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Energy transfer and grain size effects during the Standard Penetration Test (SPT) and Large Penetration… Daniel, Christopher Ryan 2008

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ENERGY TRANSFER AND GRAIN SIZE EFECTS DURING THE STANDARD PENETRATION TEST (SPT) AND LARGE PENETRATION TEST (LPT)   by  CHRISTOPHER RYAN DANIEL  B.A.Sc., The University of British Columbia, 1997 M.A.Sc., The University of British Columbia, 2000      A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY   in   THE FACULTY OF GRADUATE STUDIES  (Civil Engineering)       THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)       April, 2008  © Christopher Ryan Daniel, 2008   ii ABSTRACT  The Standard Penetration Test (SPT) is the most widely used in-situ soil test in the world. “Large Penetration Test” (LPT) is a term used to describe any scaled up version of the SPT. Several types of LPT have been developed around the world for the purpose of characterizing gravel deposits, as SPT blow counts are less reliable in gravels than in sands.  Both tests suffer from the lack of a reliable means of determining transferred energy.  Further, the use of LPT blow counts is generally limited to calculation of equivalent SPT blow counts using correlation factors measured in sands.  Variation of LPT blow counts with grain size is assumed to be negligible. This research shows that safety hammer energies can be reliably estimated from measurements of hammer impact velocity for both SPT and LPT.  This approach to determining transferred energy is relatively simple, and avoids the primary limitation of existing methods, which is the inability to calibrate the instrumentation. Transferred energies and hammer impact velocities are collected from various sources. These data are used to determine the ratio between the hammer kinetic energy and the transferred energy (energy transfer ratio, ETR), which is found to follow a roughly Normal distribution for the various hammers represented.  An assessment of uncertainty is used to demonstrate that an ETR based approach could be superior to existing energy measurement methods. SPT grain size effects have primarily been characterized as the variation of an empirical relative density correlation factor, (CD)SPT, with mean grain size.  In this thesis, equivalent (CD)LPT data are back-calculated from measured SPT-LPT correlation factors (CS/L).  Results of a numerical study suggest that SPT and LPT grain size effects should be similar and related to the ratio of the sample size to the mean grain size.  Based on this observation, trend-lines with the same shape as the (CD)SPT trend-line are established for the back-calculated (CD)LPT data.  A method for generating the grain size effect trend-line for LPT is then proposed.  These trend lines provide a rational approach to direct interpretation of LPT data, or to improved prediction of equivalent SPT blow counts.   iii TABLE OF CONTENTS   ABSTRACT................................................................................................................................... ii TABLE OF CONTENTS ............................................................................................................ iii LIST OF TABLES ...................................................................................................................... vii LIST OF FIGURES ..................................................................................................................... ix LIST OF SYMBOLS ................................................................................................................. xvi ACKNOWLEDGMENTS .......................................................................................................... xx 1. INTRODUCTION............................................................................................................. 1  1.1 GENERAL ............................................................................................................. 1   1.1.1 Energy Effects............................................................................................ 1   1.1.2 Grain Size Effects ...................................................................................... 5  1.2 RESEARCH OBJECTIVES ................................................................................ 6  1.3 THESIS ORGANIZATION ................................................................................. 6 2. SPT ENERGY AND GRAIN SIZE EFFECTS IN THE LITERATURE.................... 8  2.1 ENERGY CORRECTION ................................................................................... 8   2.1.1 Typical Values............................................................................................ 9   2.1.2 Direct Measurement ................................................................................ 11  2.2 GRAIN SIZE EFFECTS .................................................................................... 16   2.2.1 Fundamental Grain Size Effects ............................................................ 19   2.2.2 Relative Density Correlations................................................................. 21   2.2.3 SPT-CPT Correlations ............................................................................ 38   2.2.4 SPT-LPT Correlations ............................................................................ 41  2.3 CHAPTER SUMMARY ..................................................................................... 48 3. ENERGY TRANSFER RATIO APPROACH TO ENERGY CORRECTION........ 49  3.1 BACKGROUND ................................................................................................. 49  3.2 HISTORY OF THE ENERGY TRANSFER RATIO...................................... 51  3.3 CHAPTER SUMMARY ..................................................................................... 62 4. SAFETY HAMMER ENERGY TRANSFER RATIO DATABASE ......................... 63  4.1 GENERAL ........................................................................................................... 63  4.2 DATA FROM THE LITERATURE ................................................................. 63  4.3 FIELD STUDIES ................................................................................................ 66   iv  4.4 DISTRIBUTION OF ETR DATA ..................................................................... 70  4.5 ANALYSIS OF POTENTIAL CORRELATIONS .......................................... 75   4.5.1 Effect of Rod Type................................................................................... 76   4.5.2 Effect of Anvil Weight............................................................................. 78   4.5.3 Effect of Rod Length ............................................................................... 78   4.5.4 Effect of Test Type .................................................................................. 81   4.5.5 Effect of Blow Count ............................................................................... 81  4.6 CHAPTER SUMMARY ..................................................................................... 88 5. COMPARISON OF ENERGY MEASUREMENT APPROACHES......................... 89  5.1 INTRODUCTION ............................................................................................... 89  5.2 QUANTIFYING UNCERTAINTY ................................................................... 89   5.2.1 Taylor Series Expansion ......................................................................... 91   5.2.2 Application to SPT and LPT Blow Counts ........................................... 91  5.3 UNCERTAINTY OF AVERAGE ROD ENERGY RATIO ........................... 94   5.3.1 “Typical” Rod Energy Ratios................................................................. 96   5.3.2 Directly Measured Rod Energy Ratios.................................................. 97   5.3.3 Energy Transfer Ratio Approach .......................................................... 97  5.4 DISCUSSION .................................................................................................... 102   5.4.1 Comparison of Energy Correction Procedures .................................. 102   5.4.2 Recommended Procedure and Sample Application........................... 104  5.5 CHAPTER SUMMARY ................................................................................... 107 6. GRAIN SIZE EFFECT DATA .................................................................................... 108  6.1 INTRODUCTION ............................................................................................. 108  6.2 (CD) GRAIN SIZE EFFECTS .......................................................................... 108   6.2.1 Calibration Chamber Studies............................................................... 108   6.2.2 Field Measurements .............................................................................. 114   6.2.3 Discussion ............................................................................................... 114  6.3 (CS/L) GRAIN SIZE EFFECTS ........................................................................ 125   6.3.1 Available Methods for Prediction of SPT-LPT     Correlation Factors .............................................................................. 133   6.3.2 Comparison of (CS/L) Data for Different Types of LPT..................... 135   6.3.3 Discussion ............................................................................................... 137  6.4 DISCUSSION .................................................................................................... 138   v   6.4.1 Uncertainty............................................................................................. 138   6.4.2 Assessment of Existing Grain Size Effect Relationships.................... 139  6.5 CHAPTER SUMMARY ................................................................................... 143 7. NUMERICAL STUDY OF PLUGGING AND GRAIN SIZE EFFECTS............... 144  7.1 INTRODUCTION ............................................................................................. 144   7.1.1 Finite vs. Distinct Elements .................................................................. 144   7.1.2 Methodology........................................................................................... 146  7.2 SINGLE PLATEN SIMULATIONS ............................................................... 149   7.2.1 Simulation Details.................................................................................. 149   7.2.2 Effect of Particle Size on Penetration Energy..................................... 150   7.2.3 Effect of Particle Size on Shear Zone Development ........................... 154 7.3 DUAL PLATEN SIMULATIONS ................................................................... 159   7.3.1 Simulation Details.................................................................................. 159   7.3.2 Effect of Platen Spacing on Plugging................................................... 159   7.3.3 Effect of Particle Size on Plugging ....................................................... 167   7.3.4 Effect of Particle Size on Penetration Energy..................................... 174  7.4 DISCUSSION .................................................................................................... 178   7.4.1 Major Findings ...................................................................................... 178   7.4.2 Limitations ............................................................................................. 179   7.4.3 Preliminary Comparison of Experimental and Numerical    Grain Size Effects ................................................................................. 180  7.5 CHAPTER SUMMARY ................................................................................... 183 8. PREDICTION OF LPT GRAIN SIZE EFFECTS .................................................... 185  8.1 INTRODUCTION ............................................................................................. 185  8.2 INVERSION OF (CS/L) DATA......................................................................... 185   8.2.1 Measurement Uncertainty .................................................................... 186   8.2.2 Inverted Data ......................................................................................... 188   8.2.3 Discussion ............................................................................................... 194  8.3 PREDICTION OF GRAIN SIZE EFFECT TRENDS .................................. 196  8.4 DISCUSSION .................................................................................................... 199   8.4.1 Procedure for Predicting LPT Grain Size Effects.............................. 199   8.4.2 SPT-LPT Correlation Trends and Selection of LPT Equipment ..... 199   8.4.3 Illustrative Example – “Hypothetical” Large Penetration Test ....... 203   vi   8.4.4 Illustrative Example – Liquefaction Susceptibility Trends ............... 207  8.5 CHAPTER SUMMARY ................................................................................... 212 9. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH...............................................................................................215  9.1 RESEARCH SUMMARY ................................................................................ 215  9.2 ETR APPROACH TO ENERGY CORRECTION ....................................... 215  9.3 PREDICTION OF LPT GRAIN SIZE EFFECTS ........................................ 217  9.4 RECOMMENDATIONS FOR FURTHER RESEARCH............................. 218 BIBLIOGRAPHY ................................................................................................................. 220 Appendix A  –  Stress Wave Formation and Propagation in Safety and    Donut Hammers .............................................................................................229 Appendix B  – Summary of Patterson Park Test Program .................................................238 Appendix C – Energy Transfer Ratio Data..........................................................................247 Appendix D  – CRIEPI Calibration Chamber Data ............................................................287 Appendix E – Field Measurements of (CD) ..........................................................................300 Appendix F  – Distinct Element Method (DEM) Simulation Details .................................307   vii LIST OF TABLES  2.1 Rod energy ratios from the literature (Howie et al., 2003) .................................................9  2.2 Summary of relative density correlation grain size effect relationships ...........................36  2.3 Properties of KJ and T-gravels..........................................................................................38  2.4 Test details of the SPT and two types of LPT...................................................................44  3.1 ETR data presented by Schmertmann and Palacios (1979) ..............................................53  4.1 Sources of directly measured safety hammer ETR values ................................................64  4.2 Details of studies performed during the course of this research ......................................67  4.3 Nominal details of SPT, NALPT and RLPT.....................................................................68  4.4 Statistical summary of safety hammer ETR database .......................................................71  4.5 Summary of available rod type information......................................................................76  4.6 Summary of data subset for which ETRm measurements are available ............................86  5.1 Monte Carlo simulation and Taylor series expansion estimates of variability for ETR estimated (ERr) values ............................................................................................100  5.2 Reduction of Ω(ERr)avg with (N) for ETR approach .......................................................101  5.3 Estimated values of Ω(ERr)avg and corresponding values of Ω(N60) ..............................102  5.4 Data and calculations for sample application of recommended procedure.....................106  6.1 WES and CRIEPI calibration chamber test details and results .......................................109  6.2 Short rod correction factors from the literature (after: Daniel et al., 2005)....................111  6.3 Summary of available (CD) measurements......................................................................115  6.4 Test details for the SPT and several types of LPT ..........................................................126  6.5 Summary of available (CS/L) measurements....................................................................128  6.6 Comparison of expected and observed uncertainty of (CD) and (CS/L) ...........................139  7.1 Details of PFC2D samples used during particle size effect study...................................150  7.2 Estimated shear zone thickness for single platen simulations.........................................156   viii  7.3 Extrapolation of single platen penetration energies ........................................................176  8.1 Best-fit lines for SPT and back-calculated LPT (CD) data ..............................................194  8.2 Modified best-fit lines for SPT and back-calculated LPT (CD) data...............................196  8.3 Relationship between fines content and mean grain size ................................................207     ix LIST OF FIGURES  1.1 Standard SPT split spoon sampler (ASTM D1586-84).......................................................2  1.2 (a) Simple, (b) safety and (c) donut type SPT hammers .....................................................4  2.1 Illustration of (a) the rope and cathead method used with a donut hammer (Robertson et al., 1992, adapted from Kovacs and Salomone, 1982) and (b) a “Dando” trip release hammer that could be lifted using a rope and cathead or a winched cable (Clayton, 1990)..........................................................................................10  2.2 Typical force and velocity data recorded using research quality equipment during an SPT performed at 13.7 m depth (ERr = 0.59, (ERr)avg = 0.56, N = 18, N60 = 17). .......14  2.3 Relationship between selected accelerometer baseline and resulting FV energy for data shown in Figure 2.2. ..................................................................................................15  2.4 Comparison of grain size classification schemes adopted for British Code  of Practice and Unified Soil Classification System...........................................................17  2.5 Sample grain size distribution curves (after: Craig, 1994) ...............................................18  2.6 Increase of sand-steel interface friction angle (δ) with increasing surface roughness (Rmax) and decreasing mean grain size from simple shear tests.  (after: Uesugi et al., 1988)............................................................................................................................20  2.7 Radiograph image showing development of low-density shear zones (light areas) during trap-door tests for sample with mean grain size of 0.4 mm (after: Stone and Muir Wood, 1992).............................................................................................................22  2.8 Empirical correlation between SPT blows per 152 mm (6”) and soil density (Burmister, 1962) ..............................................................................................................24  2.9 Variation of (N1)60/Dr2 with mean grain size (after: Skempton, 1986).  In-situ soil densities determined primarily from conventional samples..............................................26  2.10 Revised interpretation of Skempton (1986) data by Kulhawy and Mayne (1990). NC = Normally Consolidated............................................................................................27  2.11 Aging effect observed by Kulhawy and Mayne (1990) ....................................................29  2.12 Variation of (CD)78 with mean grain size (after: Cubrinovski and Ishihara, 1999). In-situ soil densities determined primarily from frozen samples ......................................30  2.13 Empirical correlations between void ratio range (emax – emin) and mean grain size (Cubrinovski and Ishihara, 1999)......................................................................................32     x 2.14 Empirical correlation between (CD)78 and void ratio range (after: Cubrinovski and Ishihara, 1999)...................................................................................................................33  2.15 Variation of (CD) with mean grain size (after: Chen, 2004).  In-situ soil densities determined from either frozen or conventional samples ...................................................35  2.16 Cross-section of a typical modern electric piezocone (after: Davies, 1999) ....................39  2.17 Empirical correlation between SPT-CPT correlation factor and mean grain size (after: Robertson et al., 1982) ...........................................................................................40  2.18 Concept of an effective cone diameter showing one layer of particles adjacent to the cone (Gui and Bolton, 1998) .............................................................................................42  2.19 Variation of (a) SPT-JLPT correlation factor and (b) recommended SPT and JLPT blow count correction factors with mean grain size (Tokimatsu, 1988) ...........................43  2.20 Variation of (a) simplified Tokimatsu (1988) grain size correction factors and (b) corresponding SPT-JLPT correlation factor with mean grain size ...................................46  2.21 Variation of SPT-ILPT correlation factor with mean grain size (Jamiolkowski and Lo Presti, 1998).  STD = standard deviation.....................................................................47  3.1 Definitions of various energy terms (PE = potential energy, KE = kinetic energy, E = stress wave energy) ........................................................................................................50  3.2 Energy data and blow counts for SPT performed in adjacent test-holes using  different test equipment (after: Schmertmann and Palacios, 1979)..................................52  3.3 Reflected light system for measurement of hammer impact velocities (after: Kovacs et al., 1981)...........................................................................................................55  3.4 Histograms of energy transfer ratio measurements for different hammer and rod combinations (after: Kovacs et al., 1983) .........................................................................56  3.5 Sample Hammer Performance Analyzer (HPA) strip chart data showing ideal free- fall and impact velocity (Daniel et al., 2003) ....................................................................58  3.6 Field data comparing energy transfer ratio versus rod length (a) all data, (b) average values (after: Morgano and Liang, 1992) .........................................................................59  3.7 SPT stress wave energy measured using the FV method versus hammer set per blow (d) (after: Odebrecht et al., 2005) ............................................................................60  4.1 Histograms of safety hammer ETR data from studies A, B and C. Solid lines show equivalent Normal distributions ........................................................................................65  4.2 Histograms of safety hammer ETR data from studies D, E, F and G. Solid lines show equivalent Normal distributions...............................................................................69    xi  4.3 Examples of (a) Normal and (b) LogNormal probability density functions for a generic random variable (x) ..............................................................................................72  4.4 Relationship between some useful confidence intervals and the standard deviation (σ) of a Normally distributed random variable (after: Figliola and Beasley, 2000) .........73  4.5 Histograms of safety hammer ETR data for (a) entire database plus 39 excluded points and (b, c) entire database.  Solid lines show equivalent Normal and LogNormal distributions, as indicated ..............................................................................74  4.6 Box and whisker plot illustrating negligible relationship between ETR and rod area for 1,310 safety hammer blows .........................................................................................77  4.7 ETR plotted as a function of total rod length (L) for 1,427 safety hammer blows ...........80  4.8 Comparison of SPT ETR frequency distribution to that of (a) the NALPT and (b) the RLPT ...........................................................................................................................82  4.9 Comparison of ETR values for 768 safety hammer blows to permanent set calculated from (a) blows per 25 mm, (b) blows per 152 mm and (c) blow count (N) ....83  4.10 Comparison of average ETR values for 768 safety hammer blows to permanent set calculated from (a) blows per 25 mm, (b) blows per 152 mm, and (c) blow count (N) .....................................................................................................................................85  4.11 Histograms showing distribution of (a) ETR and (b) ETRm for 768 safety hammer blows.  Solid lines show equivalent Normal distributions ................................................87  5.1 Definition of precision and bias errors (after: Figliola and Beasely, 2000)......................90  5.2 Visual representation of error propagation analysis using the Taylor series expansion approach (( x ) and ( y ) are mean values of measurement (x) and result (y), after: Figliola and Beasley, 2000) ..............................................................................92  5.3 Relationships between Ω(N60) and Ω(ERr)avg for selected values of Ω(N) ......................95  5.4 Monte Carlo simulation details (ERv = 0.60) including: (a) velocity distribution by system (b) hammer mass and ETR distributions and (c) resulting rod energy ratio distributions (10,000 realizations per velocity measurement system) ..............................99  5.5 Relationships between Ω(N60) and Ω(ERr)avg for various values of Ω(N).  Ranges of Ω(ERr)avg shown for each energy measurement approach ..............................................103  5.6 Recommended ETR procedure for energy correction of SPT or LPT safety hammer blow counts......................................................................................................................105     xii 6.1 (a) Current and (b) proposed interpretations of CRIEPI data.  Error bars indicate ± one standard deviation.....................................................................................................110  6.2 Effect of short rod corrections on WES calibration chamber data set (after: Daniel and Howie, 2006) ............................................................................................................113  6.3 Current SPT (CD) data set.  Solid and dashed lines represent proposed average trend and ± one standard deviation, respectively .....................................................................118  6.4 Variation of (CD)1mm with soil age in sands.....................................................................121  6.5 Variation of (CD)1mm with coefficient of uniformity in sands .........................................122  6.6 Detailed review of T-gravel data showing approximate contours of (a) measured (N1)60 values and (b) measured (Dr) values.....................................................................124  6.7 Sampler dimensions and test details for the MPT, SPT, NALPT and RLPT..................127  6.8 Variation of (CS/L) with mean grain size for the MPT and several types of LPT ...........132  6.9 Comparison of measured and predicted SPT-LPT correlation factors for the MPT and several types of LPT.................................................................................................134  6.10 (CS/L) grain size effects in (a) measured and (b,c) converted format.  Solid and dashed lines represent proposed average trend and ± one standard deviation, respectively......................................................................................................................136  6.11 Comparison of previously proposed relationships to (a) (CD) and (b) (CS/L ⋅ FL) grain size effect trends identified herein .........................................................................140  6.12 Comparison of (CD)SPT and (CD)JLPT relationships derived from Tokimatsu (1988) grain size corrections to trends identified herein.............................................................142  7.1 Comparison of basic model components for (a) Finite Element and (b) Distinct Element Method with circular elements and linear walls ...............................................145  7.2 Model geometry (excluding particles) for a dual platen simulation.  Platens shown at full penetration of 457 mm (18”).................................................................................147  7.3 Typical output from a PFC2D sampler penetration simulation ......................................148  7.4 Penetration energies recorded during single platen penetration trials (energies have been multiplied by two)...................................................................................................151  7.5 Comparison of smoothed toe and friction loads for single platen penetration in 4.75, 8.00 and 19.0 mm samples ..............................................................................................152     xiii 7.6 Comparison of end-of-test contact force distributions for 4.75, 8.00 and 19.0 mm samples.  Thickness of lines is proportional to magnitude of total contact force (i.e. normal  and shear components).......................................................................................153  7.7 End-of-test configurations for single platen trials showing disturbance of originally horizontal grid lines.........................................................................................................155  7.8 Patterns of particle displacement adjacent to platen during single platen penetration trials in 4.75 and 19.0 mm samples .................................................................................157  7.9 Patterns of particle displacement adjacent to platen during single platen penetration trial in oversized 19.0 mm sample showing well-developed shear zone.  Sample is 1.0 m wide by 2.0 m high................................................................................................158  7.10 End-of-test geometry following penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 4.75 mm sample ...........................................................................................160  7.11 End-of-test distribution of contact forces following penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 4.75 mm sample......................................................................161  7.12 IFR profiles recorded during penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 4.75 mm sample ...........................................................................................163  7.13 Commonly observed deformation patterns for originally horizontal layers within soil samplers (Hvorslev, 1949)........................................................................................164  7.14 Hypothesized passive arching mechanism for sampler and pile plugging (Paikowsky, 1990)...........................................................................................................166  7.15 Dual platen penetration energies recorded in the 4.75 mm sample plotted as a function of (a) platen spacing and (b) final plug length ratio..........................................168  7.16 End-of-test geometry and contact forces following penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 6.30 mm sample......................................................................169  7.17 End-of-test geometry and contact forces following penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 8.00 mm sample......................................................................170  7.18 End-of-test geometry and contact forces following penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 13.2 mm sample......................................................................171  7.19 End-of-test geometry and contact forces following penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 19.0 mm sample......................................................................172  7.20 Final plug length ratio (PLR) plotted as a function of (a) mean particle size and (b) ratio of platen spacing to mean particle size for all samples and samplers.....................173     xiv 7.21 Relationship between single and dual platen energies and mean particle size. Single platen penetration energies have been multiplied by two for comparison purposes...........................................................................................................................175  7.22 Penetration energies plotted against the ratio of the internal platen spacing to the mean particle size, illustrating (a) basic data (b) single platen energies extrapolated to (Emax) values and (c) penetration energies normalized to (Emax) for each sample ......177  7.23 Comparison of (a) widely adopted (qc/N) versu (D50) relationship (after: Robertson et al., 1982) and (b) (Emax/E) versus (D50) relationship from current study showing similar increase with increasing mean grain or particle size...........................................181  7.24 Penetration energy ratio trends determined using Equations 7.3 and 7.4 .......................182  8.1 Ω(CD)SPT trend observed in Chapter 6 and Ω(CD)LPT trend believed to be applicable to back-calculated values of (CD)LPT ...............................................................................187  8.2 Back-calculated (CD)MPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation...................................................189  8.3 Back-calculated (CD)JLPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation.  Circled data points were not used to determine sand trend ...........................................................................................190  8.4 Back-calculated (CD)NALPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation.  Circled data points were not used to determine sand trend ...........................................................................................191  8.5 Back-calculated (CD)RLPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation...................................................192  8.6 Back-calculated (CD)ILPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation...................................................193  8.7 Comparison of (CD)SPT to all interpreted (CD)LPT trends.  Trends in plot (b) have been forced through point (CD)0.1mm = 32........................................................................195  8.8 (CD)1mm plotted as a function of (E60/ATE) showing best fit correlation .........................198  8.9 Recommended procedure for prediction of LPT grain size effects.................................200  8.10 Predicted variation of SPT-LPT correlation factors with mean grain size......................202  8.11 Variation of (CD) uncertainty above critical mean grain size..........................................204  8.12 Grain size effect trend predicted for Hypothetical LPT (HLPT) and (b) corresponding prediction of SPT-HLPT correlation factor (CS/L)HLPT as a function of the mean grain size......................................................................................................206     xv 8.13 Curves for calculation of cyclic resistance ratio (CRR) from SPT blow counts, Magnitude 7.5 earthquake (after: Youd et al., 2001)......................................................208  8.14 Predicted clean sand (D50 = 0.4 mm) cyclic resistance ratio trends for the SPT and four different types of LPT..............................................................................................210  8.15 Back-calculated relationships between cyclic resistance ratio and relative density .......211  8.16 Preliminary extrapolated SPT-based cyclic resistance ratio trends for soils with mean grain sizes greater than 0.4 mm .............................................................................213     xvi LIST OF SYMBOLS  a empirical constant A cross-sectional area ATE effective sampler bearing area b empirical constant B CPT cone diameter B’ CPT effective cone diameter c stress wave propagation velocity (~ 5,120 m/s for steel rods) CA SPT age correction factor CD relative density correlation factor for average rod energy ratio of 0.60 (CD)0.1mm relative density correlation factor at D50 = 0.1 mm (CD)1mm relative density correlation factor at D50 = 1.0 mm (CD)78 relative density correlation factor for average rod energy ratio of 0.78 (CD)max relative density correlation factor for D50 ≥ D50’ CE arbitrary constant energy CLg JLPT grain size correction factor CN overburden stress correction factor COCR SPT overconsolidation correction factor CR short rod correction CRR cyclic resistance ratio CSg SPT grain size correction factor CSR cyclic stress ratio CS/L SPT-LPT correlation factor (CS/L)1mm SPT-LPT correlation factor at D50 = 1.0 mm CU coefficient of uniformity CZ coefficient of curvature d hammer / rod set per blow D10 grain diameter for which 10% of the sample is finer D30 grain diameter for which 30% of the sample is finer D50 mean grain size, grain diameter for which 50% of the sample is finer (also used to describe mean particle size in PFC2D simulations). D50’ critical mean grain size for onset of plugging effects   xvii D60 grain diameter for which 60% of the sample is finer Di sampler inner diameter (at shoe) Do sampler outer diameter Dr relative density e void ratio E stress wave energy measured for a single hammer blow E60 60% of nominal hammer energy Eavg average stress wave energy during an SPT or LPT Em Young’s Modulus emax maximum void ratio Emax ∆(Ep) value corresponding to 1.0 m platen spacing emin minimum void ratio eo in-situ void ratio Ep PFC2D platen penetration energy ERhs hammer set energy ratio (ERhs)avg average hammer set energy ratio during an SPT or LPT ERr rod energy ratio (ERr)d=0 hypothetical rod energy ratio corresponding to zero hammer / rod set (ERr)avg average rod energy ratio during an SPT or LPT (ERr)i rod energy ratio corresponding to hammer blow number (i) ERv velocity energy ratio Es selected standard energy ETR energy transfer ratio (ETR)d=0 hypothetical energy transfer ratio corresponding to zero hammer / rod set ETRm modified energy transfer ratio F axial force measured on rods F2 force-squared method of stress wave energy measurement FL LPT conversion factor Fliq factor of safety against liquefaction fs CPT sleeve friction F(t) axial force measured on rods as function of time Fp peak force measured in rods FV force-velocity method of stress wave energy measurement   xviii Go small strain shear modulus H hammer drop height ID PFC2D platen spacing IFR incremental filling ratio k coefficient of permeability KE kinetic energy L length of rod between plane of impact and base of sampler L’ length of rod between measurement location and base of sampler Le average sampler embedment length M hammer mass n porosity N measured blow count (blows / 0.3m) (N1)60 energy corrected blow count corresponding to (σ’v = 1 ton/ft2) N60 blow count corrected to average rod energy ratio of 0.60 60 1mm(N )  blow count in soil with mean grain size of 1.0 mm corrected to average rod energy ratio of 0.60 5060 D(N )  blow count in soil with mean grain size (D50) corrected to average rod energy ratio of 0.60 Nce measured blow count corresponding to arbitrary constant energy (CE) sE LPT(N )  LPT blow count corrected to selected standard energy (Es) NS uncorrected SPT blow count NL uncorrected JLPT blow count PE potential energy PLR plug length ratio p(x) probability density function of random variable (x) P(x) probability that variable (x) will fall within a given interval Q CPT normalized cone tip pressure qc CPT cone tip stress Rf CPT friction ratio Rmax indicator of surface roughness t time U1 CPT pore water pressure on cone tip   xix U2 CPT pore water pressure behind cone tip U3 CPT pore water pressure behind friction sleeve V particle velocity measured on rods Vo hammer impact velocity (Vo2)avg average squared hammer impact velocity Vs volume of solids Vv volume of voids V(t) particle velocity measured on rods as function of time W weight of hammer x random variable Y arbitrary result Z impedance Z1 impedance of hammer Z2 impedance of rods Z3 impedance of donut hammer guide rod or safety hammer cylinder δi interface friction angle ∆(Ep) change in PFC2D dual platen penetration energy over interval 152 to 457 mm ηd dynamic efficiency π pi σ standard deviation σ( ) standard deviation of term in brackets σ’v vertical effective stress µ mean value Ω coefficient of variation Ω( ) coefficient of variation of term in brackets    xx ACKNOWLEDGMENTS  The author is grateful for the financial support of the Killam Trusts, which was provided as a Pre-Doctoral Scholarship.  In addition, the research could not have been completed without support from the geotechnical community, particularly the financial and in-kind contributions of the following:  • British Columbia Hydro and Power Authority (BC Hydro); • British Columbia Ministry of Transportation (BC MoT); • Dr. R.G. (Dick) Campanella, Professor Emeritus, UBC Department of Civil Engineering; • Conetec Investigations Ltd., Richmond, BC; • Corporation of Delta, BC; • Dr. Liam Finn, Professor Emeritus, UBC Department of Civil Engineering; • Foundex Explorations Ltd. of Surrey, BC; • Klohn-Crippen Berger Ltd., Burnaby, BC; • United States Army Corp of Engineers (USACE); and, • United States Bureau of Reclamation (USBR).  Special thanks to my research supervisor, Dr. John Howie, for his efforts and support over the years.  He has been a pleasure to work with, and I look forward to future collaborations.  I greatly appreciate the time and effort of those who have reviewed this thesis, including:  Dr. Oldrich Hungr, Dr. Rodrigo Salgado, Dr. Dawn Shuttle, Dr. Alex Sy, Dr. Carlos Ventura, and Dr. Dharma Wijewickreme.  Their comments were of great value to the writer.  Thanks to Dr. Misko Cubrinovski, Dr. William Kovacs and Dr. Takeji Kokusho, who provided data and reference materials for this research effort.  Scott Jackson and Harald Schrempp of the UBC Department of Civil Engineering provided outstanding technical support throughout my time at UBC.  I thank them both for helping to make so many interesting studies possible.   xxi Many undergraduate and graduate students have helped during this research effort.  I appreciate all of their efforts, especially Abdul, Ali, Brady, Chris, Kumar, Mavi and Ricardo, who volunteered during the Patterson Park field program.  I thank my wife Kim most of all, for her love, balance and understanding.   1 CHAPTER 1 INTRODUCTION  1.1 GENERAL  The Standard Penetration Test (SPT) is the most widely used site characterization tool in the world.  The test consists of driving a standard split-spoon sampler (Figure 1.1) into the soil at the base of a clean, supported borehole.  The sampler is driven by repeatedly dropping a 63.5 kg (140 lb) hammer from a height of 0.762 m (30”) onto the top of a string of drill rods extending from the top of the sampler to above the ground surface.  The numbers of hammer blows required for each 152 mm (6”) of sampler penetration are recorded and the total number of blows required for the 152 to 457 mm (6” to 18”) penetration interval is referred to as the blow count (N).  The sampler is then retrieved and the sample used for soil classification and laboratory testing purposes.  SPT’s are typically performed at 1.52 m (5’) depth intervals to obtain profiles of blow count and soil type. Precursors to the SPT were introduced in the early 1900’s in the United States, and the test had evolved into its current state by the 1930’s.  Since then, the test has been widely adopted around the world, and correlations have been developed between the blow count and a variety of soil properties. Though the general equipment and procedural details of the SPT have been standardized (ASTM D1586-84; Decourt et al., 1988), it is possible to obtain a variety of blow counts in a given soil without violating those standards.  Two relationships of interest and practical significance are those between blow counts and driving energy (energy effects), and between blow counts and soil grain size (grain size effects).  1.1.1 Energy Effects  The most important procedural factor controlling the magnitude of the measured blow count is the dynamic energy transferred to the drill rods during hammer impact, referred to as the “stress wave energy”.  Schmertmann and Palacios (1979) showed that the blow count is inversely proportional to the stress wave energy.  Several researchers have since demonstrated that the energy can be quite sensitive to variations of equipment and test details.  For example, 2Figure 1.1  Standard SPT split spoon sampler (ASTM D1586-84). 3Figure 1.2 shows three types of hammers used for SPT, all of which conform to the basic weight and drop height requirements.  The different hammer types provide different energy, and hence different blow counts.  The known relationship between the blow count and the stress wave energy can be used to correct measured blow counts to those that would have been recorded if a standard stress wave energy had been provided.  Seed et al. (1985) recommended adopting 60% of the nominal hammer potential energy as the standard, and this practice has been widely adopted.  Energy corrected blow counts are denoted (N60). Energy correction requires a reliable measurement of energy.  Stress wave energies were measured using the “force-squared” (F2) method during early SPT energy studies in the 1970’s and early 1980’s, input for which is a force history recorded on the rods below the anvil.  Sy and Campanella (1991, 1993) demonstrated that required assumptions of the F2 method are commonly violated during SPT.  They recommended  use of the theoretically correct “force- velocity” (FV) method, which uses time histories of both force and velocity to calculate the stress wave energy. Stress wave energy measurement practice has always suffered from the lack of a reliable calibration procedure, and this creates uncertainty about the accuracy of the measured energies. While the F2 method suffers from important theoretical limitations, the FV method is hampered by the difficulty of obtaining reliable velocity records during steel-on-steel SPT impacts. Lacking a calibration procedure, engineers have resorted to the use of somewhat arbitrary methods of assessing the reliability of measured energies.  These approaches are useful for identifying obviously erroneous data, but the approach becomes unreliable when the data begin to appear “reasonable” to the reviewer. In response to the additional expense of measuring stress wave energies, and the perceived uncertainty of those energies, engineers typically only record stress wave energies during larger, high-risk projects.  The majority of SPT blow counts used for design purposes are either corrected using “typical” published stress wave energies for the hammer type used or not corrected at all. 4Figure 1.2 (a) Simple, (b) safety and (c) donut type SPT hammers. 51.1.2 Grain Size Effects The term grain size effect generally refers not to a fundamental relationship between grain size and SPT blow counts, but to the manner in which an empirical SPT correlation varies with grain size.  Limited data and the lack of a fundamental understanding of grain size effects have led to much speculation about how empirical correlations developed in sands could be used in gravels.  In order to make use of available SPT-based design procedures, engineers often use arbitrary “short interval” equivalent SPT blow counts, or estimate equivalent SPT blow counts from the results of tests using oversized equipment (Large Penetration Tests, LPT) or the Becker Penetration Test (BPT) in order to characterize gravels. Short interval equivalent SPT blow counts are extrapolated from records of blows per 25 mm (1”) or other short interval of penetration.  This approach is based on the optimistic assumption that the effect of over-sized particles on penetration histories can be detected and removed. The LPT is a scaled-up version of the SPT utilizing larger hammers and samplers with outer diameters as high as 140 mm (5.5’).  The test is non-standardized, and several versions have been developed independently around the world.  Other than equipment dimensions, an LPT is essentially the same as SPT.  The BPT is a markedly different test that involves driving a closed-end steel casing with an outer diameter of either 140, 170 or 230 mm into the ground using a diesel pile-driving hammer.  The hammer blows per 305 mm of penetration are counted to yield a continuous profile of blow counts.  The BPT is better suited for testing gravels than the LPT due to the robust nature of the equipment and the fact that traditional drilling methods, many of which are poorly suited to gravel, are not required.  The primary advantage of the LPT is its similarity to the SPT, which greatly simplifies SPT-LPT correlations (e.g. Daniel et al., 2003; Jamiolkowski and Lo Presti, 2003; Yoshida et al., 1988).  In contrast, SPT-BPT correlations must account for a more complex energy transfer process and the friction acting on the casing, which increases with depth of penetration (Sy, 1993).  Both SPT-LPT and SPT-BPT correlation factors have typically been determined or confirmed through side-by-side testing in sands. The current approach to addressing grain size effects can be summarized as follows: the SPT is used in sands incorporating grain size effect adjustments when available.  In gravelly sands or fine gravels, the practitioner may use short-interval equivalent SPT blow counts or switch to an LPT.  In even coarser materials, LPT or BPT are employed, the BPT being preferred 6when difficult drilling conditions are encountered.  Increasing equipment size with grain size is a logical approach, but it stands to reason that LPT and even BPT blow counts must also vary with grain size, and will eventually become equally unreliable as grain size increases. 1.2 RESEARCH OBJECTIVES The objectives of this research were: 1. To critically examine two currently contentious issues in dynamic penetration testing systems, i.e. transferred energy and grain size effects, which have important implications in design practice. 2. To develop an alternate approach to estimating stress wave energy and to quantify the uncertainty of the resulting energy corrected blow counts. 3. To investigate the cause and nature of SPT and LPT grain size effects. Both experimental and numerical studies of the SPT and LPT were conducted in support of these objectives.  The research involved field investigations at four sites using the SPT and scaled versions of the test.  Energy data collected during these studies and from the literature were used to develop the energy measurement approach, and the reliability of the approach was evaluated using basic statistical methods.  Data from the studies were also used to investigate the variation of SPT-LPT correlation factors with grain size.  Numerical simulations of particulate behavior were conducted in order to gain insight into the processes contributing to the observed variation. Finally, the experimental data were reviewed in light of the findings of the numerical study. 1.3 THESIS ORGANIZATION Chapter 2 presents a literature review of SPT energy measurement practice and grain size effects.  Chapter 3 describes a proposed alternate approach to energy correction of SPT blow counts based on the hammer kinetic energy. A database of hammer kinetic energy and stress wave energy measurements is compiled in Chapter 4, and used to investigate the relationship between these two quantities.  The 7propagation of uncertainty from energy measurements to the final energy corrected blow count is investigated in Chapter 5 and the proposed energy correction procedure is shown to be superior to traditional procedures. Grain size effect data as evidenced in relative density and SPT-LPT correlations are compiled and compared in Chapter 6.  Chapter 7 describes a 2-dimensional numerical study of grain size effects during which the effect of particle and sampler size on penetration energy is characterized.  The available experimental grain size effect data are reviewed in light of the results of the numerical study and a method for predicting LPT grain size effects is proposed in Chapter 8. Chapter 9 summarizes the major findings and conclusions of the research, and presents recommendations for future research.   8 CHAPTER 2 SPT ENERGY AND GRAIN SIZE EFECTS IN THE LITERATURE  2.1 ENERGY CORRECTION  SPT equipment and procedural details were partially standardized in ASTM D1586-99, but a wide range of blow counts can be recorded for a given soil without violating the requirements of the standard.  Most of these variations can be attributed to variations of the stress wave energy provided during the test.  Schmertmann and Palacios (1979) demonstrated that SPT blow counts are inversely proportional to the stress wave energy, and Seed et al. (1985) recommended correction of blow counts to a standard energy equal to 60% of the nominal hammer potential energy using the formula:  (2.1) avg60 N E N 0.60 475 J ⋅= ⋅  where (Eavg) is the average stress wave energy.  Although not explicitly stated, this is presumably the average energy transferred during the blows contributing to the blow count.  The ratio of the stress wave energy measured during a single hammer blow to the nominal hammer energy (475 J) is called the rod energy ratio (ERr).  The energy ratio is commonly written as a percentage but will be expressed as a simple ratio herein.  Equation (2.1) is then written as:  (2.2) r avg60 N (ER ) N 0.60 ⋅=  where (ERr)avg is the average rod energy ratio.  Equation (2.2) has also been used to account for energy variations during other dynamic penetration tests like the LPT (e.g. Jamiolkowski and Lo Presti, 1998). The need for energy correction is addressed in ASTM D6066-96, the standard SPT procedure for the assessment of soil liquefaction potential.  The standard indicates that average rod energy ratios can be obtained from the literature (“typical” values) or through direct measurement.    9 Table 2.1 Rod energy ratios from the literature (Howie et al., 2003). Reference Hammer / Lift and Release Method ERr Schmertmann et al. (1978) Safety / Rope and Cathead 0.45 – 0.70 Goble and Ruchti (1981) Safety / Rope and Cathead 0.76 – 0.96 Kovacs et al. (1981) Safety / Rope and Cathead 0.34 – 0.83 Safety / Rope and Cathead 0.80 (3 operators) Riggs et al. (1984) Automatic Trip 0.88 Safety / Rope and Cathead 0.63 – 0.72 Seed et al. (1985) Automatic Trip 0.76 – 0.90 Riggs (1986) Safety / Rope and Cathead 0.65 – 0.90 Skempton (1986) Safety / Rope and Cathead 0.55 Safety / Rope and Cathead 0.55 – 0.60 Clayton (1990) Automatic Trip 0.60 – 0.73 Safety / Rope and Cathead 0.51 Batchelor et al. (1995) Automatic Trip 0.69 – 0.81 Safety / Rope and Cathead 0.67 Lamb (1997) Automatic Trip 0.80  2.1.1 Typical Values  ASTM D6066-96 states that typical rod energy ratios can be used in Equation (2.2) when directly measured values are not available.  Rod energy ratios are known to vary with test details such as the type of hammer and the method used to lift and release the hammer (Table 2.1).  In North America, hammers are commonly operated using the rope and cathead technique shown in Figure 2.1a, for which the hammer is released by “throwing” the rope off the cathead. Alternatively, some hammers incorporate an integral trip-release mechanism to release the hammer at the prescribed drop height (Figure 2.1b).  ASTM D6066-96 recommends using the average rod energy ratio previously recorded for a given driving system if available, or a documented value for a similar system otherwise.  It states that a typical rod energy ratio of 0.60 may be assumed for most tests performed using safety hammers, but specifically recommends   (a ) (b ) Fi gu re  2 .1  Ill us tra tio n of  (a ) t he  ro pe  a nd  c at he ad  m et ho d us ed  w ith  a  d on ut  h am m er  (R ob er ts on  e t a l.,  1 99 2,  a da pt ed  fr om  K ov ac s an d Sa lo m on e,  1 98 2)  a nd  (b ) a  “ D an do ” tri p re le as e ha m m er  th at  c ou ld  b e lif te d us in g a ro pe  a nd  c at he ad  o r a  w in ch ed  ca bl e (C la yt on , 1 99 0) . 10   11  against assuming energy values for “unusual undocumented systems”.  Donut and trip hammers are noted to often have unknown energy transmission characteristics. The use of typical rod energy ratios for energy correction has the potential to produce highly unreliable (N60) values.  Youd et al. (2001) state that safety hammer rod energy ratios typically vary between 0.42 and 0.72.  If, for example, the true average rod energy ratio was 0.42 or 0.72 but was assumed to be 0.60, the resulting (N60) estimates would be 30% higher or 20% lower than the correct values, respectively.  Despite the relatively high uncertainty associated with this approach, it is widely used because no additional costs are incurred.  2.1.2 Direct Measurement  Timoshenko and Young (1955) showed that the stress wave energy generated during an impact (E) can be calculated using the equation:  (2.3) 0 E F(t) V(t) dt ∞ = ⋅∫  where F(t) and V(t) are the axial force and particle velocity measured at a point on the rods as a function of time (t), respectively.  Equation (2.3) is known as the force-velocity (FV) method. The FV method records all stress wave energy passing the measurement point over the integration period, which should be of sufficient length to allow stress wave activity in the rods to cease. The force and velocity of a downward propagating stress wave (i.e. a stress wave propagating toward the base of the rods) are proportional as follows:  (2.4) mE AF V Z V c ⋅= ⋅ = ⋅  where (Em) is the Young’s Modulus, (A) is the cross-sectional area, (c) is the stress wave propagation velocity and (Z) is the impedance.  (Em) and (c) are roughly constant for hammer and rod components made of steel, and thus the impedance is primarily an indicator of cross-   12 sectional area.  To remain in compliance with accepted sign conventions, the following modified relationship is required for an upward propagating stress wave (i.e. a stress wave propagating toward the top of the hammer):  (2.5) F Z V= − ⋅  The axial force and particle velocity when both upward and downward propagating stress waves are present at the measurement location are equal to the algebraic sums of the force and velocity of the two stress waves, respectively.  Though force-velocity proportionality is still valid for the individual waves, review of Equations (2.4) and (2.5) reveals that the total force will no longer be proportional to the total velocity. Upward propagating stress waves are generated in the rods when the original, downward propagating stress wave encounters a change of impedance such as a rod coupling or the sampler-soil interface. During each hammer blow there is a period of time during which the measured force and velocity will be proportional as per Equation (2.4), prior to the arrival of such reflections.  For the special case of uniform rods, this length of time is equal to (2L’/c), where (L’) is the length of rod between the measurement location and the base of the sampler. Stress wave energies in uniform rods can be measured during this time period using the “force- squared” (F2) method:  (2.6) 0 2L ' c 21E (F(t)) dt Z = ∫  The F2 method requires only a time history of axial force.  Due to the technical difficulty of measuring V(t), early SPT energy studies favoured the F2 method, relying on the assumption that the effect of stress wave reflections from rod couplings would be negligible.  Semi-empirical correction factors were developed to correct F2 energies to those that would have been calculated if F(t) had been recorded at the top of the rod string and if the total rod length (L) had been greater than 10 m.  The F2 method and associated correction factors were recommended for use during SPT by Decourt et al. (1988) and were specified in ASTM D4633-86.  The latter was allowed to lapse in 1998.  F2 energies contain errors related to violations of the uniform rod   13 assumption, inaccuracies of the correction factors and the inability to measure energy transferred during secondary impacts, as discussed by Sy and Campanella (1991, 1993), and others. Sy and Campanella (1991) first recommended the use of the force-velocity (FV) method to measure SPT stress wave energies.  Modern energy measurement systems typically utilize the FV method, using strain gauges bonded directly to the drill rod below the anvil to measure force, and one or more accelerometers bonded nearby on the same rod to measure acceleration, which is then integrated to obtain the velocity history.  Figure 2.2 shows typical force and velocity data recorded using research quality equipment during a SPT hammer blow and the resulting record of (ERr).  The velocity has been multiplied by the rod impedance (Z), and the initial time period during which the force and velocity are roughly proportional can be seen in the plot.  The maximum calculated value of (ERr) is the correct value to use to calculate (ERr)avg. Direct measurement of stress wave energies using the FV method is technically challenging.  The instrumentation is expensive and somewhat delicate, and large amounts of data must be collected and stored during each hammer blow.  For example, University of British Columbia (UBC) studies typically record between 8,000 and 16,000 force and acceleration data points per hammer blow.  The data from each hammer blow must then be reviewed by an experienced engineer to identify and remove questionable traces, a process for which there is no accepted procedure. Velocity data are particularly susceptible to errors due to high peak accelerations and the cumulative effect of minor baseline errors during integration of the acceleration history.  Figure 2.3 has been prepared to demonstrate this sensitivity.  The plot shows the relationship between the selected accelerometer baseline and the calculated FV energy for the data shown in Figure 2.2.  Changing the baseline by a very small amount, less than the resolution of the instrument, is seen to have a significant effect on the calculated energy.  Due to this sensitivity and the potential for minor baseline shifts to occur during impact, accelerometer baselines are commonly selected based on the assumption that the final velocity is zero.  Violations of this assumption due to insufficient record length lead to systematic errors, the nature of which depends on whether the sampler was in the process of penetrating (soft soils) or rebounding (stiff soils) at the end of the record.    14 Time (ms) -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 ER r 0.0 0.2 0.4 0.6 0.8 Fo rc e an d Ve lo cit y * Z (k N) -100 -50 0 50 100 150 200 Force Velocity * Z                                                Figure 2.2 Typical force and velocity data recorded using research quality equipment during an SPT performed at 13.7 m depth (ERr = 0.59, (ERr)avg = 0.56, N = 18, N60 = 17).   15 Accelerometer Baseline (mV) 0 2 4 6 8 10 12 14 Ca lc ul at ed  E R r 0.4 0.6 0.8 1.0 1.2 Instrument Resolution (5 mV) Baseline for zero final velocity                                                Figure 2.3 Relationship between selected accelerometer baseline and resulting FV energy for data shown in Figure 2.2.   16 2.2 GRAIN SIZE EFFECTS  Individual soil grains range in size from thousandths of a millimetre to hundreds of millimetres.  Figure 2.4 compares grain size classification schemes recommended in the British Code of Practice on Site Investigations (BSI, 1981) and the Unified Soil Classification System (Casagrande, 1948).  The British and Unified schemes identify gravel particles as those with diameters greater than 2.0 and 4.75 mm, respectively.  The BSI system is adhered to in the Canadian Foundation Engineering Manual (CFEM, 2006) and will be adopted herein. Soils are assemblages of grains, and are largely classified on the basis of grain size distribution (GSD).  The GSD is determined by filtering a sample through a set of increasingly finer sieves and plotting the percentage (by weight) retained on each sieve against the logarithm of the sieve opening size (Figure 2.5).  The GSD of the portion of the soil that is finer than 0.075 mm is characterized using a sedimentation test.  Cohesionless soils (containing no clay) are then classified based on GSD parameters including the effective grain size (D10), mean grain size (D50), coefficient of uniformity (CU) and coefficient of curvature (CZ).  (D10) and (D50) are the diameters corresponding to 10% and 50% finer portions of the sample, respectively.  (CU) and (CZ) characterize the gradation of the soil and are defined as:  (2.7) 60U 10 DC D =  (2.8) 2 30 Z 10 60 DC D D = ⋅  where (D30) and (D60) are defined as per (D10) and (D50). SPT blow counts are known to vary with grain size, but the nature of the variation is poorly understood.  The term “grain size effect” is used very broadly to describe such variations, which are generally evidenced as variations of SPT-based empirical correlations.  Extension of what little is known of grain size effects in sands into the gravel range of grain sizes has proven to be difficult.  It is generally believed that SPT blow counts will be unreasonably high in gravels (e.g. Ross et al., 1969; U.S. National Research Council, 1985; Rollins et al., 1998), but some researchers have reported blow counts that were much lower than expected in gravels (e.g. Andrus and Youd, 1989).   17 Grain Size Boundaries (mm) - British Code of Practice 0.002 0.006 0.02 0.06 0.2 0.6 2 6 20 60 200 Cobbles BouldersClay Fine Medium CoarseFine Medium CoarseFine Medium Coarse Silt GravelSand GravelSand Fine CoarseFine Medium Crs. Silt Cobbles BouldersClay 0.002 2 4.76 19 75 3000.074 0.42 Grain Size Boundaries (mm) - Unified Soil Classification System                                                Figure 2.4 Comparison of grain size classification schemes adopted for British Code of Practice and Unified Soil Classification System.   18                                                 Figure 2.5 Sample grain size distribution curves (after: Craig, 1994).   19 The current understanding of grain size effects is reviewed in the following sections. Fundamental grain size effects are reviewed first, followed by grain size effects as evidenced in relative density correlations, and finally grain size effects evident in the ratio of in-situ test results including the cone penetration test (CPT) and the LPT.  2.2.1 Fundamental Grain Size Effects  SPT grain size effects must ultimately be due to variation with grain size of the micro- mechanical processes through which soils accommodate sampler penetration.  None of these processes are particularly well understood.  This section summarizes some fundamental micro- mechanical grain size effect studies believed to be relevant to the current study. The relationship between the coefficient of permeability (k) and grain size was empirically characterized by Hazen (1892) as:  (2.9) 210 1k (D ) 100 ≈ ⋅  where (k) is in units of (m/s).  Equation (2.9) states that soil permeability increases with grain size.  Soil permeability likely contributes to SPT grain size effects by introducing a systematic variation of the rate at which excess pore pressures generated during sampler penetration are dissipated.  Excess pore pressures will dissipate rapidly in coarse soils, possibly while sampler penetration is still occurring.  In contrast, excess pore pressures may persist between hammer blows in finer soils, introducing an unwanted hammer blow rate effect.  Very little is known about the magnitude, rate of dissipation or effect of excess pore pressures generated during SPT. Variation of the sand-steel interface friction angle (δi) with grain size is another fundamental grain size effect.  Uesugi et al. (1988) and Jardine et al. (1992) demonstrated through direct shear soil-steel interface testing that yield and critical state interface friction angles, respectively, decrease with increasing mean grain size for a given surface roughness (Figure 2.6).  Whether this trend continues into the gravel range of grain sizes is unknown. These observations suggest that the interface friction component of the total penetration resistance during an SPT may decrease with increasing (D50), all other factors held constant. Lastly, Stone and Muir Wood (1992) describe a fundamental investigation of the relationship between grain size and shear zone development.  They prepared dense sand samples   20                                               Figure 2.6 Increase of sand-steel interface friction angle (δi) with increasing surface roughness (Rmax) and decreasing mean grain size from simple shear tests (after: Uesugi et al., 1988). Rmax   D50 Ta n (δ i )   21 in a box and slowly lowered a trap door at the base of the sample.  Radiograph images were recorded at several stages of the test (Figure 2.7), allowing them to analyze density variations. Areas of concentrated strain (shear zones) were associated with reduced density in the dense, dilative samples.  Uniform sands with mean grain sizes of 0.4, 0.85 and 1.5 mm were tested.  As the trap door was lowered beneath the 0.4 mm sample, a series of increasingly steep shear bands developed, labeled “A”, “B”, “C1” and “C2” in Figure 2.7.  The study authors suggested that the orientation of each newly developing shear band was kinematically admissible for a dilating shear zone, and that the shear bands were sequentially abandoned as the shearing sand approached a constant volume (critical state) condition.  They observed that the 1.5 mm sample had only developed shear band “A” at the final displacement and thus concluded that shear zone “A” was still dilating at the end of the test.  These observations suggest that the macroscopic strain required for the soil in a shear band to reach a constant volume, post-peak state increases with grain size.  This trend would be expected to lead to increased SPT penetration resistance in coarser soils.  2.2.2 Relative Density Correlations  The relative density (Dr) is a measure of soil density relative to approximate maximum and minimum values, and is defined as:  (2.10) max or max min e eD e e −= −  where (emax), (eo) and (emin) are the maximum, in-situ and minimum void ratios, respectively. The void ratio (e) is defined as:  (2.11)  v s Ve V =  where (Vv) and (Vs) are the volume of voids and solids in a soil sample, respectively.  There are standard procedures for determining (emax) and (emin) for a given soil.   22                                               Figure 2.7 Radiograph image showing development of low-density shear zones (light areas) during trap-door tests for sample with mean grain size of 0.4 mm (after: Stone and Muir Wood, 1992). A B C C1 C2   23 The effect of mean grain size on the relationship between SPT blow counts and soil relative density is an example of the use of an empirical correlation to characterize grain size effects.  Indeed, many would consider this to be the definition of SPT grain size effects. Examples of grain size effects defined in this manner are presented in chronological order of publication below.  Burmister (1948, 1962):  Burmister observed that the SPT penetration resistance increases with the relative density of the soil, and suggested that the nature of this relationship varies with grain size as shown in Figure 2.8.  Meyerhof (1957):  Meyerhof observed that the relationship between the SPT blow count, vertical effective stress (σ’v) and relative density (Dr) for a particular soil could be written as:  (2.12) v2 r 'ba D N σ⋅+=  where (a) and (b) are empirical constants and (σ’v) is in units of (ton/ft2).  Skempton (1986):  Skempton noted that it is more appropriate to write Equation (2.12) in terms of (N60), and that it was convenient to characterize a given sand by the parameter (N1)60/Dr2, where (N1)60 is the energy corrected blow count corresponding to (σ’v = 1 ton/ft2 = 98 kPa).  This can be written as:  (2.13) 21 602 r (N ) a b (1 ton / ft ) D = + ⋅    24                                                Figure 2.8 Empirical correlation between SPT blows per 152 mm (6”) and soil density (Burmister, 1962).   25 Skempton compiled a set of blow counts measured during a United States Army Corp of Engineers (USACE) Waterways Experiment Station (WES) calibration chamber study as well as during several sets of field data (Figure 2.9).  The field test data were recorded in two normally consolidated (NC) sand fills in Japan, in four natural deposits of NC sands near Niigata, Japan and in one overconsolidated (OC) natural sand deposit near Sizewell in the United Kingdom.  In- situ densities were primarily measured using conventional tube or block sampling methods, though frozen samples were collected at one of the Niigata sites.  Typical energy corrections were selected based on the type of hammer used and the country in which the tests were performed.  For all but one test site, (N1)60/Dr2 was determined by plotting (N60/Dr2) versus (σ’v) and interpolating the value corresponding to (σ’v = 1 ton / ft2).  In the one case where insufficient data was available for this approach, he estimated (N1)60/Dr2 as follows:  (2.14) 1 60 60 60N2 2 2 vr r r (N ) N N2 C 1 'D D D = ⋅ = ⋅+ σ  where (CN) is an overburden stress correction factor.  For comparison purposes, he also plotted, as shown in Figure 2.9, a relationship proposed by Peck and Bazaraa (1969) for dense, coarse sands.  Kulhawy and Mayne (1990):  Kulhawy and Mayne reviewed and made some minor modifications to the data compiled by Skempton (Figure 2.10).  One of the changes they made was the use of the more commonly used Liao and Whitman (1986) approach to determining (CN):  (2.15) 0.5 N v 98 kPaC '  =  σ    where (σ’v) is in units of (kPa).  Based on their revised data, they proposed the following Equations to describe the Peck and Bazaraa, WES and Niigata sand data:   26                                                Figure 2.9 Variation of (N1)60/Dr2 with mean grain size (after: Skempton, 1986).  In-situ soil densities determined primarily from conventional samples.   27                                                Figure 2.10 Revised interpretation of Skempton (1986) data by Kulhawy and Mayne (1990). NC = Normally Consolidated.   28 (2.16) 1 602 r (N ) 85 D =  (Peck and Bazaraa)  (2.17) 1 60 502 r (N ) 60 25 log(D ) D = + ⋅  (WES)  (2.18) 1 60 502 r (N ) 80 25 log(D ) D = + ⋅    (Niigata Sand)  They suggested that Equation (2.17) representing the WES data is a base curve that can be shifted upwards to account for the effects of ageing (as demonstrated by the Niigata sand data) and overconsolidation effects.  Their proposed corrections for ageing (CA) and overconsolidation effects (COCR) were given as:  (2.19) AC 1.2 0.05 Log(t /100)= + ⋅  (2.20) 0.18OCRC OCR=  where (t) is the time since deposition in years and OCR is the overconsolidation ratio, (ratio of the maximum past to current vertical effective stress).  The unaged, normally consolidated value of 2r601 D)N( calculated using Equation (2.17) is multiplied by (CA) and (COCR) to determine the value appropriate for a given soil.  Equation (2.19) and the available aging data are shown in Figure 2.11.  The Niigata sand data have been incorrectly plotted as having an age of 30 to 40 years rather than the correct value of roughly 125,000 years (1.25 ⋅ 104).  Cubrinovski and Ishihara (1999):  Cubrinovski and Ishihara presented a largely new data set based primarily on frozen sample density measurements (Figure 2.12).  They corrected blow counts to a reference overburden pressure of 98 kPa using the Liao and Whitman (1986) approach, and to a reference rod energy ratio of 0.78 using typical (ERr) values recommended by Skempton (1986).  They proposed the following convenient notation:   29                                                 Figure 2.11 Aging effect observed by Kulhawy and Mayne (1990).   30                                                Figure 2.12 Variation of (CD)78 with mean grain size (after: Cubrinovski and Ishihara, 1999). In-situ soil densities determined primarily from frozen samples. Eq. (2.23) (C D ) 7 8   31 (2.21) 1D 2 r NC D =  the following slightly modified form of which will be adopted herein:  (2.22) 1 60D 2 r (N )C D =  In recognition of their correction of blow counts to an energy ratio of 0.78, their data are identified using the symbol (CD)78 herein.  They proposed the following fit-line:  (2.23) 1.7 D 78 50 0.06(C ) 9 0.23 D − = ⋅ +     Cubrinovski and Ishihara (1999) explored the use of indices other than (D50) to predict grain size effects.  Based on their own data and the results of a study conducted by Miura et al. (1997), they suggest that (emax – emin) varies systematically with mean grain size, fines content and particle angularity, as shown in Figure 2.13.  The best-fit line in the plot is described by the equation:  (2.24) 50 minmax D 06.023.0ee +=−  They suggest that Equation (2.24) provides an average value of (emax – emin), while the actual value of (emax – emin) tends to increase for a given (D50) as the fines content and particle angularity increase. Figure 2.14 illustrates the relationship between (CD)78 and (emax – emin) for the data compiled by Cubrinovski and Ishihara (1999).  The gravel data are on the left side of the plot, and they appear to follow a relatively consistent trend compared to the equivalent (D50) plot shown in Figure 2.12.  The grain size effect relationship is defined as:   (2.25) 1.7D 78 max min(C ) 9 (e e ) −= ⋅ −   32                                                Figure 2.13 Empirical correlation between void ratio range (emax - emin) and mean grain size (Cubrinovski and Ishihara, 1999).   33                                                Figure 2.14 Empirical correlation between (CD)78 and void ratio range (after: Cubrinovski and Ishihara, 1999). (C D ) 7 8   34 Equations (2.23) and (2.25), representing the (D50) and (emax – emin) relationships, respectively, are related by Equation (2.24).  Based on the apparently superior correlation shown in Figure 2.14, Cubrinovski and Ishihara (1999) recommend the use of Equation (2.25) to calculate (Dr) values.  They noted, however, that (emax) and (emin) are more difficult to measure than (D50), particularly in gravels.  For this reason they recommend the use of the (D50) based relationship (Equation 2.23) when (emax – emin) is not known.  Chen (2004):  Chen (2004) compiled a data set including calibration chamber test results collected during a Central Research Institute of the Electric Power Industry (CRIEPI) study conducted in Japan.  In addition, interpreted average (CD) and (D50) values were presented for 43 different soil deposits.  Of these, seven were man-made fills, four were mine tailings and five were volcanic deposits.  The 27 data points representing “normal” natural deposits are plotted with the CRIEPI and WES data in Figure 2.15. The CRIEPI data are seen to follow roughly the same trend as the WES data.  Based on these data and a review of aging and OCR effects, Chen (2004) concluded that the particle size effect relationship proposed by Kulhawy and Mayne (1990) and the associated (CA) and (COCR) correction factors are suitable for use in native soils with mean grain sizes as high as 20 mm.  He notes, however, that the upper limit for use of the SPT is likely about 5 mm.  Discussion:  The available data demonstrate that (CD) generally increases with mean grain size.  This is reflected in the grain size effect relationships proposed by the different researchers, which are summarized in Table 2.2.  The number of available (CD) measurements is limited, and it would be advantageous to directly compare data from all sources.  There are several issues that must be addressed first.  These issues range from repetition of data between sets, and use of averaged data versus individual measurements to differing energy correction procedures between studies. These issues are addressed and the data compiled into a single data set in Chapter 6. Regarding the use of (emax – emin) as a predictor of grain size effects, as proposed by Cubrinovski and Ishihara (1999), several limitations of the supporting data and the subsequent interpretation are apparent:   35                                                Figure 2.15 Variation of (CD) with mean grain size (after: Chen, 2004).  In-situ soil densities determined from either frozen or conventional samples. Eq. (2.17) T ab le  2 .2  Su m m ar y of  re la tiv e de ns ity  c or re la tio n gr ai n si ze  e ff ec t r el at io ns hi ps . T es t C on di tio ns  D 50  (m m ) D es cr ip tiv e E qu at io n a R ef er en ce  ~ 0. 5 to  1  D C 65  Pe ck  a nd  B az ar aa  (1 96 9) , (S ke m pt on , 1 98 6 in te rp re ta tio n)  D en se , c oa rs e sa nd s. Fi el d te st s. ~ 1 to  4  D C 85  Pe ck  a nd  B az ar aa  (1 96 9) , (K ul ha w y an d M ay ne , 1 99 0 in te rp re ta tio n)  M ed iu m  to  c oa rs e sa nd . W ES  C al ib ra tio n ch am be r t es ts . 0. 23  to  2 .0  D 50 C 60 25 lo g( D )   ˜ K ul ha w y an d M ay ne  (1 99 0)  M ed iu m  to  c oa rs e N iig at a sa nd . Fi el d te st s w ith  fr oz en  o r un di st ur be d sa m pl es . 0. 28  to  0 .6 3 D 50 C 80 25 lo g( D )   ˜ K ul ha w y an d M ay ne  (1 99 0)  1. 7 D 78 50 0. 06 (C ) 9 0. 23 D  § ·  ˜  ¨ ¸ © ¹ C ub rin ov sk i a nd  Is hi ha ra  (1 99 9)  Fi ne  sa nd  to  m ed iu m  g ra ve l. Fi el d te st s w ith  fr oz en  sa m pl es . 0. 16  to  1 8. 5 1. 7 D 78 m ax m in (C ) 9 (e e )  ˜  C ub rin ov sk i a nd  Is hi ha ra  (1 99 9)  a.  C D  =  (0 .7 8/ 0. 60 ) ˜  (C D ) 7 8 36   37 1. Data were collected in two gravel deposits, KJ-Gravel and T-Gravel, represented as open triangles pointing up and down, respectively in Figures 2.12 through 2.14. These (CD) values were recorded using “Japanese LPT” (JLPT) equipment, while the sand data points are derived from SPT blow counts.  It would be surprising if a single, continuous grain size effect relationship represented both the SPT sand data and the JLPT gravel data. 2. Figure 2.13 demonstrates that (emax – emin) is a useful parameter for differentiating between sands and gravels, but is relatively insensitive to variations of (D50) within the gravel range of grain sizes.  It would be difficult to differentiate between two soils with (D50) values of 2.0 and 20 mm given only the (emax – emin) values, yet these two soils would certainly lead to very different grain size effects during an SPT or LPT. 3. The slope of the (CD) versus (emax – emin) relationship approaches infinity in coarse soils (Figure 2.14) while that of the (CD) versus (D50) relationship approaches zero (Figure 2.12).  While this can be explained by noting that (emax – emin) is inversely proportional to (D50) in Equation (2.24), it is difficult to reconcile these conflicting predictions. 4. Close inspection of the gravel data in Figure 2.12 reveals that the KJ- and T-gravels form two relatively distinct groups, with the KJ-gravel (CD) values generally being higher.  The properties of these two gravels are compared in Table 2.3 and they are seen to be similar except for the small strain shear modulus (Go), which is much higher in the KJ-gravels.  High (Go) values are often related to the presence of naturally occurring cementation between soil particles.  Cementation would increase the blow count and hence (CD), but would be destroyed during the tests performed to determine (D50), (emax) and (emin).  Again, it would be surprising if a single, continuous grain size effect relationship represented both non-cemented and cemented soils.  For these reasons, the use of (emax – emin) as a predictor of grain size effects will not be pursued herein.   38 Table 2.3 Properties of KJ and T-gravels. Property KJ-gravel T-gravel Percent Fines a 1 – 14 1 – 8 Percent Gravel a 51 – 70 35 – 86 D50 (mm) a 2.1 – 7.8 1.1 – 18.5 CU b ~ 10 – 300 ~ 5 – 140 Dr a 0.32 – 0.70 0.21 – 0.81 Age (years) b 11,000 – 1.8 Million (Pleistocene) 11,000 – 1.8 Million (Pleistocene) Go, frozen samples (MPa) b 260 – 560 ~ 150 – 290 Go, field (MPa) b ~ 850 ~ 250 – 450   a.  Source: Cubrinovski and Ishihara (1999). b. Source: Kokusho and Tanaka (1994).  2.2.3 SPT-CPT Correlations  The cone penetration test (CPT) is another type of in-situ test that is widely used for site characterization.  The test involves pushing a 60° cone with a base area of 10 cm2 into the ground at a constant rate of 2 cm/s (Figure 2.16).  Output from the test includes the cone tip stress (qc) and the friction acting on a 150 cm2 friction sleeve located directly behind the tip (fs). SPT-CPT correlations have been developed so that CPT data may be used as input for the numerous SPT based design approaches.  Figure 2.17 shows one empirical relationship between the ratio (qc / N) and the mean grain size. Modern cones are equipped with instruments to measure pore water pressure on the cone tip (U1), between the cone tip and the friction sleeve (U2) and/or behind the friction sleeve (U3), and are referred to as piezocones.  The development and dissipation of excess pore water pressures in the vicinity of a penetrating cone is a complex topic that is still under review.  In general, however, piezocone data recorded in clean sands typically show little or no deviation from the original pore water pressure profiles, while those recorded in finer sands or silts do. This observation suggests that CPT data is affected by systematic variations of permeability with   39                                                 Figure 2.16 Cross-section of a typical modern electric piezocone (after: Davies, 1999).   40                                                Figure 2.17 Empirical correlation between SPT-CPT correlation factor and mean grain size (after: Robertson et al., 1982).   41 grain size within the sand range of grain sizes.  A similar phenomenon may affect SPT results, as discussed earlier with respect to fundamental grain size effects. It is instructive to consider the possibility of other sources of grain size effects on both test types.  Gui and Bolton (1998) performed cone penetration tests in a centrifuge using cones of varying diameter in three sands of differing mean grain size.  The sands were unsaturated and thus any observed grain size effects could not be due to variations of permeability.  They noted that the soil particle size did not significantly affect the peak normalized cone tip pressure (Q), provided the ratio of the cone diameter to the mean grain size was greater than 28.  As the ratio decreased below 28, the (Q) value increased.  This trend was attributed to an increase of the effective cone diameter (B’), equal to the  actual diameter (B) plus the mean grain size (Figure 2.18).  SPT results are likely similarly affected by the ratio of the sampler wall thickness to the mean grain size.  2.2.4 SPT-LPT Correlations  Different types of LPT have been developed independently around the world.  As for the CPT, researchers have sought to make use of existing SPT based design approaches through SPT-LPT correlation factors.  In some cases, these correlation factors have been observed to vary with grain size.  Table 2.4 presents details of the SPT and two types of LPT, including the JLPT and the Italian LPT (ILPT). Tokimatsu (1988) compared SPT-JLPT correlation factors recorded by Hatanaka and Suzuki (1986), Goto et al. (1987) and Yoshida et al. (1988) in well-graded soils with (D50) values ranging from 0.34 to 8.0 mm.  He noted that the correlation factor seemed to increase with (D50) above a base value of 1.5 in fine sands, as shown in Figure 2.19a, and suggested that this trend contained information about the variation of both SPT and JLPT blow counts with grain size.  He proposed that SPT and JLPT blow counts, denoted as (NS) and (NL), respectively, could be corrected to equivalent fine sand values using the equations:  (2.26) Sg SN C N= ⋅  (2.27) Lg LN C N= ⋅    42                                                Figure 2.18 Concept of an effective cone diameter showing one layer of particles adjacent to the cone (Gui and Bolton, 1998).   43                        (a)                    (b)    Figure 2.19 Variation of (a) SPT-JLPT correlation factor and (b) recommended SPT and JLPT blow count correction factors with mean grain size (Tokimatsu, 1988).   44 Table 2.4   Test details of the SPT and two types of LPT. Test Detail SPT a JLPT b ILPT c Sampler Outer Diameter, cm (in.) 5.08 (2.0) 7.3 (2.9) 14.0 (5.5) Sampler Inner Diameter:  Shoe, cm (in.) 3.49 (1.375) 5 (2.0) 10 (3.9)  Barrel, no liner, cm (in.) 3.81 (1.5) 5.4 (2.13) 11 (4.3) Hammer Weight, N (lb.) 623 (140) 981 (220) 5592 (1256) Hammer Drop Height, cm (in.) 76.2 (30) 150 (59.1) 50 (19.7) Nominal Hammer Energy:  kJ (ft⋅kip) 0.475 (0.350) 1.472 (1.084) 2.796 (2.062)  % of SPT Nominal Energy 100 311 591 a.  Source:  ASTM D1586-84 b. Source:  Kaito et al. (1971), Yoshida et al. (1988). c. Source:  Jamiolkowski and Lo Presti (1998).   where (NS/NL) varies with (D50), as shown in Figure 2.19a.  The resulting variation of (CSg) with (D50) is shown in Figure 2.19b.  He then drew a second, steeper relationship for (CSg) to account for the assumed increase of LPT blow counts with (D50).  Figure 2.19b shows this revised relationship as well as a third parallel relationship defining (CLg).  Tokimatsu (1988) thus assumed that the LPT would exhibit the same grain size where (N) is the equivalent fine sand SPT blow count and (CSg) and (CLg) are correction factors for the SPT and JLPT, respectively. To develop the correction factors, he first hypothesized that the LPT blow counts would not be subject to grain size effects, in which case (CSg) could be calculated as:  (2.28) Sg S L 1.5C N / N =  effects as the SPT, beginning at a slightly coarser grain size.   His recommended correction factors can be simplified as:  (2.29a) SgC 1.0=  0.1 mm ≤ D50 ≤ 0.27 mm   45 (2.29b) 50Sg DC 1.0 0.5 Log 0.27  = − ⋅     0.27 mm < D50 ≤ 3.0 mm and  (2.30a) LgC 1.5=  0.1 mm ≤ D50 ≤ 0.35 mm  (2.30b) 50Lg DC 1.5 0.5 Log 0.35  = − ⋅     0.35 mm < D50 ≤ 10.0 mm  where (D50) is in units of (mm), as shown in Figure 2.20a.  Referring to Equations (2.26) and (2.27), the relationship between (NS/NL), (CSg) and (CLg) can be written as:  (2.31) Sg LgS L Lg Sg N / C CN N N / C C = =  This relationship is plotted in Figure 2.20b, using the simplified correction factors (Equations (2.29) and (2.30)) to quantify the variation of (CSg) and (CLg) with (D50).  The plot demonstrates that the grain size corrections proposed by Tokimatsu (1988) were consistent with the SPT-JLPT correlation data available at the time. Jamiolkowski and Lo Presti (1998) presented SPT-ILPT correlation values recorded in soils with a range of mean grain size values (Figure 2.21).  Stress wave energies measured using the F2 method were used to correct the SPT and ILPT blow counts to 60% of the nominal hammer energies.  Unlike the SPT-JLPT correlation, the SPT-ILPT correlation factor seems to decrease slightly with increasing (D50), indicating that SPT blow counts decreased relative to ILPT blow counts. Jamiolkowski and Lo Presti (2003) postulated that both SPT and ILPT samplers would become plugged during tests in gravels, leading to much greater increases in sampler-end bearing area for the ILPT than the SPT.  They suggested that both SPT and  ILPT blow counts would increase due to this plugging, but that the increase would be greater for the ILPT, leading to a decrease of the correlation factor.  Very little is known of the actual prevalence of sampler plugging during SPT and LPT.     46 D50 (mm) 0.1 1 10 N S  /  N L 0 1 2 3 4 5 0.1 1 10 Si mp lif ie d Gr ai n Si ze Co rr ec tio n Fa ct or s 0.0 0.5 1.0 1.5 2.0 (a) (b)Hatanaka and Suzuki (1986) Yoshida et al. (1988) Goto et al. (1987) CSg CLg NS    CLg NL    CSg =                                                Figure 2.20 Variation of (a) simplified Tokimatsu (1988) grain size correction factors and (b) corresponding SPT-JLPT correlation factor with mean grain size.   47                                                Figure 2.21 Variation of SPT-ILPT correlation factor with mean grain size (Jamiolkowski and Lo Presti, 1998).  STD = standard deviation.   48 It is unknown why SPT-JLPT correlation factors increase in gravels while SPT-ILPT correlation factors decrease.  It may be that the plugging effect hypothesized by Jamiolkowski and Lo Presti (2003) is only one contributor to grain size effects, and is less evident in the SPT- JLPT data due to the smaller size of the JLPT sampler.  2.3 CHAPTER SUMMARY  SPT energy and grain size effects were reviewed in this chapter.  It was shown that a reliable estimate of the average rod energy ratio is required to correct SPT blow counts to a standard energy, and that current practices for determining the average rod energy ratio, including the use of typical values and direct measurement, suffer serious limitations.  The use of typical rod energy ratios can lead to very large systematic errors in energy corrected blow counts.  Direct measurement of stress wave energies is limited by the technical difficulty of recording velocity during SPT impacts and the lack of an independent means of calibrating the energy measurement equipment.  In particular, new data was presented demonstrating that measured stress wave energies are highly sensitive to the magnitude of the accelerometer baseline (Figure 2.3).  In this thesis, the uncertainty associated with existing energy approaches is estimated and compared to that of a third method based on hammer velocity measurements. Evidence of fundamental and empirical grain size effects was reviewed.  Fundamental grain size effects were defined as those occurring at the scale of the soil particles and include the effect of grain size variations on the soil hydraulic conductivity, the sand-steel interface friction angle (δi) and the development of shear zones.  SPT grain size effects are most commonly defined as the variation of the blow count – relative density relationship with the mean grain size.  Several grain size effect data sets of this type have been published, and while they appear to support the same general trend of (CD) increasing with (D50), direct comparison of the results is complicated by the different data processing applied during each study.  Grain size effects are also evident in SPT-CPT and SPT-LPT correlation factors.  These approaches to studying grain size effects are advantageous in that direct soil density measurements are not required.  In this thesis, fundamental grain size effect observations, as well as SPT-CPT and SPT-LPT correlation data are used to assess trends noted in a numerical study of grain size effects.  In addition, (CD) and SPT-LPT correlation data from various sources are compiled into larger datasets and used to establish updated SPT grain size effect trends and a procedure for predicting LPT grain size effect trends.   49 CHAPTER 3 ENERGY TRANSFER RATIO APPROACH TO ENERGY CORRECTION  3.1 BACKGROUND  Two methods for determining (ERr)avg were described in the previous chapter, including the use of “typical” values based on equipment details and direct measurement using the FV method.  The former was shown to have accuracy limitations, while the latter was shown to suffer from technical limitations.  The FV method also leads to cost increases due to the costs of the equipment and the additional time required to analyze and assess the quality of the data.  In this chapter, relationships between the hammer kinetic energy at impact and the transferred energy in the drill rod is explored as a possible alternate approach to determining the dynamic energy. Figure 3.1 illustrates various definitions of energies and energy ratios that are of interest during a dynamic penetration test.  Prior to release of the hammer, the energy in the system consists of the potential energy of the hammer, which is commonly calculated relative to the plane of impact.  Just prior to hammer impact, the energy exists as the kinetic energy of the hammer, which is determined by measuring the hammer impact velocity (Vo), and is commonly quoted as the velocity energy ratio (ERv):  (3.1) 2 o v 0.5 M VER 475 J ⋅ ⋅=  where (M) is the hammer mass in units of (kg), and (Vo) is in units of (m/s).  The velocity energy ratio quantifies the efficiency with which potential energy is converted to kinetic energy.  As described in Chapter 2, the proportion of the potential energy that is converted to stress wave energy is characterized by the rod energy ratio (ERr).  The efficiency with which the hammer kinetic energy is transferred to the drill rods can thus be quantified by the energy transfer ratio (ETR), defined as:  (3.2) r 2 v o ER EETR ER 0.5 M V = = ⋅ ⋅    50                                               Figure 3.1 Definitions of various energy terms (PE = potential energy, KE = kinetic energy, E = stress wave energy). Prior to hammer release. Just prior to hammer impact. During hammer impact. End of hammer blow. H d d 2 oVM2 1 KE ⋅⋅= J475 HgMPE = ⋅⋅= ∫ ⋅= dt)t(V)t(FE PE KE ERv = PE E ERr = H d ERhs = Energy Ratios v r ER ER ETR = hsv r m ERER ER ETR += Energy Transfer Ratios Vo Measure F(t), V(t)   51 as per Kovacs et al. (1981).  Rearranging Equation (3.2) leads to an alternate approach to measuring the rod energy ratio:  (3.3) 2 o r 0.5 M VER ETR 475 J ⋅ ⋅= ⋅  Similarly, the average rod energy ratio can be measured as follows:  (3.4) 2 o avg r avg 0.5 M (V ) (ER ) ETR 475 J ⋅ ⋅= ⋅  where (Vo2)avg  is the average squared impact velocity (as opposed to the square of the average impact velocity) measured during the penetration interval 152 to 457 mm (6” to 18”).  (ERr)avg values calculated using Equation (3.4) can be used with Equation (2.2) for energy correction of blow counts. The energy transfer ratio was referred to as the “dynamic efficiency” (ηd) by Skempton (1986).  In addition, the supporting software for the popular Pile Dynamics Inc. (PDI) Pile Driving Analyzer (PDA) stress wave energy measurement equipment refers to the rod energy ratio (ERr) as the energy transfer ratio (ETR).  In this thesis, the ratio of the stress wave energy to the hammer kinetic energy will be referred to as the energy transfer ratio (ETR) as per the original definition (Equation 3.2).  3.2 HISTORY OF THE ENERGY TRANSFER RATIO  The ETR approach to energy correction of blow counts has been considered in the past, but the results of earlier studies did not support its use.  Schmertmann and Palacios (1979) presented average rod energy ratios and average hammer kinetic energies recorded during five safety hammer and six donut hammer tests performed in adjacent boreholes (Figure 3.2).  The energy ratios in the figure are presented as percentages rather than ratios.  They noted that the average ratio of (N) values for blow counts measured at the same depth was 1.61, which is in good agreement with the corresponding average ratio of rod energy ratios (1.65) but in poor agreement with the average ratio of velocity energy ratios (1.22).  Based on these observations they concluded that “only the [stress wave energy] can produce the sampler penetration that   52                                                Figure 3.2 Energy data and blow counts for SPT performed in adjacent test-holes using different test equipment (after: Schmertmann and Palacios, 1979). ERv ERr - Safety Hammer - Donut Hammer   53 Table 3.1 ETR data presented by Schmertmann and Palacios (1979). Safety Hammer, AW rods  Donut Hammer, N rods Test Depth (m) ERv ERr ETR  ERv ERr ETR 6.1  -   -   -   0.66 0.40 0.61 6.7 0.63 0.51 0.81   -   -   - 9.1  -   -   -   0.47 0.28 0.60 10.4 0.75 0.52 0.69   -   -   - 12.1  -   -   -   0.47 0.23 0.49 13.5 0.75 0.52 0.69   -   -   - 14.6  -   -   -   0.69 0.30 0.43 17.0 0.75 0.58 0.77  0.53 0.38 0.72 18.8 0.59 0.45 0.76  0.59 0.28 0.47 Average 0.69 0.52 0.74  0.57 0.31 0.55  determines the N value….”.  They also noted that the ETR appeared to vary with hammer and rod type (Table 3.1). Schmertmann and Palacios (1979) were the original proponents of the F2 method for SPT applications.  They measured force histories and thus rod energy ratios using piezo-electric load cells inserted between two rods near the top of the rod string.  Their use of the F2 method will have introduced several important limitations as discussed in the previous chapter, including errors due to non-uniform rods and an inability to measure energy transferred during secondary impacts, which can be significant for rod lengths less than 10 to 15 m.  Perhaps more importantly, Schmertmann and Palacios (1979) estimated rather than directly measured hammer impact velocities and hence velocity energy ratios.  The impact velocities were estimated using a formula applicable to an ideal simple hammer (Figure 1.2) striking a uniform rod:  (3.5) 1 2o p 1 2 Z ZV F Z Z += ⋅⋅  (simple hammer)  where (Fp) is the peak force measured in the rods and (Z1) and (Z2) are the impedances of the hammer and rod, respectively.  Equivalent impact formulae for donut and safety hammers (derived in Appendix A) are:    54 (3.6) 1 2 3o p 1 2 Z Z ZV F Z Z + += ⋅⋅  (donut hammer)  and  (3.7) 1 2 3o p 2 1 3 Z Z ZV F Z (Z Z ) + += ⋅⋅ +  (safety hammer)  in which (Z3) is the impedance of the donut hammer guide rod and the safety hammer outer cylinder in Equations (3.6) and (3.7), respectively.  These two equations reduce to Equation (3.5) as (Z3) approaches zero, and thus the error associated with use of Equation (3.5) to calculate donut or safety hammer impact velocities is proportional to the relative magnitude of (Z3). Schmertmann and Palacios (1979) do not provide the hammer dimensions necessary to calculate (Z1), (Z2) and (Z3), and so the expected error in their (Vo), (ERv) and ETR values cannot be estimated.  These limitations are sufficient, however, to demonstrate that their conclusions regarding the ETR should be considered preliminary. Kovacs et al. (1981, 1983) described two studies during which donut and safety hammer energy transfer ratios were measured.  They also used a piezo-electric load cell to record the force in the rods and the F2 method to calculate stress wave energies.  Hammer impact velocities were measured using an innovative reflected light system illustrated in Figure 3.3, which consists of stationary light beam sources aimed at a target with alternating light and dark strips that is attached to the hammer.  The fall of the hammer and target through the light beams caused systematic variations of the reflected light intensity that were monitored, recorded and interpreted to estimate both hammer drop heights and impact velocities.  Using this approach they observed that the energy transfer ratio was quite variable for donut hammers and slightly less variable for safety hammers, with variations possibly related to rod type (Figure 3.4).  Based on these results they concluded that: “the hammer to rod transfer of energy (ETR) is important, variable, and unpredictable.  Therefore, the energy in the drill rods, [ERr] cannot be predicted from hammer kinetic energy but needs to be measured directly in the rods.…”  Their results will be compared to those of more recent studies in Chapter 4. Skempton (1986) summarized published values of velocity and rod energy ratios for different hammer types, release methods and anvil weights.  Based on hammer impact velocities measured for a trip-release system by Kovacs (1979), he assumed that all trip- release hammers   55                                                Figure 3.3 Reflected light system for measurement of hammer impact velocities (after: Kovacs et al., 1981).   56                                                Figure 3.4 Histograms of energy transfer ratio measurements for different hammer and rod combinations (after: Kovacs et al., 1983). N U M B ER  O F H A M M ER  B LO W S   57 would produce a velocity energy ratio of 1.0.   He then compared blow counts recorded using identical test setups but different hammer release methods to estimate velocity energy ratios for release methods other than trip-release.  Finally, he reviewed rod energy ratio data from the literature and, using estimated velocity energy ratios based on the hammer release method, calculated energy transfer ratios.  Based on his review and analysis, he suggests that ETR varies with anvil weight, tending to decrease from 0.7 - 0.8 for light anvils (2 to 3 kg) to 0.6 - 0.7 for heavy anvils (12 to 19 kg).  This insightful analysis provided useful guidance for future investigations, but the ETR values presented must be recognized as very preliminary estimates because none were based on velocity and rod energy ratios recorded during the same hammer blow, and in most cases the velocity energy ratios were deduced from ratios of blow counts rather than calculated from measured impact velocities. Morgano and Liang (1992) performed numerical and experimental studies in order to characterize the relationship between the ETR and rod length (L).  Rod energy ratios were measured by the FV method using a Model GCPC PDA system.  The PDA consists of a pair of strain transducers and a pair of accelerometers bonded and bolted, respectively to a transducer rod and associated signal conditioning and processing equipment.  Hammer impact velocities were measured using a radar-based PDI Hammer Performance Analyzer (HPA).  This system consists of an antenna that is placed at the base of the rod string and aimed at the hammer and signal processing equipment, generating a strip chart record of hammer velocity (Figure 3.5). Their field data suggest that ETR decreases with decreasing rod length (Figure 3.6).  Numerical simulations of SPT using the wave equation analysis software GRLWEAP commonly used for modeling pile driving supported the rod length effect and suggested that the ETR would also decrease with blow count in very soft soils.  The use of the FV method during this study will have allowed the measurement of energy transferred during secondary impacts, which is an improvement over the F2 method.  An explanation for why the ETR would vary with rod length and blow count was not provided. Odebrecht et al. (2005) used a strain-gauged rod with bolt-on accelerometers similar to the PDA system to measure stress wave energies using the FV method.  They observed a relationship between stress wave energy and the permanent set achieved during each hammer blow, indicated by the symbol (d) in Figure 3.7.  The tests were performed under controlled conditions for which it can be assumed the velocity energy ratio was relatively consistent, and thus the increase in energy shown in Figure 3.7 can be interpreted as an increase of the ETR. They noted that additional potential energy proportional to the permanent set of the hammer and   58 Ideal Free-Fall Time Fa ll V el oc ity  (f t/s ) 0 8 16 Impact Velocity = 10.4 ft/s                                                Figure 3.5 Sample Hammer Performance Analyzer (HPA) strip chart data showing ideal free- fall and impact velocity (Daniel et al., 2003).   59                                                Figure 3.6 Field data comparing energy transfer ratio versus rod length (a) all data, (b) average values (after: Morgano and Liang, 1992). Rod Length, L (m) 0 4 8 12 16 20 Av er ag e ET R 0.75 0.80 0.85 0.90 0.95 0 4 8 12 16 20 En er gy  T ra ns fe r Ra tio , ET R 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 (a) (b)   60                                                Figure 3.7 SPT stress wave energy measured using the FV method versus hammer set per blow (d) (after: Odebrecht et al., 2005). Hammer and Rod Set, d (m)   61 rods would become available during each hammer blow, and postulated that this was the cause of the observed relationship.  This additional energy may or may not be detected by the instrumentation, depending on the location of the force and velocity measurements and the manner in which the force baseline is selected.  The potential energy that is transformed due to permanent set of the rods will only be detected if the force and velocity measurements are made at the bottom of the rods and the weight of the rods is included in each force measurement (i.e. if the force baseline is determined   before the instrumented rod is placed in the rod string).  In contrast, the potential energy that is transformed due to permanent set of the hammer will be included in FV energies measured anywhere on the rods, provided the force baseline is determined while the hammer is suspended from the mast of the drill rig.  Because stress wave energies are typically recorded at the top of the rod string and force baselines are typically determined prior to each hammer blow, while the hammer is suspended from the mast, most FV stress wave energies will include the potential energy transformed due to the set of the hammer but not of the rods. The hammer set energy can be characterized using a “hammer set energy ratio” (ERhs), defined as:  (3.8) hs dER H =  where (d) and (H) are the permanent set and the hammer drop height, respectively, as shown in Figure 3.1.  For the SPT, the average hammer set energy ratio (ERhs)avg can be estimated as (0.4 / N).  More accurate values for individual hammer blows can be obtained using blows counted over shorter penetration intervals.  Assuming that roughly the same proportion of the energy derived from the impact and the hammer set is lost during any given hammer blow, the following “modified energy transfer ratio” (ETRm), is proposed to describe the effect of additional energy due to hammer set:  (3.9) rm v hs ERETR ER ER = +  as indicated in Figure 3.1.  The rod energy ratio for a single blow can then be estimated as:    62 (3.10) 2 o r m 0.5 M V dER ETR 475 J H  ⋅ ⋅= ⋅ +     and the average rod energy ratio during an SPT as:  (3.11) 2 o avg r avg m 0.5 M (V ) 0.4(ER ) ETR 475 J N  ⋅ ⋅= ⋅ +      According to Equations (3.10) and (3.11), the transferred energies should be directly proportional to the hammer set (d), as shown in Figure 3.7, and inversely proportional to the blow count (N).  These results suggest that the proposed approach based on ETRm is theoretically superior to the ETR approach, but the hammer set energy effect has yet to be independently confirmed.   3.3 CHAPTER SUMMARY  A method of estimating the rod energy ratio based on measurements of the hammer impact velocity using the energy transfer ratio (ETR) was described.  This method was discounted by authors of early energy studies, who found that the ETR was too variable to be of use.  Those studies were limited by their use of the F2 method, and two of the studies were based on deduced, rather than measured, hammer impact velocities.  One recent study noted that the total energy available to be converted into stress wave energy is equal to the sum of the hammer kinetic energy and the potential energy associated with the hammer and rod set.  The “modified energy transfer ratio” (ETRm) was proposed as a means of accounting for additional hammer set energy (Figure 3.1), and the procedure for estimating rod energy ratios from measurements of (ETRm) was demonstrated.   63 CHAPTER 4 SAFETY HAMMER ENERGY TRANSFER RATIO DATABASE  4.1 GENERAL  The variability of the energy transfer ratio was cited by early researchers as the reason an ETR based approach to dynamic energy measurement is not feasible.  The ETR data presented by Kovacs et al. (1981) and Kovacs et al. (1983) shown in Figure 3.4 suggest that donut hammer ETR values are quite variable and that those of safety hammers are not significantly better. Additional safety hammer ETR data were presented by Morgano and Liang (1992).  In this chapter, further details of these three studies are presented, as well as the details and results of four studies performed during the course of this research.  A total of 1,442 measurements from these seven sources are compiled into a database that is used to assess the distribution of safety hammer ETR values and to investigate potential correlations between the ETR and test details such as rod length.  Donut hammer ETR values are not reviewed because no new data have become available.  4.2 DATA FROM THE LITERATURE  Summary details for the studies described by Kovacs et al. (1981), Kovacs et al. (1983) and Morgano and Liang (1992) are provided in Table 4.1, wherein they are identified as studies A, B and C, respectively.  Histograms showing the data distributions for each study are presented in Figure 4.1. The data from studies A and B are shown in Figures 4.1a and 4.1b, respectively.   Figure 4.1b is equivalent to the original histogram plotted by Kovacs et al. (1983) that is shown in Figure 3.4d.  For both studies, rod energy ratios measured during short rod tests were corrected to those that would have been recorded for a rod length of 9.1 m (30’) using the correction procedure recommended by Schmertmann and Palacios (1979).  This correction attempts to address the inability of the F2 method to measure energy transferred during secondary impacts, which can be significant when short rods are used.  The use of the F2 method is likely the primary limitation of these two data sets. T ab le  4 .1  So ur ce s o f d ire ct ly  m ea su re d sa fe ty  h am m er  E TR  v al ue s. St ud y R ef er en ce  So ur ce  o f ER v So ur ce  o f E R r Te st  D et ai ls  R od  T yp e N um be r o f H am m er  B lo w s A . K ov ac s e t a l. (1 98 1)  R ef le ct ed  L ig ht  Sy st em  F2  m et ho d Fo ur  ri gs , m ul tip le  o pe ra to rs  an d ha m m er s N , A W  27 2 SP T 1 B . K ov ac s e t a l. (1 98 3)  R ef le ct ed  L ig ht  Sy st em  F2  m et ho d Si x rig s, m ul tip le  o pe ra to rs  an d ha m m er s B W , N W  14 1 SP T 2 C . M or ga no  a nd  L ia ng  (1 99 2)  H PA  (R ad ar ) FV  m et ho d D at a fr om  th re e si te s A W  18 8 SP T D . K oe st er  e t a l. (2 00 0) , D an ie l ( 20 00 ) H PA  (R ad ar ) FV  m et ho d O ne  ri g an d op er at or , t w o ha m m er s A N W J 6 SP T 6 N A LP T E.  D an ie l ( 20 00 ), D an ie l e t a l. (2 00 3)  H PA  (R ad ar ) FV  m et ho d O ne  ri g an d op er at or , t w o ha m m er s A W J, N W J N W J 87  S PT  11 8 N A LP T F.  D an ie l ( 20 00 ) H PA  (R ad ar ) FV  m et ho d O ne  ri g an d op er at or , o ne  ha m m er N W  72  N A LP T G . U np ub lis he d H PA  (R ad ar ) FV  m et ho d O ne  ri g an d op er at or , t w o ha m m er s A W N W 32 3 SP T 22 9 R LP T 1.  O ne  d at a po in t w ith  E TR  =  1 .6 78  e xc lu de d.  2. 39  A W  ro d da ta  p oi nt s e xc lu de d.  64   65                                                Figure 4.1 Histograms of safety hammer ETR data from studies A, B and C.  Solid lines show equivalent Normal distributions. ETR 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 ETR 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 10 20 30 40 50 60 70 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.40.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 10 20 30 40 50 60 70 Set A (272 Observations) Mean = 0.976 σ = 0.092 Set B plus 39 excluded points (180 Observations) Mean = 0.839 σ = 0.199 Set B (141 Observations) Mean = 0.935 σ = 0.087 Set C (188 Observations) Mean = 0.870 σ = 0.070 (a) (d)(c) (b)   66 The safety hammer ETR values measured during studies A and B are reasonably consistent except for a subset of 39 data points from study B with values ranging from 0.39 to 0.58.  These data were recorded during SPT performed by one experienced driller operating a CME-45 drill rig, using the rope and cathead method to lift and release the safety hammer.  AW rods were used with total rod lengths (L) ranging from 4.15 to 14.81 m.  Kovacs et al. (1983) suggested that the low ETR values could have been related to details of the specific hammer or rods used.  It is also possible that some consistent measurement error occurred on that day of testing.  Such an error could be due to a problem with the instrumentation or due to the sensitivity of stress wave energies measured using the F2 method to variations of rod geometry. For example, if the same load cell were used for all of the rod types tested, a variety of short adaptor rods would have been required to insert the load cell into the different rod strings.  Each rod type would thus be associated with a unique set of impedance interfaces both above and below the load cell.  Impedance interfaces below the load cell generate upward propagating stress waves that violate the force-velocity proportionality assumption upon arrival at the load cell.  Variations of the location and characteristics of these impedance interfaces with rod type would lead to systematic errors in F2 energy measurements.  When the data from the low ETR subset are removed (Figure 4.1c), it can be seen that the data from studies A and B are similar in magnitude and distribution.  These data have been removed for subsequent analyses. The data from study C were originally described by Morgano and Liang (1992) and were made available for review by Morgano (2005, personal communication).  As shown in Figure 4.1d, the distribution of the data ends abruptly at an ETR value of 1.0.  Morgano (2005) stated that ETR values greater than 1.0 were likely discarded from the dataset.  This practice, while defensible for the original application of the data, is equivalent to assuming that the measurement error was zero for all measurements and serves to artificially decrease the mean value of the data set.  For example, if the true value had been equal to 1.0 for every hammer blow, one would expect roughly half of the measurements to be greater than 1.0 due to measurement error.  The results of this slightly biased study will be included in the database due to the limited number of measurements available, but this limitation should be borne in mind when reviewing the results.  4.3 FIELD STUDIES  Studies D, E, F and G were conducted during the course of this research.  The details of Study G have not previously been published and are presented in Appendix B for completeness. T ab le  4 .2 D et ai ls  o f s tu di es  p er fo rm ed  d ur in g th e co ur se  o f t hi s r es ea rc h.   Te st  D et ai ls   St re ss  W av e En er gy  M ea su re m en t D et ai ls  St ud y Lo ca tio n  Ty pe  H am m er , kN  (l b)  D ro p H ei gh t, m  (i n. )  In st ru m en te d R od A cc el er om et er  C ap ac ity , M ou nt in g D et ai ls  Sa m pl in g R at e,  k H z R ec or d Le ng th , m s  SP T 0. 61  (1 37 ) 0. 76 (3 0)  0. 61  m  (2 ’)  A W  R od  6, 00 0g , p la st ic  m ou nt in g bl oc k bo nd ed  a nd  b ol te d to  ro d.  10 0 40  D . R es ur re ct io n R iv er , Se w ar d,  A la sk a  N A LP T 1. 31  (2 94 ) 0. 86 (3 4)  0. 61  m  (2 ’)  A W  R od  6, 00 0g , p la st ic  m ou nt in g bl oc k bo nd ed  a nd  b ol te d to  ro d.  10 0 40   SP T 0. 64  (1 44 ) 0. 76 (3 0)  0. 61  m  (2 ’)  A W  R od  6, 00 0g , p ot te d w ith  e la st om er  in  al um in iu m  b lo ck , b ol te d to  ro d.  40  10 0 E.  K id d2  S ub st at io n,  R ic hm on d,  B C   N A LP T 1. 46  (3 28 ) 0. 76 (3 0)  0. 61  m  (2 ’)  N W J R od  6, 00 0g , p ot te d w ith  e la st om er  in  al um in iu m  b lo ck , b ol te d to  ro d.  40  10 0 F.  K ee nl ey si de  D am , C as tle ga r, B C   N A LP T 1. 46  (3 28 ) 0. 76 (3 0)  0. 61  m  (2 ’)  A W  R od  6, 00 0g , p la st ic  m ou nt in g bl oc k bo nd ed  a nd  b ol te d to  ro d.  10 0 40   SP T 0. 62  (1 38 ) 0. 76 (3 0)  0. 97  m  (3 8” ) A W  R od  20 ,0 00 g,  ti ta ni um  m ou nt in g bl oc k bo nd ed  a nd  b ol te d to  ro d.  10 0 80  G . Pa tte rs on  P ar k,  La dn er , B C   R LP T 1. 46  (3 28 ) 0. 61 (2 4)  1. 17  m  (4 6” ) N W  R od  20 ,0 00 g,  ti ta ni um  m ou nt in g bl oc k bo nd ed  a nd  b ol te d to  ro d.  10 0 80  67   68 Table 4.3   Nominal details of SPT, NALPT and RLPT. Sampler Details  Hammer Details Inner Diameter, mm (in.)  Test Outer Diameter, mm (in.) Shoe Barrel Weight, kN (lb) Drop Height, m (in.) Energy, kJ (ft-lb) SPT 50.8 (2.0) 34.9 (1.37) 38.1 (1.50)  0.623 (140) 0.762 (30) 0.475 (350) NALPT 76.2 (3.0) 61.0 (2.40) 64.0 (2.52)  1.334 (300) 0.762 (30) 1.017 (750) RLPT 114.3 (4.5) 98.4 (3.87) 101.6 (4.00)  1.334 (300) 0.610 (24) 0.814 (600)  As indicated in Table 4.1, the ETR values were recorded during “North American Large Penetration Tests” (NALPT) and “Reference Large Penetration Tests” (RLPT), in addition to SPT.  Details of these tests specific to each study are provided in Table 4.2, and nominal details of each test type are listed in Table 4.3.  Rod and velocity energy ratios presented herein are calculated relative to the nominal hammer energies listed in Table 4.3.  While different rigs, rods and operators were used during each study, the same two safety hammers were used for all SPT, NALPT and RLPT performed during studies E – G, with some minor modifications to the SPT hammer between studies.  Histograms of the ETR data collected during each study are presented in Figure 4.2. Hammer impact velocities were measured during studies D – G using an HPA system similar to the model used by Morgano and Liang (1992).  Details of the custom-built FV stress wave energy measurement systems varied between studies, as summarized in Table 4.2.  Each system consisted of four orthogonal pairs of strain gauges bonded to a short drill rod, and a high capacity accelerometer mounted on a block attached in close proximity to the same rod.  The signal conditioning and processing equipment were designed to sample the output from the strain gauges and accelerometer, digitally integrate the accelerometer data to yield velocity and calculate FV energies during each hammer blow in the field.  In general, the quality of the stress wave data tended to improve during each successive study as the measurement systems were modified to address issues noted during previous studies.    69                                                Figure 4.2 Histograms of safety hammer ETR data from studies D, E, F and G.  Solid lines show equivalent Normal distributions. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.40.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 10 20 30 40 50 60 70 Set D (12 Observations) Mean = 0.976 σ = 0.056 Set E (205 Observations) Mean = 0.907 σ = 0.133 ETR 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 ETR 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 10 20 30 40 50 60 70 Set F (72 Observations) Mean = 1.021 σ = 0.105 Set G (552 Observations) Mean = 1.030 σ = 0.088 (a) (d)(c) (b)   70 No special measures were taken to identify hammer impact velocity and stress wave energy measurement pairs during studies E – G.  To overcome this limitation, all tests for which the number of hammer blows recorded using the two systems were not equal were excluded. Such a difference might occur if the HPA strip chart was turned off during a temporary halt in testing to conserve paper and the marking device was not properly warmed up prior to continuation of the test, or if the stress wave system failed to trigger.  All of the potentially useable stress wave data were then reviewed and obviously erroneous or questionable data were excluded.  Data were excluded, for example, if the force-velocity proportionality prior to time (2L/c) was strikingly different than for other blow during the same test.  It is possible that the HPA and stress wave measurement systems may have missed different blows during the same test, but it is unlikely that this would have occurred systematically.  It is also possible that a subtle bias was introduced based on what the writer considers to be reliable data.  This is unfortunately one of the fundamental limitations of the direct measurement approach.  4.4 DISTRIBUTION OF ETR DATA  The measured ETR can be thought of as a continuous random variable that will always contain random scatter, regardless of how well controlled the measurement process is.  It is convenient to describe the distribution of a random variable (x) using a probability density function, p(x).  Two commonly encountered distributions are the Normal distribution:  (4.1) 2 0.5 1 1 (x )p(x) exp 2(2 )  − µ= ⋅ − ⋅ σσ⋅ ⋅π     and the LogNormal distribution:  (4.2) 2 0.5 1 1 (x )p(x) exp ln 2x (2 )  − µ= ⋅ − ⋅ σ⋅σ ⋅ ⋅π     where (µ) and (σ) are the true mean value and standard deviation of (x), respectively.  The standard deviation is often normalized to the mean value to provide a dimensionless indicator of variability referred to as the coefficient of variation (Ω):   71 Table 4.4   Statistical summary of safety hammer ETR database. Study or Test Sample Size Mean Value, µ Standard Deviation, σ 1 Coefficient of Variation, Ω (%) 1 A. 272 0.976 0.092 9.4 B. 141 0.935 0.087 9.3 C. 188 0.870 2 0.070 2 8.0 2 D. 12 0.976 0.056 5.7 E. 205 0.907 0.133 14.7 F. 72 1.021 0.105 10.3 G. 552 1.031 0.088 8.5 SPT 1,017 0.961 0.110 11.4 NALPT 196 0.970 0.129 13.3 RLPT 229 1.017 0.091 8.9 All Data 1,442 0.971 0.112 11.5  1. Represents the 68.26% confidence interval for a Normally distributed random variable. 2. Expected to be lower than true values due to exclusion of ETR values greater than 1.0.   (4.3) 100%σΩ = ⋅µ  Examples of Normal and LogNormal distributions are shown in Figure 4.3.  The probability, P(x), that the variable (x) will assume a value within some interval can be estimated by determining the area under p(x) over that interval.  Figure 4.4 illustrates intervals around the true mean value of a normally distributed random variable within which various percentages of observations are expected to fall.  These intervals are commonly referred to as confidence intervals and are identified by their associated probability.  For example, the 95% confidence interval for a Normally distributed random variable (x) corresponds to the range (µ -  2σ ≤ x ≤ µ + 2σ).  Simple, closed-form expressions for the areas under Normal and LogNormal distribution curves are not available, but P(x) is easily determined using descriptive tables or special functions incorporated into spreadsheet software.  Some special measures are required when the sample size is less than 60. A complete listing of all relevant data from studies A to G is provided in Appendix C. The sample size, mean, standard deviation and coefficient of variation for each study, each test type and the entire database are listed in Table 4.4.  Figure 4.5a is a histogram representing the   72 x p( x) p( x) (a) (b)                                                Figure 4.3 Examples of (a) Normal and (b) LogNormal probability density functions for a generic random variable (x).   73 p( x) µ µ + σ µ + 2σ µ + 3σµ − σµ − 3σ µ − 2σ 68.27% 95.45% 99.73%                                                Figure 4.4 Relationship between some useful confidence intervals and the standard deviation (σ) of a Normally distributed random variable (after: Figliola and Beasley, 2000).   74                                               Figure 4.5 Histograms of safety hammer ETR data for (a) entire database plus 39 excluded points and (b, c) entire database.  Solid lines show equivalent Normal and LogNormal distributions, as indicated. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 25 50 75 100 125 150 All Data plus 39 excluded points (1,481 Observations) Mean = 0.959 σ = 0.135 (a) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 25 50 75 100 125 150 (b)All Data (1,442 Observations) Mean = 0.971 σ = 0.112 ETR 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 25 50 75 100 125 150 (c)All Data (1,442 Observations) Mean = 0.971 σ = 0.112 Normal Distribution Normal Distribution LogNormal Distribution   75 entire database plus the 39 data points excluded from study B.  The 1,442 ETR measurements that have been included in the database range in value from 0.61 to 1.33 while the values for the excluded 39 measurements ranged from 0.39 to 0.58.  This complete lack of overlap is strong evidence that the low ETR values of the excluded data points were caused by a systematic error and can be treated as outliers.  Figure 4.5b is a revised histogram showing only the data points included in the database. Equivalent Normal and logNormal distributions for the entire database were developed using the “NORMDIST()” and “LOGNORMDIST()” functions in Microsoft Excel 2000 (Excel) and are plotted in Figure 4.5, as labeled.  In Figure 4.5a, for which the 39 AW rod data points excluded from Study B have been included, the equivalent Normal distribution is a poor representation of the histogram.  In contrast, when the excluded points are removed (Figure 4.5b), the equivalent Normal distribution represents the data quite well.  As shown in Figure 4.5c, the minor asymmetry of the LogNormal distribution does not appear to be supported by the available data.  Thus it can be assumed that the safety hammer energy transfer ratio is a Normally distributed random variable with a mean value (µ) of 0.971, a standard deviation (σ) of 0.112 and a coefficient of variation (Ω) of 11.5%.  Equivalent Normal distributions for the data from each study were also developed and are shown on Figures 4.1 and 4.2.  Review of these figures suggests that the data from individual studies are also reasonably well represented by the equivalent Normal distributions, though the histograms are generally less symmetric. The extent to which the statistical descriptors listed in Table 4.4, particularly those of the entire database, should be adjusted or qualified for sample size is unclear.  The total number of ETR measurements (1,442) is much greater than 60, but the database could also be described, for example, in terms of the number of contributing studies (7), or the number of different equipment configurations tested.  Intuitively, it seems likely that (σ) and (Ω) will increase as additional data become available.  Until such data become available, however, it can be assumed that the observed values are representative.  4.5 ANALYSIS OF POTENTIAL CORRELATIONS  The standard deviation and coefficient of variation of the safety hammer ETR database reflects both natural variability and measurement error, but may also reflect systematic variation of the ETR with factors such as rod type (Kovacs et al., 1983), anvil weight (Skempton, 1986), rod length (Morgano and Liang, 1992), blow count (Odebrecht et al., 2005) or test type (e.g. SPT   76 Table 4.5   Summary of available rod type information. Rod Area (cm2) Nominal Rod Type Sample Size Study Test Type Mean ETR 4.839 AWJ 79 E SPT 0.863 7.361 BW 114 B SPT 0.939 7.594 AW 70 A SPT 7.613 AW 188 C SPT 7.639 AW 323 G SPT   0.968 8.310 N 103 A SPT 1.003 NWJ 6 D NALPT 9.161 NW 72 F NALPT    1.018 NWJ 118 E NALPT 9.806 NWJ 8 E SPT    0.934 13.226 NW 229 G RLPT 1.017  versus LPT).  Possible correlations between the (ETR) and these five potential controlling factors are reviewed in the following sections.  4.5.1 Effect of Rod Type  Kovacs et al. (1983) suggested that ETR variations may be related to variations of rod size.  Rod type information was unavailable for 132 hammer blows included in the database, leaving a total of 1,310 useable data points, as summarized in Table 4.5.  The data have been categorized according to rod cross-sectional area rather than rod type because the area is the factor that is most likely to affect the energy transfer ratio.  In addition, rod areas vary between manufacturers for a single nominal rod type.  Rod type descriptors ending in a “J” indicate that the rod couplings utilize tapered threads as opposed to square threads, a factor which may also affect the energy transfer ratio. The mean energy transfer ratios listed in Table 4.5 increase slightly with the rod cross- sectional area, a trend that is confirmed in Figure 4.6.  Figure 4.6 is a “box and whisker” plot in which the lower and upper limits of the box indicate the 25th and 75th percentiles, respectively, and the horizontal line within the box indicates the median value.  The error bars extending from the box indicate the 10th and 90th percentiles and the circles indicate data points that fall outside of these limits, which are often assumed to be outliers.     77                                              Figure 4.6 Box and whisker plot illustrating negligible relationship between ETR and rod area for 1,310 safety hammer blows. Rod Cross-Sectional Area, A (cm2) 2 4 6 8 10 12 14 16 En er gy  T ra ns fe r Ra tio , ET R 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Data collected during single study (Study E), susceptible to bias error.   78 Careful review of Table 4.5 reveals that most of the rod area data subsets were collected during a single study, indicating that there is considerable potential for measurement bias errors from a single study to create false trends.  For example, if the AWJ rod data (Area = 4.84 cm2) collected during study E were excluded from Figure 4.6 the trend of increasing ETR with rod area would become insignificant relative to the variability within each rod area group.  The other study E data points were recorded using 9.81 cm2 NWJ rods, and the mean ETR value is also low relative to the surrounding subsets.  This suggests that the ETR values recorded during study E may have been systematically lower than those of the other studies, possibly due to a stress wave energy measurement bias error or to the use of “J” series rods with tapered threads. Additional data recorded using rods with cross-sectional areas less than 7 cm2 and non-tapered threads are required to determine whether rod areas do affect the ETR.  Based on the available data, it can only be concluded that the effect of rod type on ETR, if any exists, appears to be minor.  4.5.2 Effect of Anvil Weight  Skempton (1986) inferred that the ETR varied with the weight of the anvil.  Anvil masses are available for the hammers used during studies D – G.  The masses of the SPT and NALPT hammer anvils used during study D were roughly 2.1 and 2.8 kg, respectively, while those of the SPT and NALPT / RLPT hammers used during studies E – G were roughly 4.6 and 4.9 kg, respectively.  Since very few data points are available from study D, and the two hammers used during studies E – G had roughly the same anvil weight, it is not possible to observe the relationship, if any, between the anvil weight and ETR using the database.  The study E – G hammer anvil masses fall between the high and low efficiency groupings identified by Skempton (1986), but the ETR values observed are significantly higher than the high efficiency range of 0.7 to 0.8 that he postulated.  The available data are thus not in agreement with Skempton’s observations, but are too limited in range to provide a suitable test of his anvil weight hypothesis.  4.5.3 Effect of Rod Length  The effect of rod length on the magnitude of the stress wave energy has been a topic of interest since the first SPT stress wave energies were recorded, primarily due to use of the F2 method during early studies (Daniel et al., 2005).  It has been suggested that rod energy ratios are lower when short rods are used, and that short rod blow counts should be reduced when the rod   79 energy ratio has not been measured to account for these assumed reduced energies (e.g. ASTM D6066-96, Youd et al., 2001).  Rod length effects are difficult to assess using stress wave energy measurements alone because there are many potential causes of energy variations related to hammer, rig and operator details.  A more direct approach is to determine if there is a relationship between rod length and ETR.  Study C was conducted by Morgano and Liang (1992) specifically for this purpose. Rod lengths are available for 1,427 of the 1,442 data points in the database.  The ETR values for these data points are plotted as a function of rod length in Figure 4.7.  The bulk of the data represent rod lengths greater than 7.0 m and these do not appear to exhibit any trend with rod length.  The 79 data points recorded using rod lengths less than 7.0 m do suggest that the ETR is reduced for shorter rod lengths leading to a linear correlation coefficient of 0.37.  Closer scrutiny of the data, however, reveals that this may be a false trend.  The data for the three shortest rod lengths (2.74, 4.27 and 5.79 m) represent three SPT performed in the field during Study C.  As noted earlier, all ETR values greater than 1.0 are believed to have been discarded from this data set, and thus it is possible that the trend of decreasing ETR with rod length actually represents an increase in the scatter of the data with decreasing rod length.  This is plausible because measurement of stress wave energy during short rod tests is often problematic. This is likely primarily due to the need to accurately measure energy transferred during post (2L/c) secondary impacts, where minor accelerometer bias errors have a greater effect on the calculated energy.  The remaining data of interest (rod length = 6.30 m) are from study A and thus are based on stress wave energies measured using the F2 method.  These F2 energies would have been corrected to “infinite” rod length values using a theoretically derived correction that is based on the idealization of a simple hammer striking a uniform rod string.  Real hammers, anvils and rod strings are considerably different than the idealized case, and the error inherent in this correction is unknown. Daniel et al. (2005) demonstrated numerically and experimentally that SPT energy transfer during what is thought of as a single hammer blow occurs during one primary impact and several secondary impacts.  The number of secondary impacts and the proportion of energy transferred during those impacts tend to increase with decreasing rod length and blow count.  It is possible that the efficiency of the energy transfer process decreases as the number of secondary impacts increases, but no reliable data have been presented to prove or disprove this hypothesis.  In contrast Matsumoto et al. (1992), Tsai et al. (2004) and Daniel et al. (2005) recorded stress wave energies during short rod SPT that were roughly equal to the original   80                                                 Figure 4.7 ETR plotted as a function of total rod length (L) for 1,427 safety hammer blows. Total Rod Length, L (m) 0 5 10 15 20 25 30 En er gy  T ra ns fe r Ra tio , ET R 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Data collected during three SPT (Study C), ETR values >1.0 discarded. Measured using F2 method (Study A).   81 potential energy of the hammer, suggesting that the ETR values were roughly equal to one.  The rod lengths used during this small number of tests ranged from 3.12 to 6.49 m.  These results suggest that either the ETR did not vary with rod length, or the variations were too small to be reliably recorded using currently available instrumentation.  Despite these observations, it can only be stated that the data do not support the conclusion that rod length effects do occur, and do not support the values in general use.  4.5.4 Effect of Test Type  The mean and standard deviation of the ETR for each of the three types of tests represented in the database are provided in Table 4.4.  ETR frequency distributions for the two types of LPT are compared to that of the SPT in Figure 4.8. Frequency distributions are equivalent to histograms except the number of occurrences are normalized by the total number of observations to ease comparison between tests.  It is evident in both the tabulated data and the plots that the SPT and NALPT ETR data are similar while slightly higher values were recorded during the RLPT.  The difference could represent a simple bias error in the RLPT data, which were all collected during a single study.  Alternatively, the hammer drop height (H) was lower for the RLPT than for the SPT and NALPT (Table 4.3) and thus, referring to Equation (3.8), the hammer set energy ratio for a given hammer set (d) or blow count (N) would be higher for the RLPT.  In that case, the ETR values would tend to be higher for the RLPT while the ETRm values should be roughly consistent between tests.  The effect of permanent hammer set is discussed in greater detail below.  4.5.5 Effect of Blow Count  Hammer blows per 25 mm penetration are available for 768 of the hammer blows from studies D – G.  Inverting these values provides a measure of the permanent set per blow (d).  The hammer blows per 25 mm were used to calculate the hammer blows per 152 mm and the (N) values normally recorded during an SPT, and these two terms were also inverted to obtain alternate estimates of (d).  Irregularities in the penetration history will be better represented by the short interval values of (d) but the latter two methods of obtaining (d) are more likely to be used during regular practice.  Figure 4.9 compares measured ETR values to (d) values calculated using the three methods.  In this plot, the ETR appears to decrease slightly with increasing permanent set, regardless of the source of (d).  This is in contrast with the results of Odebrecht et   82 ETR 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Fr eq ue nc y (% ) 0 5 10 15 20 25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Fr eq ue nc y (% ) 0 5 10 15 20 25 (a) (b) SPT (1,017 Observations) NALPT (196 Observations) SPT (1,017 Observations) RLPT (229 Observations)                                                Figure 4.8 Comparison of SPT ETR frequency distribution to that of (a) the NALPT and (b) the RLPT.   83 0 20 40 60 80 100 120 En er gy  T ra ns fe r Ra tio , ET R 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 (a) Expected range of SPT ETR due to hammer set effects (∆d = 95mm, ERv = 0.4) Permanent Set, d (mm) 0 20 40 60 80 100 120 En er gy  T ra ns fe r Ra tio , ET R 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 (c) Expected range of SPT ETR due to hammer set effects (∆d = 95mm, ERv = 0.4) 0 20 40 60 80 100 120 En er gy  T ra ns fe r Ra tio , E TR 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 (b) Expected range of SPT ETR due to hammer set effects (∆d = 95mm, ERv = 0.4)                                               Figure 4.9 Comparison of ETR values for 768 safety hammer blows to permanent set calculated from (a) blow per 25 mm, (b) blows per 152 mm, and (c) blows per 305 mm.   84 al. (2005) shown in Figure 3.7, which show an increase in measured stress wave energy with increasing (d) over a similar range of (d).  Recall that the hammer impact velocity was likely close to constant during this well-controlled study and thus the ETR would likely have been observed to increase with (d) as well, had the impact velocity been measured. Odebrecht et al. (2005) suggest that the rod energy ratio measured at the top of the rods increases with permanent set (d).  If this were true, the rod energy ratio measured during any blow count could be written as:  (4.5) H/d)ER(ER)ER(ER 0drhs0drr +=+= ==  where (ERr)d=0 is a hypothetical rod energy ratio that would have been measured if (d) had been equal to zero.  The measured energy transfer ratio would then be equal to:  (4.6) HER d)ETR( ER H/d)ER( ETR v 0d v 0dr ⋅+= += ==  where (ETR)d=0 is the hypothetical energy transfer ratio that would have been recorded if (d) had been equal to zero.  Equation (4.6) demonstrates that ETR should increase with (d) at a rate of (1 / ERv⋅H), assuming the potential energy associated with the permanent set of the hammer is converted into stress wave energy.  (H) is equal to 762 mm for the SPT and NALPT, and a conservatively large estimate of the range of (ERv) is 0.4 to 1.0.  The slope of the relationship can thus be expected to vary between roughly (1 / 1.0 ⋅ 762 mm = 0.0013) and (1 / 0.4 ⋅ 762 mm = 0.0033) ETR units per mm.  These slopes should be increased by (762 mm / 610 mm = 1.25) for the RLPT due to the reduced value of (H) applicable for that test.  Referring to Figure 4.9, the (d) values represented in the database range from roughly 5 to 100 mm.  The expected variation of ETR for SPT over this range would vary from a low value of (95 ⋅ 0.0013 = 0.12) to a high value of (95 ⋅ 0.0033 = 0.31), depending on the applicable value of (ERv).  The latter range has been included in Figure 4.9 for comparison and it can be seen that the ETR scatter at any one value of (d) is comparable to the variation of ETR expected over the entire observed range of (d). Figure 4.10 compares average ETR values recorded during different studies as a function of (d) and demonstrates that some of the scatter shown in Figure 4.9 is due to systematic variation of ETR between studies.  The tendency for ETR values recorded during study E to be somewhat   85 0 20 40 60 80 100 120 Av er ag e En er gy  T ra ns fe r Ra tio , ET R 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 (b) Permanent Set, d (mm) 0 20 40 60 80 100 120 Av er ag e En er gy  T ra ns fe r Ra tio , E TR 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 (c) 0 20 40 60 80 100 120 Av er ag e En er gy  T ra ns fe r Ra tio , E TR 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 (a) Study D (12 Observations) Study E (191 Observations) Study F (71 Observations) Study G (494 Observations)                                               Figure 4.10 Comparison of average ETR values for 768 safety hammer blows to permanent set calculated from (a) blows per 25 mm, (b) blows per 152 mm, and (c) blow count (N).   86 lower than those recorded during other studies was noted during the earlier discussion of rod type effects.  Figure 4.10 demonstrates that most of the data points with high (d) values were recorded during study E and, as a result, a false trend of decreasing (ETR) with increasing (d) is suggested when sources of data points are not differentiated, as in Figure 4.9.  Close review of Figure 4.10 reveals that, within any single study, there is no discernible trend of ETR with (d).  It is believed that the ETR has not been measured with sufficient accuracy to allow detection of the relatively small variations that could be caused by hammer set effects (0.12 to 0.31 per 95 mm). A modified energy transfer ratio (ETRm) equal to the rod energy ratio divided by the sum of the velocity and hammer set energy ratios was introduced in Chapter 3.  Referring to Equation (4.5), the equation for ETRm can be written as:  (4.7) H/dER H/d)ER( ERER ER)ER(ETR v 0dr hsv hs0dr m + +=+ += ==  Because the numerator and denominator vary in the same manner with (d), it is expected that ETRm should be less sensitive than ETR to variations of (d).  This observation suggests a second approach to assessing whether potential energy associated with the set of the hammer is converted into stress wave energy.  If the measured rod energy ratio does vary systematically with (d), one would expect the ETRm histogram to demonstrate lower variability than an equivalent ETR histogram.  Figure 4.11 compares histograms of ETR and ETRm for the same 768 hammer blows discussed above.  The ETRm values were calculated using (d) values determined from the blows per 25 mm data.  Statistical details for this particular subset of data are included in Figure 4.11 and summarized in Table 4.6.  The average ETRm values are roughly 0.03 lower than the corresponding ETR values, and the ETRm standard deviations are generally the same or higher than those of the ETR.  This may be due to additional errors associated with measurement of (d), or due to the relatively minor variations of ETR expected for the range of (d) represented in the database, as discussed above.  These observations confirm that, at this stage, the ETRm approach to estimating average rod energy ratios (Equation 3.11) is only theoretically superior to the ETR approach (Equation 3.4). Finally, it was demonstrated in Table 4.4 and Figure 4.8 that the mean ETR value was somewhat higher for RLPT hammer blows than for those of the SPT and NALPT.  It was suggested in Section 4.5.4 that this may be due to more significant hammer set effects in the   87 ETRm 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 20 40 60 80 100 (b)Displacement Subset (768 Observations) Mean = 0.969 σ = 0.118 ETR 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Nu mb er  o f Oc cu re nc es 0 20 40 60 80 100 (a)Displacement Subset (768 Observations) Mean = 1.000 σ = 0.117 Normal Distribution Normal Distribution                                                Figure 4.11 Histograms showing distribution of (a) ETR and (b) ETRm for 768 safety hammer blows.  Solid lines show equivalent Normal distributions.   88 Table 4.6   Summary of data subset for which ETRm measurements are available. ETR ETRm Test Sample Size Mean Standard Deviation Coefficient of Variation (%) Mean Standard Deviation Coefficient of Variation (%) SPT 412 1.002 0.116 11.6 0.971 0.116 11.9 NALPT 183 0.968 0.130 13.4 0.933 0.133 14.3 RLPT 173 1.029 0.094 9.1 1.002 0.090 9.0 All 768 1.000 0.117 11.7 0.969 0.118 12.2  RLPT results, due to the lower hammer drop height (H) employed during that test.  The data in Table 4.6 demonstrate, however, that even the mean values of ETRm, which should be insensitive to hammer set effects, are higher for the RLPT than for the SPT or NALPT.  This observation suggests that the observed test type effect most likely represents a systematic error in (ERr) values between studies, because all of the RLPT data were recorded during study G.  4.6 CHAPTER SUMMARY  The development of an updated database consisting of 1,442 measurements of safety hammer energy transfer ratios was described in this chapter.  The data were gathered from three studies described in the literature and from four field studies conducted during the course of this research.  A variety of ETR measurement systems and equipment configurations and even test types (SPT, NALPT and RLPT) are represented in the database.  The available data follow a roughly Normal distribution with a mean value (µ) of 0.971 and a standard deviation (σ) of 0.112.  Potential systematic variations of ETR with rod type, anvil weight, rod length, test type and blow count were investigated.  In all cases, the effect of any potential relationship was insignificant relative to data scatter within individual studies and to observed systematic variations between the results of different studies.  It is possible that some other factor that was not considered caused the variations between studies, but it is clear that a significant component of the variability can be attributed to measurement error.  The assessment of possible correlations also revealed some of the limitations of the direct measurement approach, such as the difficulty of measuring stress wave energy during short rod tests, demonstrating that a more robust approach to determining stress wave energies is needed.   89 CHAPTER 5 COMPARISON OF ENERGY MEASUREMENT APPROACHES  5.1 INTRODUCTION  It would be useful to be able to predict the uncertainty of SPT or LPT blow counts during the planning phase of a geotechnical investigation.  As noted in previous chapters, the dynamic energy is the primary factor controlling the magnitude of the blow counts, and there is considerable uncertainty associated with available energy measurement methods.  In this chapter, a method of predicting the uncertainty of energy corrected blow counts is described and, in the process, the relative merits of the various energy measurement methods are assessed.  The prediction process is described for the specific case of SPT or LPT performed in North America using safety hammers, as these are the operating conditions for which the ETR database is believed to be representative.  Finally, a recommended ETR based procedure for calculation of energy corrected blow counts and associated uncertainties is summarized.  5.2 QUANTIFYING UNCERTAINTY  Consider a result (Y) that is a function of (n) independent variables identified as (x1, x2, … , xn):  (5.1) 1 2 nY f (x , x ,..., x )=  For engineering applications, the independent variables are typically measured quantities and/or correlation factors subject to both precision and bias errors.  Precision errors are random and are often considered to lead to a distribution of possible measurements around a mean value.  Bias error decribes the offset between the mean value and the true value (Figure 5.1).  Bias errors are eliminated when possible through instrument calibration, and are very difficult to quantify below the resolution of the calibrator. Precision and bias errors of (xi)terms ultimately lead to errors in the result (Y).  If a large number of measurements are made under fixed operating conditions, the distribution of (Y) can be quantified and used to identify the most probable value of (Y).  In many cases, however, only one set of measurements can be made and hence only one value of (Y) can be calculated.  In that   90 Measured Variable Fr eq ue nc y (% ) bias error true value precision error represented as Normal distribution                                                 Figure 5.1 Definition of precision and bias errors (after: Figliola and Beasely, 2000).    91 situation, we estimate the probable error of (Y), known as the uncertainty, which is the interval about (Y) within which the true value is expected to lie (Figliola and Beasely, 2000).  5.2.1 Taylor Series Expansion  Kline and McClintock (1953) demonstrated that the uncertainty of a result (Y) can be estimated using the first order terms of a Taylor series expansion of Equation (5.1):  (5.2) 2n i ii 1 Y(Y) (x ) x=  ∂σ = ⋅σ ∂ ∑  where σ(Y) and σ(xi) are the uncertainty of (Y) and (xi), respectively, expressed here as standard deviations.  The implication of using standard deviations to characterize the contributing uncertainties is that the result uncertainty will roughly correspond to a 68% confidence interval. The Taylor series expansion method relies on a linear (first order) approximation of the sensitivity of (Y) to each of the random variables to estimate σ(Y), as demonstrated for a single variable in Figure 5.2.  Deviations from linear relationships introduce error in the predicted uncertainty.  A further limitation of the approach is that the nature of the distribution of (Y) must be interpreted from the distributions of (xi) and from f(x1,x2,…,xn).  A sum or difference of Normally distributed random variables will be Normally distributed, while multiplication or division of Normally distributed random variables produces a Log-Normally distributed variable. The latter can often be adequately represented as Normal distributions.  5.2.2 Application to SPT and LPT Blow Counts  The situation described above is the case when recording SPT or LPT energy corrected blow counts.  Many of the factors that control the magnitude of  energy corrected blow counts (e.g. sampler dimensions, borehole details, measured energies) are susceptible to both precision and bias errors.  Energy corrected blow counts are calculated using Equation (2.2), reprinted here for ease of reference:      92                                              Figure 5.2 Visual representation of error propagation analysis using the Taylor series expansion approach (( x ) and ( y ) are mean values of measurement (x) and result (y), Figliola and Beasley, 2000).    93 (5.3) r avg60 N (ER ) N 0.6 ⋅=  Applying Equation (5.2) to Equation (5.3) relates the uncertainty of the energy corrected blow count σ(N60) to the uncertainties of the measured blow count σ(N) and the average rod energy ratio (σ (ERr)avg):  (5.4) 22 60 60 60 r avg r avg N N(N ) (N) (ER ) N (ER )  ∂ ∂ σ = ⋅σ + ⋅σ    ∂ ∂      Taking the first derivative of Equation (5.3) with respect to (N) and (ERr)avg, yields:  (5.5) 22 r avg60 60 r avg (ER )(N ) (N)100% 100% 100% N N (ER )  σσ σ ⋅ = ⋅ + ⋅          or:  (5.6) 2 260 r avg(N ) ( (N)) ( (ER ) )Ω = Ω + Ω  Equation (5.6) incorrectly suggests that Ω(N60) will always be higher than Ω(N).  The root of this misunderstanding can be traced to the adopted notation, and clarified by noting that the measured value of (N) is actually a function of (ERr)avg:  (5.7) ce r avg N CEN (ER ) ⋅=  where (Nce) is the raw blow count that would be recorded at an arbitrary constant energy (CE). Substitution of Equation (5.7) into Equation (5.3) leads to the expression:  (5.8) r avgce ce60 r avg (ER )N CE N CEN (ER ) 0.6 0.6 ⋅ ⋅= ⋅ =    94 from which the following relationship for Ω(N60) can be derived:  (5.9) 2 260 ce(N ) ( (N )) ( (CE)Ω = Ω + Ω  Equation (5.9) correctly shows that the uncertainty of energy corrected blow counts is due to the uncertainty of the raw blow count at an arbitrary constant energy and the uncertainty associated with measurement of that energy.  Zekkos et al. (2004) published a study of the reliabilty of SPT blow counts and noted this distinction, but did not adopt an equivalent “constant energy” notation.  It is anticipated that the introduction of these terms would tend to confuse rather than clarify the origins of Ω(N60) and, for this reason, Equation (5.6) will be adopted herein, with the understanding that Ω(N) refers strictly to non-energy related uncertainty of (N).  It should be noted that the uncertainties calculated using these equations does not account for the effects of the inherent spatial variabilty of soils. Equation (5.6) is plotted for several values of Ω(N) in Figure 5.3.  Zekkos et al. (2004), citing a lack of available data, assumed that Ω(N) would be in the order of 10%.  Thus it is suggested that the thicker Ω(N) = 10% line in Figure 5.3 can be used to estimate the uncertainty of SPT or LPT energy corrected blow counts.  The same curve can be used to assess the relative merits of the three approaches to energy correction.  5.3 UNCERTAINTY OF AVERAGE ROD ENERGY RATIO  The uncertainty of an energy corrected blow count is a function of the measurement error of the average rod energy ratio, as opposed to that of a single hammer blow.  The average rod energy ratio recorded during a test is calculated as follows:  (5.10) N r 1 r 2 r N r avg r i i 1 (ER ) (ER ) ... (ER ) 1(ER ) (ER ) N N = + + += = ∑  where (ERr)i are the rod energy ratios measured during the (N) hammer blows contributing to the blow count.  Applying Equation (5.2) to Equation (5.10) yields:     95 Ω (ER r)avg (%) 0 5 10 15 20 25 30 35 Ω (N 60 ) (% ) 0 10 20 30 40 20% 5% 10% 15% Ω(N)                                                 Figure 5.3 Relationships between Ω(N60) and Ω(ERr)avg for selected values of Ω(N).    96 (5.11) N 2 r r avg r i2 i 1 (ER )1(ER ) (ER ) N N= σσ = σ =∑  wherein it has been assumed that σ(ERr) is roughly the same for each hammer blow.  Equation (5.11) demonstrates that σ(ERr)avg will decrease rapidly as the blow count increases.  This is valid for precision errors but not for bias errors, as only random precision errors will tend to cancel as the number of measurements increases. Estimates of Ω(ERr)avg are developed for each of the three energy measurement approaches in the following sections.  The prevalence of precision versus bias errors, and hence the applicability of the averaging effect, is also discussed.  5.3.1 “Typical” Rod Energy Ratios  Zekkos et al. (2004) assumed that the average rod energy ratio for a North American safety hammer has an equal probability of assuming any value in the range 0.42 to 0.72, the “typical” range suggested by Youd et al. (2001).  This is a conservative assumption, as (ERr)avg almost certainly has a higher probability of assuming a value of 0.6 than 0.42 or 0.72.  In the absence of a representative dataset, a more balanced approach is to assume a Normal distribution with a conservatively high standard deviation.  One accepted approach to estimating standard deviations is the three-sigma rule, based on the fact that 99.73% of observations of a Normally distributed random variable will fall within roughly three standard deviations of the mean value (e.g. Duncan, 2000).  The standard deviation can thus be estimated by dividing the widest conceivable range of values by six.  For SPT safety hammers, this range can be estimated as 0.60 ± 0.45 (0.15 to 1.05), leading to a standard deviation of 0.15 and a coefficient of variation of 25%. The difference between the assumed and actual magnitude of (ERr)avg is a simple bias error, and thus no beneficial averaging effect will be realized.  There is also no reliable means of estimating the magnitude of the bias error, though the engineer may be able to determine if the (N60) values are consistently high or low if other in-situ test results are available (which partially defeats the purpose of performing the SPT).  For the sake of discussion, it is suggested that the uncertainty of the average rod energy ratio (Ω(ERr)avg) when the “typical” value is used for a North American safety hammer will be in the order of 20 to 30%.    97 5.3.2 Directly Measured Rod Energy Ratios  Both precision and bias measurement errors must be considered when estimating the uncertainty of directly measured rod energy ratios.  The magnitude of the precision error for a particular stress wave energy measurement system could be estimated by making repeated measurements under carefully controlled testing conditions (e.g. in a laboratory) and assuming that the true stress wave energy was constant.  Based on experience it is suggested that stress wave energies recorded under those conditions using modern FV instrumentation would produce a standard deviation in the order of 0.05 to 0.10.  The precision error component of the uncertainty will decrease significantly due to the averaging effect described earlier, and is expected to be negligible relative to bias error. As noted in Chapter 2, there is no reliable means of calibrating stress wave energy measurement equipment, and thus there is considerable potential for bias error in directly measured stress wave energies.  For the purpose of discussion, it is estimated that the uncertainty of the average rod energy ratio (Ω(ERr)avg) will be primarily due to bias error,  and will be in the order of 5 to 10%.  5.3.3 Energy Transfer Ratio Approach  The energy transfer ratio approach is defined by Equation (3.3), reprinted here for ease of reference:  (5.12) 2 o r 0.5 M VER ETR 475 J ⋅ ⋅= ⋅  Applying the Taylor series expansion yields:  (5.13) 22 2 r r r r o o ER ER ER(ER ) (M) 4 (V ) (ETR) M V ETR     σ = ⋅σ + ⋅ ⋅σ + ⋅σ           or:     98 (5.14) ( ) ( ) ( )2 2 2r o(ER ) (M) 4 (V ) (ETR)Ω = Ω + ⋅ Ω + Ω  Estimates of the uncertainty of the hammer mass, impact velocity and ETR are thus required to estimate Ω(ERr).  ASTM D1586-99 states that the hammer mass must be equal to 63.5 ± 1.0 kg. Thus it is reasonable (and likely slightly conservative) to adopt σ(M) and Ω(M) values of 1.0 kg and 1.6%, respectively.  The hammer impact velocities in the ETR database were measured using one of two systems.  Kovacs (1979) estimated the measurement uncertainty of his reflected light system as 1.5%.  It will be assumed that this was his estimate of Ω(Vo).  Based on his description of the measurement procedure, it is believed that this uncertainty is primarily due to resolution considerations.  The magnitude of σ(Vo) due to resolution considerations will be constant for all (Vo), and hence Ω(Vo) is expected to vary with (Vo).  Assuming the estimate provided is appropriate for a velocity energy ratio of 0.60, corresponding to an impact velocity of 2.996 m/s, σ(Vo) can be estimated as 0.045 m/s.  The uncertainty of impact velocities measured using the hammer performance analyzer (HPA) will also be primarily due to resolution considerations, and the uncertainty can be estimated as one half of the resolution of the strip chart, or 0.061 m/s and 0.122 m/s for the high and low resolution settings, respectively.  ETR for safety hammers was shown to follow a roughly Normal distribution with a mean value of 0.97, standard deviation of 0.11 and coefficient of variation of 11.3% in Chapter 4. Unlike the typical value and direct measurement approaches, good estimates of all contributing uncertainties are available for the ETR approach.  A Monte Carlo simulation is useful for demonstrating the manner in which these uncertainties will combine, and for predicting the resulting distribution of rod energy ratios.  Consider a hammer blow with a measured impact velocity of 2.996 m/s, corresponding to an (ERv) value of 0.60.  10,000 Normally distributed possible (Vo) values were simulated with a mean value of 2.996 m/s, and standard deviations of 0.045, 0.061 and 0.122 m/s, representing the measurement uncertainty of the reflected light system, the HPA on high resolution and the HPA on low resolution, respectively.  The three resulting distributions are shown in Figure 5.4a.  Figure 5.4b shows 10,000 possible (M) values (representing the uncertainty of the mass of the hammer mobilized to site) and 10,000 possible ETR values (representing the uncertainty of the energy transfer ratio). Finally, Figure 5.4c shows the distribution of (ERr) values calculated for each of the 10,000 realizations of (Vo), (M) and (ETR), and for each velocity measurement system.  The possible (ERr) values are reasonably well represented by equivalent Normal distributions, descriptive Fi gu re  5 .4  M on te  C ar lo  s im ul at io n de ta ils  ( ER v = 0. 60 ) in cl ud in g:  ( a)  v el oc ity  d is tri bu tio n by  s ys te m  ( b)  h am m er  m as s an d ET R  di st rib ut io ns  a nd  (c ) r es ul tin g ro d en er gy  ra tio  d is tri bu tio ns  (1 0, 00 0 re al iz at io ns  p er  v el oc ity  m ea su re m en t s ys te m ). En er gy  T ra ns fe r Ra tio , ET R 0. 5 0. 6 0. 7 0. 8 0. 9 1.0 1.1 1.2 1.3 1.4 0 20 0 40 0 60 0 80 0 10 00 Ha mm er  M as s,  M  ( kg ) 58 59 60 61 62 63 64 65 66 67 68 Observations 0 20 0 40 0 60 0 80 0 10 00 Me an  =  0 .9 7 V = 0. 11 Me an  =  6 3. 5 V = 1.0 Ro d En er gy  R at io , ER r 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 0 20 0 40 0 60 0 80 0 10 00 HP A - Lo w Re s. Me an  =  0 .5 84 V = 0. 08 2 Ro d En er gy  R at io , ER r 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 0 20 0 40 0 60 0 80 0 10 00 HP A - Hi gh  R es . Me an  =  0 .5 83 V = 0. 07 0 Ro d En er gy  R at io , ER r 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 Observations 0 20 0 40 0 60 0 80 0 10 00 Re fl ec te d Li gh t Sy st em Me an  =  0 .5 83 V = 0. 06 9 Im pa ct  V el oc ity , V o  ( m/ s) 2. 6 2. 7 2. 8 2. 9 3. 0 3. 1 3. 2 3. 3 3. 4 Observations 0 20 0 40 0 60 0 80 0 10 00 Re fl ec te d Li gh t Sy st em Me an  =  2 .9 96 V = 0. 04 5 Im pa ct  V el oc ity , V o  ( m/ s) 2. 6 2. 7 2. 8 2. 9 3. 0 3. 1 3. 2 3. 3 3. 4 0 20 0 40 0 60 0 80 0 10 00 HP A - Hi gh  R es . Me an  =  2 .9 96 V = 0. 06 1 Im pa ct  V el oc ity , V o  ( m/ s) 2. 6 2. 7 2. 8 2. 9 3. 0 3. 1 3. 2 3. 3 3. 4 0 20 0 40 0 60 0 80 0 10 00 HP A - Lo w Re s. Me an  =  2 .9 96 V = 0. 12 2 (a ) (b ) (c ) 99 T ab le  5 .1 M on te  C ar lo  si m ul at io n an d Ta yl or  se rie s e xp an si on  e st im at es  o f v ar ia bi lit y fo r E TR  e st im at ed  (E R r) va lu es .  M on te  C ar lo  S im ul at io n 1  Ta yl or  S er ie s 1  V el oc ity   En er gy  T ra ns fe r R at io   R od  E ne rg y R at io   H am m er  Im pa ct  V el oc ity  M ea su re m en t S ys te m  ER v V( V o) : (V o) V( ET R ) : (E TR ) V( ER r) : (E R r) : (E R r) fr om  Eq ua tio n (5 .1 4)  0. 2  0. 04 5 4. 5  0. 11  11 .3   0. 02 4 12 .5   12 .6  0. 4  0. 04 5 2. 3  0. 11  11 .3   0. 04 7 12 .0   12 .0  0. 6  0. 04 5 1. 5  0. 11  11 .3   0. 06 9 11 .8   11 .8  0. 8  0. 04 5 1. 1  0. 11  11 .3   0. 09 1 11 .7   11 .7  R ef le ct ed -L ig ht  Sy st em , V( V o) = 0. 04 5 m /s  1. 0  0. 04 5 0. 9  0. 11  11 .3   0. 11 3 11 .7   11 .7  0. 2  0. 06 1 6. 1  0. 11  11 .3   0. 02 6 13 .4   13 .4  0. 4  0. 06 1 3. 1  0. 11  11 .3   0. 04 8 12 .5   12 .5  0. 6  0. 06 1 2. 0  0. 11  11 .3   0. 07 1 12 .1   12 .2  0. 8  0. 06 1 1. 5  0. 11  11 .3   0. 09 3 12 .0   12 .0  H PA , H ig h R es ol ut io n,  V( V o) = 0. 06 1 m /s  1. 0  0. 06 1 1. 2  0. 11  11 .3   0. 11 5 11 .9   11 .9  0. 2  0. 12 2 12 .2   0. 11  11 .3   0. 03 6 18 .3   18 .2  0. 4  0. 12 2 6. 1  0. 11  11 .3   0. 05 9 15 .3   15 .2  0. 6  0. 12 2 4. 1  0. 11  11 .3   0. 08 2 14 .1   14 .1  0. 8  0. 12 2 3. 1  0. 11  11 .3   0. 10 5 13 .5   13 .4  H PA , Lo w  R es ol ut io n,  V( V o) = 0. 12 2 m /s  1. 0  0. 12 2 2. 4  0. 11  11 .3   0. 12 7 13 .1   13 .1  1. V( M ) =  1 .0  k g,  : (M ) =  1 .6 % . 100    101 Table 5.2   Reduction of Ω(ERr)avg with (N) for ETR approach.  Coefficient of Variation, Ω(ERr)avg Ω(ERr) N = 1 N = 10 N = 20 N = 30 12% 12% 3.8% 2.7% 2.2% 18% 18% 5.7% 4.0% 3.3%  statistics for which are listed in Table 5.1. Additional simulations were run for measured (ERv) values of 0.2, 0.4, 0.8 and 1.0, and these results are also listed in Table 5.1.  Ω(ERr) values predicted using Equation (5.13) are provided in the final column of Table 5.1, and are seen to be in good agreement with the results of the Monte Carlo simulations.  This analysis demonstrates that Equation (5.14) can be used to predict Ω(ERr), and that (ERr) follows a roughly Normal distribution for values of Ω(M), Ω(Vo) and Ω(ETR) likely to be encountered in practice.  Ω(ERr) is expected to range from 12 to 18%, depending on the system used to measure the hammer impact velocity. These estimates of Ω(ERr) are applicable to individual hammer blows.  Random precision errors in rod energy ratios determined using the ETR approach will tend to cancel as per Equation (5.11), and reliable methods for identifying and eliminating bias errors in impact velocity measurements are readily available.  For example, tuning forks whose ends vibrate at a known velocity were used to confirm HPA calibration factors during studies D – G in the ETR database. Thus the significant potential for reduction of variability suggested by Equation (5.11) is likely realized to some extent when the ETR approach is used.  Table 5.2 summarizes the expected relationship between Ω(ERr) and (N) for the ETR approach.  Ω(ERr)avg is expected to vary between roughly 2 and 6% for blow counts ranging from 10 to 30.     102 Table 5.3   Estimated values of Ω(ERr)avg and corresponding values of Ω(N60). Method Ω(ERr)avg Ω(N60) Typical Value Approach 20 to 30% 22 to 32% Direct Measurement Approach (N > 10) 5 to 10% 11 to 14% ETR Approach (N > 10) 2 to 6% 10 to 12%   5.4  DISCUSSION  5.4.1 Comparison of Energy Correction Procedures  Table 5.3 summarizes what are believed to be reasonable estimates of the uncertainty of the average rod energy ratio for use during the planning stage of a geotechnical investigation. The uncertainty chart from Figure 5.3 is re-printed here as Figure 5.5 with these ranges superimposed to illustrate the corresponding ranges of Ω(N60), which are also listed in Table 5.3. The direct measurement and ETR approaches offer a significant reduction of Ω(N60) relative to the use of typical energies.  The difference between the direct measurement and ETR approaches is negligible because Ω(N60) is controlled by Ω(N) when Ω(ERr)avg decreases below 10%. Again, it should be noted that the estimated uncertainties plotted in Figure 5.5 do not account for the effects of the inherent spatial variability of soils, which will lead to additional uncertainty during geotechnical investigations. The proposed uncertainties for the typical energy and direct measurement approaches are estimates based largely on experience.  This is not uncommon when uncertainty is primarily due to bias error, as bias errors are notoriously difficult to quantify.  It has long been recognized that the lack of a calibration procedure (i.e. a means of quantifying bias error) is a major limitation of the direct measurement approach (e.g. Bosscher and Showers, 1986).  It is appropriate to take into account the fact that the uncertainty cannot be reliably characterized when selecting a representative quantifier of uncertainty. Each individual ETR measurement in the ETR database was calculated using a directly measured energy, and hence each measurement contains an unquantified and possibly significant bias error.  It is unlikely, however, that the bias errors would be consistent between different    103 Ω (ER r)avg (%) 0 5 10 15 20 25 30 35 Ω (N 60 ) (% ) 0 10 20 30 40 20% 5% 10% 15% Ω(N) 20 - 30% "Typical" Energies 5 - 10% Direct Measurement ETR Approach 2 - 6%                                                Figure 5.5 Relationships between Ω(N60) and Ω(ERr)avg for various values of Ω(N).  Ranges of Ω(ERr)avg shown for each energy measurement approach.    104 tests, boreholes and studies, and thus the bias errors can be considered to evolve into randomly distributed precision errors as the number of observations in the database increases.  The ETR approach thus provides a practical means of addressing the bias error problem which plagues any study involving the direct measurement of stress wave energies.  5.4.2 Recommended Procedure and Sample Application  For the reasons noted in the previous section, and because it is technically much easier to measure hammer impact velocities than stress wave energies, the ETR approach is recommended as the superior method for energy correction of SPT or LPT blow counts recorded using safety hammers in North America.  The recommended procedure is detailed in Figure 5.6, the end result being an energy corrected blow count and an estimate of the uncertainty of the blow count, expressed as one standard deviation. For example, consider a hypothetical SPT performed using a safety hammer, the impact velocity of which was recorded using an HPA on the high resolution setting (resolution = 0.122 m/s).  The blows per 150 mm (6”) were (3 / 4 / 8), and thus the blow count (N) is equal to 12. The mass of the safety hammer was measured as 64.5 kg on a scale with a resolution of 0.5 kg prior to testing, and the measured impact velocities for the blows contributing to the blow count are listed in Table 5.4.  Referring to Figure 5.6, the uncertainty of the hammer mass can be estimated as one half of the resolution:  • kg25.0)M( =σ • %4.0%100 kg5.64 kg25.0)M( =⋅=Ω  Similarly, the uncertainty of the hammer impact velocity can be estimated as one half of the HPA resolution and, noting the average hammer impact velocity of 3.350 m/s Table 5.4), we can write:  • s/m061.0)V( o =σ • %8.1%100 s/m350.3 s/m061.0)V( o =⋅=Ω  Fi gu re  5 .6  R ec om m en de d ET R  p ro ce du re  fo r e ne rg y co rr ec tio n of  S PT  o r L PT  sa fe ty  h am m er  b lo w  c ou nt s. 105 A.  Pr ep ar at or y W or k B.  Fi el d W or k C.  Ca lc ul at io ns 1. Ca lc ul at e               f or  e ac h ha mm er  b lo w. 2. Ca lc ul at e (E R v ) av g fo r bl ow s co nt rib ut in g to  N . * r av g v av g v av g (E R ) ET R (E R ) 0. 97 (E R ) = ⋅ = ⋅ 3. Ca lc ul at e r av g 60 (E R ) N N 0. 60 = ⋅ 4. Ca lc ul at e 5. Ca lc ul at e (V o) a vg fo r bl ow s co nt rib ut in g to  N . * 6. Ca lc ul at e 2 2 2 r o 2 2 2 o (E R ) ( (M )) 4 ( (V )) ( (E TR )) ( (M )) 4 ( (V )) (11 .3 % ) Ω = Ω + ⋅ Ω + Ω = Ω + ⋅ Ω + 7. Ca lc ul at e r r av g (E R ) (E R ) N Ω Ω = 8. Ca lc ul at e 2 2 60 r av g 2 2 r av g (N ) ( (N )) ( (E R ) ) (10 % ) ( (E R ) ) Ω = Ω + Ω = + Ω 9. Ca lc ul at e 60 60 (N ) (N ) N 1.0 10 0% Ω σ = ⋅ ≥ 10 .C al cu la te  Ha mm er  M as s (M ): Op tio n 1 :  m ea su re  h am me r we ig ht , W , i n un its  o f (N ) Op tio n 2 :  as su me  M  =  6 3. 5 kg W M g = (g  =  9 .8 1 m/ s2 ) (M ) σ = po st ed  a cc ur ac y or ½ re so lu tio n of  s ca le (M ) (M ) 10 0% M σ Ω = ⋅ 1.0 kg (M ) 10 0% 1.6 % 63 .5 kg Ω = ⋅ = Im pa ct  V el oc ity  U nc er ta in ty : Op tio n 2 :  as su me  σ (V o)  =  ½ re so lu tio n of  in st ru me nt Op tio n 1 :  pe rf or m la bo ra to ry  t ria ls  a t fix ed  ( V o ) to di re ct ly  m ea su re  σ (V o)  σ (M ) = 1.0  k g Bl ow  C ou nt  ( N) : * If N < 10 , us e al l av ai la bl e me as ur em en ts  f ro m te st . 1.  R ec or d (N ) as  p er  a pp lic ab le  s ta nd ar d. Ha mm er  Im pa ct  V el oc ity  ( V o ): 1.  P er fo rm  r eg ul ar  f ie ld  c al ib ra tio n if po ss ib le . 2.  Re co rd  ( V o ) du rin g ea ch  h am me r bl ow  in  u ni ts  o f (m /s ). 2.  A ss um e Ω (N ) = 10 % 2 o v V M 21 J 47 51 ER ⋅ ⋅ ⋅ = Re su lt : ) N( N 60 60 σ ± % 10 0 ) V( ) V( ) V( av g o o o ⋅ σ = Ω    106 Table 5.4   Data and calculations for sample application of recommended procedure. Hammer Blow 1 Vo (m/s) KE (J) 2  ERv ERr 4 3.355 363 0.76 0.74 5 3.294 350 0.74 0.72 6 3.355 363 0.76 0.74 7 3.233 337 0.71 0.69 8 3.355 363 0.76 0.74 9 3.355 363 0.76 0.74 10 3.294 350 0.74 0.72 11 3.233 337 0.71 0.69 12 3.538 404 0.85 0.83 13 3.477 290 0.82 0.8 14 3.355 363 0.76 0.74 15 3.355 363 0.76 0.74 Average: 3.350  0.76 0.74 1. Hammer blows 4 to 15 contribute to blow count of 12. 2. Measured hammer mass, M = 64.5 kg.  The kinetic energy of the hammer just prior to impact (KE) and the velocity energy ratio (ERv) is calculated for each hammer blow in Table 5.4 using the measured hammer mass of 64.5 kg. The average velocity energy ratio (ERv)avg is equal to 0.76, and thus the average rod energy ratio and energy corrected blow count are calculated as:  • 74.076.097.0)ER( avgr =⋅= • 8.14 60.0 74.012N60 =⋅=  In order to estimate the uncertainty of the energy corrected blow count, we estimate the uncertainty of the rod energy ratios and average rod energy ratio as:  • %8.11)35.11(%)8.1(4%)4.0()ER( 222r =+⋅+=Ω    107 • %4.3 12 %8.11 N )ER()ER( ravgr ==Ω=Ω  Finally, we estimate the uncertainty of the energy corrected blow count:  • %6.10%)4.3(%)10()N( 2260 =+=Ω • 6.1 %100 %6.108.14)N( 60 =⋅=σ  The energy corrected blow count is thus estimated as 14.8 ± 1.6.  corresponding to a 68.3% confidence interval (± one standard deviation).  The 99.7% confidence interval is equivalent to ± three standard deviations, or 14.8 ± 4.8.  5.5  CHAPTER SUMMARY  The problem of estimating the uncertainty of energy corrected blow counts was considered in this chapter, and was used to assess the relative merits of the typical value, direct measurement and ETR approaches to energy correction.  Contributing measurement uncertainties were estimated for each of the three methods, and a method based on Taylor series expansion was used to estimate uncertainties of energy corrected blow counts.  The uncertainty due to the typical value and direct measurement approaches is primarily due to bias error and is difficult to quantify.  In contrast, the uncertainty of the ETR approach is primarily due to precision errors that are relatively easy to quantify.  The direct measurement and ETR approaches were both shown to be clearly superior to the typical value approach, but roughly equivalent to each other in terms of result uncertainty.  Due to the relative ease of measuring and interpreting hammer impact velocity data, and the considerable potential for undetected bias error when using the direct measurement approach, the ETR approach is recommended as the superior method for energy correction of SPT or LPT blow counts recorded using safety hammers.  The recommended ETR based approach (Figure 5.6) was demonstrated using hypothetical SPT data in Section 5.4.2.  The first half of this thesis has led to an assessment of the uncertainty of energy corrected blow counts.  The results of this assessment should be borne in mind when considering other factors affecting blow counts, such as grain size effects.   108  CHAPTER 6 GRAIN SIZE EFFECT DATA  6.1 INTRODUCTION  SPT grain size effects have primarily been characterized in the literature as a variation of the relationship between blow counts and relative density (CD).  Tokimatsu (1988) used an innovative approach to back-calculate SPT and JLPT grain size effects from the observed variation of SPT-JLPT correlation factors with (D50).  Both approaches were briefly reviewed in Chapter 2.  In this chapter, (CD) data from the literature are reviewed in greater detail and compiled into a single data set.  SPT-LPT correlation factors from the literature and from this study are then compiled in a similar manner, and existing grain size effect relationships are assessed in light of the updated data sets.  For ease of notation, SPT-LPT correlation factors will be denoted using the symbol (CS/L), as per the equation:  (6.1) 60 SPTS/ L 60 LPT (N )C (N ) =  6.2 (CD) GRAIN SIZE EFFECTS  (CD) measurements from both calibration chamber and field studies are available in the literature.  Data from these two sources are discussed separately and then combined into a single data set in the following sections.  6.2.1 Calibration Chamber Studies  (CD) grain size effects were investigated using a calibration chamber approach during the Waterways Experiment Station (WES) study described by Bieganousky and Marcuson (1976, 1977) and the Central Research Institute of the Electric Power Industry (CRIEPI) study described by Yoshida et al. (1988).  Data from the WES study were considered by Skempton (1986) and Kulhawy and Mayne (1990), while Chen (2004) considered data from both studies. Chen (2004) scaled the CRIEPI data from figures available in the literature and provided tables of these values (Chen, 2006).  A full listing of the CRIEPI data obtained directly from one of the   109  Table 6.1 WES and CRIEPI calibration chamber test details and results, SPT data.  CD  (Current Int.)  CD  (Proposed Int.) c Study Soil D50 (mm) Uc  Mean Std. Dev. Ω (%)  Mean Std. Dev.  Ω (%) RBM 0.23 1.8  43.0  -   -   57.3  -   - SCS 0.51 2.5  58.0  -   -   77.3  -   - WES a PRS 2.00 5.3  63.0  -   -   84.0  -   - TS 0.34 1.95  48.1 14.4 29.9  64.2 19.2  29.9 G25 1.13 5.65  68.5 19.7 28.8  91.3 26.3 28.8 G50 2.28 11.3  75.0 20.1 26.8  100.0 26.8 26.8 CRIEPI b G75 7.30 31.1  86.0 34.9  40.6  68.5 30.6 44.7 a. Rod length = 2.4 m, prescribed CR = 0.75 (Youd et al., 2001). b. Rod length = 3.0 m, prescribed CR = 0.75 (Youd et al., 2001). c. Short rod corrections (CR) removed, original (emax) and (emin) values used for G75 data.  original researchers (Kokusho, 2003) is given in Appendix D.  Currently accepted interpretations of both the WES and CRIEPI data are listed in Table 6.1.  Also listed are new interpretations proposed herein.  Differences between the current and proposed interpretations are due to the use of short rod corrections (both data sets, all soils) and modified relative density parameters (CRIEPI data set, soil G75 only).  These modifications are discussed below. The proposed CRIEPI data are compared to the current values in Figure 6.1.  Previous interpretations of the CRIEPI data have used modified (emax) and (emin) values proposed for soil G75 by the original researchers.  They suggested that the (emax) and (emin) values measured for soil G75 were unreliable due to the presence of large grain sizes, and instead used values that they extrapolated from those of the three other soils.  While it is valid to point out deficiencies in the procedures used to determine (emax) and (emin), extrapolation from other soils does not represent an improvement and, as shown in Figure 6.1, leads to a significantly different trend of (CD) with (D50).  It is suggested that a more balanced approach is to use the measured values with the caveat that the G75 data are more susceptible to error. The use of short rod corrections (CR) during calibration chamber studies leads to a uniform reduction of all measured blow counts as per the equation:  (6.2) corrected R measuredN C N= ⋅    110 0.1 1 10 (C D) 0 25 50 75 100 125 150 175 200 D50 (mm) 0.1 1 10 (C D) 0 25 50 75 100 125 150 175 200 (b) (a)Current Interpretation Proposed Interpretation                                                Figure 6.1 (a) Current and (b) proposed interpretations of CRIEPI data.  Error bars indicate ± one standard deviation.   111  Table 6.2 Short rod correction factors from the literature (after: Daniel et al., 2005).  Short Rod Correction, CR Rod Length, L (m)  Seed et al. (1985) Skempton (1986) ASTM D4633-86 a Morgano and Liang (1992) a Youd et al. (2001) >10  1.00  1.00 0.98 – 1.00 1.00 1.00 6 – 10  1.00 0.95 0.89 – 0.98 0.96 – 0.99 0.95 4 – 6   1.00 0.85 0.76 – 0.89  0.90 – 0.96 0.85 3 – 4  1.00 0.75 0.69 – 0.76 0.86 – 0.90 0.80 <3  0.75 0.75 0.69 0.86 0.75 a. Ranges interpolated from published values.  Table 6.2 summarizes recommended (CR) values from several sources in the literature. Skempton (1986), Kulhawy and Mayne (1990) and Chen (2004) all applied short rod corrections to the calibration chamber data that they reviewed. The purpose of short rod corrections is to account for the effect of reduced or delayed energy transfer when short rods are used.  It is a fact of stress wave theory that the energy transferred prior to (2L’/c), known as the initial impact energy, will decrease with rod length. The question of whether short rod corrections should be applied is really a question of whether the blow count is controlled by the initial impact energy, or the total transferred energy (i.e. the initial impact energy plus any energy transferred during secondary impacts).  The need for short rod corrections was inferred from a limited number of tests performed in the late 1970’s and early 1980’s using the F2 method, which is incapable of measuring total transferred energy, and known to be highly susceptible to systematic error.  Practitioners who currently measure energy using the FV method almost universally use the total transferred energy to correct blow counts. Short rod corrections have become entrenched in practice, however, and continue to be recommended in “state-of-practice” articles such as Youd et al. (2001). Short rod corrections lead to a conservative reduction of blow counts when used in practice, but their use during the development of empirical correlations is potentially unconservative.  This is especially problematic for calibration chamber studies, during which all the tests are performed using short rods (Daniel and Howie, 2006).  For example, Skempton (1986) proposed the following relationship between (N1)60 and relative density (Dr) for soil RBM tested during the WES study:  (6.3) 21 60 r(N ) 36 D= ⋅   112 He applied a correction of 0.65 to the data due to the use of a 2.4 m rod length.  The measured relationship without a short rod correction would thus have been:  (6.4) 2 21 60 r r 36(N ) D 55 D 0.65 = ⋅ = ⋅  Consider the interpretation of an (N1)60 value of 20 recorded in a field deposit of the same sand using rods of greater than 10 m length.  The interpreted relative density would be 75% if the short rod corrected relationship were used (Equation 6.3), compared to 60% if the measured relationship were used (Equation 6.4).  The higher value is only correct if the calibration chamber blow counts were actually controlled by the initial impact energy rather than the total transferred energy. Kulhawy and Mayne (1990) and Chen (2004) applied short rod corrections of 0.75 to the WES and CRIEPI data, respectively.  Figure 6.2 illustrates the effect of applying a short rod correction of 0.75 to the WES data.  Kulhawy and Mayne (1990) suggested that the observed difference between the short rod corrected calibration chamber data and the Niigata sand field data represented an ageing effect, and proposed the dashed best-fit line to represent un-aged soils.  Figure 6.2 demonstrates, however, that the “uncorrected” WES data are in good agreement with the field data, suggesting that the postulated ageing effects may be entirely due to the use of short rod corrections. To summarize, it is potentially unconservative to use short rod corrections in the context of a calibration chamber study, and the corrections may have led to misinterpretation of results in some cases.  Perhaps the most relevant observation was made by Kokusho and Yoshida (1998) who, in their description of the CRIEPI study, noted that blow counts recorded using rods of 3 and 6 m length were not significantly different.  Based on these observations, it is suggested that the proposed interpretations of the WES and CRIEPI data listed in Table 6.1, from which the short rod corrections have been removed, and the measured (emax) and (emin) were used to calculate (CD) for soil G75, are the correct values to use for subsequent analyses described below.    113  D50 (mm) 0.1 1 C D 30 40 50 60 70 80 90 100 110 CD = 60 + 25 Log (D50) Kulhawy and Mayne (1990) Unaged Soils WES Data (CR = 0.75) WES Data (CR = 1.00) Niigata Sand Data                                                Figure 6.2 Effect of short rod corrections on WES calibration chamber data set (after: Daniel and Howie, 2006).   114  6.2.2 Field Measurements  Four sets of (CD) field data compiled during previous studies were compiled into a single data set during this study.  No new measurements of (CD) were made.  The four contributing data sets were: Skempton (1986), Kulhawy and Mayne (1990), Cubrinovski and Ishihara (1999) and Chen (2004).  The data selected for use from each of the four studies, referred to as references R1, R2, R3 and R4, respectively, are listed in Table 6.3.  A total of 70 natural and 7 fill soil measurements were incorporated.  The set includes 32 averaged data points (bracketed values in Table 6.3) and 45 non-averaged data points.  Repeat measurements and those representing volcanic soils, cemented soils and mine tailings were excluded.  Appendix E contains a full listing of the data from each contributing reference and describes the vetting process that was followed. Energy correction procedures represented in the data set range from the use of typical rod energy ratios to direct energy measurement.  In-situ soil densities were measured using techniques ranging from conventional sampling (e.g. tube sampling) to collection of frozen samples.  Soil ages generally range from less than one year to 125,000 years, with four older soils ranging from 980,000 to 170,000,000 years old.  Most of the soil ages listed in the table are average values based on general descriptions of the geological period or epoch, rather than a specific measurement (e.g. carbon dating), and are considered accurate to within an order of magnitude at best.  6.2.3 Discussion  The calibration chamber data summarized in Table 6.1 (proposed values) and the field data listed in Table 6.3 are plotted as a function of (D50) in Figure 6.3.  Averaged and non- averaged data points are indicated by filled and open symbols, respectively.  The mean value and variability of (CD) are seen to increase with mean grain size.  The following bi-linear relationship is proposed to describe the variation of the mean value:   (6.5a) D 50C 88 56 Log(D )= + ⋅   0.15 mm ≤ D50 ≤ 2.0 mm  (6.5b) DC 105=    2.0 mm ≤ D50 ≤ 20 mm    115 Table 6.3  Summary of available (CD) measurements. Source 1 Soil Age (years) Sampling Method 2 D50 (mm) CU Dr (%) CD 3 R1 Ogishama sand 0.25 CS 0.30 4 54 (34)  Kawagishi-cho sand 35 CS 0.35 2.4 51 (44) R2 Niigata, south bank 125,000 CS 0.28  -  67 60     0.29  -  82 56  Niigata, road site 125,000 CS 0.30 1.7 46 (62)     0.45 1.8 49 (76)  Niigata, river site 125,000 CS 0.46 2.0 43 72     0.63 2.8 36 83  Norwich Crag sand 980,000 CS 0.20 2.0 50 (122)  Bagshot sand 42,000,000  -  0.20  -   -  (112)  Folkstone sand 100,000,000  -  0.17  -   -  (145)  Grantham sand 170,000,000  -  0.16  -   -  (189) R3 F1 sand Natural CS 0.33 -  73 24     0.32 - 92 31     0.19 - 66 15     0.33 - 76 13     0.20 - 63 44     0.27 - 71 36  F2 sand Natural CS 0.38 - 81 15     0.72 - 92 30  F3 sand Natural CS 0.30 - 118 12     0.16 - 109 34     0.18 - 112 29     0.17 - 110 24  TOFL sand  Natural FS 0.16 - 92 37     0.16 - 100 37     0.17 - 87 49     0.16 - 71 60  Nagoya sand 125,000 FS / CS 0.54 - 76 56      continued… - Not available. 1. Sources:  R1 - Skempton (1986), R2 - Kulhawy and Mayne (1990), R3 - Cubrinovski and Ishihara (1999), R4 - Chen (2004). 2. CS = Conventional Samples, FS = Frozen Samples 3. Values in brackets are averages.    116 Table 6.3 continued… Source 1 Soil Age (years) Sampling Method 2 D50 (mm) CU Dr (%) CD 3 R3 (con.) Narita sand 125,000 FS / CS 0.19  -  81 (34)     0.16  -  74 (21)  IK2-1 sand 1,000 FS / CS 0.25 - 72 (43)  IK2-2 sand 1,000 FS / CS 0.39 - 57 (68)  Niigata sand -1 125,000 FS 0.30 - 64 56     0.23 - 54 81     0.23 - 84 48     0.25 - 78 56     0.29 - 86 52  Niigata station 125,000 FS 0.28 - 87 53     0.30 - 87 54     0.29 - 82 60  T-Gravel 30,000 FS 10.50 - 53 213     14.40 - 65 110     13.00 - 53 133     16.40 - 81 70     12.10 - 53 216     9.00 - 53 93     6.30 - 56 143     3.50 - 42 262     12.50 - 44 149     10.20 - 53 189     18.50 - 65 57     9.00 - 66 46     12.30 - 66 91     1.05 - 25 837     7.60 - 53 116     13.30 - 60 79     8.20 - 21 1652 R4 Higashi-Ohgishima (1) 3 FS 0.22 2.1 91 (42)      continued… - Not available. 1. Sources:  R1 - Skempton (1986), R2 - Kulhawy and Mayne (1990), R3 - Cubrinovski and Ishihara (1999), R4 - Chen (2004). 2. CS = Conventional Samples, FS = Frozen Samples 3. Values in brackets are averages.    117 Table 6.3 continued… Source 1 Soil Age (years) Sampling Method 2 D50 (mm) CU Dr (%) CD 3 R4 (con.) Higashi-Ohgishima (2) 30 FS 0.28 1.7 26 (56)  IK1 sand Fill  FS / CS 0.29 1.7 50 (59)  Duncan Dam sand 10,400 FS 0.20 2.5 44 (65)  TAMU sand (1) 32,000  -  0.16 2.2 55 (79)  TAMU sand (2) 32,000  -  0.19 1.6 55 (51)  NWU sand 23  -  0.25 1.2 48 (84)  SO gravelly sand 125,000 CS 0.43 8.3 56 (54)  SO sand 125,000 CS 0.33 2.6 60 (57)  Masado gravel 2 FS 2.43 22.3 117 (9)  Mandano gravel 125,000 FS 1.93 8.2 83 (119)  Tokyo gravel 125,000 FS 10.75 66.1 58 (335)  Tadotsu gravel 125,000 FS 9.98 27.1 99 (68)  Tone river gravel 1,000 FS 10.77 39.9 49 (138)  K-site gravel 20,000 FS 21.33 44.9 62 (506)  A-Site gravel layer 1 125,000 FS 1.81 11.8 61 (102)  A-Site gravel layer 3 125,000 FS 1.71 5.0 73 (93)  SO sandy gravel 125,000 CS 9.17 32.3 47 (52)  Bishop's Falls gravel 125,000 CS 4.50 12.4 60 (101) - Not available. 1. Sources:  R1 - Skempton (1986), R2 - Kulhawy and Mayne (1990), R3 - Cubrinovski and Ishihara (1999), R4 - Chen (2004). 2. CS = Conventional Samples, FS = Frozen Samples 3. Values in brackets are averages.  This relationship is shown as a solid line in Figure 6.3.  A more complex relationship is considered to be unwarranted considering the level of scatter. The standard deviations and coefficients of variation of the CRIEPI data are listed in Table 6.1, and are represented by error bars in Figure 6.3.  The coefficient of variation increases from roughly 25 to 30% in sands to roughly 45% for soil G75.  These values characterize the variability of (CD) under carefully controlled laboratory testing conditions, and represent a lower bound for the variability of the field data.  The coefficient of variation for the entire data set is estimated as:      118 D50 (mm) 0.1 1 10 C D 0 50 100 150 200 250 300 (335) (506)(837) (1652) CD = 88 + 56 Log (D50) CD = 105   Averaged, Field WES CRIEPI   Non-averaged, Field                                                Figure 6.3 Current SPT (CD) data set.  Solid and dashed lines represent proposed average trend and ± one standard deviation, respectively.    119 (6.6a) D(C ) 35%Ω =    0.15 mm ≤ D50 ≤ 2.0 mm  (6.6b) ( )D 50(C ) 35 60 Log D / 2.0 mmΩ = + ⋅   2.0 mm ≤ D50 ≤ 20 mm  The proposed value of Ω(CD) increases from 35 to 95% as the mean grain size increases from 2.0 to 20 mm.  The dashed lines in Figure 6.4 represent ± one standard deviation around the mean value.  No statistical analysis was undertaken to develop this estimate.  Recall, however, that 68% of observations are expected to fall within ± one standard deviation of the mean value.  For the sand and gravel data shown, 67% and 70% of the data points, respectively, fall between the dashed lines in the figure, making no distinction between averaged and non-averaged data. It is suggested that Equations 6.5 and 6.6 may be used as a first approximation of the mean value and coefficient of variation, respectively, for both field and calibration chamber data. The observed scatter is expected to be largely due to measurement errors and limitations of the (CD) term, which is only expected to be reasonably constant for (Dr) ranging from 0.35 to 0.85 (Skempton, 1986).  The potential for systematic variations (underlying trends) contributing to the observed variability is discussed for sands and gravels below.  Underlying Trends:  Sands  Skempton (1986) suggested that (CD) varies in sands with age (t) and overconsolidation ratio (OCR).  Kulhawy and Mayne proposed Equations (2.19) and (2.20), reprinted here for ease of reference:  (6.7) AC 1.2 0.05 Log(t /100)= + ⋅  (6.8) 0.18OCRC OCR=  to describe the manner in which (CD) values measured in sands increase with soil age and overconsolidation ratio, respectively.  In addition to these two factors, it is postulated that (CD) might also vary with soil gradation, as characterized by the coefficient of uniformity (CU).  For the purpose of investigating these effects, (CD) measurements were corrected to equivalent 1.0 mm mean grain size values, (CD)1mm, as follows:    120  (6.9) D 1mm D 50 88(C ) C 88 56 Log(D ) = ⋅ + ⋅   D50 ≤ 2.0 mm  The (CD)1mm term is derived from Equation (6.5a), and is intended to account for the variation of (CD) with (D50) so that underlying trends may be assessed. (CD)1mm values calculated for the sand data in Tables 6.1 and 6.3 are plotted against soil age in Figure 6.4.  For comparison, the mean value and range corresponding to ± one standard deviation at a mean grain size of 1 mm (88 ± 31) are also plotted.  The four oldest sands in order of increasing age are the Norwich Crag, Bagshot, Folkstone and Grantham sands.  These are fine sands for which relatively high (CD) values were observed, represented as closed and open square symbols in Figures 6.3 and 6.4, respectively.  Chen (2004) noted that OCR values proposed for these soils increase from 10 to 157 from youngest to oldest.  These estimates were used by Chen (2004) to calculate (COCR) and hence equivalent normally consolidated (CD) values.  The effect of this correction, in terms of (CD)1mm, is illustrated by the arrows in Figure 6.4.  It should be noted that Equation (6.8) was derived for an OCR range of roughly 1 to 3, so the use of (COCR) in this case represents an extremely large extrapolation. According to Equation (6.7) proposed by Kulhawy and Mayne (1990), (CD)1mm should increase by roughly 50% as soil age increases from 10-2 to 108 years.  A (CD)1mm value of, for example, 70 at t = 10-2 years would thus be expected to increase to roughly 105 at t = 108 years. This increase of 35 would fall entirely within the range of ± one standard deviation proposed for the current data set.  Identification of ageing trends is hampered by the fact that soil ages are generally not known very accurately.  The cluster of 20 data points at 1.25 x 105 years are all Pleistocene epoch soils that could range in age from 11 x 103 to 1.8 x 106 years old.  For this reason, it is suggested that ageing effects are negligible relative to the accuracy with which soil ages are typically determined. (CD)1mm values calculated for the sand data in Tables 6.1 and 6.3 are plotted against coefficient of uniformity in Figure 6.5.  The same mean value and range (88 ± 31) are plotted for comparison.  (CU) values were unavailable for roughly half of the available (CD) measurements. It is considered that grain size effects will be controlled by mean grain size to a greater extent than soil gradation.  For this reason, and due to the fewer number of tests for which soil gradation is available, it is believed to be reasonable to neglect the effect of soil gradation at this time.    121 Age (years) 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109 (C D) 1 mm 0 50 100 150 200 250 300 350 400 450 10 34 96 Estimated OCR = 157 20 Data Points Non-averaged, Field Averaged, Field WES CRIEPI OC Soils, no correction (CD)1mm = 88 +/- 31                                                 Figure 6.4 Variation of (CD)1mm with soil age in sands.    122 Coefficient of Uniformity, CU 0 2 4 6 8 10 12 14 (C D) 1 mm 0 50 100 150 200 250 300 10 = Estimated OCR (CD)1mm = 88 +/- 31 Non-averaged, Field Averaged, Field WES CRIEPI OC Soil, no correction                                                 Figure 6.5 Variation of (CD)1mm with coefficient of uniformity in sands.    123 Underlying Trends:  Gravels  Some of the very high and low values of (CD) measured in gravels can be attributed to (Dr) values falling outside of the range of 0.35 to 0.85 over which (CD) is expected to be reasonably constant.  The T-gravel data points with (CD) values of 837 and 1652 correspond to (Dr) values of 0.25 and 0.21 respectively.  Similarly, the averaged data points at (D50 = 7.8 mm, CD = 256) and (D50 = 2.43 mm, CD = 8.5) represent soils with relative densities of 0.27 and 1.17, respectively, and thus fall outside of the applicable range.  Similar violations of the allowable (Dr) range occur within the sand data, however, without generating equivalent levels of scatter. The T-gravel data cover a wide range of (CD) values and can provide insight into the cause of the observed increase of variability in gravels.  (N1)60 and (Dr) values are written beside each T-gravel data point in Figure 6.6.  Very general contours have been sketched on the plots to demonstrate that (CD) was varying systematically with both of these terms, tending to increase with increasing (N1)60 and with decreasing (Dr).  These trends reflect the fact that CD is proportional to (N1)60 and inversely proportional to the square of (Dr). Based on these observations, it is suggested that the relationship between SPT blow counts and soil relative density becomes less consistent in gravels.  For example, consider the six data points in Figure 6.6a marked with an asterisk (*).  The data points fall within a reasonably narrow range of (D50), and all were derived from a measured relative density of 53%, yet the measured (N1)60 values varied from 26 to 62.  SPT performed in gravels likely characterize a reduced number of soil grains, the response of which to sampler penetration is not as well correlated to the relative density of the soil mass.  This trend will be addressed in subsequent sections of this thesis, when the uncertainty of SPT blow counts in gravels is assessed.     124   3 4 5 6 7 8 9 20 3010 C D 0 50 100 150 200 250 300 62* 53* 28 47 37* 45 29 4026* 46 33* 20 46 24 (N1)60 = 60 * 30 60 50 40 20 D50 (mm) 3 4 5 6 7 8 9 20 3010 C D 0 50 100 150 200 250 300 53 53 44 42 53 56 60 6653 65 53 66 81 65 Dr = 53% 60 50 Contours of (Dr) Contours of (N1)60 (a)  Variation with (N1)60 (b)  Variation with (Dr)                                                Figure 6.6 Detailed review of T-gravel data showing approximate contours of (a) measured (N1)60 values and (b) measured (Dr) values.    125 6.3 (CS/L) GRAIN SIZE EFFECTS  Descriptions of the variation of SPT-JLPT and SPT-ILPT correlation factors with (D50) drawn from the literature were reviewed in Chapter 2.  Additional (CS/L) data were collected from the literature and during several field programs conducted during this study.  The new field data were collected using several types of LPT, including the Miniature Penetration Test” (MPT), the “North American LPT” (NALPT) and the “Reference LPT” (RLPT).  Equipment details are summarized for each test type in Table 6.4, and the equipment used for the MPT, SPT, NALPT and RLPT are compared in Figure 6.7. Table 6.5 is a full listing of the available (CS/L) data.  All of the MPT, NALPT and RLPT data were collected during this study, and each (CS/L) measurement represents a single side-by- side comparison.  In some cases, two SPT and/or two LPT were performed at the same depth, and the blow counts listed are then average values.  A Tonbi hammer rod energy ratio of 0.78 was assumed for both the SPT and JLPT data in the JLPT studies, resulting in no net correction to the measured correlation factors.  The mean grain sizes shown for Tokyo sand and gravel are believed to be averages for the sand and gravel layers tested.  The ILPT data are averaged values that were presented previously in Chapter 2.  The bracketed number beneath the (CS/L) value is the coefficient of variation. Continuing the reference identification scheme initiated for the (CD) data (R1, R2, etc…), the contributing references are tabulated at the bottom of Table 6.5.  The NALPT studies at the Resurrection River and Kidd2 sites were identified as studies D and E, respectively, in Chapter 4.  Similarly, the Patterson Park RLPT study was identified as Study G in Chapter 4.  (CS/L) is plotted as function of (D50) for each type of LPT in Figure 6.8. In the following sections, an existing approach to predicting SPT-LPT correlation factors is described and then modified to allow more direct comparison of (CS/L) values measured for different types of LPT.  Trends of the mean value and standard deviation are then discussed. T ab le  6 .4 Te st  d et ai ls  fo r t he  S PT  a nd  se ve ra l t yp es  o f L PT . Te st  D et ai l M PT  a SP T b JL PT  c N A LP T d B ur m is te r L PT  e R LP T a IL PT  f Sa m pl er  O ut er  D ia m et er , c m  (i n. ) 2. 54  (1 .0 ) 5. 08  (2 .0 ) 7. 3 (2 .9 ) 7. 62  (3 .0 ) 9. 21  (3 .6 25 ) 11 .4 3 (4 .5 ) 14 .0  (5 .5 ) Sa m pl er  In ne r D ia m et er :         Sh oe , c m  (i n. ) 1. 27  (0 .5 ) 3. 49  (1 .3 75 ) 5 (2 .0 ) 6. 1 (2 .4 ) 7. 44  (2 .9 3)  9. 84  (3 .8 75 ) 10  (3 .9 )  B ar re l, no  li ne r, cm  (i n. ) 1. 59  (0 .6 25 ) 3. 81  (1 .5 ) 5. 4 (2 .1 3)  6. 4 (2 .5 2)   -  10 .1 6 (4 .0 ) 11  (4 .3 ) H am m er  W ei gh t, N  (l b. ) 63 .5  (1 40 ) 62 3 (1 40 ) 98 1 (2 20 ) 13 35  (3 00 ) 11 12  (2 50 ) 13 35  (3 00 ) 55 92  (1 25 6)  H am m er  D ro p H ei gh t, cm  (i n. ) 50 .8  (2 0)  76 .2  (3 0) 15 0 (5 9. 1)  76 .2  (3 0)  50 .8  (2 0)  60 .9 6 (2 4)  50  (1 9. 7)  N om in al  H am m er  E ne rg y:        kJ  (f t˜k ip ) 0. 31 6 (0 .2 33 ) 0. 47 5 (0 .3 50 ) 1. 47 2 (1 .0 84 ) 1. 02  (0 .7 50 ) 0. 56 5 (0 .4 17 ) 0. 81  (0 .6 00 ) 2. 79 6 (2 .0 62 )  %  o f S PT  N om in al  E ne rg y 66 .6  10 0 31 1 21 4 11 9 17 1 59 1 C or re la tio n Fa ct or , C S/ L       Pr ed ic te d g 1. 78  - 1. 58  1. 38  0. 56  0. 69  0. 95   O bs er ve d in  S an d 1. 52  - 1. 5 h 1. 29  0. 42  h 0. 73  1. 14  C on ve rs io n Fa ct or  (F L) i 0. 39  - 0. 44 0. 50  1. 23   -  0. 73  a. So ur ce : Pr ev io us ly  u np ub lis he d.  b. So ur ce : A ST M  D 15 86 -8 4 c. So ur ce : K ai to  e t a l. (1 97 1) , Y os hi da  e t a l. (1 98 8) .  d. So ur ce : D an ie l ( 20 00 ), K oe st er  e t a l. (2 00 0) . e. So ur ce : B ur m is te r ( 19 62 ). f. So ur ce : Ja m io lk ow sk i a nd  L o Pr es ti (1 99 8) . g.  Eq ua tio n (6 .1 0) , R f =  0 .0 03 5.  h.  N o en er gy  c or re ct io n ap pl ie d by  re se ar ch er . i. Eq ua tio n (6 .1 3) . 126 Fi gu re  6 .7  Sa m pl er  d im en si on s a nd  te st  d et ai ls  fo r t he  M PT , S PT , N A LP T an d R LP T.  127    128 Table 6.5  Summary of available (CS/L) measurements. Test Type Source a Soil / Site D50 (mm) CU SPT N60 LPT N60 CS/L CS/L ⋅ FL MPT R5 Fraser River Sand 0.14  -  15 9 1.60 0.62   Patterson Park 0.18  -  23 14 1.70 0.66   Ladner, BC, Canada 0.21 2.2 28 16 1.73 0.68    0.33 3.3 18 10 1.79 0.70    0.28 2.2 18 13 1.36 0.53    0.30 2.3 23 14 1.62 0.63    0.16 2.2 18 12 1.45 0.57    0.22 2.3 34 26 1.32 0.51    0.20 2.2 32 23 1.39 0.54    0.23 2.0 39 36 1.07 0.42 JLPT R6-7 Calibration Chamber b 0.34 1.95 30 23 1.30 0.57   CRIEPI Study   40 31 1.29 0.57      43 36 1.19 0.53      44 31 1.42 0.62      47 36 1.31 0.57    1.13 5.65 31 20 1.55 0.68      42 25 1.68 0.74      52 27 1.93 0.85      56 29 1.93 0.85      57 34 1.68 0.74      59 27 2.19 0.96      60 34 1.76 0.78      78 36 2.17 0.95      82 36 2.28 1.00    2.28 11.3 36 22 1.64 0.72      40 22 1.82 0.80      65 39 1.67 0.73      68 35 1.94 0.85      69 36 1.92 0.84      74 38 1.95 0.86      86 43 2.00 0.88      90 46 1.96 0.86       continued… - Not available. a. List of references provided below table. b. Average rod energy ratio of 0.78 (Tonbi hammer) assumed for both SPT and JLPT blow counts.    129 Table 6.5  continued… Test Type Source a Site D50 (mm) CU SPT N60 LPT N60 CS/L CS/L ⋅ FL JLPT R6-7 CRIEPI (con.)   125 55 2.27 1.00  R7-9 Tokyo Sand and Gravel 0.20  -  9 8 1.13 0.50   Tokyo, Japan b   12 9 1.33 0.59      14 10 1.40 0.62      14 14 1.00 0.44      17 23 0.74 0.33      18 10 1.80 0.79      20 16 1.25 0.55      26 21 1.24 0.54      26 23 1.13 0.50      27 12 2.25 0.99      52 26 2.00 0.88      114 72 1.58 0.70      122 72 1.69 0.75    8.00 66 85 38 2.24 0.98      108 39 2.77 1.22      122 46 2.65 1.17      130 46 2.83 1.24      139 68 2.04 0.90      151 68 2.22 0.98  R10 T-Gravel b 10.5  -  69 43 1.60 0.71    14.4  -  60 40 1.50 0.66    13.0  -  48 42 1.14 0.50    16.4  -  60 40 1.50 0.66    12.1  -  70 42 1.67 0.73    9.00  -  35 43 0.81 0.36    6.30  -  51 34 1.50 0.66    3.50  -  60 38 1.58 0.69    12.5  -  39 42 0.93 0.41    10.2  -  73 34 2.15 0.94    18.5  -  35 35 1.00 0.44    9.00  -  29 39 0.74 0.33    12.3  -  56 34 1.65 0.72       continued… - Not available. a. List of references provided below table. b. Average rod energy ratio of 0.78 (Tonbi hammer) assumed for both SPT and JLPT blow counts.    130 Table 6.5  continued… Test Type Source a Site D50 (mm) CU SPT N60 LPT N60 CS/L CS/L ⋅ FL JLPT R10 T-Gravel b  (con.) 1.05  -  72 33 2.18 0.96    7.60  -  48 35 1.37 0.60    13.3  -  42 35 1.20 0.53    8.20  -  98 30 3.27 1.44  R11-12 Site B 1.80 8.6 88 52 1.69 0.74   Chiba Prefecture, Japan b 2.80 10.3 144 56 2.57 1.13   Site C 8.90 18.9 107 40 2.68 1.18   Kagawa Prefecture, Japan b 7.20 19 79 38 2.08 0.91    10.7 46.6 88 39 2.26 0.99    11.3 39.5 30 29 1.03 0.46   Site D 16.9 59 33 31 1.06 0.47   Saitama Prefecture, Japan b 10.8 37.2 57 34 1.68 0.74    5.60 23.8 59 35 1.69 0.74 NALPT R13-14 Fraser River Sand 0.34 2.6 8 4 2.00 1.00   Kidd2 Substation 0.23 2.9 7 7 1.00 0.50   Richmond, BC, Canada 0.43 4.1 11 11 1.00 0.50    0.57 3.7 26 18 1.44 0.72    0.49 6.2 20 13 1.54 0.77    0.22 2.3 22 13 1.69 0.85    0.21 2.3 16 12 1.33 0.67    0.22 2.5 19 13 1.46 0.73    0.27 2.1 24 20 1.20 0.60    0.28 2.4 31 20 1.55 0.78  R14-15 Fluvial Sand and Gravel 7.90 52 20 27 0.73 0.36   Resurrection River 0.50 18 8 19 0.40 0.20   Seward, AK, USA 0.20  -  20 26 0.77 0.38    4.00 67 52 33 1.58 0.79    6.60 55 40 51 0.79 0.39    4.70 60 26 29 0.89 0.44    1.40 30 19 11 1.76 0.88    2.30 42 37 23 1.60 0.80    0.50  -  50 32 1.55 0.78       continued… - Not available. a. List of references provided below table. b. Average rod energy ratio of 0.78 (Tonbi hammer) assumed for both SPT and JLPT blow counts.    131 Table 6.5  continued… Test Type Source a Site D50 (mm) CU SPT N60 LPT N60 CS/L CS/L ⋅ FL NALPT R14-15 Resurrection River (con.) 0.30  -  32 29 1.11 0.56 RLPT R5 Fraser River Sand 0.14  -  15 19 0.79 0.79   Patterson Park 0.18  -  23 17 1.38 1.38   Ladner, BC, Canada 0.21 2.2 28 37 0.77 0.77    0.33 3.3 18 21 0.87 0.87    0.28 2.2 18 27 0.65 0.65    0.30 2.3 23 30 0.76 0.76    0.16 2.2 18 22 0.81 0.81    0.22 2.3 34 49 0.69 0.69    0.20 2.2 32 28 1.15 1.15    0.23 2.0 39 73 0.53 0.53 ILPT R16 0.24  -   -   -  0.97  (30%) 0.71   Po River Sand, Holocene Sand and Gravel, Pleistocene Sand and Gravel Messina Strait, Italy 0.38  -   -   - 1.1 (19%) 0.80    (number in brackets is the coefficient of variation) 0.71  -   -   - 1.04 (32%) 0.76     1.44  -   -   -  0.92 (25%) 0.67     2.50  -   -   -  0.75 (23%) 0.55     4.00  -   -   -  1.03 (46%) 0.75     7.80  -   -   -  0.77 (39%) 0.56     13.0  -   -   -  0.53 (30%) 0.39  - Not available. a. List of references provided below table. b. Average rod energy ratio of 0.78 (Tonbi hammer) assumed for both SPT and JLPT blow counts.  List of References:  R5 -  Daniel et al. (2003a) R11 -  Goto et al. (1987) R6 -  Yoshida et al. (1988) R12 -  Suzuki et al. (1993) R7  -  Tokimatsu (1988) R13 -  Daniel (2000) R8  -  Hatanaka and Suzuki (1986) R14 -  Daniel et al. (2003b) R9  -  Hatanaka et al. (1988) R15 -  Koester et al. (1999) R10  -  Tanaka et al. (1991) R16  -  Jamiolkowski et al. (1998) D 5 0 (m m) 0. 1 1 10 C S/L 01234 0. 1 1 10 C S/L 01234 D 5 0 (m m) 0. 1 1 10 C S/L 01234 0. 1 1 10 C S/L 01234 JL PT MP T RL PT NA LP T IL PT  ( er ro r ba rs  =  + /-  1  x  V ) Fi gu re  6 .8  V ar ia tio n of  (C S/ L)  w ith  m ea n gr ai n si ze  fo r t he  M PT  a nd  se ve ra l t yp es  o f L PT . 132    133 6.3.1 Available Methods for Prediction of SPT-LPT Correlation Factors  Burmister (1948, 1962) proposed a theoretical approach to predicting SPT-LPT correlation factors.  The method addressed differences in hammer size and sampler end-bearing area.  Daniel (2000) and Daniel et al. (2003a) used a wave equation modeling approach to develop the following similar procedure that, in addition to hammer size and sampler end- bearing area, accounts for friction acting on the sides of the sampler and hammer efficiency:  (6.10) s 60 SPT s LPT TE SPT S/ L E LPT 60 SPT TE LPT (N ) (E ) (A )C (N ) (E ) (A ) ⋅= = ⋅  where sE LPT(N )  is the LPT blow count at a selected standard energy (Es)LPT, and (E60)SPT is equal to 0.285 kJ.  The effective sampler bearing areas for the SPT (ATE)SPT and LPT (ATE)LPT are calculated as follows:  (6.11) 2 2TE o i o i fA (D D ) L (D D ) R4 π= ⋅ − + π⋅ ⋅ + ⋅  where (Do), (Di) and (Le) are the sampler outer diameter, inner diameter (shoe) and average embedment length (305 mm), respectively, and (Rf) is the cone penetration test (CPT) friction ratio.  A value of 0.0035 was recommended for the latter if no CPT data are available. Correlation factors predicted for each type of LPT are listed in Table 6.4.  Also listed are average SPT-LPT correlation factors determined during side-by-side tests in sands and presented in previous studies.  Energies were not measured during the tests performed to measure the SPT- JLPT and SPT-Burmister LPT correlation factors, and an assumption about the average rod energy ratio for each test type was required.  Lacking details about either LPT hammer, it was assumed that the SPT and LPT average rod energy ratios were equal.  Despite the need for such assumptions, and other factors such as soil variability during side-by-side tests, the predicted and observed values are seen to be in reasonably good agreement (Figure 6.9).        134 0 10 20 30 40 (N 60 ) SP T (N 60 ) LP T 0.0 0.5 1.0 1.5 2.0 Burmister LPT JLPT NALPT ILPT RLPT E60 ATE (J/cm2) Observed (sand sites) Predicted Equation (6.10) MPT C S /L  =                                                Figure 6.9 Comparison of measured and predicted SPT-LPT correlations factors for the MPT and several types of LPT.   135 6.3.2 Comparison of (CS/L) Data for Different Types of LPT  The (CS/L) data plotted in Figure 6.9 are average values measured in sands, but it is the variability of (CS/L) with grain size (e.g. Figure 6.8) that is of interest during this study.  A general trend of (CS/L) increasing with (D50) in sands and decreasing with increasing (D50) in gravels is observed in the JLPT, NALPT and ILPT data.  Insufficient data are available to discern any trends in the MPT or RLPT data.  Considering that the number of (CS/L) measurements for any one type of LPT is limited, it would be beneficial to be able to directly compare (CS/L) values recorded for different types of LPT.  The theoretical correlation procedure described in the previous section can be adapted to that end.  As a first approximation, the (CS/L) values measured for each type of LPT can be converted to those that would have been measured using the RLPT as follows:  (6.12)  60 SPT 60 SPT L 60 RLPT 60 LPT (N ) (N ) F (N ) (N ) = ⋅  where the conversion factor (FL) is derived from Equation (6.10):  (6.13a) 60 LPTL 60 RLPT (N )F (N ) =  (6.13b) 60 LPT 60 SPTL 60 SPT 60 RLPT (N ) (N )F (N ) (N ) = ⋅  (6.13c) 60 RLPT TE LPTL 60 LPT TE RLPT (E ) (A )F (E ) (A ) ⋅= ⋅  Conversion factors predicted using Equation (6.13) for each type of LPT are listed in Table 6.4. The RLPT was selected as the test to which the other LPT results would be converted because it was the largest sampler used during this study.  Conversion factors could just as easily be calculated for any one of the other types of LPT. Figure 6.10 compares the measured (CS/L) values (Figure 6.10a) to the converted values (Figures 6.10b and 6.10c).  The range of correlation factors recorded for a given (D50) in Figure   136 D50 (mm) 0.1 1 10 C S /L  *  F L 0.0 0.5 1.0 1.5 0.1 1 10 C S /L 0 1 2 3 4 0.1 1 10 C S /L  *  F L 0 1 2 3 4 (a) (c) (b) MPT JLPT NALPT RLPT ILPT                                               Figure 6.10 (CS/L) grain size effects in (a) measured and (b, c) converted format.  Solid and dashed lines represent proposed average trend and ± one standard deviation, respectively.   137 6.10a is seen to be quite large, reflecting the wide range of LPT equipment used.  For example, SPT-LPT correlation factors predicted based on equipment considerations alone (no grain size effects), are 1.58 for the JLPT and 0.95 for the ILPT (Table 6.4).  This effect must be addressed as well as possible before correlations for the two test types can be directly compared and used to investigate grain size effects.  Application of the conversion factors leads to a considerable reduction of the range of (CS/L) for a given mean grain size (Figure 6.10b).  Figure 6.10c shows the same converted data plotted at a larger scale to allow closer review.  6.3.3 Discussion  A total of 93 field and 23 calibration chamber measurements of (CS/L) are plotted in Figure 6.10.  All of the data are non-averaged except the eight SPT-ILPT data points.  The data in Figure 6.10c show a generally consistent trend of (CS/L) increasing with (D50) in sands, and then decreasing with increasing (D50) in gravels.  The following bi-linear relationship is proposed to describe the variation of the mean value with (D50):  (6.14a) S/ L L 50C F 0.85 0.35 Log(D )⋅ = + ⋅   0.15 mm ≤ D50 ≤ 1.0 mm  (6.14b) S/ L L 50C F 0.85 0.23 Log(D )⋅ = − ⋅   1.0 mm ≤ D50 ≤ 20 mm  This relationship is shown as a solid line in Figure 6.10c. The coefficient of variation for the SPT-ILPT correlation factor ranges from roughly 20 to 30% for sands and 20% to 45% for gravels (Table 6.5).  These characterize the variability of an SPT-LPT correlation factor measured under field conditions.  Considering these values and the scatter observed for all data, the coefficient of variation for the entire data set is estimated as:  (6.15a) S/ L(C ) 25%Ω =   0.15 mm ≤ D50 ≤ 1.0 mm  (6.15b) S/ L 50(C ) (25 27 Log(D ))Ω = + ⋅   1.0 mm ≤ D50 ≤ 20 mm  The dashed lines in Figure 6.10c indicate a range of ± one standard deviation around the mean value.  The coefficient of variation is thus estimated to be 25% for (D50 < 1.0 mm) and to   138 increase from 25 to 60 % as the mean grain size increases from 1.0 to 20 mm.  No statistical analysis was undertaken to develop this estimate.  Roughly 78% and 77% of the data fall between the dashed lines for (D50 < 1.0 mm) and (D50 > 1.0 mm), respectively, making no distinction between averaged and individual measurements.  The estimated coefficient of variation for both sands and gravels could thus be slightly reduced.  It is suggested, however, that Equations 6.14 and 6.15 are suitable first approximations of the mean value and coefficient of variation, respectively, for both field and calibration chamber data.  6.4 DISCUSSION  Updated sets of (CD) and (CS/L) data have been compiled and descriptive equations proposed for the mean values and coefficients of variation as a function of (D50).  A basic assessment of uncertainty and a comparison of existing grain size effect relationships to the new data are presented in the following sections.  6.4.1 Uncertainty  A procedure for estimating the uncertainty of energy corrected SPT blow counts was described in Chapter 5.  This approach can be used to evaluate and guide the analysis of grain size effect data defined in terms of (CD) and (CS/L).  Recall that (CD) is defined as:  (6.16) N 60D 2 r C NC D ⋅=  Applying the Taylor series expansion technique to Equations (6.1) and (6.16) yields:  (6.17) 2 2 2D N 60 r(C ) (C ) (N ) 4 (D )Ω = Ω +Ω + ⋅Ω  (6.18) 2 2S/ L 60 SPT 60 LPT(C ) (N ) (N )Ω = Ω +Ω  Noting that Ω(N60)LPT should be roughly equal to Ω(N60)SPT, Equation (6.18) can be written as:    139 Table 6.6  Comparison of expected and observed uncertainty of (CD) and (CS/L). Term Expected Range Observed Value Ω(CS/L) 15 to 40% 25% (D50 < 1.0 mm) Ω(CD) > Ω(CS/L) 35% (D50 < 2.0 mm)   (6.19) S/ L 60 SPT(C ) 1.4 (N )Ω ≈ ⋅Ω  From Chapter 5, Ω(N60)SPT is expected to be in the order of 10 to 30%, depending on the energy correction method used.  Accordingly Ω(CS/L) is expected to be in the range of 15 to 40%. While the appropriate values of Ω(CN) and Ω(Dr) are currently unknown, it is anticipated that Ω(CD) will be somewhat higher than Ω(CS/L).  These estimates, while extremely general in nature, are compared to the estimated coefficients of variation in Table 6.6, and found to be in reasonable agreement.  6.4.2 Assessment of Existing Grain Size Effect Relationships  Existing grain size effect relationships include (CD) trends proposed by Kulhawy and Mayne (1990) and Cubrinovski and Ishihara (1999), and the JLPT (CS/L) trend that was interpreted by Tokimatsu (1988).  Figure 6.11 compares these three relationships to the corresponding trends noted herein.  The two (CD) trends are seen to fall within the ± one standard deviation range proposed herein.  The Kulhawy and Mayne (1990) trend was recommended for unaged soils, and would be shifted up for aged soils.  As discussed earlier, their proposed age effect is believed to reflect their use of short rod corrections and is considered to be unnecessary. The Cubrinovski and Ishihara (1999) relationship has been corrected to represent (CD) rather than (CD)78 values, and is seen to be in reasonably good agreement with the proposed trend, despite the fact that it is based on gravel JLPT blow counts. The Tokimatsu JLPT trend shown in Figure 6.11b is the simplified version shown in Figure 2.20, multiplied by (FL = 0.44) to allow direct comparison.  The Tokimatsu trend is seen to run somewhat counter to the proposed trend.  A group of 5 or 6 JLPT (CS/L) data points follow a sharply rising trend in gravels (Figure 6.8), supporting Tokimatsu’s trend, while the majority   140 Kulhawy and Mayne (1990) Unaged Soils 0.1 1 10 C D 0 50 100 150 200 250 300 Cubrinovski and Ishihara (1999) D50 (mm) 0.1 1 10 C S /L  *  F L 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Tokimatsu (1988) Equation 6.15 Equation 6.14 Equation 6.6 Equation 6.5(a) (b)                                                Figure 6.11 Comparison of previously proposed relationships to (a) (CD) and (b) (CS/L ⋅ FL) grain size effect trends identified herein.   141 support the proposed trend. Recall from Chapter 2 that Tokimatsu interpreted the JLPT (CS/L) trend he identified by making certain assumptions about how blow counts would vary with grain size during the SPT and JLPT, and ultimately generated grain size correction factors (CSg, CLg).  The variation of these correction factors with grain size is analogous to that of (CD), and can be compared by identifying an appropriate average magnitude of (CD)SPT for the (D50) range 0.1 to 0.27 mm, within which Tokimatsu predicts no variation of SPT blow counts with grain size.  Referring to Equation (6.5a), the geometric average value of (CD) over this range is 44.  The variation of (CD) for the SPT predicted by Tokimatsu (1988) can then be written as:  (6.20a) D SPT Sg 44(C ) 44 C = =  0.1 mm ≤ D50 ≤ 0.27 mm  (6.20b) D SPT 50Sg 44 44(C ) DC 1.0 0.5 Log 0.27 = =  − ⋅     0.27 mm < D50  and that of the JLPT as:  (6.21a) D JLPT Lg 44(C ) 29 C = =  0.1 mm ≤ D50 ≤ 0.35 mm  (6.21b) D JLPT 50Lg 44 44(C ) DC 1.5 0.5 Log 0.35 = =  − ⋅     0.35 mm < D50  Equations (6.20) and (6.21) are compared to the SPT (CD) trend identified herein in Figure 6.12. As expected, the JLPT trend in Figure 6.12 is distinct from the SPT trend.  This is the reason that direct comparison of JLPT and SPT (CD) data as per Cubrinovski and Ishihara (1999) is incorrect.  Figure 6.12 demonstrates that use of the Tokimatsu (1988) grain size corrections is equivalent to assuming that both (CD)SPT and (CD)JLPT increase rapidly with (D50) in gravels.  The rate of increase becomes very high above (D50 = 10 mm) for the SPT, and would presumably reach a similar rate of increase for the JLPT for larger grain sizes.  This demonstrates that   142 D50 (mm) 0.1 1 10 C D 0 50 100 150 200 250 300 SPT JLPT Equation 6.6 Equation 6.5 Tokimatsu (1988)                                                Figure 6.12 Comparison of (CD)SPT and (CD)JLPT relationships derived from Tokimatsu (1988) grain size corrections to trends identified herein.   143 Tokimatsu assumed that the JLPT grain size effects would be the same as SPT grain size effects, but offset due to the use of a larger sampler.  Comparison with the trend proposed herein, which adequately represents all currently available data, suggests that he may have underestimated the rate of SPT blow count increase in sands and over-estimated the rate in gravels. It is often assumed that SPT and LPT samplers will meet refusal in coarse materials, and this is reasonable for very coarse materials such as cobbles and boulders.  Very little is known, however, about what happens to blow counts during the transition from “normal” sampling in sands to refusal in cobbles and boulders.  In particular, sampler plugging is often cited as the dominant factor controlling grain size effects in gravels, yet very little is known of the relationship between grain size and plugging.  Geotechnical practice would benefit from an improved understanding of the processes underlying plugging and grain size effects.  6.5 CHAPTER SUMMARY  (CD) and (CS/L) grain size effect data were reviewed and compiled into two data sets in this Chapter.  Average trends were identified for both data sets, and visual estimates made of the coefficient of variation.  The latter were in reasonable agreement with predictions made using the uncertainty approach described in Chapter 5. (CD) was observed to increase with mean grain size in sands and reach a constant value of 105 in gravels, whereas (CS/L) was observed to increase and decrease with increasing mean grain size in sands and gravels, respectively.  These trends are related, and further insight can be gained by a joint interpretation of the two, as per Tokimatsu (1988).  The SPT-JLPT correlation factor trend that Tokimatsu interpreted was shown to be different than that observed in the larger, updated data set, suggesting that there may be value in revisiting his approach.   144 CHAPTER 7 NUMERICAL STUDY OF PLUGGING AND GRAIN SIZE EFFECTS  7.1 INTRODUCTION  Hvorslev (1949) reviewed the effects of sampler geometry on sample disturbance and noted the importance of the sampler opening size, the depth of penetration, the area ratio (a measure of the wall thickness) and the inside clearance ratio (a measure of the increase in sampler inner diameter behind the sampler opening).  He observed that sample disturbance was often directly due to partial or full plugging of the sampler.  Sampler plugging is often assumed to be the end-member grain size effect corresponding to very large soil particles, but a direct relationship between the variation of (CD) with mean grain size and sampler plugging has yet to be demonstrated.  It seems likely, however, that similar aspects of sampler geometry will control grain size effects. Previous studies have relied on field and calibration chamber data to characterize grain size effects.  These types of studies are limited by the difficulty of performing parametric studies during which only one parameter, such as a detail of the sampler geometry, is varied.  In contrast, numerical studies are well suited for parametric studies and provide complete knowledge of the factors affecting the results at all times.  The results of numerical studies must be interpreted with caution, however, due to the assumptions and simplifications necessary to develop the numerical model.  It was considered that a modest numerical investigation of the factors controlling grain size effects and sampler plugging would serve as a useful complement to the existing field and calibration chamber data.  7.1.1 Finite vs. Distinct Elements  Finite Element (FE) numerical simulations are widely used for geotechnical applications by both practicing engineers and those involved in research.  The basic unit used to represent the problem geometry is a deformable element that is connected to adjacent elements at shared nodes (Figure 7.1a).  Displacements must be continuous both within individual elements and between adjacent elements.  Because the deformation of granular soils is ultimately accommodated by inter-particle slip, it is only reasonable to assume that displacements are continuous if the elements are many times larger than the soil grains under consideration.  For   145                    (a)                     (b)       Figure 7.1 Comparison of basic model components for (a) Finite Element method and (b) Distinct Element Method with circular elements and linear walls. Element Nodes Particles Walls   146 the purpose of modeling SPT grain size effects in gravels, the soil grains are comparable in size to components of the sampler (e.g. wall thickness and sampler opening) and it becomes impossible to satisfy this requirement.  For this reason, the FE method was not considered to be suitable for the current study. The Distinct Element Method (DEM) is an alternate approach to numerical simulation of geomaterials.  It was initially developed for rock-mechanics applications by Cundall (1971) and subsequently modified for soil-mechanics applications by Cundall and Strack (1979).  During DEM simulations, each element is independent and unattached to adjacent elements (Figure 7.1b), thus eliminating the required assumption of a continuous displacement field, simplifying the modeling of large-strain problems such as sampler penetration, and allowing for inclusion of soil particles that are comparable in size to the sampler dimensions.  7.1.2 Methodology  A DEM approach to numerical simulation was adopted for this study.  The DEM software “Particle Flow Code in 2-Dimensions” (PFC2D) version 3.00, distributed by Itasca Consulting Group, Inc. (Itasca), was selected for the investigation.  A review of the DEM approach as implemented in PFC2D and a description of the study methodology are provided in Appendix F.  Only a brief summary of the methodology is presented here. The study methodology consisted of creating 1.0 m wide by 0.75 m high DEM samples with known particle size distributions and boundary stresses, and then pushing “platens” into the samples at a constant rate of penetration of 0.2 m/s.  The platen geometry was based on the cross-section of a standard SPT split-spoon sampler.  Simulations were performed using single platens to represent one half of a sampler or a pair of platens to represent the full cross-section of a sampler.  Figure 7.2 shows the model geometry (excluding particles) for a dual platen simulation.  The platens possess no curvature in the third dimension.  Simulations were conducted using samples with a range of particle size distributions and platens at various spacings. Output from the simulations included parameters such as the end bearing and friction forces acting on the sampler, the soil plug height and the patterns of particle displacement around the platen(s).  Typical profiles of total resistance and internal friction are shown in Figure 7.3. These profiles have been smoothed to eliminate the high frequency oscillations typical of DEM output.  Also shown are profiles of the cumulative penetration energy, calculated by integrating   147                                                Figure 7.2 Model geometry (excluding particles) for a dual platen simulation.  Platens shown at full penetration of 457 mm (18”). Platens Boundary Walls   148 Penetration Energy, Ep (kJ/m) 0 4 8 12 16 Smoothed Total Resistance (kN/m) 0 10 20 30 40 50 Pe ne tr at io n De pt h (m ) 0.0 0.1 0.2 0.3 0.4 0.5 Smoothed Internal Friction (kN/m) 0 5 10 15 Smoothed IFR (%) 0 25 50 75 100 125 ∆ Ep = 10.8 Onset of Partial Plugging                                                 Figure 7.3 Typical output from a PFC2D sampler penetration simulation.   149 the total resistance as a function of platen penetration, and the incremental filling ratio (IFR), defined as:  (7.1) Plug LengthIFR 100% Penetration Depth ∆= ⋅∆  The IFR characterizes the instantaneous plugging behaviour and ranges from 0 to 100 for fully plugged and fully coring penetration, respectively.  The change in penetration energy over the interval 152 to 457 mm (6” to 18”) is denoted as (∆Ep), and is roughly analogous to the blow count recorded during a dynamic test. In this chapter, particle size effects observed during single platen simulations are discussed first, followed by the more complex particle size effects that occur during dual platen simulations.  Some preliminary comparisons of PFC2D particle size effects and experimental SPT grain size effects are then made.  7.2 SINGLE PLATEN SIMULATIONS  Particle size effects related to platen dimensions were investigated by simulating the penetration of a single platen (the “right half” of a sampler) into samples with varying mean particle size (D50).  This approach avoids platen spacing effects encountered in dual platen simulations.  Simulation details and the observed effect of particle size on penetration energy and shear zone development are described below.  7.2.1 Simulation Details  Five 1.00 m wide by 0.75 m high samples with mean particle sizes of 4.75, 6.30, 8.00, 13.2 and 19.0 mm were created for these tests.  For each sample, particles that would be distributed on two sequential standard sieves were placed at a target initial porosity of 0.17. These samples will be referred to as the 4.75, 6.30, 8.00, 13.2 and 19.0 mm samples herein.  All tests were run at an initial isotropic stress of 100 kPa. Table 7.1 compares the initial sample porosities, defined as the void area per unit area, to those determined just prior to sampler penetration, demonstrating that it was necessary to move the boundaries outward to attain the target isotropic stress.  The sensitivity of the simulation   150 Table 7.1 Details of PFC2D samples used during particle size effect study.  Porosity (n) Mean Particle Size, D50 (mm) Number of Particles  Initial At Target Isotropic Stress 4.75 35,911  0.170 0.175 6.30 20,642  0.170 0.171 8.00 12,681  0.170 0.176 13.2 4,290  0.170 0.176 19.0 2,246  0.170 0.175  results to these variations of porosity is unknown.  Five single platen simulations were performed in each of the samples.  The platen size was held constant, but the location was shifted horizontally to a different position within a 63.5 mm (2.5”) window on either side of the sample centreline between simulations.  This approach was used to assess the sensitivity of the penetration energy to the location of the platen.  7.2.2 Effect of Particle Size on Penetration Energy  The penetration energies (∆Ep) recorded during the 25 single platen simulations are shown in Figure 7.4.  It is apparent that both the mean value and standard deviation of (∆Ep) increases with (D50).  An increasing standard deviation is the logical result of increasing particle size because the heterogeneity of the sample, at the scale of the platen, increases with (D50).  The cause of the increase in mean penetration energy is less apparent.  Review of Table 7.1 indicates that the sample porosity did not vary systematically with (D50).  Figure 7.5 compares the smoothed toe and friction loads for single platen simulations performed in the 4.75, 8.00 and 19.0 mm samples.  The profiles demonstrate that the trend of increasing penetration energy with mean particle size is due to the presence of frequent peaks in the toe load profiles of the coarser samples. Figure 7.6 compares the end-of-test configuration for the three simulations represented in Figure 7.5.  The short lines shown at the particle-particle and particle-wall contacts are proportional in thickness to the net contact force.  In this plot, the scaling factor for these lines is the same in each sample and thus the line thicknesses may be directly compared.  The plots illustrate the expected decrease in the number of particle-particle and particle-platen contacts with increasing particle size, and an associated increase in contact force magnitude.   151 Mean Particle Size (mm) 3 4 5 6 7 8 9 20 3010 Si ng le  P la te n Pe ne tr at io n En er gy  x  2  ( kJ /m ) 12 14 16 18 20 22 Mean + σ − σ                                                Figure 7.4 Penetration energies recorded during single platen penetration trials (energies have been multiplied by two).   152 Smoothed Toe Load (kN/m) 0 10 20 30 40 50 Pe ne tr at io n De pt h (m ) 0.0 0.1 0.2 0.3 0.4 0.5 Smoothed Friction (kN/m) 0 10 20 30 40 50 D50 = 4.75 mm D50 = 8.00 mm D50 = 19.0 mm                                                Figure 7.5 Comparison of smoothed toe and friction loads for single platen penetration in 4.75. 8.00 and 19.0 mm samples. Fi gu re  7 .6  C om pa ris on  o f e nd -o f- te st  c on ta ct  fo rc e di st rib ut io ns  fo r 4 .7 5,  8 .0 0 an d 19 .0  m m  s am pl es . Th ic kn es s of  li ne s is  p ro po rti on al  to m ag ni tu de  o f t ot al  c on ta ct  fo rc e (i. e.  n or m al   a nd  sh ea r c om po ne nt s) . 153 D 50  =  4 .7 5 m m  D 50  =  1 9. 0 m m D 50  =  8 .0 0 m m 0 15 0 m m    154 The net contact forces shown in Figure 7.6 include both normal and shear components, indicating that the magnitude of normal and shear contact forces in the vicinity of the platen increased with (D50).  As the (D50) value increases, the number of contacts in the vicinity of the platen toe decreases.  The forces generated by the penetrating platen were distributed through a reduced number of particle contacts in coarser samples, leading to an increase in the average normal force and hence the average allowable shear force.  Higher allowable shear forces are expected to lead to higher peak toe loads.  The reduced number of contacts also led to greater variability of the toe load because shear failure at a handful of contacts can rapidly cause chains of contacts distributing loads through the particle assemblages to fail.  This was likely the dominant process through which single platen penetration energies increased with particle size.  7.2.3 Effect of Particle Size on Shear Zone Development  Particles that are in contact with or near the platens tend to be dragged in the direction of platen penetration.  The area adjacent to the platen in which these relatively large displacements occur is referred to as a shear zone.  Uesugi et al. (1988), summarizing observations from the literature and from their own simple shear experiments, suggested that the shear zone adjacent to a moving steel surface was generally 3 to 10 times the mean grain size in thickness, depending on the surface roughness. Figure 7.7 illustrates the disruption of originally horizontal grid lines that occurred during single platen penetration tests in each of the five samples tested.  The thickness of the shear zone can be estimated from these plots as the distance between the platen edge and the undisturbed horizontal line.  Disruption of the horizontal lines was mildly asymmetric due to the bevelled toe of the platen.  Estimated shear zone thicknesses measured on the side of the platen representing the inside of the sampler (i.e. the left side) are summarized in Table 7.2 in units of length and length over (D50).  The thickness of the shear zone in units of millimetres is seen to be reasonably consistent between samples of different mean grain size.  As a result, the ratio of shear zone thickness to particle size decreases with increasing (D50).  Figure 7.8 compares particle displacement vectors for the single platen simulations performed in the 4.75 and 19.0 mm samples.  The plots confirm that the thickness of the zone in which concentrated particle displacement occurred was roughly the same in the two samples, but illustrates that the characteristics of the shear zones were significantly different.  Fi gu re  7 .7  En d- of -te st  c on fig ur at io ns  fo r s in gl e pl at en  tr ia ls  sh ow in g di st ur ba nc e of  o rig in al ly  h or iz on ta l g rid  li ne s. 155 0 15 0 m m D 50  =  4 .7 5 m m  D 50  =  6 .3 0 m m  D 50  =  8 .0 0 m m  D 50  =  1 3. 2 m m  D 50  =  1 9. 0 m m    156 Table 7.2 Estimated shear zone thickness for single platen simulations.  Shear Zone Thickness (mm) Shear Zone Thickness / Mean Particle Size Mean Particle Size (mm)  Mean Standard Deviation Mean Standard Deviation 4.75  29.7 4.6 6.3 1.0 6.30  28.5 4.4 4.5 0.7 8.00  37.2 1.1 4.6 0.1 13.2  26.9 2.7 2.0 0.2 19.0  38.5  n.a. 2.0  n.a. n.a. – not applicable because estimate is based on a single measurement.  Three stages of shear zone development are visible in the 4.75 mm sample in Figure 7.8. Immediately behind the toe of the platen, a single layer of particles adjacent to the platen has been dragged down.  Further up the platen a thicker shear zone has developed, with downward displacement of particles gradually decreasing with increasing distance from the platen edge. Finally, particles near the top of the platen have moved inward to fill the space vacated by the down-dragged particles (this last stage is obviously specific to the problem geometry).  In contrast, only two stages of shear zone development are visible in the 19.0 mm sample: the initial stage involving a single layer of down-dragged particles and the uppermost stage in which particles move in toward the platen.  The three intermediate samples (not shown) demonstrated behaviour between these end-members. Some aspects of the relationship between shear zone development and grain size were reviewed in Chapter 2.  Recall that Gui and Bolton (1998) used the concept of an effective cone diameter (Figure 2.18) to explain the variation of peak cone tip resistance with grain size.  This concept is clearly supported by the single platen simulation results, all of which demonstrated that shear zone development began with the downward dragging of a single layer of particles adjacent to the platen tip. The trap-door tests described by Stone and Muir Wood (1992) demonstrated that the strain required for a shear zone to mature into a constant volume state increases with grain size. This observation also seems to be supported by the single platen simulations results, during which the same interface strain (i.e. the final platen penetration depth) was held constant.  It was observed that the mean shear zone thickness decreased from roughly 6 to 2 times the mean particle size as the particle size was increased (Table 7.2).  It seems likely that this thickness is an indicator of the shear zone maturity, and thus that the shear zones in the finer samples had matured to a more advanced state at the end of the simulations.  In order to test this hypothesis, a   157                                                Figure 7.8 Patterns of particle displacement adjacent to platen during single platen penetration trials in 4.75 and 19.0 mm samples.                                              1. 1. D50 = 4.75 mm D50 = 19.0 mm Fi gu re  7 .9  Pa tte rn s of  p ar tic le  d is pl ac em en t a dj ac en t t o pl at en  d ur in g si ng le  p la te n pe ne tra tio n tri al  in  o ve rs iz ed  1 9. 0 m m  s am pl e sh ow in g w el l-d ev el op ed  sh ea r z on e.   S am pl e is  1 .0  m  w id e by  2 .0  m  h ig h.  158 2.1. 2. 1.   159 sample with a mean particle size of 19.0 mm, height of 2.0 m and width of 1.0 m was created.  A single platen was then penetrated to a depth of 1.5 m (compared to 0.4572 m in previous simulations), leading to the set of displacement vectors shown in Figure 7.9.  The three stages of shear zone development observed in the 4.75 mm sample can be seen in this plot.  The mean value of the shear zone thickness was estimated as 126.0 mm with a standard deviation of 25.5. This corresponds to 6.6 times the mean particle size, which is similar to the value listed in Table 7.2 for the 4.75 mm sample (6.3).  These observations confirm that shear zones require greater platen penetration to mature to a given level in coarser samples.  The systematic variation of shear zone thickness with grain size is a likely candidate for an underlying cause to grain size effects during penetration of samplers.  7.3 DUAL PLATEN SIMULATIONS  Sampler penetration was simulated during this study by penetrating pairs of platens. Constant platen dimensions were maintained in order to simplify interpretation of the resulting data, as any variations of penetration energy may then be attributed to either the single platen effects described in the previous section or to platen spacing effects.  Simulation details, and the results of the simulations in terms of platen spacing and particle size are described in the following sections.  7.3.1 Simulation Details  Five sampler penetration simulations were completed in each of the five original samples described in the previous section, with simulated sampler outer diameters of 2.54, 5.08, 7.62, 10.2 and 12.7 cm (1”, 2”, 3”, 4” and 5”).  These samplers will be referred to as the 1”, 2”, 3”, 4” and 5” samplers herein.  7.3.2 Effect of Platen Spacing on Plugging  End-of-test configurations and contact force distributions for the five samplers in the 4.75 mm sample are presented in Figures 7.10 and 7.11, respectively.  The plug length is seen to vary with platen spacing in Figure 7.10.  The final plug lengths provide an indication of the severity of the plugging that occurred during sampler penetration, but it is more instructive to compare Fi gu re  7 .1 0 En d- of -te st  g eo m et ry  fo llo w in g pe ne tra tio n of  1 ”,  2 ”,  3 ”,  4 ” an d 5”  si m ul at ed  sa m pl er s i n 4. 75  m m  sa m pl e.  160 0 15 0 m m 1”  S am pl er  2”  S am pl er 3”  S am pl er 4”  S am pl er 5”  S am pl er Fi gu re  7 .1 1 En d- of -te st  d is tri bu tio n of  c on ta ct  f or ce s fo llo w in g pe ne tra tio n of  1 ”,  2 ”,  3 ”,  4 ” an d 5”  s im ul at ed  s am pl er s in  4 .7 5 m m  sa m pl e. 161 0 15 0 m m 1”  S am pl er  2”  S am pl er 3”  S am pl er 4”  S am pl er 5”  S am pl er   162 profiles of the IFR.  Figure 7.12 compares IFR profiles recorded during the five simulations and illustrates the manner in which the various final plug lengths developed.  The penetration mode of the 1” sampler very quickly became fully plugged, with several slip episodes during which the plug length would have increased slightly.  The penetration depth at which the initial deviation from 100% occurs is seen to increase with platen spacing, suggesting that all of the samplers would have plugged given sufficient penetration depth. The factors controlling sampler plugging are poorly understood.  During static or quasi- static loading, sampler plugging is expected to occur when the combined internal friction and self weight of the soil plug exceed the load required to cause a bearing failure of the soil below the sampler opening.  Note that the term “plug” is commonly used to describe the soil inside a sampler or pile, regardless of the mode of penetration.  The internal friction and plug weight increase with plug length, leading to an increased likelihood of plugging with increasing penetration depth.  For three-dimensional samplers, the internal friction and end-bearing area are proportional to the plug diameter and the square of the plug diameter, respectively, leading to an increased likelihood of plugging with decreasing sampler inner diameter, as observed in Figures 7.10 and 7.12.  It has long been believed, however, that the factors controlling the mode of penetration are more complex than this description would suggest, and that one or more unique loading mechanisms are associated with the onset of plugging. Hvorslev (1949) performed an extensive review of soil sampling practice.  His conclusions were based primarily on deformation patterns observed in layered clays.  He observed that originally horizontal layers commonly progressed from concave-down to horizontal to concave up as one moved from the top to the bottom of the sample (Figure 7.13). He suggested that the concave-down pattern was due to heaving at the base of the test hole, that the horizontal material represented an ideal sampling stage, and that the concave-up pattern is created during an “over-driving” stage during which soil is deformed prior to entering the sampler.  He also suggested that over-driving would eventually lead to full plugging and the development of a cone of soil in front of the sampler.  The originally horizontal grid lines in Figure 7.10 do exhibit a concave-down trend throughout the soil plug but, in this case, the pattern is known to reflect the development of shear zones adjacent to the two platens. The prediction of plugging is a topic of considerable interest for pile design, and many plugging studies have been conducted using model piles that are similar in dimensions to SPT and LPT samplers.  Murff et al. (1990) performed a model pile study and suggested that the lower portion of the soil plug becomes wedged in the pile, leading to high frictional forces in the   163 Smoothed IFR (%) 0 25 50 75 100 125 Pe ne tr at io n De pt h (m ) 0.0 0.1 0.2 0.3 0.4 0.5 Smoothed IFR (%) 0 25 50 75 100 125 Smoothed IFR (%) 0 25 50 75 100 125 Smoothed IFR (%) 0 25 50 75 100 125 Smoothed IFR (%) 0 25 50 75 100 125 1" Sampler 5" Sampler4" Sampler3" Sampler2" Sampler                                                Figure 7.12 IFR profiles recorded during penetration of 1”, 2”, 3”, 4” and 5” simulated samplers in 4.75 mm sample.   164                                                Figure 7.13 Commonly observed deformation patterns for originally horizontal layers within soil samplers (Hvorslev, 1949).   165 lower, “active” portion of the plug.  The occurrence of relatively high friction forces in the lower portion of the soil plug has been experimentally confirmed during static loading of instrumented model piles by several researchers (e.g. Lehane and Gavin, 2001; Paik and Lee, 1993; Paik and Salgado, 2003).  Paikowsky (1990) suggested that this trend could be attributed to the development of stress arches in the soil plug (Figure 7.14).  He hypothesized that active and passive arches develop above and below a “hydrostatic” location, at which the vertical and horizontal stresses are equal.  Above the hydrostatic location, the vertical stress due to the self- weight of the soil is the major principal stress.  Below the hydrostatic location, the horizontal stress is the major principal stress, leading to the development of very high internal friction forces and an increased vertical load capacity for the plug.  Hight et al. (1996) suggest that this arching mechanism would be affected by shear-induced volumetric straining at the plug-pile interface, which would lead to increases and decreases of interface normal stress in dilative and contractive soils, respectively.  They noted that the magnitude of the volumetric strain would be largely independent of the pile diameter and hence that the effect would be of greater significance for smaller piles.  Randolph et al. (1991) suggested that the undrained nature of driven pile installation would prevent the changes of effective stress necessary to develop arching. The plots of contact force in Figure 7.11 can be used to qualitatively assess the distribution of internal friction for each mode of penetration.  The contact forces in the particles using the three largest samplers appear to increase in magnitude at a steady rate with depth.  In the 2” sampler, for which some plugging did occur, the contact forces are disproportionately high near the base of the plug, possibly due to arching as suggested by Paikowsky (1990).  In the 1” sampler, high contact forces are observed throughout the relatively short plug, indicating some wedging of particles has occurred, though the inner diameter is likely too small relative to the grain size for the development of arches. The arching mechanism is believed to promote plugging through an increase of internal friction.  Paikowsky (1990) suggested that the development of a soil cone ahead of the sampler, as noted by Hvorslev (1949), was a natural extension of the development of passive arches in the lower portion of the soil plug.  The contact force plots shown in Figure 7.11 suggest a complementary plugging mechanism that has perhaps not been accounted for in previous studies. The contact forces that develop at the leading edge of each platen are amongst the highest in the sample throughout the simulation.  These very high loads are distributed below the leading edges along numerous chains of particle contacts.  During penetration of the larger simulated samplers   166                                                Figure 7.14 Hypothesized passive arching mechanism for sampler and pile plugging (Paikowsky, 1990).   167 there is little interaction between the distributed loads.  As the platens are moved closer, however, it is inevitable that the load distribution patterns will begin to interact and, under certain conditions, may form a “leading arch” founded on the tips of the platens.  This appears to be the case for the 2” sampler shown in Figure 7.11.  A leading arch would effectively transfer some of the load required to cause a bearing failure of the soil beneath the plug to the platens, thus reducing the internal friction required to initiate a fully or partially plugged penetration mode.  The leading arch mechanism would naturally lead to the development of soil cones ahead of the sampler when plugging does occur. Penetration energies for the five samplers are plotted as a function of platen spacing and final plug length ratio in Figure 7.15.  The first plot demonstrates that the energy increased with increasing platen spacing, despite the fact that the dimensions of the platens did not change between simulations.  The second plot demonstrates that the energy also increased with increasing plug length ratio but several different energies were recorded for final plug length ratios of roughly 100%.  These results suggest that the occurrence of sampler plugging due to the mechanisms identified (passive arching within the soil plug and development of a leading arch) tends to decrease penetration energy, and that the decrease in energy is initiated prior to the onset of plugging.  7.3.3 Effect of Particle Size on Plugging  Model geometries and contact force distributions following penetration of the five samplers in the 6.30, 8.00, 13.2 and 19.0 mm samples are shown in Figures 7.16, 7.17, 7.18 and 7.19, respectively.  Equivalent plots for the 4.75 mm sample were presented in Figures 7.10 and 7.11.  The contact force bars in Figures 7.16 to 7.19 are drawn at the same scale and thus can be directly compared. The plots show that, in general, the degree of plugging tended to increase with (D50) for a given platen spacing.  Figure 7.20a compares the final plug length ratio to the mean particle size and shows a clear decrease of PLR with increasing mean particle size for the 2”, 3” and 4” samplers.  Figure 7.20b shows the same PLR results plotted against the ratio of the internal platen spacing (at the platen toe) to the mean particle size.  The data from all of the samples follow a single trend with the onset of plugging occurring when the internal platen spacing decreases below roughly 5 to 8 times the mean particle size.   168                                                Figure 7.15 Dual platen penetration energies recorded in the 4.75 mm sample plotted as a function of (a) platen spacing and (b) final plug length ratio. Internal Platen Spacing (mm) 0 25 50 75 100 125 Pe ne tr at io n En er gy , ∆E p (k J/ m) 9 10 11 12 13 Final Plug Length Ratio, PLR (%) 0 20 40 60 80 100 120 Pe ne tr at io n En er gy , ∆E p (k J/ m) 9 10 11 12 13 Fi gu re  7 .1 6 En d- of -te st  g eo m et ry  a nd  c on ta ct  fo rc es  fo llo w in g pe ne tra tio n of  1 ”,  2 ”,  3 ”,  4 ” an d 5”  si m ul at ed  sa m pl er s i n 6. 30  m m  sa m pl e.  169 0 15 0 m m 1”  S am pl er  2”  S am pl er 3”  S am pl er 4”  S am pl er 5”  S am pl er Fi gu re  7 .1 7 En d- of -te st  g eo m et ry  a nd  c on ta ct  fo rc es  fo llo w in g pe ne tra tio n of  1 ”,  2 ”,  3 ”,  4 ” an d 5”  si m ul at ed  sa m pl er s i n 8. 00  m m  sa m pl e.  170 0 15 0 m m 1”  S am pl er  2”  S am pl er 3”  S am pl er 4”  S am pl er 5”  S am pl er Fi gu re  7 .1 8 En d- of -te st  g eo m et ry  a nd  c on ta ct  fo rc es  fo llo w in g pe ne tra tio n of  1 ”,  2 ”,  3 ”,  4 ” an d 5”  si m ul at ed  sa m pl er s i n 13 .2  m m  sa m pl e.  171 1”  S am pl er  2”  S am pl er 3”  S am pl er 4”  S am pl er 5”  S am pl er 0 15 0 m m Fi gu re  7 .1 9 En d- of -te st  g eo m et ry  a nd  c on ta ct  fo rc es  fo llo w in g pe ne tra tio n of  1 ”,  2 ”,  3 ”,  4 ” an d 5”  si m ul at ed  sa m pl er s i n 19 .0  m m  sa m pl e.  172 1”  S am pl er  2”  S am pl er 3”  S am pl er 4”  S am pl er 5”  S am pl er 0 15 0 m m   173 Mean Particle Size (mm) 2 3 4 5 6 7 8 9 20 301 10 Fi na l Pl ug  L en gt h Ra tio , PL R (% ) 0 20 40 60 80 100 120 1" Sampler 2" Sampler 3" Sampler 4" Sampler 5" Sampler Internal Platen Spacing / Mean Particle Size 0 5 10 15 20 25 Fi na l Pl ug  L en gt h Ra tio , PL R (% ) 0 20 40 60 80 100 120 D50 = 4.75 mm D50 = 6.30 mm D50 = 8.00 mm D50 = 13.2 mm D50 = 19.0 mm                                                Figure 7.20 Final plug length ratio (PLR) plotted as a function of (a) mean particle size and (b) ratio of platen spacing to mean particle size for all samples and samplers.   174 Plugging occurred due to wedging of an oversized particle in the sampler opening during penetration of the 1” sampler in the 13.2 and 19.0 mm samples (Figures 7.18 and 7.19).  The underlying cause of plugging for the remaining simulations is clearly related to the ratio of the platen spacing to the mean particle size.  It seems likely that this relationship is related to shear zone thickness.  Some degree of plugging would be expected if all of the particles between the platens were within the shear zones of the two platens.  Shear zone thickness varied from 2.0 to 6.3 times the mean particle size for the penetration depth considered (0.4572 m).  Thus plugging would be expected to occur for platen spacings varying from 4 to 12.6 times the mean particle size, a range which brackets the observed range of 5 to 8. The fact that the degree of plugging was observed to increase with mean particle size even though the shear zone thickness (in units of length) was relatively independent of particle size suggests that the final thickness of the well-developed or critical state shear zone is a better predictor of plugging behaviour.  Consider the shear zone displacements shown in Figure 7.8 for the 4.75 and 19.0 mm samples.  While the shear zone thickness is similar for the two samples, the zone is only one particle wide in the coarse sample, leading to much higher displacements and contact forces at the edge of the zone.  These conditions are likely to encourage the formation of passive arches within the soil plug.  Indeed, arches with very high contact forces can be seen in the 13.2 and 19.0 mm samples (Figures 7.18 and 7.19).  Some of these arches have formed high in the soil plug and are likely unstable, but would still have contributed to the occurrence of plugging.  7.3.4 Effect of Particle Size on Penetration Energy  Penetration energies (∆Ep) measured for each of the five samplers in each of the five samples are plotted in Figure 7.21 as a function of (D50).  The single platen energies (multiplied by two) are also shown for comparison.  The trend of penetration energy increasing with platen spacing that was observed in Figure 7.15 for the 4.75 mm sample is observed for the other samples as well.  Some variation of order occurred in the two coarser samples, presumably due to the relative heterogeneity of those samples. The single platen energies were higher than the double platen energies in all samples. The single platen trials can be thought of as double platen trials with a platen spacing equal to two times the distance between the platen edge and the sample edge (i.e. a spacing of roughly 1.0 m).  Figure 7.21 thus confirms that the particle size effect noted during the single platen trials   175 Mean Particle Size (mm) 3 4 5 6 7 8 9 20 3010 Pe ne tr at io n En er gy , ∆ E p (k J/ m) 8 10 12 14 16 18 20 22 1" Sampler 2" Sampler 3" Sampler 4" Sampler 5" Sampler Single Platen                                               Figure 7.21 Relationship between single and dual platen energies and mean particle size. Single platen penetration energies have been multiplied by two for comparison purposes.   176 Table 7.3 Extrapolation of single platen penetration energies.  2 x Single Platen Energy (kJ/m) Mean Particle Size (mm) Single Platen ID/D50  Actual Extrapolated  to ID/D50 = 212 (Emax) 4.75 212  14.393 14.393 x 1.000 = 14.393 6.30 159  14.670 14.670 x 1.001 = 14.685 8.00 125  16.209 16.209 x 1.004 = 16.274 13.2 76  17.569 17.569 x 1.024 = 17.991 19.0 53  20.465 20.465 x 1.056 = 21.611  and the platen spacing effect noted during the dual platen trials were consistent during the trials and were additive (i.e. energy increased with both particle size and platen spacing). The single and dual platen penetration energies varied in a systematic manner.  Figure 7.22a compares penetration energies to the sampler-particle size ratio (ID/D50), where (ID) is the internal platen spacing (at the toe).  The single platen penetration energies have been assumed to correspond to an (ID) of 1.0 m.  It is reasonable to assume that the penetration energy would cease to vary above some critical value of platen spacing.  A curve conforming to this assumption has been fitted to the penetration energy data from the 4.75 mm sample data (Figure 7.22b).  The curve is defined as:  (7.2) ( )500.03514 (ID / D )pE 9.435 4.948 1 e− ⋅∆ = + ⋅ −  Since the penetration energy was observed to vary in a relatively smooth and systematic fashion with platen spacing and particle size, it is reasonable to assume that similar relationships will exist for the four other samples.  Penetration energies corresponding to an (ID/D50) ratio of 212 have been extrapolated from the single platen data for each sample using Equation 7.2.  The extrapolated values, referred to as (Emax), are listed in Table 7.3 and plotted in Figure 7.22b.  The differences between the actual single platen energies and the (Emax) values are minor. The (Emax) values reflect the single platen particle size effects between samples as well as factors such as porosity variations and boundary effects.  Normalization of dual platen energies using the corresponding (Emax) values (Figure 7.22c) reveals that the penetration energy for any of the simulations can be predicted reasonably well given the platen spacing, mean particle size and (Emax) for that sample.  The relationship between these factors can be written as:   177                                              Figure 7.22 Penetration energies plotted against the ratio of the internal platen spacing to the mean particle size, illustrating (a) basic data (b) single platen energies extrapolated to (Emax) values and (c) penetration energies normalized to (Emax) for each sample. Internal Platen Spacing / Mean Particle Size 0 20 40 60 80 100 120 140 160 180 200 220 Pe ne tr at io n En er gy , ∆ E p (k J/ m) 5 10 15 20 25 30 Internal Platen Spacing / Mean Particle Size 0 20 40 60 80 100 120 140 160 180 200 220 Pe ne tr at io n En er gy , ∆ E p (k J/ m) 5 10 15 20 25 30 Internal Platen Spacing / Mean Particle Size 0 5 10 15 20 25 30 ∆ E p / E m ax 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Extrapolated Values (Emax) Curve used for extrapolation D50 = 4.75 mm D50 = 6.30 mm D50 = 8.00 mm D50 = 13.2 mm D50 = 19.0 mm Equation 8.2 (a) (c) (b) Equation 7.3   178 (7.3a) p max 50E / E 0.6 0.03 (ID / D )∆ = + ⋅    for ID/D50 < 5  (7.3b) p max 50E / E 0.75 0.006 (ID / D 5)∆ = + ⋅ −    for ID/D50 ≥ 5  It was observed in Figure 7.20b that the onset of plugging occurred for (ID/D50) values less than roughly 5 to 8.  The change of slope in the energy figure is likely related to the onset of plugging.  These relationships are specific to the simulations that were run.  Simulations using different boundary pressures, particle size gradations, sample porosity or platens, for example, would likely follow different relationships, though there is no reason to believe that the nature of the relationship would change significantly.  7.4 DISCUSSION   Reviews of the major findings and limitations of the study are presented in this section, followed by a comparison of experimental and numerical grain size effects.  7.4.1 Major Findings  During the single platen simulations the mean value and standard deviation of the penetration energy were observed to increase with particle size.  The increasing penetration energy reflected the development of higher inter-particle normal contact forces and hence higher allowable shear forces in coarser samples.  Unique stages of shear zone development were observed adjacent to the platen, beginning with immature, single layer shear zones immediately behind the platen tip and proceeding to mature shear zones further up the platen that were roughly 6 particle diameters wide.  The platen penetration required for development of mature shear zones was seen to increase with particle size. During the dual platen simulations the penetration energy was observed to increase with particle size and with platen spacing.  This trend reflects the increase of contact forces with particle size, as for single platen simulations, as well as plugging effects.  Partial plugging was first observed when the sampler-particle size ratio (ID/D50) decreased to between 5 and 8, and the degree of plugging increased as the ratio decreased further.  Plugging due to particle jamming occurred as the ratio approached one.  The relationship between plugging severity and   179 (ID/D50) is believed to reflect the interaction of the platen shear zones.  This interaction encourages arching between platens and the development of a leading arch ahead of the sampler opening, both of which reduce the internal friction required for plugging and lead to a reduction of penetration energy.  7.4.2 Limitations  The study performed did not directly investigate the effect of factors such as sample porosity, gradation and stress state.  In addition, the sample size was held constant during all but one simulation, and the effect of varying particle size at a fixed sample size was not investigated. The simulated particles are circular cylinders of unit length.  As a result, both the inner frictional and end bearing areas are directly proportional to the platen spacing.  For a real sampler, however, the inner frictional and end bearing areas are proportional to the sampler inner diameter and the square of the sampler inner diameter, respectively.  This difference can be expected to affect the ratio of sampler to particle/grain size at which plugging begins to occur.  It also seems likely that passive arches within the plug and leading arches ahead of the sampler are more likely to develop in real samplers because reduced span out-of-plane arches can develop and instigate the formation of larger arches spanning the full inner diameter of the sampler. Other limitations of the adopted simulation approach include the use of a steady and relatively slow penetration rate and the inability to consider pore water pressure effects.  These two factors are related because the rate of loading will ultimately control the state of soil drainage in the vicinity of the sampler.  In general, plugging is considered to be more likely to occur during quasi-static sampling than dynamic sampling.  Drainage effects are expected to be of greater importance in finer soils with lower permeability, and thus may be responsible for trends observed at lower (D50) values, while plugging effects may become more important in coarser soils.  A more complete discussion of the study limitations, including consideration of previous work by Huang et al. (1992), Jiang et al. (2002), Morgan (1999), Morgan and Boettcher (1999), McDowell and Harireche (2002 a,b) and O’Sullivan et al. (2002), is provided in Appendix F.       180 7.4.3 Comparison of Experimental and Numerical Grain Size Effects  Particle size effect trends observed during the PFC2D study may provide insight into the processes controlling grain size effects in real soils.  The term (∆Ep/Emax) was shown to vary consistently with the sampler-particle size ratio.  This term would be analogous to the blow count ratio between the SPT and an LPT utilizing a very large sampler or even a pile. Alternatively, the (Emax) term can be approximated as the penetration resistance of a solid penetrometer that is not subject to plugging effects, such as a CPT piezocone.  The variation of SPT-CPT correlations with the logarithm of the mean grain size was discussed in Chapter 2 and illustrated in Figure 2.17, reproduced here as Figure 7.23a for ease of reference.  Figure 7.23b is an analogous plot of (Emax/∆Ep) versus (D50).  In both plots, the penetration resistance or energy of the penetrometer that is not subject to plugging effects (i.e. the CPT or single platen) is seen to increase relative to that of the penetrometer that is subject to plugging effects (i.e. the SPT or a pair of platens) with increasing (D50).  Although not directly comparable, the general agreement between the numerical and experimental results provides some support for the use of the PFC2D results to guide the interpretation of experimental data. A more direct comparison is possible for SPT-LPT correlation factors.  The ratio of penetration energies for any two PFC2D samplers can be estimated as follows:  (7.4) p A p A max p B p B max ( E ) ( E ) / E ( E ) ( E ) / E ∆ ∆=∆ ∆  where the subscripts (A) and (B) refer to the two samplers under consideration and the (∆Ep/Emax) values are determined using Equation (7.3).  The (Emax) terms cancel in Equation (7.4) because they are independent of platen spacing for a given sample.  The ratio of the 2” sampler penetration energy to that of each of the other sampler sizes is plotted in Figure 7.24. The ratios of the 3”, 4” and 5” samplers are seen to increase as (D50) increases to 7 mm, at which point the 2” sampler energy begins to decrease at a greater rate due to plugging effects, causing a decrease in the energy ratio.  The energy ratio continues to decrease until the other sampler also begins to plug, at which point the energy ratio begins to increase again.  A slightly different trend is observed for the 1” sampler, which begins to plug before the 2” sampler.   181 Mean Particle Size (mm) 3 4 5 6 7 8 9 20 3010 E m ax  /  ∆E p 0.8 1.0 1.2 1.4 1.6 1.8 2.0 4" 3" 2" 1" 5" Sampler                       (a)                    (b)    Figure 7.23 Comparison of (a) widely adopted (qc/N) versus (D50) relationship (after: Robertson et al., 1982) and (b) (Emax/E) versus (D50) relationship from this study showing similar increase with increasing mean grain or particle size.   182 Mean Particle Size (mm) 3 4 5 6 7 8 9 20 3010 Pe ne tr at io n En er gy  R at io 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 2" : 5" 2" Sampler : 1" Sampler 2" : 4" 2" : 3"                                                 Figure 7.24 Penetration energy ratio trends determined using Equations 7.3 and 7.4.   183 The trends in Figure 7.24 compare favourably with the concave-down trend of SPT-LPT correlation factors observed in Figure 6.10.  The experimental data exhibit a slope break well before the 7 mm mean grain size indicated in the numerical results.  This may reflect the delayed onset of plugging in the numerical results due to 2-dimensional limitations. A meaningful procedure for determining the maximum and minimum porosity and hence the relative density of a particle assemblage in the two-dimensional DEM environment has yet to be developed.  As a result, there can be no direct analogy between PFC2D particle size effects and real world grain size effects as indicated by the variation of (CD).  It was shown in Chapter 6 that (CD) increases with (D50) in the sands.  The results of the single platen PFC2D trials suggest that, in the absence of plugging effects, penetration energies increased with increasing particle size.  It seems likely, however, that these trends represent two different phenomena. It was observed in Chapter 6 that the slope of the (CD) versus Log(D50) relationship is higher in sands than gravels.  The fact that the slope appears to decrease could signify the onset of efficient plugging similar to that observed in PFC2D.  If the change of slope is related to plugging effects, the PFC2D study results support the use of a critical sampler-grain size ratio for differentiating between plugged and partially plugged penetration modes.  7.5 CHAPTER SUMMARY  An investigation of grain size effects using the two-dimensional DEM code “PFC2D” was described in this Chapter.  Single and dual platen penetration trials were used to investigate grain size effects related to platen dimensions and platen spacing, respectively.  It was observed that the required single platen penetration energy increases with increasing mean particle size.  It was suggested that this trend was due to higher inter-particle contact forces in coarser samples that led to higher allowable inter-particle shear forces.  Dual platen penetration energy was also observed to increase with mean particle size for a given platen spacing.  In addition to this trend, the penetration energy was observed to decrease with decreasing platen spacing.  The latter trend was attributed to the onset of efficient plugging during which passive and leading arches form within and ahead of the plug, respectively, leading to an overall reduction in the energy required to penetrate the simulated sampler.  Both types of arches are more likely to develop both in smaller samplers and in coarser samples.  This observed particle size effect appears to be related to the thickness of the shear zone that develops in the particle assemblage adjacent to the platens, which increases with particle size.  The onset of partial plugging was observed to occur when the   184 sampler-particle size ratio decreased below roughly 5.  Particle size effect trends were compared to experimental observations of grain size effects observed in SPT-CPT and SPT-LPT correlations.  It was suggested that the reduction of slope observed in (CD) versus Log(D50) when progressing from sands into gravels may be related to the onset of efficient plugging.   185 CHAPTER 8 PREDICTION OF GRAIN SIZE EFFECTS  8.1 INTRODUCTION  Particle size effects were observed to vary in a relatively smooth and continuous manner during the DEM study.  Plugging was triggered when the ratio of sampler to particle size decreased below a certain value, and was due to efficient mechanisms that tended to decrease the required penetration energy.  It is postulated that the decreased slope of the (CD)SPT versus (D50) relationship observed in gravels is due to similar processes in real soils, and that 2.0 mm is the critical mean grain size (D50’) above which SPT results begin to be affected by plugging.  The inner diameter of an SPT sampler opening is 35 mm, and thus the corresponding critical ratio of sampler to grain size can be estimated as (35 / 2 = 17.5).  Shear zone overlap within a sampler, which will be conducive to plugging, is expected to occur when the sampler to grain size ratio is in the range of 6 to 20 (Uesugi et al. 1988).  It is logical for the estimated critical sampler to grain size ratio of 17.5 to fall within this range. SPT or LPT blow counts recorded in soils for which the sampler to grain size ratio is less than 17.5 are expected to exhibit greater variability and to be, on average, slightly lower than would be expected based on extrapolations of grain size effect trends observed in finer soils. Grain size effects observed in finer soils are presumably due to processes other than plugging, such as drainage effects, which were not addressed in the DEM study.  In this chapter, an inversion approach similar to that employed by Tokimatsu (1988) is used to back-calculate (CD)LPT values from available measurements of (CS/L).  The data are interpreted based on an assumption of similarity between SPT and LPT grain size effects, and an empirical approach to predicting LPT grain size effects is proposed.  8.2 INVERSION OF (CS/L) DATA  (CD)LPT can be back-calculated from actual measurements of (CS/L) as follows:  (8.1) D SPTD LPT S/ L (C )(C ) C =    186 where (CD)SPT will vary according to the mean grain size of the soil in which (CS/L) was recorded.  Equation (6.5), reprinted here for ease of reference, can be used to estimate the appropriate value of (CD)SPT:  (8.2a) D SPT 50(C ) 88 56 Log(D )= + ⋅  0.15 mm ≤ D50 ≤ 2.0 mm  (8.2b) D SPT(C ) 105=   2.0 mm ≤ D50 ≤ 20 mm  and can be used with Equation (8.1) to back-calculate (CD)LPT.  The coefficient of variation of (CD)SPT is known to vary with (D50), however, and to become quite high in gravels.  The uncertainty of back-calculated (CD)LPT values is assessed taking this into account in the following sections.  8.2.1 Measurement Uncertainty  If a large number of (CD) values were directly measured for a particular type of LPT, it is expected that the coefficient of variation would vary with mean grain size in a manner similar to that observed for the SPT.  A generic description of this variation, referenced to the critical mean grain size (D50’), can be written as:  (8.3a) D(C ) 35%Ω =   0.15 mm ≤ D50 ≤ D50’  (8.3b) D 50 50(C ) 35 60 Log(D / D ')Ω = + ⋅  D50’ ≤ D50 ≤ 10 ⋅ (D50’)  Ω(CD) as defined by Equation (8.3) is equal to 35% below (D50’) and increases from 35 to 95% as the mean grain size increases from (D50’) to 10 ⋅ (D50’).  This relationship is shown for the case of an SPT (D50’ = 2.0 mm) as a dashed line in Figure 8.1. Back-calculated values of (CD)LPT are subject to greater uncertainty.  Taylor series expansion of Equation (8.1) leads to the following relationship:  (8.4) 2 2D LPT D SPT S/ L(C ) ( (C ) ) ( (C ))Ω = Ω + Ω  (Inverted Data)   187 D50 (mm) 0.1 1 10 Ω( C D ) 0 20 40 60 80 100 120 140 Ω(CD)SPT, Observed Ω(CD)LPT , for Back-Calculated (CD)LPT                                               Figure 8.1 Ω(CD)SPT trend observed in Chapter 6 and Ω(CD)LPT trend believed to be applicable to back-calculated values of (CD)LPT.   188 Ω(CD)SPT is defined by Equation (8.3) and, as a first approximation, the estimate of Ω(CS/L) from Chapter 6 can be used:  (8.5a) S/ L(C ) 25%Ω ≈  0.15 mm ≤ D50 ≤ 1.0 mm  (8.5b) )D(Log2725)C( 50L/S ⋅+≈Ω  1.0 mm ≤ D50 ≤ 20 mm  The resulting relationship between Ω(CD)LPT and mean grain size for inverted (CS/L) data is plotted as a solid line in Figure 8.1.  Ω(CD)LPT is predicted to have a minimum value of 43% in sands and to increase as (D50) becomes greater than 1.0 mm, reaching values of 60, 80 and 100% at mean grain sizes of roughly 3.0, 6.5 and 12.5 mm, respectively.  This analysis demonstrates that back-calculated (CD)LPT values will be subject to considerable uncertainty in gravels, and thus that interpretation efforts should focus on sand data.  8.2.2 Inverted Data  Back-calculated (CD) values are plotted as a function of (D50) for the MPT, JLPT, NALPT, RLPT and ILPT in Figures 8.2 to 8.6.  Recall that all SPT and LPT blow counts, including those used to calculate SPT-JLPT blow counts, were corrected to an average rod energy ratio of 0.60 in Chapter 6 prior to calculating the correlation factors.  (CD)SPT as defined by Equation (8.2) also corresponds to an average rod energy ratio of 0.6, and thus all (CD)LPT data shown in Figures 8.2 to 8.6 correspond to a rod energy ratio of 0.60. The upper plot in each figure includes error bars corresponding to a range of ± one standard deviation, calculated using Equation (8.4).  These error bars indicate that it is reasonable to identify general trends in sands and even fine gravels, but the back-calculated values in most gravels become highly uncertain.  Plot (b) in each figure shows the same data as plot (a) with no error bars, for clarity.   189 0.1 1 10 (C D) M PT 0 20 40 60 80 100 120 140 160 180 200 D50 (mm) 0.1 1 10 (C D) M PT 0 20 40 60 80 100 120 140 160 180 200 (a) (b) Interpreted Trend +/- 1 Std. Dev. (Predicted) Modified Trend                                                Figure 8.2 Back-calculated (CD)MPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation.   190 0.1 1 10 (C D) J LP T 0 25 50 75 100 125 150 175 200 D50 (mm) 0.1 1 10 (C D) J LP T 0 25 50 75 100 125 150 175 200 Interpreted Trend +/- 1 Std. Dev. (Predicted) Modified Trend (a) (b)                                               Figure 8.3 Back-calculated (CD)JLPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation.  Circled data points were not used to determine sand trend.   191 0.1 1 10 (C D) N AL PT 0 25 50 75 100 125 150 175 200 D50 (mm) 0.1 1 10 (C D) N AL PT 0 25 50 75 100 125 150 175 200 (a) (b) Interpreted Trend +/- 1 Std. Dev. (Predicted) Modified Trend                                               Figure 8.4 Back-calculated (CD)NALPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation.  Circled data points were not used to determine sand trend.   192 0.1 1 10 (C D) R LP T 0 50 100 150 200 250 300 350 400 450 D50 (mm) 0.1 1 10 (C D) R LP T 0 50 100 150 200 250 300 350 400 450 Interpreted Trend +/- 1 Std. Dev. (Predicted) (a) (b)Modified Trend                                                Figure 8.5 Back-calculated (CD)RLPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation.   193 0.1 1 10 (C D) I LP T 0 50 100 150 200 250 300 350 400 D50 (mm) 0.1 1 10 (C D) I LP T 0 50 100 150 200 250 300 350 400 Interpreted Trend +/- 1 Std. Dev. (Predicted) (a) (b)Modified Trend                                                Figure 8.6 Back-calculated (CD)ILPT data (a) with and (b) without error bars indicating uncertainty corresponding to ± one standard deviation.   194 Table 8.1  Best-fit lines for SPT and back-calculated LPT (CD) data. Test D50’ (mm) 1 Trend (0.15 ≤ D50 ≤ D50’) (CD)0.1mm (CD)max MPT 0.7 CD = 58 + 35 ⋅ Log (D50) 23 53 SPT 2.0 CD = 88 + 56 ⋅ Log (D50) 32 105 JLPT 2.9 CD = 49 + 17 ⋅ Log (D50) 32 57 NALPT 3.5 CD = 56 + 24 ⋅ Log (D50) 32 69 RLPT 5.6 CD = 136 + 107 ⋅ Log (D50) 29 216 ILPT 5.7 CD = 90 + 59 ⋅ Log (D50) 31 135 1.  D50’ = sampler inner diameter / 17.5  8.2.3 Discussion   The mean value of (CD)SPT was assumed in Chapter 6 to vary linearly with the logarithm of (D50) and to approach a maximum value ((CD)max) at (D50’).  It is proposed, as per Tokimatsu (1988), that the (CD)LPT data follow trends that are similar to the SPT trend, varying linearly with the logarithm of (D50) to a maximum value at (D50’).  Based on that assumption, best-fit lines were determined for each type of LPT using only data points corresponding to (D50 ≤ D50’). These are shown as solid black lines in Figures 8.2 to 8.6.  Descriptive equations and (D50’) and (CD)max values are listed in Table 8.1.  Corresponding parameters for the SPT are listed for comparison.  One JLPT data point and two NALPT data points were identified as outliers based on position relative to other data points and excluded, as indicated in Figures 8.3 and 8.4, respectively.  (CD) is assumed to reach a constant value defined by the sand trend for (D50 ≥ D50’).  The trends identified for each test type are directly compared in Figure 8.7a. Ranges corresponding to ± one standard deviation around the observed mean are indicated by the dashed lines in Figures 8.2 to 8.6.  These ranges were calculated using Equation (8.3), which is believed to be applicable to directly measured rather than back-calculated (CD) values, and are plotted for comparison purposes only.  Most of the back-calculated values are seen to fall within this range, which becomes quite broad for (D50 > D50’).     195 D50 (mm) 0.1 1 10 C D 0 50 100 150 200 250 300 0.1 1 10 C D 0 50 100 150 200 250 300 (a) (b) MPT RLPT JLPT NALPT SPT ILPT RLPT JLPT NALPT SPT ILPT MPT                                                Figure 8.7 Comparison of (CD)SPT to all interpreted (CD)LPT trends.  Trends in plot (b) have been forced through point (CD)0.1mm = 32.   196 Table 8.2  Modified best-fit lines for SPT and back-calculated LPT (CD) data. Test Revised Sand Trend D50’ (mm) (CD)max (CD)1mm E60/ATE (J/cm2) MPT CD = 43 + 11 ⋅ Log (D50) 0.7 41 43 a 37.4 SPT CD = 88 + 56 ⋅ Log (D50) 2.0 105 88 21.0 JLPT CD = 49 + 17 ⋅ Log (D50) 2.9 57 49 33.5 NALPT CD = 56 + 24 ⋅ Log (D50) 3.5 69 56 29.2 RLPT CD = 132 + 100 ⋅ Log (D50) 5.6 207 132 14.4 ILPT CD = 90 + 58 ⋅ Log (D50) 5.7 134 90 20.1 a. D50’ < 1.0 mm for the MPT, but (CD)1mm is still used to describe the sand trend.  8.3 PREDICTION OF GRAIN SIZE EFFECT TRENDS  SPT-LPT correlations are generally based on side-by-side SPT and LPT performed in one or more sand deposits.  The (CS/L) data presented in Chapter 6 show, however, that (CS/L) varies with grain size in both sands and gravels.  The variation of (CS/L) with (D50) could be predicted for any LPT given the (CD)LPT trend.  Thus it would be useful to be able to generate (CD)LPT versus (D50) trends for any type of LPT. Each of the trend lines listed in Table 8.1 consists of a y-intercept value and a slope (m). Because Log(1) is equal to zero, the y-intercept is equal to the value of (CD) corresponding to a mean grain size of 1.0 mm, which will be denoted (CD)1mm herein.  Either the slope or one other point on the line would fully define the trend.  The trend-lines in Figure 8.7a converge as (D50) approaches 0.1 mm.  The magnitudes of (CD) corresponding to (D50 = 0.1 mm) for each trend line, denoted (CD)0.1mm, are listed in Table 8.1.  With the exception of the MPT and possibly the RLPT, the (CD)0.1mm values all fall fairly close to the SPT value of 32, indicated by the small black circular symbol in Figure 8.7.  (CD)1mm and (CD)0.1mm  are separated by one log cycle, so the slope of the trend (m) is simply equal to (CD)1mm minus (CD)0.1mm.  It is proposed that (CD)0.1mm can be assumed to equal 32 for all of the tests shown, so that (m) is equal to (CD)1mm minus 32.  New best-fit relationships forced through this point were determined for each type of LPT.  The resulting modified trends are shown in Figure 8.7b and listed in Table 8.2.  The new trends are also shown as “dash-dot-dash” lines in Figures 8.2b to 8.6b to allow direct comparison   197 with the original trends.  Only the MPT and RLPT trends are noticeably affected, and these were based on data distributed over a relatively small range of (D50). The relationship between (CD)LPT and (D50) for the SPT or any LPT can thus be written in the following generalized form:  (8.6a) D D 1mm D 1mm 50C (C ) ((C ) 32) Log(D )= + − ⋅  0.15 mm ≤ D50 ≤ D50’