtt = 117.82 mm9 KHz sine pulseTime (ms)CCx,y(t)Figure 3.14: Time-domain cross-correlation result for specimen 261from a 9 kHz sine pulse at 10 minutes of ageing depicting avelocity of 165.4 m/set al. (2009). This cross-spectrum technique performs linear regression overa moving 4 kHz frequency window on a plot of the unwrapped phase shiftagainst frequency (Figure 3.16a). The propagation is calculated with ∆t =∆θ∆f1−2pi . For these three age times, the cross spectrum method resulted in aVS that was faster than the cross-correlation and peak to peak results, butslower than the first-arrival selection.The problem is not that these different trigger signals and interpretationmethods result in different shear wave velocities. The problem is that noth-ing in the model of a shear wave propagating through a soil specimen wouldindicate that there should be a difference. There is no informed or objec-tive means to select the correct velocity. The different time domain methodsshould converge on the same velocity. The frequency domain interpretationsshould agree with this velocity.Furthermore, there is little confidence in estimating a G0 value using801 10 100150155160165170175180185190195200Age time (min)VS (m/s)  FAPPCCFigure 3.15: Time-domain bender element test results for Specimen261 during ageing where FA is First Arrival, PP is peak topeak, and CC is cross correlationρV 2S . At the end of ageing, Specimen 261 had a bulk density of ρ = 1902kg/m3. Assuming a representative First Arrival shear wave velocity of 187m/s, this results in G0 = 67 MPa. The cross correlation and peak-peakvalues may share an average shear wave velocity of 165 m/s, resulting in G0= 52 MPa. Finally, the frequency domain cross spectrum method at thepeak correlation coefficient is close to 180 m/s, resulting in G0 = 62 MPa.Clearly, these three values are not in agreement.Additionally, the peak-peak and cross-correlation techniques resulted ina variation of 5m/s depending on the selected trigger signal. For a specimenwith an NG factor of 2 % and ρ of 1900 kg/m3, VS will increase from 165m/s to 170 m/s over 1000 minutes of ageing. The uncertainty in state ofpractice time-domain bender element testing exceeds the effect of ageing inclean sands. NG cannot confidently be determined using state-of-practice81bender element testing.0 2 4 6 8 10 12 14 16 18 20−100−80−60−40−20020Frequency (kHz)∆θ (rad)(a) Phase shift (rad)0 2 4 6 8 10 12 14 16 18 20150155160165170175180185190195200Frequency (kHz)VS (m/s)(b) VS with moving 4 kHz windowFigure 3.16: Frequency domain interpretation following Viana daFonseca et al. (2009) with 1 minute (blue), 10 minutes (red),and 100 minutes (green) bender element tests on Specimen 261Type 3 signals were observed using the installed bender elements. Theredoes not appear to be an acceptable published technique for Type 3 signalsthat can confidently determine a propagation time and shear wave velocity.82The second objective of this research has not been met by these initialresults. Further study into the application and interpretation of benderelements is required.3.5 SummaryThe improved triaxial apparatus is capable of producing results similar tothose of previous investigations (Section 3.4.1). This validates the developeddata acquisition system and data reduction procedure. The equipment hasat least the same capability to acquire secant shear stiffness curves as theequipment used in previous investigations. Additionally, the stress pathcontrol is improved and a higher density of data is obtained.Bender elements were added to the UBC triaxial apparatus. This meetsthe first research objective outlined in Section 1.1. Bender element shearwave signals can be measured over the triaxial specimens of Fraser RiverSand.The second research objective was the evaluation of the applicability ofthese bender elements to perform a study of the effect of ageing on stiff-ness. Exploratory testing was performed with the bender elements usingprevalent time domain and frequency domain interpretation techniques. Itwas concluded that these techniques were unable to confidently characterizeG0 or the NG ageing factor. The use and interpretation of bender elementtesting requires further investigation.83Chapter 4Development of a combinedtime and frequency domainbender elementinterpretation methodAccurate determination of the travel time increment has been the subjectof considerable research since the introduction of bender element testing.Methods of interpretation have been developed in both the time and fre-quency domains, as covered in Chapter 2. Section 3.4.3 investigated theapplication of these techniques for this investigation. The effect of ageingcould not be confidently determined.This chapter presents an improved method of determining the shear wavepropagation time in bender element testing. It is a combination of time andfrequency domain techniques. This technique has been published by Stylerand Howie (2013) in the ASTM Geotechnical Testing Journal.This method of interpretation minimizes the subjectivity of the processand provides a consistent approach to determination of VS . It combinesthe FD cross spectrum technique with an approach proposed by Blewettet al. (1999). This results in a determination of the phase velocity instead of84the group velocity over the bender element operating frequency range. Theproposed method is evaluated for both synthetic and experimental signals.4.1 Proposed methodThe group velocity is distorted by frequency dependent effects while the vari-ation of phase velocity with frequency characterizes frequency dependence.The phase velocity is a more appealing measure than the group velocity forbender element testing. The phase velocity at a given frequency can be cal-culated using Equation 4.1, where f is the frequency, Ltt is the propagationlength (bender element tip to tip length), ∆θr is the unwrapped phase shift,and n is the determined phase degeneracy constant.VS =−2pifLtt∆θr − 2pin(4.1)The combined TD and FD approach described in this chapter solves forthe constant integer n so that Equation 4.1 can be solved for the phasevelocity. The unwrapped phase shift, ∆θr, is calculated from the responseto a wide band trigger signal, the exact same procedure as in the crossspectrum technique. Sachse and Pao (1978) and Viggiani and Atkinson(1995) both calculated the phase shift from sine pulse triggers. Recentpublished investigations on frequency domain approaches have used linearswept sweeping sine triggers (Greening and Nash, 2004; Viana da Fonsecaet al., 2009).In the proposed technique, two trigger signal waveforms are used todetermine the absolute phase shift at a single frequency, ∆θa = ∆θr − 2pin.These are a continuous sine wave over 20 ms and a sine pulse. The longduration continuous sine wave trigger and response have almost all of theirpower at a single frequency. The cross correlation of a continuous sine wavebender test results in a series of peaks, with each peak being separatedby the period of the continuous trigger, T=1/f. The peak correspondingto the arrival of the shear wave is chosen based on the results of a sinepulse test. In this work, the sine pulse frequency is the same as that ofthe continuous sine. The propagation time for the continuous wave and the85frequency of the continuous wave are used to calculate the absolute phaseshift, ∆θa = 2pif∆t.The absolute phase shift, ∆θa, is compared to the relative phase shiftfrom the linear sweeping sine, ∆θr, to determine the phase degeneracy,−2pin. The absolute and relative phase shifts are compared at multiplefrequencies to confirm that they agree on the same phase degeneracy i.e.that n is constant for each unwrapped relative phase shift. Once the rela-tive phase shift and phase degeneracy are determined, Equation 4.1 can besolved for the phase velocity.The difference between the phase velocity and group velocity is nowdemonstrated using simulated signals. This demonstrates that they aredifferent velocities and that the group velocity is distorted by frequencydependent dispersion.4.2 Validation using simulated bender elementsignalsSynthetic bender element signals provide a controlled means to evaluate var-ious methods of propagation time interpretation. The generated syntheticsignals must be representative of the measured distortion that is found inexperimental bender element testing. This can be achieved by character-izing a series of subsystems making up the experimental system. For thisexercise, the soil subsystem for shear wave propagation is simulated usingthe boundary value solution by Cruse and Rizzo (1968). Lee and Santa-marina (2005) and Wang et al. (2007) used the same approach. AlthoughAlvarado and Coop (2012) found that a single degree of freedom oscillatorrepresentation of a bender element is often not reflected in real bender ele-ment systems that exhibit multiple resonance peaks, it is used to representthe receiving bender element as was done by Santamarina and Fam (1997)and Wang et al. (2007). The low frequency range is not measured in experi-mental bender element testing, the charge density between the piezoceramicplates dissipates and less mechanical force is generated at low frequencies.To simulate this phenomenon, a simple high pass filter was included in the86synthetic system. The high pass filter is modelled with Equation 4.2 wherefc is the corner frequency. At the corner frequency the output power is halfof the input power.HT (ω) =jωjω + 2pifc(4.2)The soil model used in the simulation had a total bulk density of ρ =1900kg/m3, a shear wave velocity VS = 200 m/s, a compression wave ve-locity VP = 1428 m/s (Poisson’s ratio equal to 0.49, simulating saturatedsoil), soil damping D = 0.025, and a propagation length r = 125 mm. Thereceiving bender element was modeled as a damped single-degree of freedomoscillator, with a resonant frequency of ω = 2pi9kHz, and damping of Dbe =0.2. The parameters for the soil damping and bender element damping arethe same as the ones used by Wang et al. (2007). The resonant frequencywas selected to match the peak energy in the experimental signals presentedlater. The trigger bender element is modelled as a high pass filter (Equa-tion 4.2), with a corner frequency fc = 2 kHz. A noise signal was added tothe simulated output. This noise signal consists of random Gaussian noisewith an amplitude of 5 % of the output and a 60 Hz sinusoidal wave with arandom phase angle and amplitude of 10 % of the output signal. The 60 Hzsine wave noise models environmental noise due to an alternating currenthouse power supply. The contribution of this noise is reduced by simulatingsignal stacking with 10 stacked signals for each simulated output signal.Figure 4.1 depicts the synthetic bender element trigger, response, andcross correlation for a 5 kHz sine pulse and a 5 kHz continuous sine wave.The near-field effect preceding the arrival of the 5 kHz sine pulse (Fig-ure 4.1c) is obscured by the noise in the signal. The peak cross correlationof the sine pulse occurs at 0.646 ms, resulting in an estimated VS = 125mm/0.646 ms = 193 m/s. The cross correlation of the continuous sine waveresults in a set of peaks [0.044, 0.244, 0.444, 0.644, 0.844 ms, ...], of which0.644 ms correlates to the sine pulse results. This propagation time is usedto solve for the absolute phase shift at 5 kHz: ∆θ(5kHz) = −2pi5kHz∆t =−2pi × 5kHz× 0.644ms = −20.30 radians.870Amplitude(a) Sine pulse trigger (b) Continuous sine trigger0Amplitude(c) Sine pulse response (d) Continuous sine response0 0.5 1 1.5 20Time (ms)ccx,y(e) CCx,y sine pulse0 0.5 1 1.5 2Time (ms)(f) CCx,y continuous sineFigure 4.1: Synthetic bender element trigger and response signals: (a)5 kHz sine pulse trigger; (b) 5 kHz continuous sine pulse trigger;(c) sine pulse response; (d) continuous sine response; (e) crosscorrelation of sine pulse trigger and response; and (f) cross cor-relation of continuous sine with circle point marking the peakcross correlation of the sine pulseFigure 4.2 depicts a synthetic bender element linear sweeping sine triggerand response. The sweeping sine trigger frequency increases linearly from 0to 10 kHz over 20 ms (Figure 4.2a). The simulated response to this trigger isdepicted in Figure 4.2b. Unlike Figure 4.1, the sweeping sine wave responsecannot be visually interpreted in the time domain. Figure 4.2c shows thatthe sweeping sine wave trigger has a wide band of uniform magnitude in thefrequency domain. Figure 4.2c shows that the magnitude of the responsewave peaked at 9 kHz, the resonant frequency of the bender element.Ten simulated bender element signals were generated for the sweeping880Amplitude(a) Sweeping sine trigger0 5 10 15 2002040Frequency (kHz)(c) Frequency magnitudesTriggerResponsedB0 5 10 15 200Time (ms)Amplitude(b) Sweeping sine responseFigure 4.2: Synthetic bender element results: (a) linear sweeping sinewave trigger; (b) response; and (c) magnitude of the trigger andresponse signals in the frequency domainsine response and the coherence function was calculated. This coherencefunction is depicted in Figure 4.3a. A drop off occurs at low frequencies andthere is a gradual decline above 12 kHz. Figure 4.3b depicts the calculatedphase shift between the trigger and response signals. This equation hasdiscontinuities at +pi and pi. The unwrapped phase shift is depicted inFigure 4.3c as a dashed line. At 5 kHz, the unwrapped phase shift is -13.92 radians. The absolute phase shift determined at this frequency inFigure 4.1 was -20.30 radians. The difference between these two values isthe phase offset, -20.30 + 13.92 = -6.38 radians ≈ −2pi. The corrected phaseshift is then depicted as a solid line in Figure 4.3c. Figure 4.3d shows thephase velocity, group velocity, and model velocity VS = 200 m/s.The phase velocity is calculated from the corrected phase shift withVS = −2pifLtt/∆θa. For the range of frequencies for which the coherencewas 1, it ranged between 195 m/s at frequencies from 4 to 7 kHz to 189m/s over frequencies from 9 to 14 kHz. The group velocity was calculatedfrom the slope of the phase shift in a moving 4 kHz frequency window. The89group velocity reached a minimum of 183 m/s as it approached the resonantfrequency of the bender element.Both the group and phase velocities underestimate the actual shear wavevelocity, with the phase velocity being within 5 to 10 % of the specifiedvelocity. This is due to the resonance model used to represent the receiverelement. As the propagation length gets shorter, the bender element transferfunction has a greater influence on the propagation time. This is a particularproblem for short specimens (Wang et al., 2007), such as those used forconsolidation testing or direct simple shear.In general, the application of the proposed combined FD and TD ap-proach to the synthetic signals has shown that the technique permits esti-mation of VS of the soil samples but that the values obtained are influencedby the bender-soil transfer functions, tending to result in phase velocitiesthat are less than the VS of the soil. The group velocities are shown to beconsiderably more variable than the phase velocities and are affected by theresonant frequency of the bender element. The proposed technique is nowdemonstrated using experimental signals.9000.51γ(a) Sine sweep coherence0∆θ (rad)−pipi(b) Phase shift−500∆θ (rad) Phase offset = −2pi  (c) Unwrapped phase shiftUnwrappedCorrected0 2 4 6 8 10 12 14 16 18 20180200Frequency (kHz)V S (m/s)  (d) Shear wave velocityVS PhaseVS GroupFigure 4.3: Interpreted synthetic frequency domain results: (a) co-herence function; (b) calculated phase shift; (c) unwrapped andcorrected phase shift; and (d) phase and group velocities914.3 Experimental demonstrationTo demonstrate that the proposed combined TD and FD method provides areproducible measure of VS , ten similar experiments were compared. Theseten specimens of Fraser River Sand were prepared in as loose an initial stateas possible using the procedures described in Chapter 3 and Appendix B.Consolidation was performed in two stages. First, the axial stress wasincreased to a stress ratio of 2.0 (σ′a/σ′r), and then both the axial and radialstresses were increased to maintain the stress ratio constant up to the desiredconfining stress state. The rate of consolidation was sufficiently slow to pre-vent generation of excess pore pressure. The final samples had consolidatedvoid ratios that ranged from 0.969 to 0.988.The consolidation was temporarily paused to perform bender elementtesting at radial stresses of 60, 70, 80, and 90 kPa. Bender element testswere performed at an axial stress of 160 kPa and radial stress of 80 kPa.Each bender element test consisted of a suite of 10 trigger signals. Theseincluded 7, 9, 11, and 13 kHz sine pulses, 20 ms duration continuous sinewaves and two linear swept sine waves from 0 to 10 kHz over 20 ms. Thetrigger signal amplitude was 3 volts.Figure 4.4 presents a 9 kHz sine pulse and continuous sine trigger andresponse for Specimen 016 at an axial stress of 159.6 kPa, radial stress of 79.2kPa, void ratio of 0.977, propagation length of 120.0 mm, and a propagationlength to diameter ratio of 1.90. Comparing Figure 4.4 and Figure 4.1, thecompression wave through water is observable prior to the shear wave arrivalin both Figure 4.4c and Figure 4.4d. It was shown in Section 3.3.2 that thisis interference from a compression wave. The amplitude of the arrivingcompression wave builds up to a peak around 0.3 ms before decaying. Thepeak cross correlation (Figure 4.4e) of the sine pulse occurs at 0.774 msand corresponds to the first major shear signal in the response. This pointcorrelates to a peak of 0.770 ms in the cross correlation of the continuoussine signal (Figure 4.4f) which leads to a determination of an absolute phaseshift at 9 kHz of -41.85 radians (−2pi × 9kHz× 0.740ms).A low amplitude pulse in the received wave was observed immediately92−303Amplitude(a) Sine pulse trigger (b) Continuous sine trigger−101Amplitude(c) Sine pulse response (d) Continuous sine response0 0.5 1 1.5 20Time (ms)ccx,y(e) CCx,y sine pulse0 0.5 1 1.5 2Time (ms)(f) CCx,y continuous sineFigure 4.4: Experimental bender element signals for saturated FraserRiver Sand Specimen 016, σa = 159.6 kPa, σr = 79.2 kPa,void = 0.977, ltt = 120.0 mm, slenderness ltt/d = 1.90: (a) 9kHz sine pulse trigger; (b) 9 kHz continuous sine pulse trigger;(c) sine pulse response; (d) continuous sine response; (e) crosscorrelation of sine pulse trigger and response; and (f) cross cor-relation of continuous sine with circle point marking the peakcross correlation of the sine pulseprior to the arrival of a major shear component. This characteristic hasbeen observed by other bender element investigations (Arulnathan et al.,1998; Brandenberg et al., 2008; Brignoli et al., 1996; Landon et al., 2004).In Figure 4.4c, following the compression wave is this initial low amplitudepulse prior to a strong shear wave pulse. In a numerical model without re-flective boundaries, Arroyo et al. (2006) showed the amplitude of the leadingshear pulse decreasing with increasing propagation distance. Consequently,93this first low amplitude cycle may represent the shear wave arrival. In anumerical model with reflecting boundaries, Arroyo et al. (2006) observed asimilar pre-arrival pulse suggesting that the experimental observation maybe due to distorting reflections. The first pulse and the main shear pulsewere both investigated as possible shear wave arrivals. The first pulse re-sulted in a phase velocity that increased without bounds with decreasingfrequency. The main shear pulse resulted in a less sensitive change withfrequency. Therefore, the main shear pulse is considered indicative of theshear wave arrival. This point is very important. It is why the developedmethod can be used to investigate Type 3 signals. Other techniques provideno guidance on the commonly observed low amplitude pre-arrival cycle.Figure 4.5 shows the applied and measured sweeping sine wave overSpecimen 016 collected in the same suite of signals in Figure 4.4. Theexperimental sweeping sine response signal is much more complex than thesimulated result in Figure 4.2 but displays the same characteristic trends.In Figure 4.5c, the amplitude of the response rises to a peak at about 11 kHzand then drops away again with increasing frequency. It has been observedthat these frequency-dependent features are systematic, but can migrate todifferent frequencies throughout an experiment.Figure 4.6 illustrates the reduction of the sweeping sine wave data forSpecimen 016. Figure 4.6a shows that the coherence drops off below 3 kHz.This range corresponds to a degraded phase shift in Figure 4.6b. The relativephase shift is plotted as a dashed line in Figure 4.6c. At 9 kHz, the relativephase shift is -35.34 radians. This results in an estimated phase degeneracyof -41.85 + 35.34 = -6.51 radians ≈ −2pi. Figure 4.6d depicts the resultingphase and group velocities. As was done for the synthetic signals, the groupvelocity is calculated over a moving 4 kHz window. In Figure 4.6d, the groupvelocity is approximately 150 m/s between 3 and 10 kHz, and then drops to105 m/s at 14.4 kHz. The phase velocity is approximately 158 m/s between3 and 10 kHz and drops to 142 m/s at 14 kHz.Table 4.1 summarizes the results for Specimen 016 at 7, 9, 11, and 13kHz. The phase degeneracy is approximately −2pi, independent of the sinepulse and continuous sine frequency. Table 4.2 presents experimental results94−303Amplitude(a) Sweeping sine trigger0 5 10 15 200204060Frequency (kHz)(c) Frequency magnitudesTriggerResponsedB0 5 10 15 20−101Time (ms)Amplitude(b) Sweeping sine responseFigure 4.5: Sweeping sine was trigger and response over saturatedFraser River Sand Specimen 016: (a) linear sweeping sine wavetrigger; (b) response; and (c) magnitude of the signals in thefrequency domainfor all ten specimens at the similar stress and volume states. This tableincludes the cross correlation from a 9 kHz sine pulse, the phase velocityat 9 kHz, and a group velocity centred at 9 kHz. The phase offsets are0,−2pi,−4pi, or−6pi. The phase and group velocities for each bender elementtest suite in Table 4.2 are plotted in Figure 4.7. This figure shows that thephase velocity converges between 5 and 14 kHz at about 155 ± 3 m/s, whilethe group velocity is much more variable.The results in Table 4.2 correspond to the third suite of bender elementtests for each specimen. This corresponds to a stress state of σ′a = 160 kPa,σ′r = 80 kPa at which a wide band of frequencies were propagated. The ob-servation of test to test reproducible phase velocities and variations in groupvelocities was made for all four suites of bender tests. At lower stresses, theresonance peak locations are more compressed, the group velocity is morevariable, and the bender element system has a smaller operating frequencyrange.95Table 4.1: Measured phase offsets at four different frequencies for sat-urated Fraser River Sand Specimen 016 at 159.6 kPa, 79.2 kPa,note that the phase offset, θo, is approximately constant and in-dependent of the input frequencyFrequency (kHz)∆t(a) (ms) Phase (radians)SP (b) CS(c) ∆θ(d)a ∆θr θ(e)o7 0.774 0.760 -33.43 -27.19 -6.249 0.778 0.774 -43.77 -37.60 -6.1711 0.778 0.772 -53.36 -47.33 -6.0413 0.778 0.786 -64.21 -58.23 -5.98(a) Cross correlation(b) Sine pulse(c) Continuous sine(d) ∆θa = −2pif∆t(e) θo = ∆θa −∆θrTable 4.2: Ten different bender element results at similar stress andvoid conditions for saturated Fraser River SandID σ′a σ′r void LttLttD(a)θo V(b)S−TD V(c)S−PH V(d)S−GRP(kPa) (kPa) ratio (mm) (rad) (m/s) (m/s) (m/s)004 159.7 80.1 0.969 118.50 1.87 −4pi 152 151 157008 161.2 80.6 0.987 118.34 1.87 −6pi 151 151 161012 160.4 80.0 0.965 119.48 1.89 0 153 153 158015 161.2 80.9 0.965 118.67 1.87 0 155 154 161016 159.6 79.2 0.977 119.96 1.90 −2pi 155 158 149020 160.7 80.1 0.977 118.68 1.87 −2pi 156 157 151021 160.2 79.7 0.988 119.81 1.90 −2pi 157 159 150023 160.3 79.7 0.974 120.85 1.91 0 154 156 150024 159.8 78.9 0.969 121.55 1.92 −2pi 154 155 146027 160.6 79.7 0.974 120.76 1.90 0 151 151 153(a) Slenderness ratio(b) Cross correlation of a 9 kHz sine pulse(c) Phase velocity at 9 kHz(d) Group velocity between 7 and 11 kHz9600.51γ(a) Sine sweep coherence0∆θ (rad)−pipi(b) Phase shift−80−400∆θ (rad)Phase offset = −2pi  (c) Unwrapped phase shiftUnwrappedCorrected0 2 4 6 8 10 12 14 16 18 20100120140160180Frequency (kHz)V S (m/s)  (d) Shear wave velocityVS PhaseVS GroupFigure 4.6: Interpreted results for specimen 016: (a) coherence func-tion; (b) calculated phase shift; (c) unwrapped and correctedphase shift; and (d) phase and group velocities9700.51γ(a) Coherence120150180(b) Phase velocityV S (m/s)0 2 4 6 8 10 12 14 16 18 20120150180(c) Group velocityFrequency (kHz)V S (m/s)Figure 4.7: Interpreted phase and group velocities for all ten experi-ments of saturated Fraser River Sand specimens at stress andvolume states indicated in Table 4.2984.4 Observing the effect of ageing on VSAs noted in Section 3.4.3, current methods of interpretation of bender re-sults were unable to provide sufficiently consistent values of G0 to assess theeffects of ageing. Published techniques to interpret bender element tests arein the time domain (Section 2.2.7) or frequency domain (Section 2.2.8). Theresults were inconclusive. More troubling, a Type 3 signal (Section 2.2.6)was observed adding considerable uncertainty to the estimation of the prop-agation time from time domain techniques.Figure 4.8 shows the interpretation of the bender element signals fromSpecimen 261 using the combined TD and FD approach. This figure demon-strates that an increase in VS does occur during ageing. It also suggests thatthe increase in VS is log-linear as the change from 1 to 10 minutes is almostequal to the change from 10 to 100 minutes. This trend may be extrapolatedto explain observed differences between laboratory reconstituted specimensand aged field results.Figure 4.8 includes some evidence that illustrates the difficulty in usingconventional time domain or cross-spectrum approaches. The velocity isfrequency dependent. Therefore, a phase velocity should be interpretedinstead of a group velocity. There are significant frequency-features at 6kHz and near 15 kHz. These are likely to be resonance peaks in the bender-soil system. A cross-spectrum velocity calculated over a resonance peak willnot give reasonable results. The data in Figure 4.8 should be interpreted atfrequencies where the VS is stable. In this figure, this range is between 6.5and 14 kHz.4.5 DiscussionBased on the results obtained with simulated and experimental bender el-ement signals, the interpreted group velocities appear to have three mainproblems: they appear sensitive to dispersion, the results are not repro-ducible test to test, and the method is contingent on unmeasured inputcriteria: the selection of a frequency window for linear regression.The effect of dispersion on the group velocity is apparent in the simulated99Figure 4.8: TD-FD technique on bender elements tests during ageingof Specimen 261 (σ′a/σ′r = 2.0, e=0.964-0.962) with annotatedstable frequency rangesignals where it is controlled by the bender element resonance model. In thesimulated signals (Figure 4.3), the group velocity reaches a minimum at thesimulated resonant frequency of the bender element. In the experimentalsignals (Figure 4.6d), the group velocity deviates from the phase velocityaround 14 kHz.Figure 4.7 depicts 9 of the 10 experimental signals exhibiting this dras-tic drop in VS above 11 kHz. The group velocity measurements are notreproducible test to test. Below 11 kHz, the group velocities do not appearto converge on a single solution over any frequency range. The multipleresonance peaks result in a highly variable group velocity characterization.Small variations in the frequency dependent dispersion are exaggerated whenthe slope is calculated.The final problem is that the group velocity measurements vary with100the selected frequency range. For the results presented, a 4kHz moving fre-quency window was used as suggested by Viana da Fonseca et al. (2009).The measured group velocity changes based on the selected frequency win-dow size and location. Recommendations have been published for selectingthe group velocity frequency window based on the coherence function orcorrelation coefficient (Viana da Fonseca et al., 2009; Viggiani and Atkin-son, 1995). However, the resulting frequency window is still selected by theinterpreter and this choice will influence the results.The results of time domain methods are also influenced by required sub-jective input. This includes the selected trigger waveform, frequency, andinterpretation method. For the same measured signals, different interpre-tations result in different velocities (Viggiani and Atkinson, 1995). Theselected waveform and frequency also bias the results due to the resonantfrequency of the bender element system (Lee and Santamarina, 2006). De-veloping objective criteria for TD bender element interpretations is difficultdue to the lack of representation of influencing factors in the model of a bulkpropagating elastic wave through a non-dispersive linear elastic continuum.The characterization of the phase velocity does not assume a bulk propagat-ing elastic wave. The effects of dispersion, while not individually isolated,all influence the resulting measured phase velocity.The proposed phase velocity method uses only measured input values.It measures the relative phase shift in the frequency domain. The absolutephase shift is measured at a point in the time domain. These two values areused to correct the unwrapped relative phase shift and calculate the phasevelocity. It was demonstrated that the sine pulse trigger signal frequency isarbitrary. In this work, frequencies of 7,9,11 and 13 kHz all resulted in thesame phase offset. The phase velocity approach measures the velocity anddoes not require any external input.4.6 ConclusionThe time domain and frequency domain approaches can be combined inorder to measure the phase velocity. The time domain cross correlation101technique was used to solve for the phase degeneracy and find the absolutephase shift. An unwrapped phase shift from a sweeping sine wave was usedto find the relative phase shift over the bender element frequency range.It was shown that the same phase degeneracy and phase offset were de-termined for four different analysed frequencies. This makes the selectedfrequency arbitrary instead of subjectively influencing the results. This canlead to a consistent frequency dependent measurement of the phase velocity.Conversely, time domain results are influenced by the trigger waveform andinterpretation method. Group velocity interpretations are influenced by theselected frequency window.The combined method was demonstrated using synthetic and experimen-tal signals. The reproducibility test to test of this method was demonstratedover ten saturated specimens of Fraser River Sand. These results were com-pared to cross spectrum group velocity measurements. It was found that:• Realistic coherence functions from simulated bender element signalscan be achieved using a high pass filter and noise signal, as shown bycomparing Figure 4.3(a) to Figure 4.6(a).• Group velocity methods are sensitive to dispersion, not reproducible,and contingent on subjective input, as demonstrated experimentallyand depicted shown inFigure 4.6(c).• The phase degeneracy can be determined at selected arbitrary frequen-cies in the bender element operating range, as detailed in Table 4.1 forfour different frequencies.• The proposed method determines the shear wave phase velocity usingonly measured values over the bender element frequency operatingrange.• The proposed method was capable of observing the small effect of ageon VS in a clean specimen of Fraser River Sand.The proposed method provides a more complete analysis of bender el-ement testing than available from time domain or cross-spectrum results.102The proposed method overcomes many drawbacks of existing techniques. Itacquires the phase velocity over the bender-soil system and is less subjectivethan other interpretation methods. One unresolved issue is the isolation ofthe soil response when using a two-bender element system to determine theshear wave velocity.In Section 3.4.3 it was observed that different trigger signals and inter-pretation methods resulted in an unacceptable range of VS interpretationsand G0 calculations. The proposed method systematically combines the re-sults from a suite of trigger signals in both the time and frequency domain.It is shown that these results all converge on a single phase velocity solution.A VS value can be selected with more confidence from the observed varia-tions in the phase velocity. The NG factor can be better quantified. Thebender element equipped triaxial apparatus can now be used to confidentlyacquire G0.103Chapter 5Development of a continuousbender element phasevelocity monitoring methodThe combined TD and FD method interpreted the phase velocity from asuite of bender element trigger signals. One of the trigger signal waveformswas a 20 ms duration continuous sine wave. This was used to find the relativephase shift at a single frequency. There is no reason to stop the continuoussine wave after 20ms. It could operate continuously and the relative phaseshift could be monitored in real time.This chapter describes a procedure by which shear wave velocities canbe monitored continuously throughout a triaxial test. To achieve this, thetriggering element is subjected to continuous excitation at one end of thesample and the response of the bender at the opposite end is recorded andanalyzed to determine the travel time. Instead of performing a bender el-ement test at a discrete point in the test over a finite amount of time, thebender element test is running throughout the experiment. The methodallows VS to be measured during dynamic phases of the experiment, such asduring changes in the stress path direction, the onset of ageing, the onset ofshearing, and during the phase transformation from contractive to dilativebehaviour. It does not require special equipment; it uses a typical bender104element setup.The proposed continuous method has been accepted for publication inthe ASTM Geotechnical Testing Journal (Styler and Howie, 2014).5.1 Continuous monitoring methodBlewett et al. (1999) monitored the change in the relative phase shift ofa continuous sinusoidal trigger signal. This was corrected to the absolutephase shift based on a square pulse trigger test. In the current approach, weuse a multi-tonal signal to transmit multiple frequencies which is comple-mented by a small number of sine pulse triggers to find the constant phaseoffsets. The multi-tonal signal addresses the challenges posed by migratingfrequency features and resonance peaks during an experiment.The relative phase shift between the two signals ∆θr is monitored formultiple frequencies in real time during an experiment. Monitoring therelative phase shift includes correcting the arc-tan discontinuities.Continuous sinusoidal signals do not provide enough information to de-termine the absolute propagation time. The evolving relative phase shift canbe monitored, but no information is provided for the phase offset correction.The phase offset is determined using a small set of discrete conventionalbender element tests.The absolute phase shift is determined using a suite of bender ele-ment tests as described in Chapter 4. The absolute phase shift at a sin-gle frequency is compared to the monitored relative phase shift at thesame frequency to determine the constant phase offset. The phase offsetis θo = ∆θa − ∆θr = n2pi, where n is an integer. At a minimum, a singleabsolute phase shift is required during an experiment to find the constantphase offset. Determining the absolute phase shift multiple times during anexperiment confirms that the phase offset from the tracked relative phaseshift is a constant for a single frequency.Migrating resonance peaks can influence the monitored shear wave veloc-ity. To address this, multiple different frequencies are monitored. These mul-tiple frequencies will be affected differently by migrating resonance peaks.105The continuous shear wave velocity method determines the shear wave veloc-ity at multiple frequencies throughout an experiment. This is accomplishedby using a continuous sinusoidal trigger signal. The continuous multi-tonalsinusoidal trigger signal may be expressed as:trg(t) = sin(2pif1t) + sin(2pif2t) + sin(2pif3t) + sin(2pif4t) (5.1)for four different constant frequencies f1, f2, f3, and f4. Every time theexperimental sensors are sampled, the phase angles of the bender triggerand response signals are measured at the multi-tonal frequencies.5.2 Experimental demonstrationProcedureThe bender element monitoring technique has two components: continu-ously measuring the relative phase shift and discrete measurements of theabsolute phase shift.Multiple phase velocities were monitored simultaneously at four frequen-cies: 6.25, 7.15, 8.35, and 10 kHz. These four frequencies are within thebender element frequency operating range for most of the soil states in thereported experiments. Approximately 3 times per second, the relative phaseshifts for the 6.25, 7.15, 8.35, and 10 kHz frequency components were mea-sured and recorded. This was accomplished by analysing a 20 ms window ofthe trigger and response bender element signals. The 20 ms windows wereused in Equation 2.3 to solve for the frequency dependent relative phaseshifts. The four phase shifts were recorded simultaneously with the fivetriaxial sensors.The multi-tonal trigger signal was temporarily suspended to perform ab-solute phase shift measurements. This was performed during consolidationat σ′r stresses of 60, 70, 80, and 90 kPa. The absolute phase shifts for the6.25, 7.15, 8.35, and 10 kHz frequency components were determined from a106suite of bender element tests using the procedure described in Chapter 4.This suite of tests included two sweeping sine waves, four sine pulses (at themulti-tonal frequencies), and four 20 ms continuous sine triggers. Each ofthe trigger signal waveforms was stacked 10 times to increase the signal tonoise ratio.The absolute phase shift was measured four times at different pointsduring consolidation. These repeated measurements demonstrated that thephase offset, θo = n2pi was constant for each frequency throughout theexperiment. The n parameter is a constant integer for each experiment ateach frequency.The four monitored frequencies are different than what was used in Chap-ter 4. A multi-tonal signal with only integer value frequencies repeats every1ms. This does not occur with the selected fractional frequencies(6.25, 7.15,8.35, and 10 kHz). It was thought that the relative phase shifts for thesefour frequencies might correspond to only one plausible absolute phase shift.Then, the absolute phase shift and phase velocity could be calculated in realtime without performing discrete bender testing. This approach proved dif-ficult to pursue due to challenges from moving resonance features. It wasnot further pursued in this research.ResultsIn order to demonstrate the continuous monitoring method, the results froma single experiment are presented in detail. Figure 5.1 depicts the 6.25 kHzcomponents of four discrete bender element tests performed on Specimen040. The 6.25 kHz component consists of two trigger signals. The firstwas a 6.25 kHz sine pulse, and the second was a 20 ms duration 6.25 kHzcontinuous sine wave (only the first 2 ms are depicted). Each subfigure inFigure 5.1 contains two plots. The upper plot is the received wave fromthe 6.25 kHz sine pulse. The lower plot is the cross correlation of the 20ms duration continuous wave. The cross correlation function resulted in aseries of peaks. The peak corresponding to the arrival of the sine pulse wasselected as the propagation time for the 6.25 kHz wave. This propagation107time was used to solve for the absolute phase shift, ∆θa = −2pif∆t. Thebender tests depicted in Figure 5.1 were performed at different stress statesduring consolidation of Specimen 040. As the stress increased, the specimenconsolidated and the absolute phase shift decreased, resulting in a fasterpropagation time.108(a) σ’a=121.2 kPa, σ’r=60.2 kPa, ∆θa=−32.3 rad, ∆t=0.822 ms(b) σ’a=141.2 kPa, σ’r=70.2 kPa, ∆θa=−30.4 rad, ∆t=0.774 ms(c) σ’a=161.0 kPa, σ’r=80.2 kPa, ∆θa=−28.9 rad, ∆t=0.736 ms(d) σ’a=181.1 kPa, σ’r=90.2 kPa, ∆θa=−27.6 rad, ∆t=0.704 ms0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2time (ms)Figure 5.1: Measured 6.25 kHz sine pulse response and cross corre-lation of 6.25 kHz continuous sine wave during drained con-solidation of loose saturated Fraser River Sand Specimen 040to acquire absolute phase shift of a 6.25 kHz wave at multiplepoints during the experiment109The relative phase shift was monitored continuously at four frequenciesusing a multi-tonal sinusoidal trigger signal. Figure 5.2 depicts a 2 mswindow of the applied and measured multi-tonal continuous trigger signalin the time domain and frequency domain immediately prior to the discretebender element test in Figure 5.1d. In the time domain, the received signalresembled the applied signal. In the frequency domain, it is shown thatthese signals contained all of their energies at the four selected frequencies:6.25, 7.15, 8.35, and 10 kHz.−505x(t)(a) Perpetual trigger signal0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.500.5y(t)Time (ms)(b) Measured response to perpetual trigger020004000|X(f)|(c) Perpetual trigger signal0 2 4 6 8 10 120500|Y(f)|Frequency (kHz)(d) Measured response to perpetual triggerFigure 5.2: Perpetual trigger and response signals in the time domain(a,b) and frequency domain (c,d) applied to and measured overdrained saturated Fraser River Sand Specimen 040 at σa = 181.1kPa, σr = 90.2 kPa to monitor the relative phase shift (∆θr) atfour frequencies, 6.15, 7.15, 8.35, and 10 kHzFigure 5.3 depicts the measured 6.25 kHz relative phase shift duringthe triaxial test of Specimen 040. The specimen was consolidated for 17.7minutes at a stress ratio of σa/σr of 2.0, followed by 100 minutes of ageing.It was then sheared along a conventional stress path of increasing σa tofailure. Figure 5.3 depicts arc tan discontinuities during consolidation, one110noise spike during ageing, and eight noise spikes during shearing. Figure 5.4depicts the unwrapped 6.25 kHz relative phase shift for the first 25 minutesof the triaxial test of Specimen 040. This figure includes the four measuredrelative phase shifts immediately prior to the discrete bender element testsdepicted in Figure 5.1.0 20 40 60 80 100 120 140 160 180 200−4−3−2−101234time (min)∆θ (rad) Age  ShearFigure 5.3: Measured relative phase shift from 6.25 kHz component ofperpetual trigger and response signals over consolidation, age-ing, and shearing of saturated Fraser River Sand specimen 040The continuous method requires a constant phase offset correction be-tween the unwrapped monitored relative phase shift and the measured dis-crete absolute phase shift. Table 5.1 details the calculated phase offsets forSpecimen 040. The absolute phase shift was measured at four frequenciesand at four different times during consolidation. Figure 5.1 depicts the 6.25kHz absolute phase shifts at these four points.The frequency of the bender element shear wave has a systematic effecton the resulting shear wave velocity. This was previously shown in Chapter 4and specifically Figure 4.8. It is further shown in Table 5.1. The ultimateobjective in a bender element test is to obtain a single velocity for the111propagation of a shear wave through the soil. A technique to correct thesystematic effect of frequency has not been developed in this work or inother published research to date. Consequently, bender element VS resultsshould be reported with the wave frequency.Figure 5.4 shows the measured relative phase shifts for the 6.25 kHz waveat four points during consolidation. The time for consolidation is due to therate of stress increase and temporary pauses to perform suites of benderelement tests to obtain the phase offsets. The consolidation test phaseslasts 17 minutes. The triaxial specimen of sand does not take 17 minutes toconsolidate.The phase offset is the difference between the discrete absolute phaseshift points and the monitored corrected relative phase shift. The differencebetween the absolute phase shift and the relative phase shift must be a mul-tiple of 2pi. For Specimen 040, the 6.25 kHz continuously monitored relativephase shift had a phase offset of −9 ∗ 2pi. Making multiple measurementsof the phase offset at different points during the experiment confirmed thisvalue.Figure 5.5 shows the monitored phase velocity at 6.25, 7.15, 8.35, and10 kHz for the saturated drained Fraser River Sand Specimen 040. Therewas a large increase in VS during consolidation up to a 6.25 kHz phasevelocity of 175 m/s. The kinks in the measured VS during consolidation aredue to pauses during the test to perform conventional bender element tests.During 100 minutes of ageing the 6.25 kHz phase velocity increased to 179m/s. When sheared along a conventional shear path the 6.25 kHz phasevelocity reached a peak of 183 m/s at σ′a = 336 kPa. This figure contains26319 measurements of the phase velocity for each of the four frequencies.This figure only contains measured phase velocities; it does not containinterpolated values or curve fitting. Before calculating VS , the monitoredchange in specimen height was used to adjust the propagation length.112Table 5.1: Measured absolute phase shifts, phase offsets, and phasevelocities for a loose saturated drained specimens of Fraser RiverSand Specimen 040Phase shift (rad)Specimen state Freq. θ(a)a θ(b)r θ(c)o n(d) VS(kHz) (m/s)σ′a = 121.2 (kPa) 6.25 -32.28 24.14 -56.42 9 144.1σ′r = 60.2 (kPa) 7.15 -37.02 19.32 -56.35 9 143.7e = 0.998 8.35 -43.44 25.13 -68.58 11 143.0Ltt = 118.426 (mm) 10.0 -48.51 26.32 -74.84 12 153.4σ′a = 141.2 (kPa) 6.25 -30.40 25.93 -56.32 9 152.9σ′r = 70.2 (kPa) 7.15 -35.13 21.18 -56.31 9 151.3e = 0.996 8.35 -41.03 27.68 -68.71 11 151.3Ltt = 118.335 (mm) 10.0 -46.00 28.90 -74.90 12 161.6σ′a = 161.0 (kPa) 6.25 -28.91 27.44 -56.35 9 160.6σ′r = 80.2 (kPa) 7.15 -33.52 22.89 -56.40 9 158.5e = 0.993 8.35 -39.14 29.64 -68.78 11 158.5Ltt = 118.250 (mm) 10.0 -43.99 30.88 -74.87 12 168.9σ′a = 181.1 (kPa) 6.25 -27.65 29.03 -56.67 9 167.8σ′r = 90.2 (kPa) 7.15 -31.99 24.45 -56.44 9 165.9e = 0.991 8.35 -37.46 31.45 -68.91 11 165.5Ltt = 118.161 (mm) 10.0 -42.23 32.74 -74.97 12 175.8(a) Interpreted from a suite of bender element trigger signals(b) Monitored unwrapped relative phase shift(c) The difference between the absolute and relative phase shifts(d) n = θo/(−2pi), constant for each frequency1130 5 10 15 20 250510152025303540time (min)∆θ (rad) 24.1 rad25.9 rad27.4 rad29.0 rad AgeConsolidation Figure 5.4: Unwrapped relative phase shift during drained consolida-tion of loose saturated Fraser River Sand Specimen 0401140 50 100 150  80100120140160180200220240σa’(kPa)V S (m/s)Consolidation10 kHz  8.35 kHz7.15 kHz6.25 kHz1 10  10 kHz6.25 kHz 7.15 kHz8.35 kHzTime (minutes)Age250 300 350 400 450 80100120140160180200220240σa’(kPa)V S (m/s)Shear  6.25 kHz7.15 kHz8.35 kHz10.0 kHzFigure 5.5: Perpetual source measured phase VS for saturated drainedFraser River Sand Triaxial Specimen 040 with consolidation ata stress ratio of σa/σr = 2.0, aged for 100 minutes, and shearedalong a conventional shear path1155.3 Interpretation challengesSome noise spikes in the monitored relative phase shift are visible on Fig-ure 5.4. Under certain circumstances, noise spikes resulted in an incorrectphase discontinuity correction. These circumstances depend on the magni-tude of the noise spike and the unwrapping algorithm used to correct thediscontinuities. Most noise spikes observed in these experiments did notexceed the threshold for a phase discontinuity correction or resulted in twosubsequent phase discontinuity corrections that cancelled each other out.However, it was occasionally observed that a noise spike resulted in a singleincorrect phase discontinuity correction. In Specimen 048 this occurred forthe 8.35 kHz monitored relative phase shift during shearing, as shown inFigure 5.6. The result is an obvious discontinuity in the measured VS . Thiseffect is corrected by incrementing the remainder of the relative phase shiftvalues by 2pi. This inconsistency is easy to identify and easy to fix.Another problem was observed at low stresses. The continuously moni-tored frequencies may not be in the bender element testing frequency range.This results in a relatively constant, but incorrect, monitored phase shiftduring the low stress portion of consolidation. Once a sufficient stress isachieved, the receiver bender element begins sensing the propagating shearwave and the relative phase shift is correct. This inconsistency is depictedin Figure 5.7 for the 10.0 kHz shear wave. At low stresses, the measuredrelative phase shift and VS are incorrect. This is easy to identify, but canonly be fixed by changing the monitoring frequency. This may be addressedby testing multiple frequencies with a multi-tonal signal as done in thisinvestigation.Migrating frequency features in the bender element transform functionresult in a phase velocity where the dominant factor causing the change invelocity is a change in the system transfer function, not a change in the shearwave propagation time. This effect is shown in Figure 5.8 during ageing forSpecimens 044 and slightly in 047.The frequency-dependent features can be observed by calculating thephase velocity over the bender element operating range. The discrete ben-116−45−40−35−30−25∆θa (rad)(a) Absolute phase shift200 250 300 350 400 450120140160180200220VS (m/s)σ’a (kPa)(b) Shear wave velocity  ErrorCorrectedFigure 5.6: Correcting a discontinuity in the 0.835 kHz phase shift inSpecimen 048 to result in a continuous measured phase velocityder element tests consisted of a suite of bender element signals including asweeping sine wave. Figure 5.9a depicts the magnitude of the transfer func-tion at two different stress states for Specimen 040. The transfer function isthe frequency dependent conversion from the input electrical signal, to themechanical wave in the soil specimen, to the output voltage signal, and thenthrough the signal amplifier. The mechanical response of the soil cannotbe isolated without characterizing the transfer functions of the trigger andreceiver bender elements. A method to characterize these transfer functionsduring an experiment has not yet been devised. They must be characterizedduring an experiment as the soil-coupling will change the response of thebender element cantilever beam. Figure 5.9b depicts the interpreted fre-quency dependent phase velocity following the method described in Chap-1170 10 20 30 40 50 60 70 80 90 10090100110120130140150σa (kPa)VS (m/s)040047048044Figure 5.7: Monitored 10.0 kHz shear wave velocities during consoli-dation of loose saturated Fraser River Sand are not within thebender element frequency operating range at low stressester 4. The frequency dependent features in the phase velocity correspond tochanges in the magnitude of the transfer function. The frequency dependentfeatures are translated to higher velocities and different frequencies as thestress increases.The phase velocity is not constant across the bender element frequencyrange. This was observed in Specimen 040 as detailed in Table 5.1 and in Fig-ure 5.5. The 10 kHz shear wave velocity was almost 10 m/s faster than thethree other frequencies. This 10 m/s difference was not constant through-out the experiment. During shear, the system transfer function changes at10 kHz. After this change, the 10 kHz signal agrees with the other threefrequencies.1180.1 1 10 100165170175180185VS 7.15kHz (m/s)040044047048Age (minutes)Figure 5.8: 7.15 kHz shear wave phase velocity during ageing of fourloose saturated Fraser River Sand specimens at σa = 200, σr =100 kPaFigure 5.9b for Specimen 040 contradicts the results in Table 5.1 with the10 kHz phase velocity being slower than the velocities at 6.25, 7.13, and 8.35kHz. The difference in the absolute phase shift between the 10 kHz resultsin Figure 5.9b and Table 5.1 is 2pi. The combination of the cross correlationof the sine pulse and continuous sine at 10 kHz resulted in the values inTable 5.1. The sweeping sine wave anchored at the absolute phase shifts for3 of the 4 signals results in Figure 5.9b. The dispersive phase velocity overthe bender-soil system makes it difficult to interpret the results.It was observed that the trends in VS with stress and void ratio aretypically consistent, even if the VS measurements at different frequenciesdisagree. The only time these trends deviate is when a significant frequencyfeature appears at the frequency being monitored, as depicted during shear119−100−5005020 log(|RES|/|TRG|) dB  (a) Transfer function peaksσ’r=60,σ’a=120kPaσ’r=90,σ’a=180kPa0 2 4 6 8 10 12100120140160180200VS (m/s)Frequency (kHz)(b) Shear wave velocityFigure 5.9: Bender element test results from Saturated Fraser RiverSand specimen 040; (a) Migration of multiple resonance peakswith increasing stress, (b) Phase velocity against frequencyof Specimen 040 for 10 kHz (Figure 5.5) and during ageing of Specimens 047and 044 (Figure 5.8). The proposed method monitors the shear wave velocityacross the soil-bender system. This compares a trigger voltage signal to areceived voltage signal, not the mechanical input and output waves sensedby the cantilever bender elements. The effect of the bender element electricalto mechanical transform function depends on the bender-soil coupling and120changes through-out the experiment. Until a method is devised to measurethe transform function during an experiment, judgement must be used tointerpret bender element VS measurements. In order to detect changes inVS with age, stress, and density; the observer can concentrate on signalsthat are not adversely affected by the system transform functions. Moreattention is placed on consistent VS results than outliers.The implementation of the continuous technique is mostly automated.In this work, the manual effort involved creating Table 5.1 in order to cal-culate the phase offset to apply to each monitored phase shift. The discretebender element tests needed to be manually aligned with the continuousmonitored relative phase shifts. The post-processing required in Figure 5.6,to correct discontinuities missed by the phase-unwrapping algorithm, wasrarely encountered.1215.4 Evaluation of bender element induceddisturbanceFor the trigger bender elements, it can be shown that for excitation in air,the bender tip deflection increases with applied voltage. To investigate thepotential disturbance to the specimens caused by continuous excitation ofthe benders and the effect of triggering voltage, the triaxial behaviour wascompared between the proposed continuous bender element method andtests without bender element testing. Disturbance was evaluated by com-paring axial and volumetric creep strains of loose specimens of Fraser RiverSand under σa = 200 kPa and σr = 100 kPa. It was expected that ifthe continuous trigger signal induced disturbance then the developed creepstrains would correlate to the trigger signal amplitude. The testing program,as detailed in Table 5.2, included three specimens without bender elementmonitoring, two specimens at ± 3 V, one at ± 6 V, and one at ± 10 V.Creep strains were measured during ageing for all seven specimens. Fig-ure 5.10 shows the measured volumetric strains during constant stress ratioconsolidation for the seven specimens. Four of these specimens includedcontinuous bender element trigger excitation. Figure 5.11 shows the mea-sured volumetric creep strains against the applied trigger signal amplitudeat 1, 10, and 100 minutes for each specimen. There is no obvious effect ofthe trigger signal amplitude on the volumetric creep strains.Table 5.2: Experimental program and specimen propertiesID B-Value Void ratio Perpetual trigger NGInitial End Consolidation amplitude (V)034 0.991 0.998 0.973 (-0.025) 0 -040 0.991 1.012 0.989 (-0.023) ± 3 2.1 %042 0.994 1.025 0.997 (-0.028) 0 -044 0.990 0.996 0.968 (-0.028) ± 10 2.2 %047 0.999 0.981 0.954 (-0.027) ± 6 2.8 %048 0.988 0.998 0.974 (-0.024) ± 3 2.3 %049 0.992 0.994 0.969 (-0.025) 0 -12240 60 80 100 150 20000.20.40.60.81p (kPa)Volumetric strain (%)  0 V3V6V10VFigure 5.10: Measured volumetric strains during constant stress ratio( σa/σr = 2.0) consolidation of loose saturated Fraser RiverSandFor the four specimens with continuous VS measurements, the measuredincrease in phase velocity during ageing is presented in Figure 5.8. This in-crease in VS at constant effective stress is similar to observations by Afifi andRichart (1973); Anderson and Stokoe (1978); Baxter and Mitchell (2004).The calculated NG factors for the specimens with continuous VS measure-ments are provided in Table 5.2.The amplitude of the bender element trigger signals did not result inan observable change in the void ratio during consolidation or in the creepstrain magnitudes. For the given loose samples of Fraser River Sand andsensor resolution of the triaxial equipment, the disturbance induced creepstrains did not exceed experimental scatter, a function of the repeatability of1230 1 2 3 4 5 6 7 8 9 1000.050.10.150.20.25Trigger signal amplitudeVolumetric strain (%)  1 min10 min100 minFigure 5.11: Volumetric strains during ageing of seven loose saturatedFraser River Sand specimens at σa = 200, σr = 100 kPathe specimens and test procedure and the uncertainty of the measurements.The increase in small strain stiffness, as quantified with NG, did not changesignificantly with changes in the trigger signal amplitude. The effect of ageon the increase of G0 does not depend on the bender element trigger signalamplitude, for the given equipment up to a trigger amplitude of ± 10 V.Based on the bender element equipment and soil, continuous monitoringwith bender elements was judged to be non-destructive.There will be a zone of disturbance adjacent to the trigger bender ele-ment. This will be due to the mechanical triggering of the shear wave fromthe bender element. The extent of this zone could not be examined withthe UBC triaxial equipment. For the triaxial specimens with a propaga-124tion length around 120 mm, this zone of disturbance was unobservable. Forshorter propagation lengths, such as in an oedometer cell, the proportionof disturbance caused by the continuous excitation of the trigger benderelement may be significant. However, it was not examined in this study.5.5 G0 during ageing of Fraser River SandThe observed Gsec at small strains along conventional stress paths is sensi-tive to specimen age duration (Lam, 2003; Shozen, 2001). There were twodifferent expectations for the effect of ageing on G0 in Fraser River Sand.The trend in results from Shozen (2001) showed an increased sensitivity toageing at lower strains. This suggests a significant increase in Gsec at theeven lower shear wave strain level. Conversely, published resonant columnresults found a negligible increase in stiffness during ageing for clean sands,as summarized in Section 2.3.4.Continuously monitored bender element measurements depicted eitherstable or unstable behaviour. Figure 5.12 is an example of stable benderelement behaviour during ageing and Figure 5.13 is an example of unsta-ble bender element behaviour during ageing. Unstable ageing was observedwithout any noticeable stability issues in the creep strain measurements.It appears to be a result of the migration of resonance peaks in the ben-der element transducer-sensor system as the soil stiffens. An advantage ofcontinuous bender element monitoring is that the results can be screenedfor stable bender element behaviour. This prevents the characterization oferroneous NG factors that may be too high or even negative.The NG factor, Equation 2.10, is the normalized change in Gvh perlog-cycle of time. The calculated NG factors are detailed in Table 5.3. Themedian stable NG factor for ageing of Gvh was 1.9±0.5 % for loose specimensand 1.0 ± 0.2 % for the stable denser specimens. These results agree withthe published values of 1-3 % for coarse grained soil (Anderson and Stokoe,1978).In this chapter Gvh corresponds to a stiffness interpreted from a benderelement shear wave velocity propagating in the vertical direction with hori-1250.01 0.1 1 10 1005353.55454.55555.55656.55757.558time (min)G vh (MPa) NG=2.1 %Figure 5.12: Example of stable ageing for Specimen 040 at 8.35 kHzzontal particle motion. Gvh represents interpreted values from measured VS .G0 is used when referencing the isotropic elastic shear stiffness, when refer-ring to theoretical equations, when discussing other publications to matchtheir nomenclature, and when presenting normalized Gsec/G0 curves.The NG equation is normalized by G0 at 1000 minutes to avoid an ap-parent change in the log-linear behaviour for fine grained specimens (Afifiand Richart, 1973; Anderson and Stokoe, 1978). For coarse-grained speci-mens Anderson and Stokoe (1978) observed a log-linear increase in G0 fromthe start of ageing. They speculated that it may not be initially log-linear,but were unable to make this observation using resonant column equipment.Figure 5.12 shows that the log-linear behaviour begins around 1 minute afterthe onset of ageing in clean Fraser River Sand.The bender element modified triaxial equipment is capable of acquiringGsec and Gvh. It can be used to characterize the Gsec/G0 degradation withshear strain during the shear phase. It can also be used to calibrate an1260.01 0.1 1 10 10046485052545658time (min)G vh (MPa)NG=−9.2 %Figure 5.13: Example of unstable ageing for Specimen 015 at 9 kHzempirical G0 equation for Fraser River Sand.5.6 Calibration of G0 equation for Fraser RiverSandThe form of the calibrated empirical equation is given in Equation 5.2. Ithas three empirical components: the leading coefficient A, the void ratiofunction f(e), and the in-plane effective stress exponent (n/2). The stressexponent is divided by two to match a convention by Hardin and Blandford(1989). The original work by Hardin raised the isotropic stress to the powerof n. When it was found that the shear wave velocity depends only on thein-plane stresses, it required the equation to be modified. If the soil is underisotropic effective stress and σ′0 replaces both σ′a and σ′r, then the originalequations are obtained as the two n/2 exponents are added together.127Table 5.3: Calculated NG factors(Equation 2.10) for continuouslymonitored bender element testsSpecimen σ′a σ′r Void ratio NG Stable004 199.0 99.9 0.966 1.8 ± 0.2 % Yes008 200.1 100.1 0.984 1.7 ± 0.4 % Yes012 199.9 99.9 0.962 2.9 ± 0.4 % Yes013 100.0 100.0 0.971 -1.3 ± 2.8 % No014 280.3 100.2 0.937 2.0 ± 0.3 % Yes015 199.9 100.2 0.962 0.8 ± 10.8 % No016 199.6 99.7 0.973 2.0 ± 0.4 % Yes018 199.6 99.6 0.760 1.0 ± 0.2 % Yes019 198.6 99.1 0.816 0.2 ± 7.2 % No020 200.0 99.9 0.974 -0.3 ± 0.4 % No023 200.3 100.0 0.970 0.1 ± 3.2 % No024 200.7 100.2 0.965 -5.8 ± 4.2 % No026 99.9 99.9 0.952 3.3 ± 2.5 % No027 200.5 100.3 0.970 3.9 ± 1.4 % No040 200.9 100.3 0.989 2.0 ± 0.5 % Yes043 194.0 100.8 0.968 2.2 ± 0.7 % Yes044 200.5 100.0 0.968 2.7 ± 1.1 % Yes047 200.4 100.1 0.954 2.8 ± 0.9 % Yes048 200.8 100.1 0.974 2.3 ± 0.4 % YesG0 = Af(e)(σ′aσ′r)n/2(5.2)An attempt to isolate the effect of the in-plane stresses on G0 was made.A dataset was compiled for the measured G0 at void ratios of 0.96, 0.97, and0.98, at stress ratios of 2.0, without any ageing. The underlying assumptionis that the void ratio term, f(e), would be approximately constant since thespecimens are at the same void ratio and stress ratio. This resulted in astress exponent (n/2) of 0.31.The stress exponent was calibrated from 18 similar experiments andresulted in n/2 = 0.31. This is slightly higher than the expected n/2 = 0.25from Hardin and Blandford (1989). It is within the range of published128empirical relationships for many sands summarized by Cho et al. (2006),and similar to some of the crushed sand types.Three potential published void ratio functions were investigated. Thefirst two are from Hardin and Black (1966), the third one is from Hardinand Blandford (1989). None of these three equations clearly provided an im-proved empirical fit. Therefore, the most recent formulation, Equation 5.3,will be used.f(e) =10.3 + 0.7e2(5.3)In this study, the intrinsic particle properties are constant - Fraser RiverSand is used for every experiment. The leading coefficient in the empiricalequation, A, should be a constant. A value of 2440 was calibrated using thepreceding f(e) function and stress exponent.5.6.1 Evaluation of calibrated equationEquation 5.4 is the final calibrated equation. This equation has been nor-malized by dividing the atmospheric pressure (P 0.38a ) out of the leading Acoefficient. The stress ratio correction proposed by (Yu and Richart, 1984)was not used. The majority of these data were measured at a stress ratio of2.0. This results in a stress ratio correction of (1−rK2N ) = (1−0.2(1/3)2) =0.978. Applying this stress-ratio correction would increase the leading coef-ficient from 420 to 429.(G0Pa)= (420)10.3 + 0.7e2(σ′aPaσ′rPa)0.31(5.4)Hardin and Blandford (1989) proposed initial values for the leading coef-ficient of 680 and for n/2 of 0.25. The calibrated Fraser River Sand equationis softer and more stress dependent.Figure 5.14 compares this calibrated empirical equation to the entiretested dataset with continuous bender element measurements. The standarddeviation for Equation 5.4 was calculated to equal 3.3 MPa as shown inEquation 5.5. This figure includes three monitored frequencies for each129experiment. One unaccounted source of error is the frequency of the benderelement testing. The bender element performance was found to be frequencydependent and this dependence could not be predicted. This effect can beseen in Figure 4.8. For example, the VS at 8 kHz is systematically differentthan at 9 kHz, despite both being within the stable range between 6 and 14kHz.0 10 20 30 40 50 60 70 80 90 1000102030405060708090100Empirical G0 (MPa)G 0=ρVS2  (MPa)Figure 5.14: Comparing empirically estimated G0 to the entiredataset of measured ρV 2Ss = 2√1n− 2∑(measured− predicted)2 =2√450998MPa240720= 3.3MPa(5.5)The empirical trends capture the effect of void ratio and in-plane effec-tive stress on G0. In triaxial testing, the void ratio and in-plane effectivestress can be confidently determined. Conversely, bender element testing ismeasuring the velocity across the entire measurement system. It includes130an unknown effect due to the bender element sensors. The different testedfrequencies do not agree - even within the same experiment. However, eachfrequency depicts the same trends with soil state. The empirical relationshipand uncertainty for G0 were developed with the multiple tested frequencies.5.6.2 Comparing to other empirical G0 equations for FraserRiver SandChillarige et al. (1997) used a laboratory calibrated VS equation for FraserRiver Sand to interpret in-situ soil state. Their empirical VS equation wasconverted to G0 using G0 = ρV 2S , with ρ =γwgravity(Se+GS1+e). Convertingtheir empirical equation for VS to G0 results in Equation 5.6. This equationsolves for G0 in terms of Pa units.G0 =γwgravity(Se+GS1 + e)(294− 143e)2(σ′vPa)0.52K0.250 (5.6)Wride et al. (2000) used an empirical equation calculated by Cunninget al. (1995) to interpret VS measurements in Fraser River Sand at theKidd-2 research site. They used this equation even though the coefficientscalculated by Cunning et al. (1995) were for Syncrude Sand, Ottawa Sand,and Alaska Sand. This empirical equation for VS has been reformulated toG0 in Equation 5.7.G0 =γwgravity(Se+GS1 + e)(359− 231e)2(σ′vPa)0.50K0.250 (5.7)Although not Fraser River Sand, Lee et al. (2004) used an equation cali-brated by Salgado et al. (2000) for a sand with no silt. The work by Salgadoet al. (2000) characterized empirical coefficients for different amounts of finescontent. Equation 5.8 is for a clean sand.G0 = 611Pa(2.17− e)21 + e(p′Pa)0.44(5.8)These three equations were compared to the calibrated empirical Equa-tion 5.4 and a continuous measurement of VS . Figure 5.15 was generated131using the measured void ratios and stresses from the consolidation of Speci-men 040. A K0 value of 0.5 was assumed for Equation 5.6 and Equation 5.7.20 40 60 80 100 120 140 160 180 200 22015202530354045505560σ’a (kPa)G 0 (MPa)  This studyChillarige et al. 1997Cunning et al. 1995Lee et al. 2004Specimen 040Figure 5.15: Empirical G0 estimates during consolidation of Spec-imen 040 (σ′a/σ′r = 2) using Equation 5.4(blue), Equa-tion 5.6(red), Equation 5.7(green), Equation 5.8(grey), andmeasured from Specimen 040 (yellow)The calibrated empirical equation compares very well with a previousinvestigation by Chillarige et al. (1997). It also fits the measured datasetbetter. This past study used Fraser River Sand, but was not performedon the same laboratory equipment using the same laboratory techniques.The improved accuracy in the interpretation of bender element tests wasnecessary for evaluating the small change in G0 during ageing, not the largechange during consolidation. The comparison is poor between the currentstudy and Cunning et al. (1995). This may entirely be a result of thedifferent sand investigated by Cunning et al. (1995). An equation calibratedby Salgado et al. (2000) and used by Lee et al. (2004) for a sand with no132silt was too high at low stresses compared to the characterized Fraser RiverSand equation and measured results.Cho et al. (2006) compiled a set of empirical coefficients for differentsand types. They fit an empirical equation with two coefficients: VS =α (σ′mean/1(kPa))β. The coefficients in this study can be manipulated toprovide an α of 39 m/s and β equal to n/2 of 0.31. The Fraser River Sandα value is less than Nevada Sand (α = 56.3) and Ticino sand (α = 70.7).The β value is greater than Nevada Sand (β = 0.242) and Ticino Sand(β = 0.231). Based on the work by Cha et al. (2014), this implies thatFraser River Sand is slightly more compressible than these two soils.5.6.3 Comparing effect of age on G0 to calibrated G0equationIt can be seen that volumetric creep strain occurs during ageing. This resultsin a decrease in the void ratio. Using Equation 5.4, a decrease in the voidratio would increase G0 and consequently increase the shear wave velocity.Therefore, it might be expected that Equation 5.4 inherently accounts forageing and that the ageing phenomenon is just a consequence of increaseddensity due to volumetric creep. This expectation is not supported by thedata.Equation 5.4 does not account for the observed increase in stiffness dur-ing ageing. This is demonstrated conclusively by Figure 5.16 which showsa plot of the calculated and measured stiffness against time for a specimenunder a stress ratio of 2.0. Additional details for this figure are provided inTable 5.4. This observation has been made before; e.g. Figure 9 in Andersonand Stokoe (1978). The effect of age on G0 is not due to volumetric creepchanges. Therefore, an NG factor must be used. An NG factor for FRS wascalibrated in Section 5.5.5.7 ConclusionThis chapter presented a method to monitor VS throughout a laboratoryexperiment with bender elements at multiple user selected frequencies. The1330 10 20 30 40 50 60 70 80 90 1005051525354555657585960Age time (minutes)G 0 (MPa)  EmpiricalMeasuredEmpiricalMeasuredFigure 5.16: Empirical G0 estimates during ageing for Specimen 040compared to measured valuesTable 5.4: Comparing empirical and measured G0 (at 7.15 kHz) dur-ing ageing of Specimen 040Time σ′a σ′r void Equation 5.4 G0 = ρV2S(min) (kPa) (kPa) (MPa) (MPa)1 200.9 100.1 0.989 53.2 55.810 200.9 100.0 0.988 53.3 57.2100 200.5 99.7 0.987 53.2 58.6equipment used is a typical two element bender system. Challenges in ap-plying the developed method were identified. Errors in the correction ofdiscontinuities in the monitored relative phase shift are easy to fix and un-representative low-stress velocities are easy to identify. The migration offrequency-dependent features is more challenging. The measured propaga-tion time across the system is correct, but it is not possible to separate the134change due to the soil from the change due to the bender element transferfunction. This effect cannot be corrected without characterizing the evolv-ing bender element transfer functions. To date, the characterization of anin-specimen bender element transfer function has not been achieved.Monitoring multiple frequencies allows detection of anomalous resultscaused by changes in the bender element transform function. Frequencydependent effects may not occur on all of the monitored frequencies simul-taneously, and the additional monitored frequencies still reflect the soil be-haviour. Conventional discrete bender element testing does not allow easyidentification of detrimental system effects. This technique permits bad datato be identified and discarded, which protects against reporting and drawingconclusions from bad results.Monitoring the relative phase velocity throughout an experiment uses acontinuous trigger signal. The value of this method would be reduced if thecontinuous excitation caused sample disturbance. For the given equipmentdetails using the metric of creep strains and NG age factor, bender elementtesting is considered to be non-destructive.There is a variation in the frequency-dependent bender element resultsbetween “identical” specimens. A portion of this is due to the natural vari-ation between identical specimens. The same exact specimen cannot berecreated. The systematic frequency dependence of the shear wave velocityis affected by differences in the geometry of the specimen and coupling ofthe soil-bender element. Figure 5.9 shows how frequency dependent featurescan migrate during a single experiment. However, as shown in Chapter 4,the phase velocity is much more consistent than group velocity measures.The empirical G0 Equation 5.4 can be used to estimate the small strainshear stiffness from the void ratio and effective stress state in Fraser RiverSand. The equation matched the form proposed by Hardin and Blandford(1989). The calibrated equation using the continuous bender element tech-nique was similar to other published relationships.This technique was further developed to create a new in-situ testingtechnique. This development is reported in Chapter 7. Before switchingto in-situ testing, the third research objective outlined in Section 1.1 is135addressed.The research into bender element testing and interpretations reported onin this chapter and Chapter 4 will now be used to integrate VS measurementsand G0 calculations into a laboratory investigation of the effect of age onshear stiffness of Fraser River Sand.136Chapter 6Characterizing normalizedstiffness degradation curvesin the laboratoryThe deformation properties of in-situ granular soils cannot be easily charac-terized through laboratory testing. The deformation is very sensitive to thestate of the soil and free-draining soils cannot be routinely sampled undis-turbed. One way to estimate the deformation properties is to measure thein-situ G0 and select an equivalent modulus based on applicable shear strain.G0 can be determined using in-situ VS measurements. Its degradation withshear strain can be captured using published or empirical normalized shearstiffness degradation curves (Gsec/G0 against shear strain). This chaptercontains measured shear stiffness degradation curves that demonstrate thesignificance of specimen age, initial stress ratio, and stress path variables.It was demonstrated in Section 3.4.1 that the triaxial equipment canbe used to produce results similar to previous studies. It was shown in Sec-tion 3.4.3 that current bender element techniques were unable to confidentlydetermine small changes in G0, such as during ageing at constant stress. Acombined time and frequency domain approach was proposed in Chapter 4.This method was shown to be reproducible for simulated and experimentalbender element signals. This method was further developed into a continu-137ous technique in Chapter 5. The continuous excitation did not influence theeffect of ageing. Bender element testing in this research can now be used toprovide consistent values of G0 that can be used to study Gsec/G0.Before integrating the bender element results into the stiffness investi-gation, this chapter first briefly covers the triaxial consolidation and creepstrain measurements. The Gsec stiffness is then evaluated to demonstratethe need for a normalization factor, G0, to compare different testing condi-tions.This investigation complemented past studies (Lam, 2003; Shozen, 2001)by adding bender elements to the triaxial investigation of the small strainbehaviour of Fraser River Sand. The test program in the current study re-peated many experiments during the development of the equipment, dataacquisition, stress control routines, and bender element techniques. Thesetests were all performed under drained conditions through the consolida-tion, ageing, and shear phases. Section 3.4.1 demonstrated that the smallstrain results in the current investigation are very similar to the past studies.Therefore, the results from the current investigation may be combined withprevious results when making observations or conclusions.6.1 Consolidation of Fraser River Sand specimensConsolidation occurs in two phases. The effective axial stress is increaseduntil the desired stress ratio is achieved. Then the axial stress and chamberpressure are increased simultaneously while maintaining the desired stressratio. The effective stresses are increased up to the desired stress state.Assuming that the specimen is a perfect cylinder, the axial and volumet-ric strains can be used to calculate the radial strain, εr = (εv − εa)/2, andshear strain, εq = 2/3(εa − εr). If the developed strains are isotropic thenthey are the same in every direction. This means that εa = εr, εv = 3εa, andεq = 0. An isotropic soil fabric will have isotropic strains when an isotropiceffective stress is applied. Zero radial strain corresponds to a K0 stress path.Zero radial strains are typical in oedometers with a fixed radial boundary.In-situ at-rest conditions are at K0 = σ′h/σ′v stress.138During the second phase of consolidation, the stress path direction isconstant. Figure 6.1 depicts the developed axial and radial strains duringconsolidation at a constant stress ratio for nine specimens. The origin of thisplot is at the top centre - it corresponds to the point at which the desiredstress ratio was achieved. The sign convention for axial compression is pos-itive. The sign convention for radial compression is positive. Compressiveradial strains mean that the radius of the cylindrical specimen is decreasing.The final point for each of these nine strain paths is labelled. This labelcontains the applied constant stress ratio (σ′v/σ′h) and an identifier for thedataset with TS being Takahiro Shozen, KL being Keith Lam, and MS beingmyself.This figure includes two lines identifying the isotropic strain path andK0 strain path. The hydrostatic stress paths (σ′v/σ′h = 1.0) have lower axialstrains than the isotropic strain path. Therefore, water pluviated specimensdo not create isotropic fabric - they are stiffer in the axial direction. Thisagrees with the observation by Negussey (1984) that WP pluviated speci-mens are anisotropic. This figure also shows that the 2.8 stress ratios resultin radial extension strains and 1.6 have compressive radial strains. The 2.0tests are near the K0 strain path.6.2 Developed creep strains during ageingAfter consolidation, the applied axial load and chamber pressure were keptconstant for an ageing duration. This ageing duration was typically 10, 100,or 1000 minutes. During the holding phase the specimen exhibits creep orsecondary compression strains. The creep strain magnitudes are summarizedin Appendix D.Figure 6.2 depicts radial strain against axial strain during secondarycompression. This is the same type of plot as Figure 6.1, but at much lowerstrain magnitudes. This shows that during ageing there is a constant strainpath direction. The test by Lam at a stress ratio of 2.5 does not appear tobe stable.Figure 6.3 compares the consolidation strain path direction to the age139−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.800.20.40.60.811.21.41.61.82.0 MS2.8 MS2.0 TS2.8 TS1.0 TS1.0 KL1.6 KL2.1 KL2.5 KLIsotropic Strains  K0radial extension  radial compressionaxial compression εr (%)ε a (%)Figure 6.1: Primary compression strains for nine specimens at six dif-ferent stress ratios from this study (MS), Shozen (TS), and Lam(KL)strain path direction. Most points plots below the 1:1 line. This meansthat during creep there is a larger ratio of axial to radial strain than duringconsolidation. This implies that K0 is lower during consolidation. Thisagrees with observations by Mesri and Vardhanabhuti (2009).6.3 Secant stiffness during shearingAll imposed shear stress paths involve an increase in σ′a/σ′r until failure. Theconventional stress path is an increase in the axial stress without changingthe chamber pressure. The constant-p stress path is ∆σ′r−2 = ∆σ′a. The−1 stress path is ∆σ′r−1 = ∆σ′a. The slope 0 stress path is a decrease inconfining pressure with an increase in axial load to maintain a constant σ′a.The axial load has to be increased to compensate for the reduction in the140−0.1 −0.05 0 0.05 0.1 0.1500.050.10.150.20.252.0 MS2.8 MS2.0 TS2.8 TS1.0 TS1.0 KL1.6 KL2.1 KL2.5 KLIsotropic Strains  K0radial extension  radial compressionaxial compression εr (%)ε a (%)Figure 6.2: Secondary compression strains for nine specimens at sixdifferent stress ratios from this study (MS), Shozen (TS), andLam (KL)chamber pressure contribution to σ′a. In the work performed by Shozen(2001) and Lam (2003), the constant-p stress path was called a -2 stresspath. This naming convention identified the slope of ∆σ′a/∆σ′r. In thiswork the -2 stress path was renamed the constant-p stress path to make itmore informative in the Cambridge stress space.Figure 6.4 compares the responses to the three different stress pathsperformed during this investigation. In this figure all three specimens wereprepared loose, consolidated along a constant stress ratio of 2.0 up to σ′a =200 kPa, σ′r = 100 kPa, and aged for 100 minutes. The −1 stress path wasnot performed in this study.Figure 6.4a shows that the three stress paths have very different ultimateshear stresses, ∆q. However, it does not show that these different failurestate effective stresses are on the same failure surface. The conventional141−1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5−1−0.500.511.522.533.5Age εr/εaConsolidation εr/εa  This studyShozen (2001)Lam (2003)Figure 6.3: Comparing the strain ratio during consolidation to agepath reaches a maximum stress ratio (σ′1/σ′3) of 3.99, slope P reaches 3.92,and slope 0 reaches 3.87. Figure 6.4b shows that the different stress pathsexperience much different volumetric strains. The conventional stress path,which involves an increasing mean stress, results in more contractive strains.The slope-P stress path is at a constant mean stress. It shows that theincreasing shear stress also results in contractive strains. The slope-0 stresspath, which involves a decreasing mean stress and increasing shear stress,also shows contractive volumetric strains. The phase transformation pointfrom contractive to dilative volumetric strain occurs at lower axial strainsas the shear stress path rotates towards the failure surface. Figure 6.4c andFigure 6.4d show the secant stiffness against shear strain. The log-plot inFigure 6.4d is more informative at the small strain. The slope-0 and slope-P stress paths appear to have an initial constant stiffness plateau beforedegrading with strain. All of these specimens were prepared loose and theshear phases began at the same stress state and age duration. They have142different secant stiffness values above 0.01 % shear strain.0 1 2 3 4 5 6 7 8 9 10020406080100120140160180200εa (%)∆ q (kPa)  CP0(a)0 1 2 3 4 5 6 7 8 9 10−0.4−0.3−0.2−0.100.10.20.30.40.50.6εa (%)ε v (%)  CP0(b)0 1 2 3 4 5 6 7 8 9 1002468101214161820εq (%)G sec (MPa)  CP0(c)0.01 0.1 1 1005101520253035404550εq (%)G sec (MPa)  CP0(d)Figure 6.4: Effect of stress path for specimens 012 (e=0.960, con-ventional, see Figure D.36), 015 (e=0.959, constant-p, see Fig-ure D.39), and 016 (e=0.971, slope-0, see Figure D.40); all pre-pared loose, consolidated at a SR 2.0 to σ′a =200 kPa and σ′r =100 kPa, and aged 100 minutesFigure 6.5 depicts a similar set of plots, but for different initial stressratios. In this figure all three specimens were aged for 100 minutes andsheared along a conventional stress path. At higher initial stress ratiosthe specimen state at the onset of shearing is closer to the failure surface.Similar to Figure 6.4a, Figure 6.5a shows that for the same conventional143stress path, a different initial stress ratio results in a very different ultimateshear stress. However, they all reach the same failure surface. The ultimatestress ratio is 4.04 for a stress ratio of 1.0, 3.98 for a stress ratio of 2.0, and4.04 for a stress ratio of 2.8. The shear path for all three tests includes anincrease in both mean stress and shear stress to failure. Figure 6.4b showsthat an increasing initial stress ratio results in a less contractive volumetricstrain. Furthermore, the phase transformation point is reached at loweraxial strains. Figure 6.4c and Figure 6.4d shows the secant stiffness againstshear strain. The log-scale plot shows that the higher stress ratio specimenshave a larger secant stiffness at very low strains. It also shows that thestiffness for the 1.0 stress ratio does not degrade as rapidly as the higherstress ratios.Figure 6.6 shows the effect of the age duration on conventional stresspaths from a stress ratio of 2.0. The strains have been corrected for con-tinued creep following the observations by Shozen (2001). The void ratiosare reported at the end of ageing. The differences between these void ratiosis due to the challenge of reproducing identical very loose specimens. Theeffect of volumetric creep during the ageing phase is very minor on the voidratio.Figure 6.6a shows that the 100 minute and 1000 minute tests reacha similar ultimate stress state. The 10 minute test was not completelysheared to failure. It has been observed elsewhere that the ageing doesnot affect the ultimate strength of the soil (Mitchell, 2008). Figure 6.6bshows that the developed volumetric strains for the three age durations didnot depict a trend. It may be experimental scatter due to differences inspecimen preparation. The secant stiffness is compared in Figure 6.6c andFigure 6.6d. Figure 6.6c is not informative. It must be a log-scale to depictthe effect of ageing. This is shown in Figure 6.6d. At 0.01 % shear strain the1000 minute test secant stiffness is more than double the 10 minute secantstiffness. Shozen (2001) normalized the stiffness results with the 10 minutetest stiffness at 0.03 % shear strain. This normalization made the effect ofageing on the secant stiffness very clear.This brief review of a subset of the investigation observed that the peak1440 1 2 3 4 5 6 7 8 9 10050100150200250300350εa (%)∆ q (kPa)  1.02.02.8(a)0 1 2 3 4 5 6 7 8 9 10−0.4−0.200.20.40.60.81εa (%)ε v (%)  1.02.02.8(b)0 1 2 3 4 5 6 7 8 9 1002468101214161820εq (%)G sec (MPa)  1.02.02.8(c)0.01 0.1 1 1005101520253035404550εq (%)G sec (MPa)  1.02.02.8(d)Figure 6.5: Effect of stress ratio for specimens 013 (e=0.969, SR=1.0,see Figure D.37), 012 (e=0.960, SR=2.0, see Figure D.36), and014 (e=0.934, SR=2.8, see Figure D.38); consolidated to σ′r =100 kPa, aged 100 minutes, and sheared along a conventionalstress pathstress ratio was independent of the shear path, initial stress ratio, and ageduration. It was also observed that the deformation is dependent on thesevariables. Predicting the deformation of in-situ sands is very difficult. Thesesoils will be at an in-situ stress ratio, possibly near σ′a/σ′r = 2.0 as identifiedby K0 in Section 6.1 and Section 6.2, and will be aged on a geological scale.These soils cannot be routinely sampled undisturbed for careful laboratory1450 1 2 3 4 5 6 7 8 9 10050100150200250εa (%)∆ q (kPa)  101001000(a)0 1 2 3 4 5 6 7 8 9 10−0.2−0.100.10.20.30.40.50.60.70.8εa (%)ε v (%)  101001000(b)0 1 2 3 4 5 6 7 8 9 1002468101214161820εq (%)G sec (MPa)  101001000(c)0.01 0.1 1 1005101520253035404550εq (%)G sec (MPa)  101001000(d)Figure 6.6: Effect of age for specimens 090 (e=0.871 at end of ageing,10 minutes, see Figure D.8), 261 (e=0.962 at end of ageing, 100minutes, see Figure D.28), and 108 (e=0.918 at end of ageing,1000 minutes, see Figure D.14); all prepared loose, consolidatedat a SR 2.0 to σ′a =200 kPa and σ′r = 100 kPa, and shearedalong a conventional stress pathtesting.6.4 Normalizing Gsec degradation curves with G0Secant stiffness curves can be normalized with G0. G0 can be obtained fromshear wave velocity measurements. The shear wave velocity can be obtained146in-situ and in the laboratory using bender elements. The shear strains forthese shear waves are estimated to be below 1.0×10−4% (Jovicic and Coop,1997; Kuwano and Jardine, 2002b). This strain range should correspondto an elastic shear modulus. Clayton (2011) questioned the existence of anelastic zone, but it cannot be examined with this equipment as it is belowthe resolution of the sensors.Normalized stiffness degradation curves can be used in practice by scalingthe curve using an in-situ measured VS . The normalized curves can beempirically estimated or measured in a laboratory.The bender element equipped triaxial apparatus can be used to investi-gate the effects of stress path, initial stress ratio, and age on the normalizedstiffness degradation curves. This equipment can also be used to examine re-cently published empirical procedures by Oztoprak and Bolton (2013) andWichtmann and Triantafyllidis (2013) for estimating normalized stiffnessdegradation curves.Figure 6.7 depicts the measured Gsec/G0 stiffness degradation curves fora set of experiments consolidated to the same stress state of σ′a = 200 kPaand σ′r = 100 kPa, aged for 100 minutes, and sheared along a conventionalstress path to failure. The specimen information for these experiments isprovided in Table 6.1. The G0 values from bender element testing havea range of 4 MPa. The reduced triaxial sensor measurements are not re-producible over the entire depicted small strain range. They deviate below0.1 % shear strain. This deviation is explained by the measurement uncer-tainty quantified in Section 3.4.2. This figure also includes two predictedcurves using the relationships covered in Section 2.4.The formulation proposed by Oztoprak and Bolton (2013) fits the ex-perimental results better than Wichtmann and Triantafyllidis (2013), butboth approaches overestimate the stiffness of loose Fraser River Sand. TheOztoprak and Bolton (2013) relationship was based on a dataset compiledfrom published stiffness degradation curves. Only one source investigatedthe effect of stress ratio. The measurements may be close to the predictedcurve due to the combined effects of an increase in Gsec due to ageing anddecrease due to testing at a higher stress ratio. Both of these studies pro-1470.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G0  Oztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013This studyFigure 6.7: Measured and predicted normalized stiffness degradationcurves for loose specimens of saturated Fraser River Sand con-solidated at SR 2.0 up to σ′a = 200 kPa and σ′r = 100 kPa, agedfor 100 minutes, and sheared conventionally where G0 rangedfrom 58 to 62 MPa with specimen details in Table 6.1vided a means to estimate a non-linear normalized shear stiffness curve fromreadily obtainable parameters.The empirical equation for reference strain from Wichtmann and Tri-antafyllidis (2013) given in Equation 2.15 was developed using a resonantcolumn apparatus. It was calibrated for stiffness degradation from a hydro-static stress state, while the results in Figure 6.7 began from a stress ratioof 2.0. Wichtmann and Triantafyllidis (2013) stated that stress anisotropywould only have a significant effect near failure, based on the work by Yu andRichart (1984). However, the work by Yu and Richart (1984) was for G0.Gsec degradation curves are significantly affected by the initial stress ratio- this parameter was not considered by either Wichtmann and Triantafyl-lidis (2013) or Oztoprak and Bolton (2013). It was demonstrated clearly148Table 6.1: Specimen variables for Figure 6.7, void ratios and G0 mea-sured at end of ageingSpecimen Void ratio G0 (MPa)008 (see Figure D.35) 0.982 58012 (see Figure D.36) 0.960 62040 (see Figure D.52) 0.987 59043 (see Figure D.54) 0.967 59044 (see Figure D.55) 0.965 57047 (see Figure D.56) 0.951 61048 (see Figure D.57) 0.972 62in Section 6.3 that the initial stress ratio has a significant effect on Gsec.Wichtmann and Triantafyllidis (2013) clearly misinterpreted the results byYu and Richart (1984). They applied the observations of the effect of stressratio on G0 by Yu and Richart (1984) to Gsec.In this investigation, the same approach was taken to characterize theeffect of ageing. For every test, the hyperbolic curve model was fitted to thedataset of measured Gsec/G0. The elastic threshold strain was estimatedusing Equation 2.12 as it is below the observable strain range with thistriaxial equipment. The laboratory triaxial apparatus is unable to observethe possible dependence of the threshold strain on age duration. It cannotbe used to measure shear strains around 1e-4 %.Better empirical relationships can be achieved using a larger dataset.A larger dataset was created by combining the results from the currentinvestigation to the previous studies by Shozen (2001) and Lam (2003).These past studies did not include VS measurements and G0 calculations.These parameters need to be empirically estimated. The form and variablesfor a proper empirical equation for G0 were previously covered in Section 2.3.A shortcoming of this dataset is that it is dominated by loose, contrac-tive, specimens. This was done to produce saturated homogeneous speci-mens with the water pluviation technique. Densifying the specimens throughmechanical disturbance during specimen preparation may not have been asreproducible or homogeneous.149The continuous bender element measurements were used to calibrate anempirical G0 equation and estimate an NG ageing factor. Both of theseare required to estimate G0 for Fraser River Sand experiments performedwithout bender element testing. This included the investigations by Shozen(2001) and Lam (2003) as well as experiments conducted in this investiga-tion that did not include VS measurements. This led to the creation of alarge dataset of Fraser River Sand Gsec/G0 strain degradation curves (Ap-pendix D).6.5 Factors influencing Gsec/G0 degradationcurvesThe empirical relationships for NG and G0 were calibrated. This permitsevery Gsec curve to be normalized by a measured or estimated very smallstrain shear stiffness. This increases the size of the dataset for makingempirical observations.6.5.1 Effect of shear stress pathAs covered in Section 2.4, the empirical equations for the hyperbolic pa-rameters proposed by Oztoprak and Bolton (2013) and Wichtmann andTriantafyllidis (2013) do not include the shear stress path as a variable.Consequently, the same normalized stiffness degradation curve is predictedfor every shear stress path. A subset of the experimental results that wereprepared loose, consolidated to an effective radial stress of 100 kPa, and ata consolidation stress ratio of 2.0 were compiled. This subset contained 29triaxial experiments. The shear paths in the current program that includedunloading and reloading loops were excluded. One of the 19 conventionalstress path experiments is 25025017 from Lam (2003), which was at a stressratio of 2.1 instead of 2.0.Table 6.2 contains the average hyperbolic parameters. For comparison,the empirical prediction from Oztoprak and Bolton (2013) results in a cur-vature of 0.96 and reference strain of 0.026 %. The curvature parameterdoes not appear to have any trend with the rotating stress path direction.150The reference strain appears to decrease as the stress path is rotated towardthe failure surface.Table 6.2: Effect of stress path on curvature(a) and referencestrain(εqr) for a hyperbolic model of the normalized secant stiff-ness curve Equation 2.11 from loose specimens consolidated at astress ratio of 2.0 up to σ′r=100 kPa and aged for 100 minutesStress path Specimens Curvature(a) Reference strain (εqr)C 19 0.61 0.009 %P 7 0.71 0.009 %-1 1 0.73 0.007 %0 2 0.64 0.002 %Figure 6.8 compares predicted stiffness degradation curves, fitted hyper-bolic curves using the parameters in Table 6.2, and the measured data. Thepredicted stiffness degradation curves from the Oztoprak and Bolton (2013)and Wichtmann and Triantafyllidis (2013) equations are identical for all fourshear stress paths. The conventional test matches the hyperbolic functionover the small strain range. The other three stress paths deviate from thiscurve at lower strains. The predicted curves overestimate the normalizedshear stiffness.It appears that the hyperbolic formulations may not fit non-conventionalstress paths at low strains. This was observed in Constant-P and Slope-0shear paths. The plateau to a shear strain beyond 0.01 % is not character-ized by the hyperbolic degradation function. There is more evidence of thisobservation included in Appendix D for different age durations and consol-idation stress ratios. The stiffness degradation of non-conventional stresspaths should be investigated with an apparatus that can measure lowerstrains.6.5.2 Effect of initial stress ratioThe developed hyperbolic relationships proposed by Oztoprak and Bolton(2013) and Wichtmann and Triantafyllidis (2013) do not account for the1510.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(a) Conventional stress path0.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(b) Constant P stress path0.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(c) Slope -1 stress path0.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(d) Slope 0 stress pathFigure 6.8: Effect of stress path on measured and hyperbolic stiffnessdegradation curves for loose specimens consolidated at SR 2.0and aged for 100 minuteseffect of the initial stress ratio. The shearing of specimens consolidatedat higher stress ratios begins closer to the failure surface. They requiremuch less deviator stress to reach failure and have softer normalized stiffnessdegradation curves. Many of the experiments used to develop the empiricalrelationships in Oztoprak and Bolton (2013) and all of the specimens inWichtmann and Triantafyllidis (2013) were on hydrostatically consolidatedspecimens. Shearing in-situ soil rarely begins at such a stress state.This effect was investigated by comparing experiments that were pre-pared loose, consolidated to a radial effective stress of 100 kPa, aged for100 minutes, and sheared along a conventional stress path. The stress ra-152tio is the variable that is being changed. This subset contained 27 triaxialexperiments.Table 6.3 details the effect of the consolidation stress ratio on the hyper-bolic model coefficients. No conclusive trend on the curvature was observedas the stress ratio increases. The reference strain decreases as the consoli-dation stress ratio increases. Higher stress ratios result in an increase in G0and decrease in Gsec, resulting in a softer normalized stiffness curve.Table 6.3: Effect of stress ratio on curvature(a) and referencestrain(εqr) for a hyperbolic model of the normalized secant stiff-ness curve Equation 2.11 from loose specimens consolidated andaged for 100 minutes and sheared along conventional stress pathsStress ratio Specimens Curvature(a) Reference strain (εqr)1.0 4 0.64 0.046 %1.6 1 0.78 0.026 %2.0 19 0.61 0.009 %2.5 1 0.62 0.005 %2.8 2 0.64 0.004 %Figure 6.9 compares predicted stiffness degradation curves against thefitted hyperbolic relationship and measured data. The parameters for thefitted hyperbolic relationships are in Table 6.3. The measured data andfitted hyperbolic curves are softer at higher stress ratios. The referencestrain decreases as the initial stress-state of the shear path is closer to failure.Equation 2.13 from Oztoprak and Bolton (2013) and Equation 2.15 fromWichtmann and Triantafyllidis (2013) both determine an increase in thereference strain at higher mean stress. Based on the results from this in-vestigation, the effect of mean stress needs to be separated from the ef-fect of stress ratio when predicting hyperbolic-strain stiffness degradationcurves. Higher initial stress ratios increase the mean stress, but decreasethe reference strain. The predictions from Oztoprak and Bolton (2013) andWichtmann and Triantafyllidis (2013) disagree with this observation.1530.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(a) Stress ratio 1.00.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(b) Stress ratio 2.00.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(c) Stress ratio 2.8Figure 6.9: Effect of stress ratio on measured and hyperbolic stiffnessdegradation curves for loose specimens, aged for 100 minutes,and sheared along a conventional stress path6.5.3 Effect of reconstituted specimen ageThe reconstituted specimen age is not a variable in the existing methods toestimate a stiffness degradation curve. On laboratory specimens, ageing hasa significant effect on the secant shear modulus (Howie et al., 2002; Lam,2003; Shozen, 2001), no effect on the strength, and a small effect on G0.A subset of the triaxial experiments consolidated at a stress ratio of 2.0,sheared along a conventional stress path, and aged for different durations,was compiled. This dataset contains 34 experiments.Table 6.4 details the fitted hyperbolic coefficients. Both the brittleness154(curvature) and reference strain increase with age duration. Figure 6.10depicts the the effect of age on the hyperbolic stiffness degradation from1 to 1000 minutes. Ageing changes the shape of the curve. The effect ofageing is not accounted for by normalizing with G0.Table 6.4: Effect of age on curvature(a) and reference strain(εqr) for ahyperbolic model of the normalized secant stiffness curve Equa-tion 2.11 from loose specimens sheared along a conventional stresspath from a stress ratio of 2.0Age(minutes) Specimens Curvature(a) Reference strain (εqr)1 2 0.49 0.002 %10 5 0.52 0.003 %100 19 0.61 0.009 %1000 5 0.66 0.011 %10000 3 0.75 0.020 %Reconstituted laboratory specimens are at a very different age than in-situ soil. To predict in-situ behaviour of Fraser River Sand, the ageingtrends for G0, the reference strain(εqr), and the curvature(a), have beenextrapolated. For loose Fraser River Sand, G0 increases with NG equal to1.9 %. For a stress ratio of 2.0, Figure 6.11 depicts the effect of age on thereference strain and curvature. The trend with age for these two variablesappears to be log-linear up to 10000 minutes. A best-fit for these data pointsresulted in Equation 6.1 and Equation 6.2.εqr(%) = 0.0044log10(ageminutes) + 0.004 (6.1)a = 0.0665log10(ageminutes) + 0.471 (6.2)For σ′a=200 kPa, σ′r=100 kPa, and a void ratio of 0.95, G0 according toEquation 5.4 is 56 MPa. Figure 6.12 depicts the effect of ageing on the non-linear secant stiffness curve for these initial properties. The extrapolated ageeffects are indicated with dashed lines. This figure also includes the stiffnessdegradation curve from Specimen 040. This specimen was consolidated at1550.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(a) 1 minute0.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(b) 10 minutes0.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(c) 100 minutes0.01% 0.1% 1% 10%00.10.20.30.40.50.60.70.80.91εq(%)=2/3(εa−εr)G sec/G 0  HyperbolicOztoprak & Bolton 2013Wichtmann & Triantafyllidis 2013MeanMean +/− std(d) 1000 minutesFigure 6.10: Effect of specimen age duration on measured and hy-perbolic stiffness degradation curves for loose specimens con-solidated at SR 2.0 and sheared along a conventional stresspatha stress ratio of 2.0, aged for 100 minutes, and sheared along a conventionalstress path.This approach captures the general trends in observations of the ef-fect of ageing. It results in an increase in the reference strain (strain toGsec/G0=0.5) and an increase in the curvature (i.e. more brittle). It doesnot capture the independence of strength due to ageing. The hyperbolicrelationships do not include a strength term and do not fit large strain mea-surements. The presented results are only for the conventional stress path.1561m 100m 10000m 1yr 10yr 100yr1000yr00.0050.010.0150.020.0250.030.0350.040.045Age timeReference strain (%)(a) Reference strain1m 100m 10000m 1yr 10yr 100yr1000yr0.40.50.60.70.80.911.11.21.3Age timeCurvature parameter, a(b) Curvature parameterFigure 6.11: Extrapolation of normalized secant stiffness curve pa-rameters6.6 DiscussionThe effects of age, initial stress ratio, and stress path were quantified withthe same approach as Wichtmann and Triantafyllidis (2013) and Oztoprakand Bolton (2013). The average of fitted hyperbolic coefficients was cal-culated. The effect of ageing was extrapolated by developing empiricalrelationships for the empirical model coefficients from the fitted stiffnessdegradation curves.The trends with age, stress ratio, and stress path can be used to modifythe predicted hyperbolic reference strain and curvature. The work in thischapter was mostly based on very loose reconstituted specimens of FraserRiver Sand aged for less than 1000 minutes. The values reported should notbe applied to other soils or densities, but the trends may be used to estimatebetter stiffness degradation curves or explain differences in observed andpredicted deformation behaviour.6.7 ConclusionThe third objective of this research project was to integrate bender elementsinto the triaxial small strain shear stiffness investigation of Fraser River1570.01 0.1 1 100102030405060G sec (MPa)εq (%)  10min1hr12hr1day1week1month1yr100yr1000yr10000yrFigure 6.12: Effect of age on secant stiffness curve for σ′a=200 kPa,σ′r=100 kPa, G0 according to Equation 5.4, NG = 1.9 %, wheresolid lines are interpolated and dashed lines are extrapolated,the solid black points correspond to Specimen 040 (see Fig-ure D.52) aged for 100 minutesSand. This objective has been achieved. This was accomplished by using theUBC bender element equipped triaxial apparatus (Chapter 3) with benderelement techniques developed and reported in Chapter 4 and Chapter 5.This study demonstrated the shortcomings of recently published empir-ical methods to estimate Gsec/G0. It was found that these methods do notcorrectly handle the initial stress ratio. It was shown that the effect of thestress path and age duration is not removed by normalizing with G0.To increase the size of the dataset the results from past investigations byShozen (2001) and Lam (2003) were included by using an empirically esti-mated G0 value. The empirical equation for G0 was developed in Section 5.6combining the data collected in this research following the theoretical back-158ground and past empirical relationships described in Section 2.3. The resultsof this research were able to show that ageing can result in the observed smallincrease in G0, large increase in Gsec, and no change in strength.The following conclusions were drawn from the research presented in thischapter:1. The developed triaxial apparatus is capable of acquiring Gsec/G0 stiff-ness degradation curves above 0.01 % shear strain.2. The effect of ageing on Gsec is not eliminated by normalizing withG0 - i.e. the stiffness degradation curves do not collapse to a singlereference curve.3. The effect of ageing on the model hyperbolic-stiffness parameters wasplotted (Figure 6.12). The parameters appeared to increase on a log-linear relationship with age duration. Ageing is a significant differencebetween reconstituted specimens and in-situ soil, particularly over thestrain range experienced by most geotechnical structures.4. The hyperbolic stiffness degradation curves did not appear to fit non-conventional stress paths, particularly slope-0 stress paths.5. Wichtmann and Triantafyllidis (2013) and Oztoprak and Bolton (2013)proposed very simple techniques to estimate a normalized stiffnessdegradation curve from readily obtained granular soil properties. Thiswork demonstrated the importance of the specimen age, stress ra-tio, and stress path on the measured normalized stiffness degradationcurves. These variables are not accounted for in the work by Wicht-mann and Triantafyllidis (2013) and Oztoprak and Bolton (2013).As mentioned at the end of Chapter 5, the next chapter concerns in-situ measurements. It describes the adaptation and preliminary evaluationof the developed continuous monitoring method to down-hole seismic test-ing. VS can be measured in-situ and used to scale the empirically predictednormalized stiffness curves to estimate deformation of sands.159Chapter 7Development of PerpetualSource SCPTuShear waves are measured in both laboratory specimens and in the field.This permits empirical normalized stiffness degradation curves (Chapter 6)to be scaled to in-situ conditions. While developing the continuous labora-tory bender element technique (Chapter 5), it was realized that it could beadapted to in-situ measurements. This chapter reports on this adaptation.This work has been the subject of three conference papers: Styler et al.(2012), Styler et al. (2013), and Styler et al. (2014).Chapter 5 presented a method to continuously monitor the shear wavevelocity with bender elements throughout a laboratory experiment. Thismethod used a continuous multi-tonal shear wave signal measured at twospatial points - the bender element locations. The phase shift of the signalsbetween these two monitoring locations were used to estimate the shearwave propagation time and VS . This chapter presents the adaptation ofthis continuous bender element technique to down-hole shear wave veloc-ity measurements. This was accomplished by creating a continuous seismicsource using a vibrator at the ground surface. The shear waves propagatingdownward from this continuous source were monitored at multiple down-hole locations. The phase shift or cross correlation of the signals measuredat these points was used to calculate the propagation time and VS . Seismic160signals were collected concurrently with CPT measurements while the conewas advanced at the standard rate of 2 cm/sec (ASTM D5778-12). Thismethod has been named “Perpetual Source SCPTu” (PS-SCPTu) to differ-entiate it from other attempts to measure a profile of VS continuously duringCPT penetration. This development provides a profile of measurements ofin-situ soil response at the in-situ state. These measurements include thecone tip resistance, friction sleeve, pore water pressure, and shear wave sig-nals. Additional details on cone testing and interpretation can be found inLunne et al. (1997).Figure 7.1 shows three different sources that can be used to generateshear waves at the ground surface. The conventional source is the sledgehammer and shear beam. The continuous-interval source uses a motor toprime a spring loaded pendulum. Both of these sources create a shear wavefrom the impact of a swinging hammer. The third source is new and is thefocus of this chapter. It does not have an impact. It generates a continuousfield of downward propagating shear waves.The objective of this chapter is to demonstrate that this new techniqueprovides a measure of the in-situ VS . This was accomplished by comparingthe results to conventional shear-beam down-hole seismic testing.161Figure 7.1: Three different shear wave sources for down-hole seismic testing during cone penetration1627.1 Existing down-hole in-situ VS measurements7.1.1 Conventional SCPTuThe cone penetrometer is an in-situ tool with almost 80 years of refine-ment in equipment, technique, and interpretation. Robertson et al. (1986)described the combination of conventional down-hole seismic testing withCPTu to provide seismic cone testing (SCPTu). A shear wave was triggeredat the ground surface and a seismic sensor behind the sleeve responded tothe downward propagating wave. The shear waves were generated by strik-ing the end of a beam with a sledge hammer. Seismic signals were generatedwhen the cone penetration was paused at 1m interval rod breaks. Adjacentdown-hole seismic signals were compared to determine the shear wave veloc-ity over the interval between measured signals. Conventional seismic testingresults in a coarse step plot of VS measurements at 1 m intervals.True-interval testing uses one set of shear waves and two seismic sensors.The seismic sensors are spaced behind the cone tip and a single shear beamhit can be used to estimate the propagation time. Pseudo interval testinguses two sets of shear waves and one seismic sensor to estimate VS . A setof seismic signals is collected, the cone is advanced to the next depth, andanother set of seismic signals is collected. The advantages of true intervaltesting are that it eliminates error of the data-acquisition trigger time andseismic sensor spacing. It also reduces the need for a reproducible shearwave. This makes true interval testing a more attractive option if less con-trollable shear sources, i.e. shotgun shells, are used. The disadvantage oftrue interval testing is that it uses multiple seismic sensors. These sensorsmust respond identically to the shear wave to avoid introducing a bias intothe signals. They must have the same frequency response and soil coupling.The advantage of pseudo-interval testing is that it only uses a single sensor.This simplifies the equipment and shortens the length of the probe. Anybias in this sensor is subtracted out when two signals, both measured fromthe same sensor, are compared.1637.1.2 Continuous SCPTuResearch over the past decade at Georgia Tech in Atlanta, Georgia hasfocused on a seismic source and interpretation procedure for a continuousprofile of VS . This method has been named Continuous Interval SeismicCone Penetration (CiSCPTU). It involves the frequent collection of ham-mer strike seismic signals down-hole during cone penetration. Casey andMayne (2002) and McGillivray and Mayne (2008) describe the developmentof the automatic seismic source, called a Roto-seis. It contains a motordriven geared wheel which primes a spring loaded short arm pendulum. Anelectronic trigger signal initiates an immediate and reproducible hammerstrike. This trigger signal is wired to a depth increment measurement sys-tem to automatically trigger shear waves at frequent depths. The Roto-seisunit is compact and weighs only 35 kg.The CiSCPTu approach creates a number of challenges for interpreta-tion of the propagation time that are not an issue for conventional down-holeseismic testing. Many more seismic signals are collected for a single sound-ing. This required the development of automated signal processing routines.The measured seismic signals include noise from external disturbance, vi-brations, stray signals, and seismic noise from the cone shearing the soil.The signals are collected while the cone is moving. This prevents the useof signal stacking to reduce random noise. It also prevents the use of theconventional left-hit right-hit cross over point identification. Further detailson these challenges and the required post-processing can be found in Kuand Mayne (2012); Ku et al. (2013).The developed PS-SCPTu technique described in this chapter differsfrom the Continuous Interval method. PS-SCPTu does not use a hammer-strike shear wave. The seismic signal is from a vibration source. This focusesthe downward propagating shear wave into a small frequency window. Theshear waves are continuous - they are arriving throughout the collected sig-nal. There is no window to select for the arrival. Furthermore, the entiremeasured signal contains useful information. With hammer strike signals,everything before the shear wave arrival is discarded and everything after164has minimal use.Confident interpretations of the shear wave propagation time require asufficient signal to noise ratio (SNR). The signal strength depends on thecontinuous vibration source, geometric radiation damping, and soil damp-ing. The power of the signal, and consequently the SNR, is reduced due togeometric damping as the depth of the receiver increases. Higher frequencyvibrations are reduced by soil damping with depth. Noise is generated bythe grinding caused by penetration of the cone tip through the soil. Thesignals are collected while the cone is moving, so signal stacking proceduresto reduce random noise are not applicable. The source has to be strongenough to overcome the noise at depth.As covered in Chapter 2 and will be demonstrated in Chapter 6, VS is aninformative soil parameter. Measuring profiles of VS during cone penetrationtesting has implications for soil profiling and soil property interpretations.Soil behaviour charts using a normalized tip resistance and G0 have beenproposed by Robertson et al. (1995a) and Schnaid and Yu (2007). Thesecharts provide an indication of the type of soil and soil properties includingcementation, age, and compressibility. In-situ measurements of VS provideadditional information that may improve existing empirical correlations.7.2 Perpetual source methodThe perpetual source technique consists of advancing a seismic cone througha continuous field of radiating shear waves from the ground surface. Imple-mentation of the technique required development of a suitable perpetualsource, the test procedure and interpretation method, and evaluation of theprofile of VS obtained against conventional results.7.2.1 Perpetual sourceThe perpetual source device consists of two motor driven rotating offsetweights. The plane of rotation for these two weights is parallel to the groundsurface. On this plane, the two offset weights constructively create a vibra-tion in one direction. Perpendicular to this direction, the vibrations pro-165duced by offset weights destructively interfere to minimize any motion. Theperpetual source device vibrates along a line parallel to the ground surface.This line is directed toward the CPT hole. Additionally, the CPT seismicsensors are aligned to respond to shear motion in this direction. This devicevibrates at a frequency of 28 Hz. Figure 7.2a is a photo of this source duringa perpetual source test at Kidd 2 in Richmond, BC.7.2.2 True interval coneA true interval cone with three seismic sensor locations was used to measurethe continuous wave at three depths simultaneously. The first geophone was0.3m behind the cone tip in a standard seismic cone. The second and thirdgeophones were 0.8 and 1.3 m behind the cone tip in a true interval module.All three of these geophones are aligned in the same direction. These threegeophones were reported to have a resonance frequency of 24 Hz.Geophone measurements depend on the velocity of a coil of wire rela-tive to a magnet (Santamarina et al., 2001). Geophones have a non-linearfrequency response and amplify shear wave frequencies (Stewart and Cam-panella, 1993). Geophones are also rugged, inexpensive, and do not needto be filtered (Laing, 1985). Geophones perform better than accelerometersfor detecting shear waves with frequencies less than 60 Hz (Hons, 2009).Accelerometers are an alternative to geophones. Accelerometers respondto the acceleration of a seismic mass on a chip (Santamarina et al., 2001).The change in capacitance between electrodes sandwiching this seismic massis measured (Hons, 2009). Campanella and Stewart (1992) recommended ahigh sensitivity, critically damped piezoresistive accelerometer with a flatresponse from 0 to above 350 hz. Accelerometers were not evaluated. Thisresearch employed geophones, but does not make a recommendation on thetype of seismic sensor.Figure 7.2b is a photo of the seismic cone attached to the true intervalmodule.166(a) Perpetual shear wave source(b) Seismic cone with true interval moduleFigure 7.2: Photos of PS equipment taken at Kidd 2 in Richmond,BC1677.2.3 ProcedureThe Perpetual Source technique supplements conventional cone penetrationtesting. ASTM standard (D5788-12) procedures for CPT were followed.This standard covers the required calibration standard, penetration rate,and data acquisition. The perpetual source device is placed on the groundsurface 1-3 m from the CPT hole. It is orientated so that the active vibrationaxis points towards the CPT. The cone is rotated so that the three geophonesare aligned with the perpetual source vibrations. The perpetual source isturned on and left on through out the PS-CPTu sounding.During penetration, a depth-wheel rotates as the cone rods are advanceddownward. This wheel has a proximity sensor that responds to small metaltags on the depth wheel every 2.5, 5.0 or 10.0 cm. This proximity sensortriggers the seismic data acquisition. At every single depth wheel trigger,the data acquisition system automatically records for 250 ms from the top,middle, and bottom geophones simultaneously at a sampling rate of 20 kHz(5000 measurements per geophone). These three signals are compared todetermine the propagation time, i.e. a true interval technique.7.2.4 Interpretation of collected signals for VSThe large number of seismic signals collected during a PS-SCPTu soundingrequire an automated approach to interpretation. Ideally, the interpretationof VS should not depend on subjective input and a general procedure appli-cable to any sounding needs to be developed and demonstrated. Automatedinterpretation is necessary to make this test a viable tool for routine siteinvestigations.Conventional approaches to down-hole seismic interpretations will notwork. As the polarity of the signal is not inverted during testing, there isno cross-over point to identify. A single point in the 250ms signals does notcorrespond to the shear wave arrival. The shear wave is continuous - it isarriving at 0ms and 250ms, and at every time in between. VS is determinedby identifying the time of travel of significant features in the shear wavesignal over known depth intervals.168Two methods were investigated to estimate the propagation time be-tween two signals collected at the same time: the cross correlation functionand the phase shift. It was found that when the measured perpetual sourcesignals were dominated by a single frequency, the two approaches gave thesame answer. However, the perpetual source was unable to generate a cleansingle frequency sine wave. The cross-correlation of the signals was used inorder to compare all of the propagating frequency components.The simplest approach to estimating the shear wave propagation distanceis the difference in the shortest line to each geophone from the perpetualsource. This may not be accurate if the shear wave direction changes due torefraction. This work is focused on the estimation of the propagation timefrom the perpetual source during cone penetration. Errors in the propaga-tion length due to refraction are beyond the scope of the early stages of thisresearch.7.3 Field testingTo demonstrate that this new approach can be used to acquire in-situ VS ,it is compared to coarse, conventional, 1m interval measurements. ThreePS-SCPTu soundings were performed. The first one was made adjacentto a previous conventional SCPTu profile. To reduce any potential spa-tial variability errors, the second sounding included concurrent conventionalmeasurements. The perpetual source was paused every metre to trigger andrecord conventional hammer-test seismic shear waves. These two tests usedthe true-interval module and measured true-interval shear wave velocitiesfrom the Top-Middle, Middle-Bottom, and Top-Bottom geophone pairs.In these two tests, it was observed that the top-middle geophone pairresulted in a faster velocity than the middle-bottom pair. The second sound-ing included concurrent seismic-hammer testing that showed the same re-sult. The true interval cone was disassembled and the geophone locationswere confirmed. The cone was placed on a vibration table and the geo-phones responded in phase. The source of this anomaly was investigated. Asix-geophone true interval module with 25cm spacing was constructed and169tested. No trend with geophone pair location was observed. It is believedthat the effect observed on the original equipment is due to a difference inmounting of one of the geophones. However, this theory has not been conclu-sively tested. To avoid this problem, the PS-SCPTu method was altered forpseudo-interval testing. Pseudo-interval testing uses the same geophone atdifferent depths to acquire the propagation time, as in conventional seismiccone testing using a single geophone probe. The third PS-SCPTu sound-ing was performed adjacent to another conventional SCPTu and used themodified pseudo-interval technique.7.3.1 PS-SCPTu-01: Feasibility testThe PS-SCPTu-01 sounding was performed at 12410 Vulcan Way, Rich-mond, BC. This test went to a depth of 45 m. Seismic data acquisition wasmanually triggered - an automatic interface to cone depth increment systemhad not yet been developed. Seismic signals were collected approximatelyevery 10 cm of cone penetration. The perpetual source was 3.16 m from thePS-SCPTu hole.Figure 7.3a shows the measured and recorded top, middle, and bottomgeophone signals at a cone tip depth of 6 m. The top geophone is at a depthof 4.7 m, the middle geophone is at 5.2 m, and the bottom geophone is at5.7 m. This demonstrates that the source is generating a periodic shearwave signal that propagates to 5.7 m, the location of the bottom geophone.Figure 7.3b shows the same three signals in the frequency domain. The peakin this plot is at the perpetual source frequency of 28 Hz. Some harmonicsof this frequency occur near 60, 90, 120, and 150 Hz.Figure 7.4 depicts the cross correlation of the three geophone signalsshown in Figure 7.3a. The peak cross correlation corresponds to the trueinterval change in propagation time. For the top-middle geophone pair thisoccurs at 4.00 ms. For the middle-bottom geophone pair this occurs at 4.50ms. For the top-bottom geophone pair, the largest propagation distance, thisoccurs at 8.75 ms. These propagation times occur with the geophone depthsat 4.7 m (top), 5.2 m (middle), and 5.7 m (bottom). The ray path distances170from the source to the geophones are 5.66 m (top), 6.08 m (middle), and6.52 m (bottom). This results in an estimated VS of 105 m/s from the topto the middle geophones, 96 m/s from the middle to the bottom, and 98m/s from the top to the bottom. At a cone tip depth of 6 m, the raw datawas interpreted with the cross correlation technique. This did not requireany subjective selection of filters, averaging, or windowing.Figure 7.5 shows the PS-SCPTu-01 profile with an adjacent conven-tional SCPTu. The first column is the corrected cone tip resistance (qt =qc+(1−a)u2). The second column is the friction ratio (Rf = fs/qt(100%)).The third column includes the measured pore water pressure and hydrostaticpore water pressure line based on the estimated ground water table (dashedblue line). The fourth column includes the interpreted cross-correlation VSfrom the top to bottom geophone pair (green line) with the adjacent con-ventional seismic interpretations (black step plot). The last column is theinterpreted soil behaviour. There is a close agreement between the VS inter-pretations in the top 15 m and in the lower silt. There are some variationsin the sand layer.One apparent advantage of the PS-SCPTu results is when the results donot agree with conventional measures. A poor quality seismic wave mea-surement from conventional testing may affect up to 2 metres of the seismicprofile. The perpetual source technique provides so many more velocity in-terpretations that apparent outliers are either confirmed with immediatelyadjacent results or confidently ignored.171(a) Time domain signals0 50 100 150 200 250−10010top (V)0 50 100 150 200 250−10010middle (V)0 50 100 150 200 250−10010time (ms)bottom (V)(b) Frequency domain signals0 50 100 150 200 250 300 350 40001020304050607080(dB)frequency (Hz)  TopMiddleBottomFigure 7.3: Collected signals at a cone tip depth of 6m1720 50 100 150 200 250−101T−M0 50 100 150 200 250−101M−B0 50 100 150 200 250−101time (ms)T−BFigure 7.4: Cross correlation of measured signals shown in Figure 7.3:T-M = 4.00 ms, M-B = 4.50 ms, T-B = 8.75 ms1730 200 400051015202530354045depth (m)qt (bar)0 2 4 6Rf (%)0 100u2 (m H2O)0 200VS (m/s)Soil BehaviourSiltSilty sandSandSiltFigure 7.5: First PS-SCPTu profile collected in Richmond, BC where the green trace in the fourth columnrepresents the perpetual source results and the black step trace is from adjacent conventional hammerbeam strike tests1747.3.2 PS-SCPTu-02: Concurrent hammer testingThe second test was performed at Kidd-2, a nearby site in Richmond, BCthat was part of the CANLEX liquefaction research project (Robertsonet al., 2000; Wride et al., 2000). This test included concurrent hammerstrike shear wave signals from 3 through 13 m. These were concurrent sig-nals, not adjacent signals. The perpetual source was turned off at rod breaksand hammer strike shear wave data was collected. The perpetual source wasthen turned back on to generate continuous shear waves during penetration.The purpose of this test was to create a dataset to allow a direct compar-ison between the Perpetual Source VS and the accepted conventional VSmeasurements that did not include an unknown spatial variability.Testing at this site also attempted to measure shear wave signals dur-ing rod retraction. It was expected that this would significantly reduce anyseismic noise generated by cone penetration. However, this data was domi-nated by noise and could not be interpreted. It may be due to poor couplingbetween the soil and cone probe. The source of this noise was not investi-gated and further developments on PS-SCPTu was focused on measurementsduring downwards cone penetration.The results of this second test are shown in Figure 7.6. The VS columnincludes four sets of data. The black line is VS from concurrent conventionalhammer testing from 3 through 13 m. The green line is the cross correlationresults of the Middle-Bottom geophone pair, the blue line is the Top-Middle,and the orange line is the Top-Bottom. The conventional hammer testingand the Top-Bottom perpetual source method are both interpreted over a1m depth interval. The Top-Middle and Middle-Bottom geophone pairs areinterpreted over a 50 cm depth interval.Figure 7.7a compares the ratio of the geophone pair velocities againstdepth for the perpetual source testing. Figure 7.7b presents the same plotfor the conventional hammer test velocities. Not only is the top-middleVS significantly faster than the middle-bottom, this inconsistency increaseswith depth. This discrepancy was only observed due to the use of three seis-mic sensor locations. A typical true interval module only has two seismic175locations and this effect would not be measurable. A literature search wasunsuccessful for other published data using a true-interval module with morethan two geophones. It is not yet clear if the observed phenomenon is iso-lated to this equipment. Two possibilities are that it is a function of surfacewaves along the cone rod-soil interface or an amplitude dependent changein the coupling between the soil motion and geophone motion (McGillivray,2013). Asalemi (2006) observed that the shear wave velocity increased withageing when multiple tests were carried out without advancing the cone. Atthe ASTM rate of 2cm/sec, the soil around the top geophone was sheared50 seconds before the soil around the bottom geophone. This ageing effectmay explain the increase in the measured shear wave velocity over the topinterval. Errors in the physical geophone locations and electronic bias wereconclusively eliminated.The hammer-strike data was collected during rod-breaks. It could beinterpreted using pseudo-interval techniques instead of true-interval. ThePseudo-interval technique estimates the propagation time from signals col-lected from the same geophone at two different depths. Any inherent biasin the geophone will subtract out when comparing pseudo-interval signals.Figure 7.8 depicts pseudo-interval interpretations from 3m to 13m usingthe hammer strike signals. No systematic trends with geophones or depthwere observed. Pseudo-interval testing does not suffer from the observedtrue-interval discrepancy.For comparison purposes, Figure 7.9 combines the data shown in Fig-ure 7.7b and Figure 7.8. The Pseudo-Interval results were generally slightlylarger than the T-B geophone pair.The two preceding sets of perpetual source signals cannot be interpretedwith the pseudo-interval technique. The source operates independently ofthe data acquisition. It is only possible to compare signals that are alignedin time. The hammer strike signals are aligned in time. For every hammerstrike signal, the time origin corresponds to the hammer strike. For per-petual source testing the time origin corresponds to a depth wheel event.This is asynchronous with any features in the perpetual source shear waves.The only aligned signals in the perpetual source testing are the set of three176simultaneously collected signals - top, middle, and bottom at each depthwheel trigger.1770 1002000510152025depth (m)qt (bar)0 2 4Rf (%)0 20u2 (m H2O)0 200VS (m/s)Soil BehaviourSiltSandSiltFigure 7.6: Second PS-SCPTu profile collected in Richmond, BC178(a) Ratio of measured velocities: blue points Kidd-2, green points Vulcan Way(feasibility test)0 0.5 1 1.5 2 2.5 30510152025303540ratio TM:MB VSdepth (m)(b) Measured true interval shear wave velocities for concurrent hammer strikes atKidd 2: blue T-M, green: M-B, orange: T-B80 100 120 140 160 180 200 22002468101214VS (m/s)depth (m)  T−MM−B T−BT−MT−BM−BFigure 7.7: True interval discrepancy17980 100 120 140 160 180 200 22002468101214VS (m/s)depth (m)Figure 7.8: Measured pseudo-interval shear wave velocities for con-current hammer strikes at Kidd 2: blue T, green: B, orange:M80 100 120 140 160 180 200 22002468101214VS (m/s)depth (m)  TMMBTBPIFigure 7.9: Comparing measured True Interval to Pseudo-Intervalshear wave velocities for hammer-test data from a 3-geophonetrue interval cone1807.3.3 PS-SCPTu-03: Pseudo IntervalFor psuedo-interval testing, the collected perpetual source seismic signalsneed to share a common time-origin. The time origin for the signals collectedat a depth of 10m needs to be the same as for the signals collected at 11m.For hammer strike testing, this time origin is the initiation of the shear wave.Perpetual source testing does not have such an event. The shear wave ispropagating continuously throughout the recorded signals. The perpetualsource is periodic. Instead of aligning the collected signals to the time originof the shear wave, they can be aligned to a constant phase angle of the sourcewave. This was accomplished by adding a proximity sensor to the perpetualsource device. This sensor is fixed in place and responds to an adjustable setscrew attached to one of the rotating weights. The proximity sensor signalhas a sharp step in voltage when this set screw is detected. In addition tothe three geophone signals (top, middle, and bottom), the proximity sensorsignal is recorded at 20 khz for 250 ms. Figure 7.10 depicts all four measuredchannels at a depth of 6 m. These signals alone can only be interpreted withthe true interval technique.Pseudo interval testing determines the shear wave propagation time us-ing a single geophone. To do this, the recorded signals are shifted in time sothat a proximity sensor edge occurs at the time origin. Once the proximitysensor edge is aligned, two signals collected with the same geophone at dif-ferent depths can be compared. Proximity sensor edges are easily identified.The cross-correlation signal comparison technique can identify the changein propagation time.These modifications were implemented on a PS-SCPTu sounding per-formed at the Vulcan Way, Richmond, BC (Fraser River Delta) site. Per-petual source seismic signals were collected every 2.5 cm from all three geo-phones. This test included an adjacent conventional SCPTu profile.Figure 7.11 shows two bottom geophone signals and proximity sensorsignals collected at 6m and 7m cone tip depth. In this figure, the timeorigin corresponds to the depth-wheel data acquisition trigger. To performpseudo-interval testing, the signals need to be shifted so that the time origin1810 50 100 150 200 250−1−0.500.5geophones (V)0 50 100 150 200 25000.511.5prox sensor (V)time (ms)Figure 7.10: Measured PI signals with perpetual source proximitysensor: blue T, green: B, orange: Mcorresponds to a step in the proximity sensor. This is shown in Figure 7.12a.A pseudo-interval velocity can be interpreted from the proximity sensoraligned signals. The cross-correlation of the results in Figure 7.12a has apeak at 8.25 ms. This corresponds to a difference in ray path length of0.97 m and a VS of 118 m/s. This is the pseudo-interval velocity. It wasestimated using the response of a single geophone at two different depths.Figure 7.12b depicts the effect of shifting the 6 m bottom geophone signalby the cross correlation result of 8.25 ms. There is a high degree of overlapbetween the two signals. The features in the signal that propagate over 8.25ms dominate these two signals.Waterfall plots can be generated for pseudo-interval measured signals.A waterfall plot contains every measured signal at the depth where it wascollected. For 1 m increment hammer testing to 30 m, this can result in60 plotted signals (left hit, right hit) at each depth. Figure 7.13 shows1820 50 100 150 200 250−1−0.500.51(V)(a) 6m0 50 100 150 200 250−1−0.500.51(V)time (ms)(b) 7mFigure 7.11: Measured bottom geophone signal and proximity sensorsignal at 6 m and 7 m, where time 0 corresponds to a depthwheel data acquisition triggera waterfall plot from the adjacent conventional testing over-plotted ontoa grey scale waterfall plot of the pseudo-interval bottom geophone. Forthe perpetual source data the time origin (time = 0 ms) for every signalcorresponds to an edge in the proximity sensor. In this plot, the shear wavevelocity is approximately equal to the slope of the seismic features. Thisslope is the change in propagation time against the change in geophonedepth. The difference between this slope and the actual shear wave velocityis due to the difference between the change in ray path length and thechange in depth. The waterfall figure depicts the aligned geophone signals.It does not directly provide an estimate of the propagation time or shearwave velocity.The propagation time was estimated over a 1m moving window for thebottom geophone. Figure 7.14 shows the resulting PS-SCPTu profile. In183this figure the black lines correspond to the adjacent conventional SCPTuprofile, the red lines correspond to the PS-SCPTu test. The VS columnshows the similarity between the perpetual source pseudo-interval VS (bot-tom geophone) and the conventional seismic cross-over point interpreted VS .184(a) Aligned 6 m and 7 m cone tip depth bottom geophone phone signals with theproximity sensor edge0 20 40 60 80 100 120 140 160 180−1−0.8−0.6−0.4−0.200.20.40.60.81time (ms)amplitude (V(b) Applied time shift to the 6 m cone tip bottom geophone signal by the crosscorrelation result of 8.25 ms0 20 40 60 80 100 120 140 160 180−1−0.8−0.6−0.4−0.200.20.40.60.81time (ms)amplitude (VFigure 7.12: Interpreting a pseudo-interval propagation time using asingle geophone with a perpetual source185Figure 7.13: Perpetual source PI and conventional PI overlapping waterfall plots1860 100 200051015202530depth (m)qt (bar)0 2 4Rf (%)0 10 20 30u2 (m H2O)0 100 200 300VS (m/s)SiltSandSiltFigure 7.14: PS-SCPTu profile for pseudo-interval testing (red) with adjacent conventional SCPTu (black)1877.3.4 Comparing to conventional pseudo-interval VSThe data presented in this chapter used two different techniques to acquirethe in-situ velocity for a downward propagating shear wave. The conven-tional method interprets the propagation of shear waves generated from animpact-hammer source. The perpetual source method measures the velocityfrom continuous shear waves.There are a few obvious differences between these types of measure-ments. The PS-SCPTu-01 and PS-SCPTu-03 had adjacent conventionalseismic profiles. There will be some spatial variability between these mea-surements. PS-SCPTu-02 had concurrent measurements. However, the per-petual source and conventional seismic beam were necessarily in differentlocation. Therefore, the ray paths for the waves in the second-hole are dif-ferent. The second hole would also contain some spatial variability. Theperpetual source method has most of its energy at a single frequency. Theconventional hammer-testing covers a wide band of frequencies with a fre-quency distribution that changes with penetration due to in-situ soil damp-ing. Any frequency-dispersion effects may cause these two measurementsto differ. The perpetual source measurements also include noise from thegrinding cone tip that is not present during conventional testing when thecone penetration is paused.The interpretation of perpetual source signals is automated. It mustbe automated to handle the large number of signals collected during eachtest. The post-processing used in this work does not require subjective filterselections or windowing. It requires significantly less post-processing thandescribed by Ku et al. (2013). Conventional testing - particularly the first-cross over technique - requires manual interpretation and has associatedoverhead.Furthermore, by collecting and interpreting a large number of shear wavevelocities - the outliers can be ignored. This cannot be done with conven-tional data without sacrificing up to 2 m of data. For example, if one set ofmeasured signals were anomalous it would affect 2 m of interpreted conven-tional data. For the perpetual source results, it would affect only two points188on the moving window interpretations.7.4 DiscussionThe Perpetual Source technique that has been proposed has some advan-tages over conventional seismic testing. First, the test is faster. It doesnot require seismic testing during rod breaks. This is a minor advantageover conventional seismic testing and does not justify the additional equip-ment and interpretation costs. Second, a high depth resolution profile of VSis determined. This is much more data than conventional seismic testingwhich results in a step plot of VS . Empirical tools need to be developedthat use VS measurements to reduce uncertainty in soil profiling and soilproperties. Once these have been developed, the additional equipment andinterpretation costs associated with perpetual source measurements may bejustified.An interesting observation was made concerning the use of true inter-val cones. True interval measurements are taken to be more accurate thanpseudo-interval (Jamiolkowski, 2012). They do not have additional randomerror from the differences in trigger time and depth. In true interval testingthere is one trigger time and the depth-spacing of the geophones is exactlyknown. Conventional pseudo-interval testing may have a random error ontrigger time. The zero time for the hammer strike may not be exactly thesame between adjacent seismic tests. Conventional pseudo-interval testingmay also have error due to the depth of the geophone. A 5cm depth reso-lution may be acceptable for CPT profiles, but may add considerable errorwhen calculating the shear wave velocity over 1 metre. The exact depthspacing of the adjacent seismic tests has more uncertainty than true intervaltesting.Despite these advantages of true interval testing, this work identifieda potential problem. Three identical geophones resulted in a significantsystematic discrepancy in VS . The exact cause of this discrepancy has notbeen conclusively determined. It was not due to the geophone location orelectronics. Another hypothesis is that the down-hole coupling between the189geophone and soil motion is not consistent between the three geophones.This effect is only observable with more than two geophones. With onlytwo, as commonly used in true-interval testing, there may be an unknownerror in the measurements. The only way to avoid this error is to comparesignals collected from the same geophone.Therefore, the highest quality in situ VS measurements can be madefrom pseudo-interval testing with careful attention paid toward the depthincrement and the repeatability of the hammer strike trigger. The Perpetual-Source testing uses a proximity sensor to ensure that the signals are aligned.The Perpetual-Source testing is triggered off a depth wheel. The depth wheeltrigger encourages consistent in-situ depth separation of the recorded seismicsignals used to calculate VS .The PS-SSCPTu method provides measurements that trend with con-ventional down-hole seismic measurements. This is depicted by the waterfallplot in Figure 7.13 that compares the actual data instead of the interpretedVS results. The waterfall plot provides additional information on the ex-act depth where the signals qualitatively change. This may be useful forprofiling and other seismic studies.7.5 ConclusionThe new perpetual source technique was developed for down-hole seismictesting. Based on the results in this chapter it is concluded that carefulpseudo-interval testing is more reliable than true-interval testing. The per-petual source technique was modified for pseudo-interval testing. Futurework on the development of perpetual-source testing should explore theeffect of changing the source frequency, seismic measurements during dissi-pation, the effect of approaching a reflective layer, and the development andimplementation of a stronger and portable seismic source.190Chapter 8ConclusionThe original intention of this research work was to examine the effect ofageing using a bender element triaxial apparatus. However, preliminaryresults found that the small effect of ageing could not be measured usingbender elements. This led to an examination of bender element testingand interpretation. More advanced signal interpretation techniques wereimplemented, which led to the contribution of a combined time domain andfrequency domain approach covered in Chapter 4. Further improvements inbender element VS measurements were realized and Chapter 5 demonstratedthat VS could be monitored with bender elements continuously throughouta triaxial experiment. This technique was able to characterize the smallincrease in stiffness due to ageing when the bender element signals werestable. This enables the equipment to be used to investigate the effect ofageing on normalized shear secant-stiffness curves for laboratory specimensof clean Fraser River Sand using bender elements. This research projectinvestigated only a small part of the effect of ageing on sands.The limitation of using bender elements is that it is still a measurementover the bender-soil-bender system. The behaviour of the soil is not isolatedand the bender element electrical-physical transformations may influencethe results. These bender element transformations are not linear - they arestrongly affected by the multiple frequency resonance peaks in the system.These resonance peaks change frequencies during a test (Alvarado and Coop,1912012). The behaviour of the bender elements can be characterized in air,but it would not be applicable to the response with soil coupling (Lee andSantamarina, 2005). This work demonstrated the significance of the sys-tematic effect of frequency. Additional research may be able to characterizeand correct the sources of these frequency effects.One important implication of the developed continuous method is thatthe stability of the bender element testing can be observed. The stabilityof the bender elements appears to be lost when a major frequency feature- such as a resonance peak - approaches or crosses one of the monitoringpoints. Without monitoring the bender elements continuously it would bechallenging to confidently disregard a measured bender element velocity. Itis even possible to measure an incorrect negative NG factor using benderelements when the results are influenced by the resonance peaks.Continuous bender element monitoring was used to characterize an em-pirical G0 equation and NG ageing coefficient in Fraser River Sand (Sec-tion 5.6). This equation was used to calculate G0 for the previous experi-ments (Lam, 2003; Shozen, 2001) and create a large dataset of normalizedsecant-stiffness (Gsec/G0) curves for different age durations, consolidationstresses, and shear stress paths.By following the same empirical technique used by Wichtmann and Tri-antafyllidis (2013) and Oztoprak and Bolton (2013), the effect of ageingcould be quantified and extrapolated. This was done by characterizing theeffect of ageing on best-fit hyperbolic function coefficients. The hyperboliccoefficients for the normalized stiffness degradation curves were found tofollow log-linear trends with age duration (Section 6.5.3).The normalized secant stiffness degradation curve is sensitive to recon-stituted specimen age over the small strain range (approximately 0.01% to1% shear strain). This may explain how ageing can result in a very smallincrease in G0 and a very large increase in Gsec. This suggests that VSinterpretations are not very useful for investigating the consequences of age-ing. However, the implications of the age induced increase in Gsec can beseen in the conceptual shear stiffness degradation curve given in Figure 1.2.Empirical shear stiffness degradation estimates will suffer if the difference in192ageing between laboratory reconstituted specimens and in-situ soils is notconsidered. Neglecting the effect of ageing may result in an overestimate ofdisplacements. The hyperbolic models do not account for the fact that thestrength is independent of ageing. They also do not explain the underlyingmechanism responsible for the observed effect of ageing. There is still a needfor more research into the fundamental mechanism responsible for ageing.Chapter 7 presented the adaptation of the continuous bender elementmethod to down-hole seismic testing. In-situ VS measurements can be usedto acquire G0 and scale estimated normalized Gsec/G0 stiffness curves. Itwas shown that this new in-situ method is capable of measuring a continuousprofile of VS . A continuous profile of VS has implications for improving em-pirical interpretations of seismic cone testing. It may be able to increase theresolution of the VS measurements by acquiring the propagation time overshorter intervals. An important outcome of the PS-SCPTu research was theobservation that the true-interval shear wave velocities may be dependenton the geophone pair location behind the cone tip. It still needs to be con-firmed if this observation is limited to the equipment used or endemic to alltrue-interval testing. Both possibilities have different implications. If it isrelated to the equipment, then a requirement for all true-interval module de-signs could be developed. If it is related to the true-interval technique, thenan improved understanding of down-hole seismic testing could be realized.Summary of research contributionsTo reach the conclusions of this thesis, a number of contributions have beenmade. Most of these contributions are related to improvements in the mea-surements of VS . These contributions are:1. Development of a combined time domain and frequency domain in-terpretation method for bender element testing (Chapter 4). Thistechnique eliminates the systematic effect of the selected trigger signalwaveform from the resulting VS measurement.2. Development of a technique for continuous bender element VS mon-itoring (Chapter 5). The developed technique is able to measure VS193at dynamic phases of the experiment - including the transition fromconsolidation to ageing, from ageing to shear, and from contractive todilative behaviour.3. An empirical Gvh and NG equation for clean Fraser River Sand (Sec-tion 5.6 and Section 5.5). These empirical coefficients can be used toestimate Gvh in reconstituted Fraser River Sand specimens. It wasused in this study to complement previous investigations by Shozen(2001) and Lam (2003).4. Extrapolation of the effect of ageing on normalized Gsec/G0 curves(Section 6.5.3) for Fraser River Sand. The extrapolated curves demon-strated a significant effect of age over the small-strain stiffness range.As shown in Figure 1.2, this strain range is critical for typical geotech-nical designs.5. Development of Perpetual Source Seismic Cone Penetration Testingand the pseudo-interval modification (Chapter 7). This technique maybe able to be used to increase the depth resolution of in-situ VS mea-surements.Summary of conclusionsThis research developed new methods for measuring VS with bender el-ements and in-situ. The laboratory and in-situ investigations led to thefollowing primary conclusions:1. The group velocity measured with bender elements is sensitive to dis-persion and contains significant scatter (see Figure 4.6). The variationin group velocity is due to the non-linear frequency response of thebender element-soil system.2. The phase velocity measures dispersion of the bender-soil system andis reproducible (see Figure 4.7). Phase velocity measurements are at asingle frequency, and unlike group velocities they are not as stronglyaffected by dispersion.1943. Bender element testing is non-destructive for loose specimens of FraserRiver Sand in the UBC triaxial apparatus (Section 5.4). No conclusivechange in behaviour was observed with the external triaxial sensors orbender elements. Continuous bender element testing can be used toevaluate the effect of ageing.4. Ageing increases the reference strain to 50 % G0 and the brittleness(curvature) of the secant stiffness curve (Section 6.5.3). This increasesthe secant stiffness over the small strain range significantly, despiteonly a small increase in G0 and negligible change in strength.5. In-situ pseudo-interval shear wave testing is more reliable than true-interval until the observed inconsistency is resolved (Section 7.3.2).The error sources in pseudo-interval testing are known and can becontrolled.Unresolved issuesThe characterization of NG and G0 with bender elements required a study ofbender element errors. This led to improvements in bender element testingand in-situ VS measurements. The following list summarizes some unre-solved issues:1. Characterization of the bender element electrical-mechanical trans-form function under evolving bender-soil coupling. Acquiring the trig-ger and receiver bender element transform functions would enable themeasure of the shear wave across the soil specimen, instead of the cur-rent practice of measuring the shear wave across the bender-soil-bendersystem. Characterizing this transform function may significantly re-duce the observed frequency dispersion in bender element testing andimprove the understanding of the frequency evolution of the resonancepeak features.2. The secant stiffness for non-conventional shear stress paths over strainsbelow 0.01 % is not clear. In the current investigation, these curves did195not appear to fit the hyperbolic relationships. They did not appear totrend towards G0 with decreasing shear strain.3. An inconsistency in true-interval measurements was observed on a 3-geophone seismic probe. This error was observed for both perpetualsource testing and conventional hammer testing. The source of thiserror was not resolved. Therefore, it is not known if this error isisolated to the used true-interval probe or endemic to all true-intervalmeasurements.Further research on the effect of age is warranted. The following pro-grams of study are suggested:1. Create an electronically and mechanically stable triaxial apparatus forlong-term age investigations. This apparatus requires constant tem-perature. It may require damping to eliminate mechanical vibrations.It may require a battery power supply to avoid electronic noise andpower outages.2. Measure Slope-0 stress paths at various age durations to investigate theeffect of the initial volumetric expansion on the stiffness degradation.3. It was observed that NG for the stable denser specimens (1.0± 0.2 %)was less than the loose specimen dataset (1.9± 0.5 %). This conflictswith an increase in NG with an increase in relative density reported byBaxter and Mitchell (2004) for Evanston Beach Sand. A test programshould investigate the effect of density on NG.4. Perform continuous bender element monitoring on Slope -1 shear paths.These shear paths to failure are at a constant in-plane effective stressstate. This investigation may provide insight into the effect of fabric,void ratio, and stress ratio on the shear wave velocity.Closing remarksThe use of bender elements for measuring VS in the laboratory has beeninvestigated and improved. The continuous method can be used to charac-196terize the effect of ageing on VS in clean sands. In practice, the effect ofageing on Gsec over the small strain range is much more significant in bothmagnitude and importance. It is more important because this strain rangegoverns the response of many geotechnical designs.The previous triaxial results at the University of British Columbia havebeen complemented with G0 estimates. The apparent contradiction betweensmall age-induced increases in G0 and large age-induced increases in Gsecare due to a change in the shape of the non-linear shear-stiffness curve. Theeffect of age is insignificant over the very small strain range and at strainsgreater than 2 %. In the small strain range that governs soil behaviour inmost geotechnical designs (Atkinson, 2000; Burland, 1989; Clayton, 2011),the effect of age cannot be ignored. Small strain behaviour is increasinglyimportant for designs that are constrained by displacement instead of fail-ure. Such designs include redevelopment adjacent to existing buildings andburied infrastructure. The advantage of the hyperbolic stiffness degradationcurves is in predicting the small strain behaviour using readily obtained soilparameters. This is of particular importance in granular soils that cannotbe routinely collected undisturbed. These hyperbolic curves can be scaledto in-situ calculated G0 values from VS measurements.197ReferencesAfifi, S. and Richart, F. (1973). Stress-history effects on shear modulus ofsoils. Soils and Foundations, 13(1):77–95.Alvarado, G. and Coop, M. (2012). On the performance of benderelements in triaxial tests. Ge´otechnique, 62(1):1–17.Anderson, D. and Stokoe, K. (1978). Shear modulus: A time dependentsoil property. Dynamic Geotechnical Testing, ASTM STP, 654:66–90.Arroyo, M., Muir Wood, D., Greening, P., Medina, L., and Rio, J. (2006).Effects of sample size on bender-based axial G0 measurements.Ge´otechnique, 56(1):39–52.Arulnathan, R., Boulanger, R., and Riemer, M. (1998). Analysis of benderelement tests. ASTM Geotechnical Testing Journal, 21(2):120–131.Asalemi, A. A. (2006). Application of seismic cone for characterization ofground improved by vibro-replacement. PhD thesis, University of BritishColumbia.Atkinson, J. (2000). Non-linear soil stiffness in routine design.Ge´otechnique, 50(5):487–508.Baldi, G. and Nova, R. (1984). Membrane penetration effects in triaxialtesting. Journal of Geotechnical Engineering, 110(3):403–420.Baxter, C. D. and Mitchell, J. K. (2004). Experimental study on the agingof sands. Journal of Geotechnical and Geoenvironmental Engineering,130(10):1051–1062.Bellotti, R., Jamiolkowski, M., Lo Presti, D., and O’Neill, D. (1996).Anisotropy of small strain stiffness in ticino sand. Ge´otechnique,46(1):115–132.198Bendat, J. and Piersol, A. (2010). Random data: analysis andmeasurement procedures. Wiley.Biot, M. (1956a). Theory of propagation of elastic waves in afluid-saturated porous solid. I. low-frequency range. Journal of theAcoustical Society of America, 28(2):168–178.Biot, M. (1956b). Theory of propagation of elastic waves in afluid-saturated porous solid. II. higher frequency range. Journal of theAcoustical Society of America, 28(2):179–191.Bishop, A. and Henkel, D. (1957). The measurement of soil properties inthe triaxial test. Edward Arnold (Publishers) Ltd.Blewett, J., Blewett, I., and Woodward, P. (1999). Measurement ofshear-wave velocity using phase-sensitive detection techniques. CanadianGeotechnical Journal, 36(5):934–939.Bohac, J. and Feda, J. (1992). Membrane penetration in triaxial tests.ASTM Geotechnical Testing Journal, 15(3):288–294.Bonal, J., Donohue, S., and McNally, C. (2012). Wavelet analysis ofbender element signals. Ge´otechnique, 62(3):243–252.Boonyatee, T., Chan, K., and Mitachi, T. (2009). Determination of shearwave velocity by bender elements using variable-path length method.Soils and Foundations, 49(3):489–494.Brandenberg, S., Kutter, B., and Wilson, D. (2008). Fast stacking andphase corrections of shear wave signals in a noisy environment. Journalof Geotechnical and Geoenvironmental Engineering, 134(8):1154–1165.Brignoli, E., Gotti, M., and Stokoe, K. (1996). Measurement of shearwaves in laboratory specimens by means of piezoelectric transducers.ASTM Geotechnical Testing Journal, 19(4):384–397.Brocanelli, D. and Rinaldi, V. (1998). Measurement of low-strain materialdamping and wave velocity with bender elements in the frequencydomain. Canadian Geotechnical Journal, 35(6):1032–1040.Burland, J. (1989). Ninth laurits bjerrum memorial lecture:” small isbeautiful”-the stiffness of soils at small strains. Canadian GeotechnicalJournal, 26(4):499–516.199Camacho-Tauta, J., Cascante, G., Santos, J., and da Fonseca, A. (2011).Measurements of shear wave velocity by resonant-column test, benderelement test and miniature accelerometers. In 2011 Pan-Am CanadianGeotechnical Society Geotechnical Conference, Toronto.Campanella, R. and Stewart, W. (1992). Seismic cone analysis usingdigital signal processing for dynamic site characterization. CanadianGeotechnical Journal, 29(3):477–486.Casey, T. and Mayne, P. (2002). Development of an electrically-drivenautomatic downhole seismic source. Soil Dynamics and EarthquakeEngineering, 22(9-12):951–957.Cha, M. and Cho, G. (2007). Shear strength estimation of sandy soils usingshear wave velocity. ASTM Geotechnical Testing Journal, 30(6):484–495.Cha, M., Santamarina, J., Kim, H.-S., and Cho, G.-C. (2014). Small-strainstiffness, shear-wave velocity, and soil compressibility. Journal ofGeotechnical and Geoenvironmental Engineering.Chan, K., Boonyatee, T., and Mitachi, T. (2010). Effect of bender elementinstallation in clay samples. Ge´otechnique, 60(4):287–291.Chang, C., Misra, A., and Sundaram, S. (1991). Properties of granularpackings under low amplitude cyclic loading. Soil Dynamics andEarthquake Engineering, 10(4):201–211.Chillarige, A., Robertson, P., Morgenstern, N., and Christian, H. (1997).Evaluation of the in situ state of Fraser River Sand. CanadianGeotechnical Journal, 34(4):510–519.Cho, G.-C., Dodds, J., and Santamarina, J. C. (2006). Particle ShapeEffects on Packing Density, Stiffness, and Strength: Natural andCrushed Sands. Journal of Geotechnical and GeoenvironmentalEngineering, 132(5):591–602.Cho, G. C. and Santamarina, J. C. (2001). Unsaturated particulatematerials-particle-level studies. Journal of Geotechnical andGeoenvironmental Engineering, 127(1):84–96.Clayton, C. (2011). Stiffness at small strain: research and practice.Ge´otechnique, 61(1):5–37.200Comina, C., Foti, S., Musso, G., and Romero, E. (2008). EIT Oedometer:an advanced cell to monitor spatial and time variability in soil withelectrical and seismic measurements. ASTM Geotechnical TestingJournal, 31(5):404–412.Cruse, T. and Rizzo, F. (1968). A direct formulation and numericalsolution of the general transient elastodynamic problem. transientproblem solution in linear elastodynamics by integral equation in laplacetransform space. Journal of Mathematical Analysis and Applications,22:244–259.Cunning, J., Robertson, P., and Sego, D. (1995). Shear wave velocity toevaluate in situ state of cohesionless soils. Canadian GeotechnicalJournal, 32(5):848–858.Darendeli, M. B. (2001). Development of a new family of normalizedmodulus reduction and material damping curves. PhD thesis, TheUniversity of Texas at Austin.d’Onofrio, A., Silvestri, F., and Vinale, F. (1999). A new torsional sheardevice. ASTM Geotechnical Testing Journal, 22(2):107–117.Drnevich, V., Hardin, B., and Shippy, D. (1978). Modulus and damping ofsoils by the resonant-column method. Dynamic Geotechnical Testing,ASTM STP, 654:91–125.Emeriault, F. and Chang, C. S. (1997). Anisotropic elastic moduli ofgranular assemblies from micromechanical approach. Journal ofEngineering Mechanics, 123(12):1289–1293.Fam, M., Cascante, G., and Dusseault, M. (2002). Large and small strainproperties of sands subjected to local void increase. Journal ofGeotechnical and Geoenvironmental Engineering, 128(12):1018–1025.Garrison, R. E., Luternauer, J. L., Grill, E. V., MacDonald, R. D., andMurray, J. W. (1969). Early diagenetic cementation of recent sands,Fraser River Delta, British Columbia. Sedimentology, 12(1-2):27–46.Ghayoomi, M. and McCartney, J. (2011). Measurement of small-strainshear moduli of partially saturated sand during infiltration in ageotechnical centrifuge. ASTM Geotechnical Testing Journal, 34.Greening, P. and Nash, D. (2004). Frequency domain determination of G0using bender elements. Geotechnical Testing Journal, 27(3):288–294.201Hamidi, B., Varaksin, S., and Nikraz, H. (2013). Relative densitycorrelations are not reliable criteria. Proceedings of the ICE-GroundImprovement, 166(4):196–208.Hardin, B. (1980). Discussion: Anisotropic shear modulus due to stressanisotropy. Journal of the Geotechnical Engineering Division,106(8):956–958.Hardin, B. and Black, W. (1966). Sand stifness under various triaxialstresses. Journal of the Soil Mechanics and Foundations Division,92(SM 2):27–42.Hardin, B. and Black, W. (1968). Vibration modulus of normallyconsolidated clay. Journal of the Soil Mechanics and FoundationsDivision, 95(SM 2):–361.Hardin, B. and Black, W. (1969). Closure: Vibration modulus of normallyconsolidated clay. Journal of the Soil Mechanics and FoundationsDivision, 95(SM 6):1531–1537.Hardin, B. and Drnevich, V. (1972). Shear modulus and damping in soils:Measurement and parameter effects. Journal of the Soil Mechanics andFoundations Division, 98(SM6):603–623.Hardin, B. and Richart Jr, F. (1963). Elastic wave velocities in granularsoils. Journal of the Soil Mechanics and Foundations Division, 89(SM1):33–65.Hardin, B. O. and Blandford, G. E. (1989). Elasticity of particulatematerials. Journal of Geotechnical Engineering, 115(6):788–805.Heyliger, P., Ledbetter, H., and Kim, S. (2003). Elastic constants ofnatural quartz. The Journal of the Acoustical Society of America,114:644.Hons, M. (2009). Seismic sensing: Comparison of geophones andaccelerometers using laboratory and field data. PhD thesis, University ofCalgary.Howie, J., Shozen, T., and Vaid, Y. (2002). Effect of ageing on stiffness ofvery loose sand. Canadian Geotechnical Journal, 39(1):149–156.Iida, K. (1938). The velocity of elastic waves in sand.202Isenhower, W., Stokoe, K., and Allen, J. (1987). Instrumentation fortorsional shear/resonant column measurements under anisotropicstresses. ASTM Geotechnical Testing Journal, 10(4):183–191.Jamiolkowski, M. (2012). Role of p-waves and s-waves in geotechnical sitecharacterization. In Third international workshop on Modern Trends inGeomechanics IW-MTG3, 4-5 September 2012.Jang, I., Kwon, O., and Chung, C. (2010). A pilot study of in-hole typecptu using piezoelectric bender elements. In 2nd InternationalSymposium on Cone Penetration Testing. Huntington Beach, California.JCGM, BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML(2008a). Evaluation of measurement data - guide to the expression ofuncertainty in measurement - GUM 1995 with minor corrections.Technical Report JCGM 100:2008.JCGM, BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML(2008b). Evaluation of measurement data - supplement 1 to the ”Guideto the expression of uncertainty in measurement” - proagation ofdistributions using a monte carlo method. Technical Report JCGM101:2008.Jovicic, V. and Coop, M. (1997). Stiffness of coarse-grained soils at smallstrains. Ge´otechnique, 47(3):545–61.Jovicic, V., Coop, M., and Simic, M. (1996). Objective criteria fordetermining Gmax from bender element tests. Ge´otechnique,46(2):357–362.Jung, Y., Cho, W., and Finno, R. (2007). Defining yield from benderelement measurements in triaxial stress probe experiments. Journal ofGeotechnical and Geoenvironmental Engineering, 133(7):841–849.Karl, L., Haegeman, W., Degrande, G., and Dooms, D. (2008).Determination of the material damping ratio with the bender elementtest. Journal of Geotechnical and Geoenvironmental Engineering,134(12):1743–1756.Ku, T. and Mayne, P. (2012). Frequent-interval SDMT and continuousSCPTu for detailed shear wave velocity profiling in soils. GeotechnicalEngineering Journal of the SEAGS & AGSSEA, 43(4):34–40.203Ku, T., Mayne, P. W., and Cargill, E. (2013). Continuous-interval shearwave velocity profiling by auto-source and seismic piezocone tests.Canadian Geotechnical Journal, (Online pre-print).Kuerbis, R. H. and Vaid, Y. P. (1990). Corrections for membrane strengthin the triaxial test. ASTM Geotechnical Testing Journal, 13(4):361–369.Kumar, J. and Madhusudhan, B. (2010). A note on the measurement oftravel times using bender and extender elements. Soil Dynamics andEarthquake Engineering, 30(7):630–634.Kuwano, R., Connolly, T., and Jardine, R. (2000). Anisotropic stiffnessmeasurements in a stress-path triaxial cell. Geotechnical TestingJournal, 23(2).Kuwano, R. and Jardine, R. (2002a). On measuring creep behaviour ingranular materials through triaxial testing. Canadian GeotechnicalJounral, 39:1061–1074.Kuwano, R. and Jardine, R. (2002b). On the applicability ofcross-anisotropic elasticity to granular materials at very small strains.Ge´otechnique, 52(10):727–749.Laing, N. (1985). Sources and receivers with the seismic cone test.Master’s thesis, University of British Columbia.Lam, C. K. K. (2003). Effects of aging duration, stress ratio during agingand stress path on stress-strain behaviour of loose fraser river sand.Master’s thesis, University of British Columbia.Landon, M., DeGroot, D., and Jakubowski, J. (2004). Comparison of shearwave velocity measured in situ and on block samples of a marine clay. InProc. of the 57th Canadian Geotechnical Conference, Quebec.Lawrence Jr, F. V. (1965). Ultrasonic shear wave velocities in sand andclay. Technical report, DTIC Document.Lee, C., Lee, J., Lee, W., and Cho, T. (2008). Experiment setup for shearwave and electrical resistance measurements in an oedometer. ASTMGeotechnical Testing Journal, 31(2):149–156.Lee, J., Salgado, R., and Carraro, J. A. H. (2004). Stiffness degradationand shear strength of silty sands. Canadian Geotechnical Journal,41(5):831–843.204Lee, J. and Santamarina, J. (2005). Bender elements: performance andsignal interpretation. Journal of Geotechnical and GeoenvironmentalEngineering, 131:1063.Lee, J. and Santamarina, J. (2006). Discussion ”Measuring Shear WaveVelocity Using Bender Elements” By Leong, EC, Yeo, SH, andRahardjo, H. ASTM Geotechnical Testing Journal, 29(5):439.Leong, E., Cahyadi, J., and Rahardjo, H. (2009). Measuring shear andcompression wave velocities of soil using bender-extender elements.Canadian Geotechnical Journal, 46(7):792–812.Leong, E., Yeo, S., and Rahardjo, H. (2005). Measuring shear wave velocityusing bender elements. Geotechnical Testing Journal, 28(5):488–498.Lunne, T., Robertson, P., and Powell, J. (1997). Cone Penetrating Testing:In Geotechnical Practice. Blackie Academic and Professional.Marjanovic, J. and Germaine, J. T. (2013). Experimental studyinvestigating the effects of setup conditions on bender element velocityresults. ASTM Geotechnical Testing Journal, 36(2):187–197.McGillivray, A. (2013). personal communication.McGillivray, A. and Mayne, P. (2008). An automated seismic source forcontinuous-push shear wave velocity profiling with SCPT and SDMT. InGeotechnical & Geophysical Site Characterization, ISC-3, Taipe.Mesri, G. and Vardhanabhuti, B. (2009). Compression of granularmaterials. Canadian Geotechnical Journal, 46(4):369–392.Mitchell, J. K. (2008). Aging of sand - a continuing enigma? In SixthInternational Conference on Case Histories in Geotechnical Engineeringand Symposium in Honor of Professor James K. Mitchell. MissouriUniversity of Science and Technology.Mitchell, J. K. and Solymar, Z. V. (1984). Time-dependent strength gainin freshly deposited or densified sand. Journal of GeotechnicalEngineering, 110(11):1559–1576.Negussey, D. (1984). An experimental study of the small strain response ofsand. PhD thesis, University of British Columbia.Oztoprak, S. and Bolton, M. (2013). Stiffness of sands through alaboratory test database. Ge´otechnique, 63(1):54–70.205Petrakis, E. and Dobry, R. (1989). Micromechanical behavior andmodelling of granular soil. Technical report, DTIC Document.Rio, J. (2006). Advances in laboratory geophysics using bender elements.PhD thesis, University College London.Robertson, P., Campanella, P., Gillespie, D., and Rice, A. (1986). SeismicCPT to measure in situ shear wave velocity. Journal of GeotechnicalEngineering, 112:791.Robertson, P., Fear, C., Woeller, D., and Weemees, I. (1995a). Estimationof sand compressibility from seismic cpt. In 48th Canadian GeotechnicalConference.Robertson, P., (Fear) Wride, C., List, B., Atukorala, U., Bigger, K., Byrne,P., Campanella, R., Cathro, D., Chan, D., Czajewski, K., Finn, W., Gu,W., Hammamji, Y., Hofmann, B., Howie, J., Hughes, J., Imrie, A.,Konrad, J.-M., Kupper, A., Law, T., Lord, E., Monahan, P.,Morgenstren, N., Phillips, R., Piche, R., Plewes, H., Scott, D., Sego, D.,Sobkowicz, J., Stewart, R., Watts, B., Woeller, D., Youd, T., andZavodni, Z. (2000). The CANLEX project: summary and conclusions.Canadian Geotechnical Journal, 37(3):563–591.Robertson, P., Sasitharan, S., Cunning, J., and Sego, D. (1995b).Shear-wave velocity to evaluate in-situ state of ottawa sand. Journal ofGeotechnical Engineering, 121(3):262–273.Roesler, S. K. (1979). Anisotropic shear modulus due to stress anisotropy.Journal of the Geotechnical Engineering Division, 105(7):871–880.Saada, A. and Townsend, F. (1981). State of the art: laboratory strengthtesting of soils. Laboratory shear strength of soil, ASTM STP, 740:7–77.Sachse, W. and Pao, Y. (1978). On the determination of phase and groupvelocities of dispersive waves in solids. Journal of Applied Physics,49(8):4320–4327.Salgado, R., Bandini, P., and Karim, A. (2000). Shear strength andstiffness of silty sand. Journal of Geotechnical and GeoenvironmentalEngineering, 126(5):451–462.Sa´nchez-Salinero, I., Roesset, J., and Stokoe, K. (1986). Analytical Studiesof Body Wave Propagation and Attenuation; a Report on Research206Sponsored by United States Air Force, Office of Scientific Research,Bolling Air Force Base. University of Texas, Geotechnical EngineeringCenter, Civil Engineering Dept.Santamarina, J. and Cascante, G. (1996). Stress anisotropy and wavepropagation: a micromechanical view. Canadian Geotechnical Journal,33(5):770–782.Santamarina, J. and Fam, M. (1997). Discussion: Interpretation of benderelement tests. Ge´otechnique, 47(4):873–877.Santamarina, J., Klein, K., and Fam, M. (2001). Soils and Waves. JohnWiley, Hoboken, NJ.Schmertmann, J. H. (1991). The mechanical aging of soils. Journal ofGeotechnical Engineering, 117(9):1288–1330.Schnaid, F. and Yu, H. (2007). Interpretation of the seismic cone test ingranular soils. Ge´otechnique, 57(3):265–272.Scholey, G. K., Frost, J. D., and Lo, P. (1995). A review ofinstrumentation for measuring small strains during triaxial testing of soilspecimens. ASTM Geotechnical Testing Journal, 18(2):137–156.Seed, H., Wong, R., Idriss, I., and Tokimatu, K. (1984). Moduli anddamping factors for dynamic analyses of cohesionless soils. College ofEngineering, University of California. Earthquake Engineering ResearchCenter.Seed, H. B., Wong, R. T., Idriss, I., and Tokimatsu, K. (1986). Moduli anddamping factors for dynamic analyses of cohesionless soils. Journal ofGeotechnical Engineering, 112(11):1016–1032.Shirley, D. (1978). An improved shear wave transducer. The Journal of theAcoustical Society of America, 63:1643.Shozen, T. (2001). Deformation under the constant stress state and itseffect on stress-strain behaviour of fraser river sand. Master’s thesis,University of British Columbia.Slawinski, M. (2003). Seismic waves and rays in elastic media. ElsevierScience.207Somfai, E., Roux, J., Snoeijer, J., Van Hecke, M., and Van Saarloos, W.(2005). Elastic wave propagation in confined granular systems. PhysicalReview E, 72(2).Stewart, W. and Campanella, R. (1993). Practical aspects of in situmeasurements of material damping with the seismic cone penetrationtest. Canadian Geotechnical Journal, 30(2):211–219.Styler, M. and Howie, J. (2013). A combined time and frequency domainapproach to the interpretation of bender element tests. ASTMGeotechnical Testing Journal, 36(5).Styler, M. and Howie, J. (2014). Continuous monitoring of bender elementshear wave velocities during triaxial testing. ASTM Geotechnical TestingJournal, 37(2):218–229.Styler, M., Howie, J., and Sharp, J. (2014). Perpetual source scptu: Signalstacking shear waves during continuous penetration. In CPT1´4 LasVegas.Styler, M., Howie, J., and Woeller, D. (2012). Perpetual Source SeismicPiezocone Penetration Testing: A new method for down-hole shear wavevelocity profiling. In GeoManitoba, Winnipeg, Manitoba. CanadianGeotechnical Conference.Styler, M., Howie, J., and Woeller, D. (2013). Measuring down-hole shearwaves from a vibrating perpetual source during Cone PenetrationTesting. In GeoMontreal, Montreal, Quebec.Thomann, T. G. and Hryciw, R. D. (1990). Laboratory measurement ofsmall strain shear modulus under K0 conditions. Geotechnical TestingJournal, 13(2):97–105.Vaid, Y. (2009). personal communication.Vaid, Y. P. and Negussey, D. (1984). A critical assessment of membranepenetration in the triaxial test. Geotechnical Testing Journal, 7(2):70–76.Vaid, Y. P. and Negussey, D. (1988). Preparation of reconstituted sandspecimens. Advanced triaxial testing of soil and rock, pages 405–417.Velea, D., Shields, F., and Sabatier, J. (2000). Elastic wave velocities inpartially saturated ottawa sand: experimental results and modeling. SoilScience Society of America Journal, 64(4):1226–1234.208Viana da Fonseca, A., Ferreira, C., and Fahey, M. (2009). A frameworkinterpreting bender element tests, combining time-domain andfrequency-domain methods. Geotechnical Testing Journal, 32(2):1.Viggiani, G. and Atkinson, J. (1995). Interpretation of bender elementtests. Ge´otechnique, 45:149.Wang, Y., Lo, K., Yan, W., and Dong, X. (2007). Measurement biases inthe bender element test. Journal of Geotechnical and GeoenvironmentalEngineering, 133:564.Wang, Y. and Mok, C. (2008). Mechanisms of small-strain shear-modulusanisotropy in soils. Journal of Geotechnical and GeoenvironmentalEngineering, 134(10):1516–1530.Wichtmann, T. and Triantafyllidis, T. (2013). Effect of uniformitycoefficient on g/g max and damping ratio of uniform to well-gradedquartz sands. Journal of Geotechnical and GeoenvironmentalEngineering, 139(1):59–72.Woods, R. (1994). Laboratory measurement of dynamic soil properties.Dynamic Geotechnical Testing II: ASTM Special Technical Publication,1213:165–165.Wride, C., Robertson, P., Biggar, K., Campanella, R., Hofmann, B.,Hughes, J., Ku¨pper, A., and Woeller, D. (2000). Interpretation of in situtest results from the canlex sites. Canadian Geotechnical Journal,37(3):505–529.Wroth, C. (1984). The interpretation of in situ soil tests. Ge´otechnique,34(4):449–489.Yamashita, S., Kawaguchi, T., Nakata, Y., Mikaml, T., Fujiwara, T., andShibuya, S. (2009). Interpretation of international parallel test on themeasurement of Gmax using bender elements. Soils and Foundations,49(4):631–650.Yimsiri, S. and Soga, K. (2000). Micromechanics-based stress-strainbehaviour of soils at small strains. Ge´otechnique, 50(5):559–571.Youn, J., Choo, Y., and Kim, D. (2008). Measurement of small-strainshear modulus gmax of dry and saturated sands by bender element,resonant column, and torsional shear tests. Canadian GeotechnicalJournal, 45(10):1426–1438.209Yu, P. and Richart, F. (1984). Stress ratio effects on shear modulus of drysands. Journal of Geotechnical Engineering, 110(3):331–345.210Appendix ATriaxial apparatuspreparationThe triaxial apparatus must be prepared prior to any testing program. Thispreparation includes cleaning, levelling, and saturating the apparatus. Itincludes calibrating the sensors, measuring the constants, and characterizingsystematic errors between the sensors and the state of the specimen. Thetriaxial equipment needs to be maintained for reliable performance. Thesensors should be re-calibrated each time the equipment is moved. Theconnections for each sensor into the signal conditioning and amplificationbox must be periodically checked, especially if a noisy signal is observed.Fully saturated water pressure transducers are necessary for responsiveand accurate volume measurements. The saturation of the system can bequalitatively checked very easily and quickly. This is accomplished by closingValve 2 in Figure 3.3 and turning up the back pressure to around 300 kPa.Any bubbles in the system will compress and possibly dissolve into the porefluid. Dissolved air in water increases the compressibility of the fluid. Ifthe system is not saturated then a significant finite drop in the water levelin the volumetric cylinders will occur. There are three primary reasonsfor a loss in saturation. First, due to testing specimens that are not fullysaturated. Second, air will dissolve into the water at the water-air boundaryin the cell pressure reservoir and differential pore water pressure volumetric211cylinders. This dissolved air will slowly dissipate through the water in theapparatus. Third, draining too much water out of the apparatus. This canoccur when the specimen is dilating or if the system is accidentally openedto atmosphere with an applied back pressure. If the system is not saturatedthen the apparatus must be flushed with boiled(and cooled) de-aired water.A more difficult problem is finding and removing any air bubbles that mayreside in the plumbing of the system. These are dislodged by cyclicallydraining and filling the system while opening and closing the valves.The apparatus is designed so that leaks can be detected. This is accom-plished by using the manual back pressure regulator to apply a pressure of atleast 200 kPa to the system. Valve 11 in Figure 3.3 is then shut. If the pres-sure indicated by the pressure gage adjacent to Valve 11 drops then thereis a leak in the system. Leaks may be detected by spraying a soapy-watersolution onto the pressurized apparatus at potential leak locations.A.1 Sensor calibrationsThe triaxial sensors were calibrated using the triaxial data acquisition sys-tem. Calibrating the the sensors using the triaxial data acquisition systemcaptures the measurement uncertainty due to the peripheral electronics andsignal conditioning in the uncertainty of the calibration factor. The sensorswere calibrated with points spread through-out the expected measurementrange. This prevents the calibration factor from being biased to a smallportion of the curve. The sensors were calibrated over a loading and un-loading loop to capture any hysteresis. Each calibration was based on atleast 12 data points. The uncertainty in the calibration factor decreaseswith diminishing returns for each additional calibration point.Calibration points are obtained with measurements against a standard.The standard for the load call calibration was a set of dead weights. Theseweights were applied to the load cell using a hanging loading frame. Theload cell was detached from the apparatus and placed on the corner of atable. The loading frame was balanced on top of the load cell and deadweights were added. THe upper range of the load cell calibration could not212be tested with this approach. The potential danger of knocking over thishanging apparatus must be acknowledged prior to calibrating.The LVDT was calibrated using an accurate screw controlled plungerdevice. The LVDT was locked into this device and a screw controlled plungerdisplaced the LVDT arm. The full range of the LVDT arm position wasmeasured. The calibration factor only applies over the linear portion ofthe LVDT response. Calibration data points outside this linear range werediscarded from the calibration. Triaxial testing is only performed over thelinear range of the LVDT.The water pressure transducers were calibrated using a digital pressureindicator (DPI). This device was not directly attached to the pressure trans-ducer swage connections. The DPI pressurizes air, while the pore pressuresensors measure water pressure. A small reservoir was used to transfer theair pressure to water pressure.The differential pore water pressure transducer(DPWPT) was calibratedusing a pipette to measure volume. The pipette used was one of the twovolumetric cylinders in the apparatus. First an initial reading is taken withboth cylinders open. Second, the large cylinder is shut and a measuredvolume of water is added to or removed from the pipette. Third, bothcylinders and opened and permitted to equalize prior to taking the finalreading.The DPWPT must also be calibrated for elevation head in order for thesubsequent calibration of the expanded membrane diameter. This was doneusing the graduated measurement tape attached to one of the volumetriccylinders.The calibration factors are detailed in Table 3.4. The conditional stan-dard deviations are included in Table 3.4. These values represent the stan-dard deviation of the measurement for a given voltage. For example, withthe LVDT this is the standard deviation of the change in height conditionalon the measured LVDT voltage. Equation A.1 calculates the conditionalstandard deviation where n is the sample size in the calibration, σy is thestandard deviation of the calibration standard displacements, and r2xy is thesquared correlation coefficient for the calibration. The conditional standard213deviation for the LVDT sensor is 0.00386 mm. The DPWPT calibration wasperformed twice and the results are combined in DPWPT*.σ(units|volts) =√n− 1n− 2σy(1− r2xy) (A.1)A.2 Apparatus constantsReducing the sensor measurements to the properties of the specimen re-quire the measurement of apparatus constants. The height of the specimenduring specimen preparation is measured using a dial gage. This dial gagehas a range of 20 mm, while the initial specimen height is between 125 and132mm. To calculate the height of the specimen, the dial gage measure-ments are corrected with respect to a datum specimen height. This datumspecimen is a solid metal cylinder with recesses to accommodate the benderelements. The height of this datum specimen was measured 12 times witha micrometer. It has a mean height of 127.0775 mm ± 0.00827 mm.An effective stress is applied to the soil specimen during specimen prepa-ration. This effective stress is sufficient for the specimen to be self-supportingwhile the triaxial chamber is constructed. The effective stress is added to thespecimen by applying an 18 kPa vacuum pressure to the pore water. Thischange in effective stress from 0 to 18 kPa induces a volumetric deformationof the soil skeleton. To calculate the initial volume of the specimen, thisvolumetric change needs to be measured. The DPWPT cylinders can notbe used for this step. A vacuum pressure should not be applied to the porewater pressure transducer. Therefore, another graduated bored cylinder wascalibrated. This bored cylinder collects the volume of water ejected fromthe specimen voids during specimen preparation.This bored glass cylinder is not a pipette. The gradations attachedto the outside of this cylinder are a measuring tape. The calibration isthen the volume of water per gradation, where each gradation correspondsto a centimetre in elevation head. This graduated cylinder was calibratedusing the DPWPT volumetric calibration. The bored glass cylinders thatmeasure changes in the specimen volume (see Figure 3.3) were filled with214de-aired water. They were then connected to the specimen preparationglass cylinder through a saturated swage tube. The water in the DPWPTvolumetric cylinders were at a higher elevation head so that when the valveis opened water would flow into the specimen preparation cylinder. Smallvolumes of water were transferred and the gradations and DPWPT voltageswere recorded. A total of 41 points were collected during four cycles oftransferring water between the glass cylinders. The specimen preparationglass cylinder has a calibration factor of -0.487 cm3/grad with a conditionalstandard deviation of ± 0.012 cm3. This standard deviation is conditionalon the person performing the measurement, as the reading of the gradationfor the meniscus of the water may be slightly subjective.The calibrated volumetric cylinder measures the change in volume duringspecimen preparation. To calculate the specimen volume, the initial volumemust be determined. The specimen is prepared within a membrane thatis held open using a membrane expander. The initial specimen volumeis calculated from the internal diameter of the expanded membrane andthe initial specimen height measured during specimen preparation. Thespecimen volume and void ratio are very sensitive to the expanded membraneinternal diameter.An accurate measure of the average internal diameter of the expandedmembrane is required. The DPWPT can be used to measure both the heightof water and the volume of water. These two measures can be used to cal-culate the average internal diameter of the expanded membrane. Figure A.1depicts the apparatus set up required and details the procedure to mea-sure the internal diameter using the DPWPT. This resulted in an internalexpanded membrane diameter of 63.877±0.046 mm.215Pore pressuretransducerDPWPTP1234 511100 mmRVacuum regulator set to -18 kPaMembraneMembraneexpanderBottom o-ringAtmosphereDrainage valver1r2ΔV1ΔV2,ΔhΔV31.  Open line (Valves 1 and 2) between expanded membrane and DWPWT      and wait for elevation head to equalize2.  Record DPWPT voltage (r1)3.  Close the DPWPT Valve 24.  Open drainage valve and drain a large volume of water (30-50mL) out of the      expanded cavity5.  Close drainage valve6.  Record the weight of the discharged water and calculate the volume, ΔV17.  Open DPWPT Valve 2 and wait for the elevation head to equalize8.  Record DPWPT voltage (r2)9.  Calculate volume of water drained out of the DPWPT cylinders from r1      and r2, ΔV210.  Calculate the change in water height in the expanded membrane from      r1 and r2, ΔH111.  Calculate the change in water volume within the expanded membrane,      ΔV3=ΔV1 - ΔV212.  Calculate the average internal diameter of the expanded membrane from      ΔV3 and ΔH113.  Repeat until expanded membrane is drainedI.D. = 63.877±0.046mmFigure A.1: Apparatus configuration to measure average internal ex-panded membrane diameter216A.3 Systematic error correctionsSystematic errors between the external sensor measurements and stress anddeformation of the soil specimen need to be corrected. These include cor-rections for the axial stress from the ram friction, uplift, elastic membrane,and dead weight; for the radial stress from the elastic membrane, and for thevolumetric strain from the membrane penetration into the specimen surface.The measured axial stress at the centre of the specimen includes theeffective weight of half of the soil, the weight of the top cap, downwardspressure on the top cap due to the chamber pressure minus the upwardspressure due to the pore water pressure, the measured applied load from theload cell minus any friction along the driving rod, and an applied load fromthe deformed elastic membrane. The weight of the top cap was measuredusing the laboratory scale and equals 0.4683 kg. The downward pressureon the top cap due to the chamber pressure acts on an area equal the crosssectional area of the specimen minus the cross sectional area of the drivingrod attached to the top cap. The cross section area of the driving rod wasmeasured 12 times with a micrometer and the mean diameter is 9.645 mm± 0.0164 mm. This is the error in the estimate of the mean height based onan unbiased measurement. It is not the measurement error. The pore waterpressure acting upwards applies over the cross section area of the specimen.The ram friction and elastic membrane corrections are not as simple.The ram friction must be overcome by the driving rod to apply a loadto the specimen. The ram friction can be measured in a pressurized triaxialchamber without a soil specimen. The triaxial chamber is placed in thetriaxial apparatus, filled with water, and the chamber pressure lines areattached. The chamber was pressurized to 300 kPa, this is a typical pressureduring a triaxial test, activates the friction reducer, and applies an upliftforce. This uplift force is the chamber pressure times the cross section areaof the driving rod, it will overcome the buoyant weight of the top cap. Thiswill apply a load to the load cell. The constant strain stepper motor is usedto slowly cycle the top cap upwards and downwards while recording themeasured load cell readings. When the top cap is being driven downwards217the load cell is measuring the friction plus the uplift minus the top capweight (Ldown = F +U−W ). When the top cap is being pulled upwards theload cell is measuring the uplift minus the friction minus the top cap weight(Lup = −F+U−W ). The driving rod friction can be found by the differencein these two measurements, Ldown−Lup = (F+U−W )−(−F+U−W ) = 2F .Figure A.2 presents the measurements for this correction. The ram frictionequals -0.0624 kg. Typical magnitudes for this correction are from -0.18 to -0.21 kPa for the axial stress. The negative sign means that the measurementby the load cell needs to be reduced, not that the rod friction is negative.0 500 1000 1500 2000 2500 3000 3500 400039.954040.0540.140.15time (seconds)load (kg)0 500 1000 1500 2000 2500 3000 3500 40002.533.5time (seconds)disp (mm)Figure A.2: Measuring the rod friction of -0.0624 kgThe triaxial specimen is enclosed in an elastic membrane. This elasticmembrane is deformed from its unstretched state and will contribute to theaxial and radial stresses experienced by the soil skeleton. The membrane isinitially stretched over the membrane expander. Once it is snapped on to218the specimen it is already deformed and contributing to the axial and radialstress. The procedure for measuring the elastic properties of the membranewas presented by Bishop and Henkel (1957). The interpretation of thesemeasurements was corrected by Kuerbis and Vaid (1990). The elastic prop-erties for the membrane are determined by measuring the deformation toan applied stretching force. Two rods are inserted through the membrane.One rod is hung from a fixed point. A loading frame is attached to the otherrod. Dead weight is added to the loading frame and the deformation of themembrane is measured. This membrane has an unstretched outer diameterof 61 mm and a wall thickness of 0.3 mm. The Young’s modulus is 976 kPa.The contributions the membrane makes to the axial and radial stresses ofthe specimen are calculating from elastic shell theory. The equations forthis correction are presented in Appendix C. Typical magnitudes for thiscorrection are 0.17 kPa for the axial stress and 0.34 kPa for the radial stress.The elastic membrane also affects the volumetric measurements. Theelastic membrane will penetrate into the voids over the surface of the soilspecimen. This penetration will increase with increasing radial effectivestress. This penetration will result in an ejection of water from the specimenthat does not correspond to a change in the volume of the void space. Thisejected water will be measured by the DPWPT.This effect has been quantified by comparing the volume change of mul-tiple specimens under hydrostatic loading. Each of these specimens had abrass rod of varying diameter along the specimen axis. This results in a setof specimens with the same surface area, but different soil volumes. Vaid andNegussey (1984) disagreed with this approach, the inclusion of brass rodswould influence the the developed volumetric strains in the soil. Vaid andNegussey (1984) assumed that soil behaved isotropically under hydrostaticunloading. They calculated the membrane penetration volume as the dif-ference between the measured volume change during hydrostatic unloadingand the isotropic volume change calculated from the axial strain. Alterna-tively, Bohac and Feda (1992) calculated the membrane penetration volumeduring K0 consolidation by comparing the measured value to the calculatedvalue assuming the radial strain was 0. Baldi and Nova (1984) presented an219equation resulting from an idealized analysis in terms of the diameter of theparticles, the membrane properties, and the effective radial stress.The hydrostatic unloading method presented by Vaid and Negussey(1984) was used to calculate the unit membrane penetration coefficient.Figure A.3 depicts one of the fifteen hydrostatic unloading loops used to cal-culate the membrane penetration coefficient. The value obtained 0.000326 isless than the value of 0.0021 used by Shozen (2001). Figure A.4 presents theunit membrane penetration volume against the logarithm of effective stress.For Fraser River Sand under a change in effective confining stress of 100 kPa,the measured unit penetration by the Vaid and Negussey (1984) method is0.00065 cm3 per square centimetre of specimen surface area. The Baldi andNova (1984) simple analytical approach results in a comparable 0.0010 cm3per square centimetre of specimen surface area. Typical magnitudes for thiscorrection are 0.18 cm3, or 0.05 % volumetric strain.Table A.1 details the measured constants for the UBC Triaxial testing ofFraser River Sand. This table includes standard deviation of the mean. Themean value is estimated from the set of measurements, it is not a constant.If an additional measurement was taken, then the mean value would change.The datum specimen was measured 12 times to result in a mean height of127.0775 mm with a standard deviation of the mean of 0.00827 mm. This isthe standard deviation of the mean value for the datum specimen height, it isnot the standard deviation of the 12 measurements. The standard deviationof a mean for a normal distribution is calculated as the standard deviationof the sample size divided by the square root of the number of samples.Table A.1 summarizes constants used in the reduction of the triaxialdata. The n column is the number of measurements performed. These valuesare expected to be constants - to have a standard deviation of 0 if measuredperfectly. Therefore, the standard deviation of the n measured samples is aresult of the measurement procedure - not the measurand. The mean valueof these n measurements is taken as the most likely point estimate for theconstant. The standard deviation of the mean value is s/√n, where s is thestandard deviation of n measurements.22040 60 80 100 120 140 160 180−0.100.10.20.30.40.50.6Effective confining pressure (kPa)Strain (%)  εa3 εa *D/4∆ V/AsFigure A.3: Measured and calculated volumetric strains during hy-drostatic unloadingTable A.1: ConstantsMeasurand n mean stdev (s/sqrt(n))Datum specimen height 12 127.0775 mm 0.00827 mmDriving rod diameter 12 9.645 mm 0.0164 mmTop cap weight 0.4683Expanded membrane ID 6 63.8772 mm 0.0456Unstretched membrane OD 61 mmUnstretched membrane thick-ness0.3 mmMembrane Young’s modulus 976 kPaUnit membrane penetration(cm3/cm2 per log(σ′r kPa))15 0.000326 0.000017Ram friction -0.0624 kg22110 100 500−0.500.511.522.53Effective confining pressure (kPa)unit membrane penetrationFigure A.4: Measured unit membrane penetration against effectiveconfining pressure222Appendix BTriaxial testing procedureB.1 Sample preparationMaintaining a fully saturated triaxial apparatus requires testing only satu-rated triaxial specimens. The procedure for testing fully saturated specimensbegins with sample preparation. Each tested specimen is reconstituted froma prepared sample of Fraser River Sand. The particles larger than 2.362 mmare removed by dry sieving and particles finer than 75 µm are washed outby wet sieving. The Fraser River sand retained on the 75 µm sieve is ovendried then air cooled. This forms a bulk sample that is used to make mul-tiple individual samples. De-aired water is added to individual samples of590 to 600 grams of dry Fraser River Sand in pycnometer flasks. These sam-ples are boiled for at least 30 minutes then stored under a vacuum. Duringperiods when the vacuum source was broken the samples were re-boiled theday before testing and then sealed with a rubber stopper while still cooling.Prior to using a sample to reconstitute a specimen the sample flask is tiltedapproximately 30 degrees and rolled rapidly about its axis in an attempt tofree any air bubbles. If no air bubbles are observed then the sample is usedto create a specimen.223B.2 Specimen reconstitution procedureThere are a few preliminary steps prior to water pluviation of the sandspecimen. The triaxial membranes do not arrive ready to use. They needto be marked in order to measure membrane deformations during speci-men preparation. This is accomplished by inserting a piece of graph paperinto the membrane cavity and tracing the lines with a ball point pen. An-other preliminary step is to get a dial gauge reading of the datum specimenplaced on to the base pedestal. This datum specimen has a known height(Table A.1). The difference between the datum specimen dial reading andthe dial reading on the actual specimen can then be used to calculate thespecimen height.The water pluviation procedure described by Vaid and Negussey (1988)is used to create saturated triaxial specimens. Figure B.1 through Figure B.3depict the creation of a specimen using water pluviation. These three figureshighlight the main steps in the specimen preparation procedure.224Specimen100 mmRRABCDE FGVacuum regulator set to -18 kPaPressure regulator used to drive de-aired water into thespecimen cavityReservoir 1Reservoir 2Calibratedvolume changeMembraneexpanderBottomo-ringSampleBoiled porousdiscBoiled de-airedwater supply1.  Jet de-aired water through base pedestal to dislodge bubbles (open C E G A) 2.  Place membrane onto base pedestal, partly fill with de-aired water3.  Remove any air trapped between membrane and base pedestal4.  Place bottom o-ring5.  Attached membrane expander, stretch membrane over the lip6.  Apply 15-20 kPa vacuum to membrane expander7.  Place siphon chamber and fill cavity with de-aired water8.  Place boiled porous disc into the specimen cavity at at angle, drop into place9.  Fill sample flask with de-aired water10.  Block end of sample flask, invert, place end into specimen cavity11.  Wait for specimen depositionFigure B.1: Specimen pluviation225100 mmRRABCDE FGVacuum regulator set to -18 kPaCalibratedvolume changeExhaustSiphonchamberSiphon tubeSet screw forsiphon level1.  Place siphon tube end under the water in the siphon chamber2.  Attach a compressed red rubber ball hand pump on the exhaust3.  Release the hand pump to create a slight vaccum in the flask4.  Once the siphon is running remove the hand pump5.  Level the specimen top surface by moving the siphon6.  The specimen top surface should be 3-5mm below the membrane expander7.  The water level should be siphoned until it is just above the specimen8.  Remove the siphon chamberFigure B.2: Specimen siphon226TopCap100 mmRRABCDE FGVacuum regulator set to -18 kPaReservoir 1Reservoir 2Calibratedvolume changeMembrane Top o-ringO-ring expander1.  Place top o-rin expander onto membrane expander2.  Open Reservoir 2 to atmosphere and valves A,D,G 3.  Brake the specimen surface water with the top cap at an angle4.  Place the top cap5.  Roll up the membrane off of the membrane expander6.  Level the top cap7.  Snap the top o-ring off of the o-ring expander8.  Level the top cap9.  Close valve D, attach graduated cylinder (GC)  to 15-20 kPa vacuum10.  Record inital dial gauge reading and GC water level11.  Open valve F to apply a vacuum to the specimen pore water12.  Record dial gauge and GC13.  Remove membrane expander14.  Record dial gauge and GC15.  Measure axial membrane strain using a micrometer 16.  Construct triaxial chamber and fill with water - the chamber must be       vented to fill without pressuring17.  Measure final dial gauge reading18.  Add supply pressure to E/P regulators19.  Float the load cell by adding a downward load on the DAS and        an upward load from the manual regulator20.  Place the triaxial chamber in the apparatus21.  Adjust the LVDT to have maximum linear range22.  Measure final GC reading23.  Shut valve A24.  Attach PWP and Chamber pressure lines25.  Apply a chamber pressure to 20 kPa26.  Open PWP transudcer to the specimen - record first PWP, it should        be between 1 and 5 kPaFigure B.3: Specimen preparation227B.3 Triaxial testing procedureOnce the specimen is in the apparatus the experiment proceeds in four se-quential phases: back pressure saturation, consolidation, ageing, and shear.Back pressure saturation serves two purposes: it provides an indicationof the specimen saturation and it increases the saturation of the specimen.Back pressure saturation is performed by increasing the chamber pressurewhile drainage is closed. The increasing back pressure causes any air in thespecimen or equipment to dissolve, which increases the saturation. B-valuescan be calculated during back pressure saturation steps of increasing hydro-static pressure. If the deviator stress changes during back-pressure satura-tion then the change in the pore water pressure is due to both Skempton’s Aand B parameters. Increasing the hydrostatic pressure requires precise com-puter control of the axial load to maintain a σ1/σ3 ratio of 1.0. B-Valuesare calculated by increasing the hydrostatic pressure by 20 kPa, waitingtwo minutes, and measuring the resulting increase in pore water pressure.The B-Value is the ratio of the increase in pore pressure to the increasein hydrostatic pressure. In an incompressible specimen saturated with anincompressible fluid, the B-Value equals 1.0. An acceptable initial B-Valueis in excess of 0.95 (Vaid, 2009). If the initial B-value is too low then thespecimen will undergo unmeasured volumetric strains during back pressuresaturation. This volumetric strain is a result of the compression of residualair in the pores of the specimen and the increased compressibility of aeratedwater. B-values in excess of 1.0 are indicative of a leaking membrane. Verylow B-values can be measured due to a leak to atmosphere pressure at thebender element in the top cap or along the pore water pressure drainageline.Back pressure saturation was performed until the pore water pressureexceeds 200 kPa. At this point Valve 2 is closed and Valve 3 is opened(see Figure 3.3). The back pressure regulator is adjusted to match the finalpore water pressure measurement. Valve 2 is then opened. The specimenshould not experience any volumetric strain when drainage is open. At thispoint the specimen is open to drainage and should have an effective stress228of approximately 20 kPa for both σ′1 and σ′3. The bender element wires arethen connected and tested prior to the start of consolidation.Consolidation occurs in two sequential stages. First the axial stress isincreased until the desired stress ratio is achieved. Then the computer con-trolled data acquisition system increases both the axial and radial stresses,maintaining the stress ratio, until the desired stress state is achieved. Con-solidation is temporarily paused when discrete bender element testing isperformed.The age phase maintains the specimen boundary conditions for a speci-fied amount of time. There are two ways to maintain the boundary condi-tions. One is to maintain the loads, the other is to maintain the stresses.The specimen experiences volumetric and axial creep strains during ageing.These strains change the cross sectional area of the specimen, resulting in adecreasing axial stress. This can be compensated for with small increases inthe axial load. It is very challenging to maintain a stable ageing environmentwith a feedback control adjusting the loads on the specimen. Consequently,the second approach was adopted and the loads were maintained duringageing.The shear phase loads the specimen to failure along a specified shearpath. The equipment is capable of shearing along three different shear paths:conventional, constant p, and slope 0. The conventional shear path increasesthe axial load until the specimen fails. The constant p shear path maintainsthe mean stress (σ1+2σ33 ) while the deviator stress (σ1 − σ3) is increased.This requires increasing the axial load and decreasing the radial load simul-taneously to maintain the mean stress. This was accomplished in a feedbackloop that estimated the succeeding axial stress and adjusted the chamberpressure accordingly. The slope 0 shear path maintains a constant axialstress while the radial stress is decreased. The axial stress is a combinationof the axial load and the cell pressure. As the computer controlled cell pres-sure is decreased, the axial load must be increased in order to maintain aconstant axial stress.The cell pressure is not adjusted during conventional shear paths. Theaxial load is increased until the specimen fails. The voltage to the chamber229pressure regulator is kept constant. As the specimen experiences volumetricchanges the differential pore water pressure volumetric cylinders change inwater elevation head. These changes are noticeable in the measured porepressure during conventional shear paths. It is possible to compensate forthese changes using the computer controlled cell pressure, but this approachwas not taken in order to match conventional triaxial tests.The equipment limits the extent of the shear phase. The differentialpore water pressure transducer can only handle pore water volume changesthat fit in the cylindrical tubes. The test must be stopped if the specimencontracts or dilates beyond this range. There is also an upper limit on theload cell and on the LVDTs. The LVDTs have a linear range that onceexceeded the interpreted specimen heights are incorrect. The shear phaseends when the specimen fails or the equipment limitations are met.230Appendix CTriaxial data reductionThe initial specimen height is calculated with Equation C.1, where df is thefinal dial reading, dd is the datum dial reading, and datum is the height ofthe datum specimen (see Table A.1).h0 = df − dd + datum (C.1)Equation C.2 is for the height of the unstretched membrane covering thesurface area of the specimen. It is calculated from d3 − dd + datum, theheight of the specimen after the membrane expander has been removed, andεma, the measured membrane axial strain. The measured membrane axialstrain is based on the distortion of markings drawn onto the membrane.hm0 = (d3 − dd + datum) ∗ (1 + εma) (C.2)The initial specimen volume is calculated with Equation C.3. In thisequation ∆v is the measured change in volume using the calibrated glasscylinder (see Table 3.4). This change in volume is taken off of the volumecalculated with the expanded membrane diameter vX (see Table A.1). Thevolume of the specimen when it is within the expanded membrane is basedon the diameter of the expanded membrane and the height of the specimenhX when it is in the expanded membrane. The height of the specimen withinthe membrane expander is found with the first dial reading and datum dial.231hX = di − dd + datumvX = pir2 ∗ hX∆V = gci − gcfv0 = ∆v + vX (C.3)The initial void ratio of the specimen is calculated with Equation C.4,where G is the specific gravity of the material, ρw is the density of waterin g/cm3, v0 is the total volume in cm3, and md is the dry mass in grams.This equation assumes that the specimen is fully saturated.e0 =GS ∗ ρw ∗ v0md− 1 (C.4)The height of the specimen during the test is calculated with Equa-tion C.5. The height is the initial height plus the change in height measuredwith the LVDT sensor. The change in height is calculated form the LVDTcalibration factor (see Table 3.4) and ∆volts, which is the change in voltsfrom the zero to current reading. The pore water pressure, chamber pres-sure, load cell, and measured change in volume are all calculated with similarequations.h = h0 + Clvdt ∗ (∆volts) (C.5)The volume of the specimen is calculated with Equation C.6, where vmis the membrane penetration volume. As the membrane penetrates intothe specimen due to the confining pressure it causes water to be drainedfrom the specimen without a corresponding volume loss of the soil skeleton.This systematic error must be corrected to calculate the volume of the soilskeleton.v = v0 + Cdpwpt ∗ (∆volts)− vm (C.6)Equation C.7 is used to calculate the membrane penetration volume.The membrane penetration constant, mp, depends on the membrane andsoil particles, and is in Table A.1. The circumferential surface area of the232specimen is pi ∗ d ∗ h, where d is the diameter of the specimen.vm = mp ∗ (pi ∗ d ∗ h) ∗ log10(cell − pwp) (C.7)Equation C.8 is for the diameter of the specimen. Note that a dependency-circle has been created, the diameter equation(Equation C.8) requires thespecimen volume (Equation C.6) and the specimen volume equation requiresthe diameter(through the membrane penetration Equation C.7). The solu-tion taken to this problem was to use the previous time steps membranepenetration value to estimate the volume and diameter - then calculate thevolume and membrane penetration with these estimates. This solution alsoassumes that there is no membrane penetration in the first time step - whenthe confining pressures are low.d = 2√vhpi(C.8)Equation C.9 is the axial strain in the membrane at any point duringthe test based on the specimen height (Equation C.5) and initial membraneheight (Equation C.2).εma =(hm0 − h)hm0(C.9)Equation C.10 is the radial strain experienced by the membrane, wheredm is the unstretched membrane diameter (see Table A.1).εmr =dm − ddm(C.10)Equation C.11 is the volumetric strain of the membrane cavity.εmv = εma + 2 ∗ εmr (C.11)Equation C.12 is the radial stress contribution on the specimen due tothe deformed elastic membrane, where Em is the Young’s modulus of themembrane and tm is the thickness of the membrane shell (see Table A.1).Equation C.13 is the axial stress contribution on the specimen due to the233deformed elastic membrane.σmr =−4Emtm(2 + εmv + εma)εmv3dm(2− εmv) + εma(C.12)σma =−4Emtm(2 + εmv + εma)(3εma + epsilonmv)3dm(2− εmv) + εma(C.13)Equation C.14 is the effective radial stress acting on the specimen. Thestresses in this equation are all acting on the cylindrical surface area of thespecimen.σ′r = cell − pwp+ σmr (C.14)Equation C.15 is the cross sectional area of the specimen.ac = pi(d2)2(C.15)Equation C.16 is the downward axial pressure applied by the combinationof chamber pressure downwards on the top cap and pore water pressureupwards. The chamber pressure exerts over an area of (ac − ar) where ac isthe cross section area from Equation C.15 and ar is the area of the drivingrod (see Table A.1).σc =cell(ac − ar)− pwp(ac)ac(C.16)Equation C.17 is the effective axial stress on the specimen, where theload cell, mass, ram friction, and dry weight are all in kilograms. Whenmultiplied by gravity (9.81 m/s2) the result is newtons, which are thendivided by 1000 to get kilo-newtons.σ′a =(loadCell + 0.5wd + capMass+ ramFriction) ∗ 9.811000 + acσma + acσcac(C.17)Equation C.18 through Equation C.21 calculate the axial strain, volu-metric strain, radial strain, and shear strain from reference height hr andvolume vr in percent. The reference height and volume may be taken as the234initial specimen properties or from the start of a phase of testing (consoli-dation, age, shear).εa =hr − hhr∗ 100 (C.18)εv =vr − vvr∗ 100 (C.19)εr =εv − εa2(C.20)εq =23(εa − εr) (C.21)Equations C.22 and C.23 are the deviator stress and mean stress.q = σ′a − σ′r (C.22)p′ =σ′a + 2σ′r3(C.23)Equation C.24 calculates the secant shear modulus. In this equation εqis divided by 100 if it is in percent. Note that the units of Gsec will be thesame units as q, so it is often divided by 1000 to get MPa.Gsec =∆q3εq/100(C.24)235Appendix DTriaxial ResultsThis appendix contains results from this investigation as well as Shozen(2001) and Lam (2003). The past results from Shozen (2001) and Lam(2003) were complemented with the empirical G0 equation in order to build alarger empirical dataset for drawing conclusions on the shape of the Gsec/G0normalized stiffness curves.D.1 Results from this studyD.1.1 Summarized creep strainsA certain amount of creep strain will occur with out without increasing theshear stress. When the shear phase occurs after short age durations, themagnitude of the continued creep strains are comparable to the observablesmall-strain measurements. Uncorrected, this will decrease the measuredGsec over small strains and make it difficult to compare the stiffness be-tween different age durations. This effect can be corrected by projectingthe developed creep strains during ageing through the shear phase. Theseprojected creep deformations are subtracted from the axial and volumetricdisplacements prior to calculating q and Gsec. For specimens that haveundergone over 100 minutes of ageing, this correction becomes negligible(Lam, 2003; Shozen, 2001).236To correct for continued creep strains after short age durations, the creepstrain rates need to be characterized. After consolidation the applied axialload and chamber pressure are kept constant for an age phase of up to 1000minutes. Creep strains occur during this phase - a continued deformationof the specimen without a significant change in the imposed effective stressstate. During ageing, the data acquisition system maintains constant axialload and chamber pressure to avoid instability. The imposed boundarycondition constants are maintained by applying a constant voltage to thetwo electronic pressure regulators. Soil creep will change the dimensions ofthe soil specimen. Creep strains that result in radial contraction or extensionchange the cross-section area of the specimen. This changes the calculatedstress for a constant axial load. Contractive volumetric strains will increasethe water head measured with the DPWPT sensor. This slightly increasesthe back pressure, and therefore reduces both the radial and axial effectivestress.Despite efforts to maintain stability during ageing, sensor drift was ob-served in some experiments. The creep strains were very small -e.g. from0.008mm to 0.088mm of axial displacement per log-cycle of age time. Anysensor drift often completely obscured the magnitude of the creep strains.Loss of stability was found to be related to the environmental conditions.Many tests were not affected and stability was maintained throughout age-ing. To quantify the log-linear creep strain behaviour the median of thetabulated creep strain rates for the full dataset were calculated. This metricis not sensitive to outliers that may have occurred due to sensor drift duringageing. Table D.1 and Table D.2 provide the median value of developedcreep strains for loose specimens for age times up to 1000 minutes.The developed creep strains quickly, but not immediately, become linearon a log-time scale. The medians of the log-linear slopes are detailed inTable D.3. This table is the amount of creep strain per log cycle of timefor each tested stress ratio. The axial creep strains increase with increasingstress ratio. The volumetric strains increase, but are not as sensitive tostress ratio. The radial and shear strains are derived from the calculatedaxial and volumetric strains. The radial strains decrease with stress ratio237Table D.1: Developed axial creep strains (%) for loose specimens withσ′r = 100 kPaDeveloped axial creep strains (%)Stress ratio (increasing axial stress)Minutes 1.0 1.6 2.0 2.1 2.5 2.81 0.01 0.01 0.03 0.03 0.05 0.0710 0.01 0.03 0.07 0.06 0.09 0.14100 0.02 0.04 0.10 0.09 0.14 0.211000 0.02 0.05 0.14 0.12 0.19 0.28Table D.2: Developed volumetric (%) creep strains for loose speci-mens with σ′r = 100 kPaDeveloped volumetric creep strains (%)Stress ratio (increasing mean stress)Minutes 1.0 1.6 2.0 2.1 2.5 2.81 0.03 0.02 0.04 0.03 0.04 0.0410 0.05 0.05 0.07 0.06 0.08 0.07100 0.08 0.07 0.11 0.10 0.12 0.111000 0.10 0.09 0.15 0.13 0.16 0.14through a transition from compression to extension at K0. The magnitudeof the creep shear strains increase with stress ratio.Table D.3: Developed creep strains (%) per log-cycle of age time forloose specimens with σ′r = 100 kPaStress ratio1.0 1.6 2.0 2.1 2.5 2.8a% 0.006 0.013 0.035 0.029 0.046 0.071v% 0.026 0.023 0.037 0.032 0.041 0.036r% 0.010 0.005 0.001 0.002 -0.003 -0.017q% -0.003 0.005 0.022 0.018 0.033 0.059The values listed in Table D.3 were used to perform creep-strain correc-tions for calculating Gsec.238D.1.2 Triaxial results239−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.0114−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.35700.10.2ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)40 60 80 100 1200200400600σ’3 (kPa)σ’ 1 (kPa)ID: styler−052.lvmeshear=0.909σ’a=200.9kPaσ’r=99.8kPaage=1000.0minConventional0100200∆ q (kPa)Shearε v (%)Compressionεv=0.38%, εq=2.46%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.62εr=0.0084%εe=0.0021%Gsec/G0Figure D.1: Styler-052.lvm: σa = 200.9 kPa, σr = 99.8 kPa,age=1000.0 min, Stress path=C240−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0472−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.39400.10.2ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−059.lvmeshear=0.879σ’a=200.9kPaσ’r=100.0kPaage=1000.2minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.01%, εq=0.02%Compressionεv=0.23%, εq=1.93%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.71εr=0.0073%εe=0.0021%Gsec/G0Figure D.2: Styler-059.lvm: σa = 200.9 kPa, σr = 100.0 kPa,age=1000.2 min, Stress path=P241−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0756−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.58800.10.2ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−060.lvmeshear=0.915σ’a=201.6kPaσ’r=100.1kPaage=1000.0minSlope ?01020∆ q (kPa)Shear−0.5ε v (%)Dilationεv=−0.29%, εq=2.08%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=2.3εr=0.0022%εe=0.002%Gsec/G0Figure D.3: Styler-060.lvm: σa = 201.6 kPa, σr = 100.1 kPa,age=1000.0 min, Stress path=?242−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0416−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.40600.51ε a (%)Creep εa (%)1 10 100 10000.51ε v (%)Creep εv (%)time (min)0 50 100 150−2000200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−061.lvmeshear=0.858σ’a=200.8kPaσ’r=100.0kPaage=1000.0minConstant P0100200∆ q (kPa)Shear0ε v (%)Dilationεv=−0.01%, εq=0.02%Compressionεv=0.21%, εq=1.84%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.63εr=0.0042%εe=0.0021%Gsec/G0Figure D.4: Styler-061.lvm: σa = 200.8 kPa, σr = 100.0 kPa,age=1000.0 min, Stress path=P243−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0571−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.43100.51ε a (%)Creep εa (%)1 10 100 10000.51ε v (%)Creep εv (%)time (min)0 50 100 150−2000200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−067.lvmeshear=0.884σ’a=200.9kPaσ’r=100.1kPaage=1000.0minConstant P0100200∆ q (kPa)Shear0ε v (%)Dilationεv=−0.01%, εq=0.02%Compressionεv=0.12%, εq=1.14%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.65εr=0.0056%εe=0.0021%Gsec/G0Figure D.5: Styler-067.lvm: σa = 200.9 kPa, σr = 100.1 kPa,age=1000.0 min, Stress path=P244−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.134−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.41600.050.1ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−070.lvmeshear=0.842σ’a=200.8kPaσ’r=100.2kPaage=1000.2minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.02%, εq=0.03%Compressionεv=0.14%, εq=1.30%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.7εr=0.0063%εe=0.0021%Gsec/G0Figure D.6: Styler-070.lvm: σa = 200.8 kPa, σr = 100.2 kPa,age=1000.2 min, Stress path=P245−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.174−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.48200.20.4ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−073.lvmeshear=0.873σ’a=281.0kPaσ’r=100.0kPaage=1000.3minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.06%, εq=2.03%Compressionεv=0.01%, εq=0.74%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.75εr=0.0044%εe=0.0021%Gsec/G0Figure D.7: Styler-073.lvm: σa = 281.0 kPa, σr = 100.0 kPa,age=1000.3 min, Stress path=P246−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0777−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.3300.05ε a (%)Creep εa (%)1 10 1000.05ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−090.lvmeshear=0.871σ’a=200.6kPaσ’r=100.3kPaage=10.0minConventional0100200∆ q (kPa)Shearε v (%)Compressionεv=0.47%, εq=2.48%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.46εr=0.0019%εe=0.002%Gsec/G0Figure D.8: Styler-090.lvm: σa = 200.6 kPa, σr = 100.3 kPa,age=10.0 min, Stress path=C247−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.087−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.38800.050.1ε a (%)Creep εa (%)1 10 1000.05ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−091.lvmeshear=0.894σ’a=200.8kPaσ’r=100.1kPaage=10.0minConstant P050100∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.23%, εq=1.67%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.64εr=0.0046%εe=0.0021%Gsec/G0Figure D.9: Styler-091.lvm: σa = 200.8 kPa, σr = 100.1 kPa,age=10.0 min, Stress path=P248−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.114−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.32200.05ε a (%)Creep εa (%)1 10 1000.05ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400600σ’3 (kPa)σ’ 1 (kPa)ID: styler−093.lvmeshear=0.876σ’a=200.7kPaσ’r=100.3kPaage=10.0minConventional0200400∆ q (kPa)Shearε v (%)Compressionεv=0.49%, εq=2.51%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.52εr=0.0033%εe=0.002%Gsec/G0Figure D.10: Styler-093.lvm: σa = 200.7 kPa, σr = 100.3 kPa,age=10.0 min, Stress path=C249−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.161−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.44400.51ε a (%)Creep εa (%)1 10 1000.51ε v (%)Creep εv (%)time (min)0 50 100 1500100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−097.lvmeshear=0.88σ’a=200.7kPaσ’r=100.3kPaage=10.1minSlope −0.5050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.03%, εq=0.03%Compressionεv=0.06%, εq=0.86%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.64εr=0.0031%εe=0.002%Gsec/G0Figure D.11: Styler-097.lvm: σa = 200.7 kPa, σr = 100.3 kPa,age=10.1 min, Stress path=-0.5250−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0896−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.44900.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−100.lvmeshear=0.893σ’a=200.8kPaσ’r=99.9kPaage=1000.0minSlope −0.5050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.04%, εq=0.06%Compressionεv=0.05%, εq=0.94%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.7εr=0.0048%εe=0.0021%Gsec/G0Figure D.12: Styler-100.lvm: σa = 200.8 kPa, σr = 99.9 kPa,age=1000.0 min, Stress path=-0.5251−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0806−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.39200.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−103.lvmeshear=0.915σ’a=200.8kPaσ’r=100.0kPaage=1000.3minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.02%, εq=0.03%Compressionεv=0.23%, εq=2.00%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.71εr=0.0075%εe=0.0021%Gsec/G0Figure D.13: Styler-103.lvm: σa = 200.8 kPa, σr = 100.0 kPa,age=1000.3 min, Stress path=P252−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0973−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.32900.10.2ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)0 50 100 1500200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−108.lvmeshear=0.918σ’a=200.7kPaσ’r=99.9kPaage=1000.3minConventional0100200∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.55%, εq=3.43%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.69εr=0.013%εe=0.0022%Gsec/G0Figure D.14: Styler-108.lvm: σa = 200.7 kPa, σr = 99.9 kPa,age=1000.3 min, Stress path=C253−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.117−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.39600.050.1ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)0 50 100 1500100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−112.lvmeshear=0.914σ’a=200.9kPaσ’r=100.0kPaage=100.3minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.01%, εq=0.02%Compressionεv=0.21%, εq=1.61%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.7εr=0.0069%εe=0.0021%Gsec/G0Figure D.15: Styler-112.lvm: σa = 200.9 kPa, σr = 100.0 kPa,age=100.3 min, Stress path=P254−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0938−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.46700.10.2ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−116.lvmeshear=0.913σ’a=200.6kPaσ’r=99.9kPaage=1000.3minSlope 0050∆ q (kPa)Shear0ε v (%)Dilationεv=−0.04%, εq=0.08%Compressionεv=0.03%, εq=0.91%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.75εr=0.005%εe=0.0021%Gsec/G0Figure D.16: Styler-116.lvm: σa = 200.6 kPa, σr = 99.9 kPa,age=1000.3 min, Stress path=0255−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.178−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.53100.20.4ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)0 50 100 1500100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−120.lvmeshear=0.891σ’a=280.2kPaσ’r=100.0kPaage=1000.0minSlope 002040∆ q (kPa)Shear−0.5ε v (%)Dilationεv=−0.13%, εq=2.02%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.8εr=0.0028%εe=0.002%Gsec/G0Figure D.17: Styler-120.lvm: σa = 280.2 kPa, σr = 100.0 kPa,age=1000.0 min, Stress path=0256−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.177−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.47400.20.4ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−122.lvmeshear=0.891σ’a=280.4kPaσ’r=100.0kPaage=1000.0minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.04%, εq=2.01%Compressionεv=0.02%, εq=0.92%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.75εr=0.0042%εe=0.0021%Gsec/G0Figure D.18: Styler-122.lvm: σa = 280.4 kPa, σr = 100.0 kPa,age=1000.0 min, Stress path=P257−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.183−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.4400.20.4ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−123.lvmeshear=0.875σ’a=279.6kPaσ’r=99.8kPaage=1000.0minConventional0100200∆ q (kPa)Shearε v (%)Compressionεv=0.14%, εq=1.96%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.72εr=0.0067%εe=0.0021%Gsec/G0Figure D.19: Styler-123.lvm: σa = 279.6 kPa, σr = 99.8 kPa,age=1000.0 min, Stress path=C258−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.195−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.47500.20.4ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)0 50 100 1500200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−124.lvmeshear=0.893σ’a=280.2kPaσ’r=100.0kPaage=1000.0minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.04%, εq=0.09%Compressionεv=0.02%, εq=0.97%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.73εr=0.0033%εe=0.002%Gsec/G0Figure D.20: Styler-124.lvm: σa = 280.2 kPa, σr = 100.0 kPa,age=1000.0 min, Stress path=P259−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.19−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.48400.20.4ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)0 50 100 1500100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−125.lvmeshear=0.895σ’a=279.0kPaσ’r=99.6kPaage=100.0minSlope 002040∆ q (kPa)Shear−0.5ε v (%)Dilationεv=−0.05%, εq=0.13%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.73εr=0.0013%εe=0.002%Gsec/G0Figure D.21: Styler-125.lvm: σa = 279.0 kPa, σr = 99.6 kPa,age=100.0 min, Stress path=0260−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = −0.295−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.46012ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)0 50 100 1500200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−126.lvmeshear=0.899σ’a=280.0kPaσ’r=99.9kPaage=100.0minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.03%, εq=0.05%Compressionεv=0.05%, εq=1.07%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.71εr=0.0028%εe=0.002%Gsec/G0Figure D.22: Styler-126.lvm: σa = 280.0 kPa, σr = 99.9 kPa,age=100.0 min, Stress path=P261−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0995−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.39200.10.2ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−129.lvmeshear=0.884σ’a=200.7kPaσ’r=99.9kPaage=999.9minConstant P050100∆ q (kPa)Shear0ε v (%)Dilationεv=−0.01%, εq=0.03%Compressionεv=0.21%, εq=1.70%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.69εr=0.0065%εe=0.0021%Gsec/G0Figure D.23: Styler-129.lvm: σa = 200.7 kPa, σr = 99.9 kPa,age=999.9 min, Stress path=P262−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.11−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.32400.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)0 50 100 1500200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−245eshear=0.968σ’a=199.7kPaσ’r=100.3kPaage=100.0minConventional0100200∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.59%, εq=3.54%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.7εr=0.018%εe=0.0022%Gsec/G0Figure D.24: Styler-245: σa = 199.7 kPa, σr = 100.3 kPa, age=100.0min, Stress path=C263−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0872−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.29900.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)0 50 100 1500200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−246eshear=0.989σ’a=199.2kPaσ’r=100.2kPaage=100.0minConventional0100200∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.69%, εq=3.77%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.59εr=0.0072%εe=0.0021%Gsec/G0Figure D.25: Styler-246: σa = 199.2 kPa, σr = 100.2 kPa, age=100.0min, Stress path=C264−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0694−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.32700.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)0 50 100 1500200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−247eshear=0.959σ’a=198.3kPaσ’r=99.9kPaage=100.0minConventional0100200∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.66%, εq=4.11%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.63εr=0.0094%εe=0.0021%Gsec/G0Figure D.26: Styler-247: σa = 198.3 kPa, σr = 99.9 kPa, age=100.0min, Stress path=C265−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0596−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.29500.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−248eshear=0.972σ’a=195.9kPaσ’r=100.3kPaage=100.0minConventional0100200∆ q (kPa)Shear0ε v (%)Dilationεv=−0.00%, εq=0.00%Compressionεv=0.81%, εq=4.69%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.58εr=0.0058%εe=0.0021%Gsec/G0Figure D.27: Styler-248: σa = 195.9 kPa, σr = 100.3 kPa, age=100.0min, Stress path=C266−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0622−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.30100.10.2ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−261eshear=0.962σ’a=198.4kPaσ’r=100.0kPaage=102.2minConventional0100200∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.72%, εq=4.27%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.61εr=0.0077%εe=0.0021%Gsec/G0Figure D.28: Styler-261: σa = 198.4 kPa, σr = 100.0 kPa, age=102.2min, Stress path=C267−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0358−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.30200.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−262eshear=0.96σ’a=199.1kPaσ’r=100.1kPaage=102.5minConventional0100200∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.70%, εq=3.34%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.55εr=0.0056%εe=0.0021%Gsec/G0Figure D.29: Styler-262: σa = 199.1 kPa, σr = 100.1 kPa, age=102.5min, Stress path=C268−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.169−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.29700.050.1ε a (%)Creep εa (%)1 10 100 10000.050.1ε v (%)Creep εv (%)time (min)90 95 100 105100200300400σ’3 (kPa)σ’ 1 (kPa)ID: styler−275eshear=0.953σ’a=199.3kPaσ’r=100.3kPaage=100.0minConstant P0100200∆ q (kPa)Shear0.5ε v (%)Compressionεv=0.71%, εq=3.95%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.58εr=0.0057%εe=0.0021%Gsec/G0Figure D.30: Styler-275: σa = 199.3 kPa, σr = 100.3 kPa, age=100.0min, Stress path=P269−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 1.6−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.19800.020.04ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)0 50 100 1500200400σ’3 (kPa)σ’ 1 (kPa)ID: styler−277eshear=0.974σ’a=100.2kPaσ’r=100.2kPaage=100.0minConstant P0200400∆ q (kPa)Shear1ε v (%)Compressionεv=1.23%, εq=5.05%0.01% 0.1% 1% 10%0.30.50.7εq(%)=2/3(εa−εr)Gsec/G0 = (1+((εq−εe)/εr)a)−1a=0.63εr=0.028%εe=0.0023%Gsec/G0Figure D.31: Styler-277: σa = 100.2 kPa, σr = 100.2 kPa, age=100.0min, Stress path=P270−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Consolidationεa/εr = 0.0906−100 −50 0 50 1000100200∆σr’ (kPa)∆σa’ (kPa)−0.5 0 0.500.51εr (%)ε a (%)Shearεa/εr = −0.25700.10.2ε a (%)Creep εa (%)1 10 100 10000.10.2ε v (%)Creep εv (%)time (min)20 40 60 80 100 1200100200300σ’3 (kPa)σ’ 1 (kPa)ID: styler−290eshear=0.987σ’a=198.3kPaσ’r=100.0kPaage=100.0minConventional050100∆ q (kPa)Shear0.2ε v (%)Compressionεv=0.24%, εq=0.44%0.01% 0.1% 1% 10%0.30.50.7Figure D.32: Styler-290: σa = 198.3 kPa, σr = 100.0 kPa, age=100.0min, Stress path=C271Figure D.33: Styler-002: σa = 199.5 kPa, σr = 100.2 kPa, age=100.0min, Stress path=C272Figure D.34: Styler-004: σD.2 Results from Lam (2003)298

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