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Seismic assessment of basement walls in British Columbia Amirzehni, Elnaz 2016

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.Seismic Assessment of Basement Walls inBritish ColumbiabyElnaz AmirzehniB.Sc., Civil Engineering, University of Tehran, Iran, 2006M.Sc., Geotechnical Engineering, University of Tehran, Iran, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Civil Engineering)The University of British Columbia(Vancouver)April 2016c© Elnaz Amirzehni, 2016AbstractThe current state of practice for seismic design of basement walls in Vancouveris based on the Mononobe-Okabe (M-O) method using a Peak Ground Accelera-tion (PGA) mandated by the National Building Code of Canada (NBCC, 2010).Because there is a little evidence of any significant damage to basement walls dur-ing major earthquakes, the Structural Engineers Association of British Columbia(SEABC) became concerned about designing the walls under the code-mandatedPGA and set up a task force to review the current procedure for seismic design ofbasement walls in British Columbia. The University of British Columbia (UBC)was asked to carry out this investigation. This thesis aims to provide solid base fordesigning the basement walls using an appropriate fraction of the code-mandatedPGA in the M-O analyses. To this end, a series of dynamic nonlinear soil–structureinteraction analyses are conducted to examine the seismic resistance of typicalbasement walls designed according to current practice in BC, for different frac-tions of the code-mandated PGA (100% to 50%). The seismic responses of thewalls are evaluated by subjecting them to ensembles of ground motions comprisedof shallow crustal, deep subcrustal, interface earthquakes from a Cascadia subduc-tion events and near-fault earthquake motions. Input motions are matched to theintensity of the seismic hazard using both spectral and linear scaling techniques.Representative 4-level and 6-level basement walls are analyzed. The nonlinear hys-teretic response of the foundation soil is characterized in order to obtain realisticestimates of an interaction between the basement wall and the surrounding soil. Inaddition, the effects of the local site conditions in terms of geometrical and geo-logical structure of soil deposits underlying the basement structure on the seismicperformance of the basement walls are evaluated. The analyses show that currentiiengineering practice for designing basement walls based on the M-O method andusing 100% PGA is too conservative. The analyses suggest that a wall designedusing 50% to 60% PGA results in an acceptable performance in terms of drift ratio.iiiPrefaceIn 2010, the Structural Engineers Association of British Columbia (SEABC) ini-tiated a voluntary task force to review current seismic design procedure for deepbasement walls and the University of British Columbia (UBC) was asked to carryout this research. Prof. Finn and Drs. DeVall and Taiebat are members of thisvoluntary task force and together with Prof. Ventura are the members of the super-visory committee of this thesis. The present study aims to evaluate the performanceof basement walls designed following the current state of practice in Vancouver andprovide a basis for recommending an acceptable reduced design loads for basementwall. The seismic design of the basement walls presented was done by Dr. DeVall,R. H., senior consultant structural engineering at Read Jones Christoffersen Ltd.,Vancouver, who is also a member of technical committee on basement walls atSEABC. The outputs of this thesis aid the advancement of the state of practice inthis area.I, Elnaz Amirzehni, am the principle contributor to all seven chapters of thisthesis. I was responsible for all major areas of concept formation, data collectionand analysis, and wiring the chapters. Some parts of the findings of this thesis havebeen published in a journal and three conferences so far.• Amirzehni, E., Taiebat, M., Finn, W. D. L., and DeVall, R. H. (2015), “Groundmotion scaling/matching for nonlinear dynamic analysis of basement walls”,Proceedings of the 11th Canadian Conference on Earthquake Engineering.Victoria, BC, Canada, p. 10 pages.This paper includes a version of some sections in Chapter 6. I conducted allthe numerical analyses and wrote the first draft of the manuscript. Prof. Finnivand Dr. DeVall provided guidance throughout the evolution of the projectand manuscript edits.• Amirzehni, E., Taiebat, M., Finn, W. D. L., and DeVall, R. H. (2015), “Seis-mic performance of deep basement walls”, Proceedings of the 6th Interna-tional Conference on Earthquake Geotechnical Engineering. Christchurch,New Zealand, p. Paper ID: 194, 8 pages.This paper includes a version of Section 5.4 in Chapter 5. I conducted all thenumerical analyses and wrote the first draft of the manuscript. Prof. Finnand Drs. DeVall and Taiebat provided guidance throughout the evolution ofthe project and manuscript edits.• Taiebat, M., Amirzehni, E., and Finn, W. D. L. (2014), “Seismic designof basement walls: evaluation of the current practice in British Columbia”,Canadian Geotechnical Journal, vol. 51, no. 9, pp. 1004-1020.This paper includes a version of some sections in Chapters 3 and 4. I con-ducted all the numerical analyses and wrote the first draft of the manuscript.Prof. Finn and Drs. Taiebat and DeVall provided guidance throughout theevolution of the project and manuscript edits.• Amirzehni, E., Taiebat, M., Finn, W. D. L., and DeVall, R. H. (2013), “Effectof near-fault ground motions on seismic response of deep basement walls”,Proceedings of the 4th International Conference on Computational Methodsin Structural Dynamics & Earthquake Engineering (COMPDYN 2013). KosIsland, Greece, p. 11 pages.This paper includes a version of some sections in Chapters 6. I conducted allthe numerical analyses and wrote the first draft of the manuscript. Prof. Finnand Drs. Taiebat and DeVall provided guidance throughout the evolution ofthe project and manuscript edits.Additional papers are under preparation to publish the remainder of the thesisfindings.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxviii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives and scope . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Organization of dissertation . . . . . . . . . . . . . . . . . . . . . 62 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Performance of basement walls during past earthquake events . . . 92.3 Building code provisions requirement . . . . . . . . . . . . . . . 102.4 State of practice in British Columbia . . . . . . . . . . . . . . . . 132.5 Seismic coefficient in basement wall design . . . . . . . . . . . . 183 Development of the computational model of a basement wall . . . . 233.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23vi3.2 Seismic design of the typical 4-level basement wall . . . . . . . . 243.3 Description of the computational model . . . . . . . . . . . . . . 283.3.1 Modeling the construction sequence . . . . . . . . . . . . 283.3.2 Input ground motions characterization . . . . . . . . . . . 303.3.3 Structural elements . . . . . . . . . . . . . . . . . . . . . 363.3.4 Representative soil properties . . . . . . . . . . . . . . . 373.3.5 Mesh refinement of the soil domain . . . . . . . . . . . . 433.3.6 Modeling soil–wall interaction using an interface elements 453.3.7 Boundary conditions . . . . . . . . . . . . . . . . . . . . 474 Seismic performance of a typical 4-level basement wall . . . . . . . 514.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2 Lateral earth forces and pressures on the wall . . . . . . . . . . . 524.3 Bending moments and shear forces on the wall . . . . . . . . . . 654.4 Displacements and drift ratios on the wall . . . . . . . . . . . . . 654.5 Sensitivity analyses . . . . . . . . . . . . . . . . . . . . . . . . . 724.5.1 Soil–wall interface element . . . . . . . . . . . . . . . . . 724.5.2 Dilation angle of the backfill soil . . . . . . . . . . . . . . 764.5.3 Friction angle of the backfill soil . . . . . . . . . . . . . . 774.5.4 Shear wave velocity of the backfill soil . . . . . . . . . . 784.5.5 Modulus reduction and Rayleigh damping . . . . . . . . . 804.5.6 Shoring pressure during excavation stage . . . . . . . . . 825 Additional studies on soil properties and wall geometries . . . . . . 845.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.2 Nonlinear stress-strain characteristics of soil . . . . . . . . . . . . 855.2.1 Description of the UBCHYST soil model . . . . . . . . . 865.2.2 Calibration of UBCHYST input parameters . . . . . . . . 885.2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . 955.3 Local site condition . . . . . . . . . . . . . . . . . . . . . . . . . 985.3.1 General subsurface conditions in Vancouver . . . . . . . . 1015.3.2 Depth to the significant impedance contrast . . . . . . . . 103vii5.3.3 Shear wave velocity and impedance contrast of the soil de-posits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.4 Effect of basement wall geometry . . . . . . . . . . . . . . . . . 1265.4.1 Seismic design of a 4-level basement wall with higher topstorey height and a 6-level basement wall . . . . . . . . . 1275.4.2 Simulation results . . . . . . . . . . . . . . . . . . . . . 1306 Selection and modification of time histories for Vancouver . . . . . . 1406.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1406.2 Seismicity of south-western British Columbia . . . . . . . . . . . 1416.3 Ground motion scaling methods . . . . . . . . . . . . . . . . . . 1456.3.1 PGA scaling . . . . . . . . . . . . . . . . . . . . . . . . 1476.3.2 Sa(T1) scaling . . . . . . . . . . . . . . . . . . . . . . . . 1476.3.3 ASCE scaling . . . . . . . . . . . . . . . . . . . . . . . . 1486.3.4 SIa scaling . . . . . . . . . . . . . . . . . . . . . . . . . 1486.3.5 MSE scaling . . . . . . . . . . . . . . . . . . . . . . . . 1486.4 Selection of ground motion records . . . . . . . . . . . . . . . . . 1496.4.1 Crustal earthquakes . . . . . . . . . . . . . . . . . . . . . 1516.4.2 Subcrustal earthquakes . . . . . . . . . . . . . . . . . . . 1616.4.3 Subduction earthquakes . . . . . . . . . . . . . . . . . . 1656.4.4 Near-fault pulse-like earthquakes . . . . . . . . . . . . . 1696.5 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . 1757 Summary and future research . . . . . . . . . . . . . . . . . . . . . 1887.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1887.2 Recommendations for future research . . . . . . . . . . . . . . . 196Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198Appendix A Foundation Walls . . . . . . . . . . . . . . . . . . . . . . . 214A.1 Wall physical properties . . . . . . . . . . . . . . . . . . . . . . . 214A.2 Load cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214A.3 Moment capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 216A.4 Shear capacity - CAN/CSA-A23.3-04 (2004) . . . . . . . . . . . 221viiiA.5 Wall curvature and rotation capacity . . . . . . . . . . . . . . . . 221ixList of TablesTable 3.1 List of the selected crustal ground motions. . . . . . . . . . . . 33Table 3.2 Soil layer material properties. . . . . . . . . . . . . . . . . . . 38Table 4.1 Soil modulus reduction and damping ratios obtained from SHAKEanalyses for different normalized shear wave velocities of topsoil layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Table 5.1 Soil parameters of the UBCHYST constitutive model used inFLAC analyses. . . . . . . . . . . . . . . . . . . . . . . . . . 94Table 5.2 Shear wave velocities of the first and the second soil layers cor-responding to ten proposed soil profiles. The numbers in theparenthesis represent the average shear wave velocities of thetop 30 m of the soil (Vs30) used for NBCC (2010) site classifi-cation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Table 5.3 Soil parameters of the UBCHYST constitutive model used inFLAC analyses. . . . . . . . . . . . . . . . . . . . . . . . . . 118Table 6.1 Scaling factors calculated for the selected crustal ground mo-tions using different linear scaling methods. . . . . . . . . . . 152Table 6.2 List of the selected subcrustal ground motions. . . . . . . . . . 161Table 6.3 List of the selected subduction ground motions. . . . . . . . . 167Table 6.4 List of the selected pulse-like ground motions. . . . . . . . . . 171Table 7.1 Summary of the sensitivity analyses conducted in this study. . . 190Table 7.2 Summary of analyses. . . . . . . . . . . . . . . . . . . . . . . 193xTable A.1 Physical properties of the foundation walls . . . . . . . . . . . 214Table A.2 Nominal moment capacity (kN−m/m) in W1 . . . . . . . . . 217Table A.3 As(mm2/m) in W1 . . . . . . . . . . . . . . . . . . . . . . . . 217Table A.4 Nominal moment capacity (kN−m/m) in W2 . . . . . . . . . 218Table A.5 As(mm2/m) in W2 . . . . . . . . . . . . . . . . . . . . . . . . 218Table A.6 Nominal moment capacity (kN−m/m) in W3 . . . . . . . . . 219Table A.7 As(mm2/m) in W3 . . . . . . . . . . . . . . . . . . . . . . . . 220Table A.8 Nominal shear capacity . . . . . . . . . . . . . . . . . . . . . 221Table A.9 Drift limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222xiList of FiguresFigure 2.1 Forces considered in the Mononobe-Okabe analysis. . . . . . 14Figure 2.2 State of practice for seismic design of the basement walls inBritish Columbia using the modified M-O method. . . . . . . 15Figure 3.1 (a) Floor heights in the 4-level basement wall and (b) the cal-culated lateral earth pressure distributions from the first loadcombination. . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.2 (a) Floor heights in the 4-level basement wall and the calcu-lated lateral earth pressure distributions from the second loadcombination using the modified M-O method with (b) 100% PGA,(c) 90% PGA, (d) 80% PGA, (e) 70% PGA, (f) 60% PGA, and(g) 50% PGA, where PGA=0.46g, based on the NBCC (2010)for Vancouver. . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.3 Moment capacity distribution along the height of the 4-levelbasement walls designed for various fractions of the code PGA.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 3.4 Different stages of the computational model building procedure. 29Figure 3.5 The 5% damped acceleration response spectra of the selected14 crustal input ground motions, all spectrally matched to thetarget NBCC (2010) UHS of Vancouver in the period range of0.02-1.7 sec. . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.6 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35xiiFigure 3.6 Acceleration time histories of the selected 14 crustal groundmotions spectrally matched to the NBCC (2010) UHS of Van-couver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 3.7 Schematic sketch of the SHAKE model reporting on the num-ber of sublayers, the assigned shear wave velocities at eachsublayer and the depth at which the ground motions are applied. 40Figure 3.8 Resulting (a) G/Gmax and (b) damping ratios along the depthof the model from the equivalent linear analyses of the free-field column of soil subjected to G1–G14. The red solid linesshow the average values of G/Gmax and damping ratio in thefirst and the second soil layers used in the subsequent nonlinearanalyses in FLAC. . . . . . . . . . . . . . . . . . . . . . . . 41Figure 3.9 Velocity response spectrum versus frequency of the selected14 crustal ground motions (G1–G14). . . . . . . . . . . . . . 42Figure 3.10 Cumulative power densities of the unfiltered selected 14 crustalground motions spectrally matched to the NBCC (2010) UHSfor Vancouver. . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 3.11 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 3.11 Shear stress time histories of the selected 14 crustal groundmotions applied at the base of the FLAC model. . . . . . . . . 50Figure 4.1 Lateral earth pressure distribution along the height of the base-ment wall designed for 100% code PGA subjected to groundmotion G1 (only the first 15 sec response is illustrated). . . . . 53Figure 4.2 The lateral earth pressure time histories at floor levels and mid-height of the floor slab levels along the 4-level basement walldesigned for 100% PGA subjected to ground motion G1. . . . 54Figure 4.3 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Figure 4.3 Time histories of the resultant lateral earth force of the walldesigned for 100% PGA subjected to 14 ground motions, com-pared with the corresponding PAE calculated from the modifiedM-O method. . . . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 4.4 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56xiiiFigure 4.4 Time histories of the normalized height of application of thelateral earth force from the base of the wall designed for 100% PGAsubjected to 14 ground motions, compared with the correspond-ing PAE calculated from the modified M-O method. . . . . . . 57Figure 4.5 Maximum resultant lateral earth forces on the walls designedfor 100% PGA subjected to 14 ground motions, compared withthe corresponding PAE values calculated from the modified M-O method using the same fraction of PGA. . . . . . . . . . . 58Figure 4.6 The normalized heights of application of the maximum resul-tant lateral earth forces from the base of the wall designed for100% PGA subjected to 14 ground motions, compared with thecorresponding normalized heights of application of PAE frombase of the wall calculated from the modified M-O method us-ing the same fraction of PGA. . . . . . . . . . . . . . . . . . 58Figure 4.7 Distribution of the maximum envelope of the lateral earth pres-sure along the height of the basement wall designed for 100% codePGA subjected to earthquake ground motion G1 (only the first15 sec response is illustrated). . . . . . . . . . . . . . . . . . 59Figure 4.8 Average of maximum envelopes, average of minimum envelopes,and residual lateral earth pressures for ground motions G1–G14, along the height of the walls designed for different frac-tions of the code PGA, compared with the corresponding pAEcalculated from the M-O method for the same fraction of PGAused for design of each wall. . . . . . . . . . . . . . . . . . . 61Figure 4.9 Average of static pressures prior to the dynamic analysis forground motions G1–G14, along the height of the walls de-signed for different fractions of the code PGA, compared withthe corresponding pA calculated from the Coulomb static theory. 62xivFigure 4.10 Average of pressure patterns at the instance of occurrence ofmaximum resultant lateral earth force for ground motions G1–G14, along the height of the walls designed for different frac-tions of the code PGA, compared with the corresponding pAEcalculated from the M-O method for the same fraction of PGAused for design of each wall. . . . . . . . . . . . . . . . . . . 63Figure 4.11 (a) Shear stress time history corresponding to earthquake groundinput motion G1 and (b) the lateral earth pressure distributionsat the instances of the maximum shear stress along the heightof the basement wall designed for 50% PGA; black-dashedlines represent the average of the maximum and minimum en-velopes of the lateral earth pressures for ground motions G1–G14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 4.12 Average of maximum envelopes, average of minimum envelopes,and residual bending moments for ground motions G1–G14,along the height of the walls designed for different fractionsof the code PGA, compared with the corresponding nominalmoment capacity, Mn(z), of each wall. . . . . . . . . . . . . . 66Figure 4.13 Average of maximum envelopes, average of minimum envelopes,and residual shear forces for ground motions G1–G14, alongthe height of the walls designed for different fractions of thecode PGA, compared with the corresponding nominal shearcapacity, Vn(z), of each wall. . . . . . . . . . . . . . . . . . . 67Figure 4.14 Definition of drift ratio for each level of the basement wall. . . 68Figure 4.15 Average of maximum envelopes, average of minimum envelopes,and residual lateral deformations (displacements relative to thebase of the basement wall) for ground motions G1–G14, alongthe height of the walls designed for different fractions of thecode PGA. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 4.16 Average of maximum envelopes, average of minimum envelopes,and residual drift ratios for ground motions G1–G14, along theheight of the walls designed for different fractions of the codePGA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71xvFigure 4.17 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 4.17 (Left-hand-side column) Average of maximum envelopes ofdrift ratios and the corresponding average ± one standard de-viation along the height of the wall;(right-hand-side column)distribution of the maximum drift ratios in the form of ex-ceedance probability of the walls designed for different frac-tions of the code PGA, subjected to ground motions G1–G14spectrally matched to NBCC (2010) UHS for Vancouver. . . . 74Figure 4.18 Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50%the code PGA, subjected to ground motions G1–G14 showingthe sensitivity of response to variation of the friction angle ofthe soil–wall interface element, including the case where noslippage and/or opening is allowed. . . . . . . . . . . . . . . 75Figure 4.19 Average of maximum envelopes of (a,c) lateral deformationsand (b,d) drift ratios along the height of the wall designedfor 50% the code PGA subjected to ground motions G1–G14,showing the lack of sensitivity of response to variation of thenormal and shear stiffnesses of the soil–wall interface element. 76Figure 4.20 Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50%the code PGA subjected to ground motions G1–G14, showingthe lack of sensitivity of the response to variation of top soildilation angle. . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 4.21 Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50%the code PGA subjected to ground motions G1–G14, showingthe lack of sensitivity of the response to variation of top soilfriction angle. . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 4.22 Different scenarios of the shear wave velocity profiles of thesoil along the depth of the model. . . . . . . . . . . . . . . . 79xviFigure 4.23 Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50%the code PGA subjected to ground motions G1–G14, showingthe sensitivity of response to variation in the normalized shearwave velocity of the top soil layer. . . . . . . . . . . . . . . 80Figure 4.24 Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50%the code PGA subjected to ground motions G1–G14, show-ing the sensitivity of the response to variation in the modulusreduction of the top soil layer. . . . . . . . . . . . . . . . . . 81Figure 4.25 Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50%the code PGA subjected to ground motions G1–G14, showingthe sensitivity of the response to variation in the damping ratioof the top soil layer. . . . . . . . . . . . . . . . . . . . . . . 82Figure 4.26 Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50%the code PGA subjected to ground motions G1–G14, showingthat the results are not sensitive to the initial shoring pressureduring excavation stage. . . . . . . . . . . . . . . . . . . . . 83Figure 5.1 UBCHYST model (Naesgaard, 2011). . . . . . . . . . . . . . 87Figure 5.2 Typical schematic stress–strain response of (a,c) Mohr–Coulomband (b,d) UBCHYST soil materials in a cyclic direct shear testin a case of 0.2% and 1% maximum shear strains. . . . . . . . 89Figure 5.3 Normalized modulus reduction and material damping curvesrecommended by Darendeli (2001) for different confining pres-sures for cohesionless sandy soils with PI=0. . . . . . . . . . 90Figure 5.4 Element cyclic simple shear (CSS) test in FLAC. . . . . . . . 91Figure 5.5 (a) The typical nonlinear shear stress versus shear strain re-sponse of soil under cyclic loading for three different levels ofshear strain, (b,c) shear modulus reduction and damping curvesthat characterize the nonlinear response of soil. . . . . . . . . 92xviiFigure 5.6 Variation of shear modulus and damping ratio with cyclic shearstrain amplitude at different depths of the first soil layer esti-mated by FLAC using UBCHYST model. . . . . . . . . . . . 94Figure 5.7 Variation of shear modulus and damping ratio with cyclic shearstrain amplitude at different depths of the second soil layer es-timated by FLAC using UBCHYST model. . . . . . . . . . . 95Figure 5.8 Average of maximum envelopes of drift ratios ± one standarddeviation along the height of the 4-level basement wall, de-signed for four different fractions of the code PGA subjectedto 14 spectrally matched crustal ground motions (G1–G14),using UBCHYST constitutive model. . . . . . . . . . . . . . 96Figure 5.9 Exceedance probability of drift ratio for 4-level basement wallsdesigned for different fractions of the code PGA subjected to14 spectrally matched crustal ground motions (G1–G14), usingUBCHYST constitutive model. . . . . . . . . . . . . . . . . 97Figure 5.10 Schematic of the 4-level basement wall model with differentmodel depths (dimensions are not to scale). . . . . . . . . . . 100Figure 5.11 Average of maximum envelopes of drift ratios ± one standarddeviation along the height of the 4-level basement wall, de-signed for 50% of the code PGA embedded in 24.3 and 40.0 msoil deposits, subjected to 14 spectrally matched crustal groundmotions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Figure 5.12 Soil type map for the Greater Regional District of Vancouver(Monahan, 2005). . . . . . . . . . . . . . . . . . . . . . . . . 102Figure 5.13 Schematic of the 4-level basement walls supported on (a) CaseI and (b) Case II soil profiles (dimensions are not to scale). . 104Figure 5.14 FLAC models of the 4-level basement walls with a total heightof 11.7 m founded on Case I and Case II soil profiles. . . . . . 104Figure 5.15 Average of maximum envelopes of drift ratios ± one standarddeviation along the height of the 4-level basement wall embed-ded in Case I soil profile, designed for four different fractionsof the code PGA subjected to 14 spectrally matched crustalground motions. . . . . . . . . . . . . . . . . . . . . . . . . 105xviiiFigure 5.16 Average of the maximum envelopes of drift ratios ± one stan-dard deviation along the height of the 4-level basement wallembedded in Case II soil profile, designed for four differentfractions of the code PGA subjected to 14 spectrally matchedcrustal ground motions. . . . . . . . . . . . . . . . . . . . . 106Figure 5.17 Exceedance probability of drift ratio of the 4-level basementwall designed for different fractions of code PGA founded on(a) Case I and (b) Case II soil profiles and subjected to 14crustal ground motions spectrally-matched to the UHS of Van-couver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Figure 5.18 Results of the nonlinear site response analyses conducted inFLAC in the form of amplification ratio at the (a) foundationlevel and (b) ground surface with respect to the base of thefree-field column of soil subjected to 14 ground motions (G1–G14), the solid red and blue lines show the mean value of theresponse for each case. . . . . . . . . . . . . . . . . . . . . . 109Figure 5.19 Results of the nonlinear site response analyses conducted inFLAC in the form of amplification ratio at the fundamentalperiod of the systems along the depth of the free-field columnof soil subjected to 14 ground motions (G1–G14), the solid redlines show the mean value of the response. The sketch of thelocation of the 4-level basement wall with respect to the soilgeometry is added for comparison. . . . . . . . . . . . . . . 110Figure 5.20 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Figure 5.20 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure 5.20 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 114xixFigure 5.20 Left-hand-side column: schematic of the 4-level basement wallssupported on 11 different soil profiles (dimensions are not toscale); Right-hand-side column: results of the nonlinear siteresponse analyses conducted in FLAC in the form of ampli-fication ratio at the fundamental period of the systems alongthe depth of the far-field column of soil subjected to 14 crustalground motions (G1–G14) spectrally-matched to the UHS ofVancouver. The solid red lines show the mean value of the re-sponse. The sketch of the location of the 4-level basement wallwith respect to the soil geometry is added for comparison. . . 115Figure 5.21 Modulus reduction and damping curves at different depths ofthe first soil layers with normalized shear wave velocities of(a) Vs1 = 150 m/s, (b) Vs1 = 250 m/s and (c) Vs1 = 300 m/sestimated by FLAC using UBCHYST model. . . . . . . . . . 116Figure 5.22 Modulus reduction and damping curves at different depths ofthe second soil layers with normalized shear wave velocities of(a) Vs1 = 250 m/s and (b) Vs1 = 300 m/s estimated by FLACusing UBCHYST model. . . . . . . . . . . . . . . . . . . . . 117Figure 5.23 Effect of the shear wave velocity of the first soil layer and thecorresponding impedance contrast among different soil layerson amplification ratio at the (a) foundation level and (b) groundsurface with respect to the base of the model. Each model issubjected to 14 crustal ground motions (G1–G14) spectrally-matched to the UHS of Vancouver. The mean values of theresponse are presented in solid lines. . . . . . . . . . . . . . 120Figure 5.24 Effect of the shear wave velocity of the second soil layer andthe corresponding impedance contrast among different soil lay-ers on amplification ratio at the (a) foundation level and (b)ground surface with respect to the base of the model. Eachmodel is subjected to 14 crustal ground motions (G1–G14)spectrally-matched to the UHS of Vancouver. The mean valuesof the response are presented in solid lines. . . . . . . . . . . 120xxFigure 5.25 Average of the maximum envelopes of drift ratios along theheight of the walls designed for 50% and 60% of the code PGAsubjected to 14 crustal ground motions spectrally-matched toUHS of Vancouver (G1–G14) and founded on different soilprofiles, showing the sensitivity of response to variation in thenormalized shear wave velocities of (a) the first and (b) thesecond soil layers. . . . . . . . . . . . . . . . . . . . . . . . 122Figure 5.26 Sensitivity of the resultant maximum drift ratios and the corre-sponding average± one standard deviation of the 4-level base-ment wall designed for 50% and 60% PGA to variation of thenormalized shear wave velocities of (a) the first and (b) the sec-ond soil layers. The walls are subjected to 14 crustal groundmotion spectrally-matched to the UHS of Vancouver. . . . . . 123Figure 5.27 Average of the maximum drift ratios and the correspondingone standard deviation of the 4-level basement wall designedfor different fractions of the code PGA and founded on ten dif-ferent soil profiles. Each wall is subjected to 14 crustal groundmotions (G1–G14) spectrally-matched to the UHS of Vancouver.125Figure 5.28 (a) Floor heights in the 4-level basement wall with 5 m topstorey and (b) the calculated lateral earth pressure distributionsfrom the first load combination. . . . . . . . . . . . . . . . . 128Figure 5.29 (a) Floor heights in the 6-level basement wall and (b) the cal-culated lateral earth pressure distributions from the first loadcombination. . . . . . . . . . . . . . . . . . . . . . . . . . . 128Figure 5.30 (a) Floor heights in the 4-level basement wall with 5 m topstorey and the calculated lateral earth pressure distributionsfrom the second load combination using the M-O method with(b) 100% PGA, (c) 70% PGA, (d) 60% PGA, and (e) 50% PGA,where PGA=0.46g. . . . . . . . . . . . . . . . . . . . . . . . 129Figure 5.31 (a) Floor heights in the 6-level basement wall and the calcu-lated lateral earth pressure distributions from the second loadcombination using the M-O method with (b) 100% PGA, (c)70% PGA, (d) 60% PGA, and (e) 50% PGA, where PGA=0.46g.129xxiFigure 5.32 Moment capacity distribution along height of (a) the 4-levelbasement wall with 5.0 m top storey and (b) the 6-level base-ment wall designed for different fractions of the NBCC (2010)PGA for Vancouver (= 0.46 g). . . . . . . . . . . . . . . . . 130Figure 5.33 (a) 4-level basement wall with 5.0 m top storey and total heightof 13.1 m and (b) 6-level basement walls with a total height of17.1 m founded on Case I soil profile. . . . . . . . . . . . . . 131Figure 5.34 (a) 4-level basement wall with 5.0 m top storey and total heightof 13.1 m and (b) 6-level basement walls with a total height of17.1 m founded on Case II soil profile. . . . . . . . . . . . . . 131Figure 5.35 Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 13.1 m 4-level base-ment walls designed for different fractions of the code PGA,founded on Case I soil profile subjected to 14 crustal groundmotions (G1–G14) spectrally-matched to the UHS of Vancouver.133Figure 5.36 Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 13.1 m 4-level base-ment walls designed for different fractions of the code PGA,founded on Case II soil profile subjected to 14 crustal groundmotions (G1–G14) spectrally-matched to the UHS of Vancouver.134Figure 5.37 Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 17.1 m 6-level base-ment walls designed for different fractions of the code PGA,founded on Case I soil profile subjected to 14 crustal groundmotions (G1–G14) spectrally-matched to the UHS of Vancouver.135Figure 5.38 Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 17.1 m 6-level base-ment walls designed for different fractions of the code PGA,founded on Case II soil profile subjected to 14 crustal groundmotions (G1–G14) spectrally-matched to the UHS of Vancouver.136xxiiFigure 5.39 Probability of drift ratio exceedance of the 13.1 m 4-level base-ment walls designed for 50%, 60%, 70% and 100% of thecode PGA, founded on Case I and II soil profiles subjectedto 14 crustal ground motions (G1–G14) spectrally-matched tothe UHS of Vancouver. . . . . . . . . . . . . . . . . . . . . . 137Figure 5.40 Probability of the maximum drift ratio exceedance of the 17.1 m6-level basement walls designed for different fractions of thecode PGA, founded on Case I and II soil profiles subjected to14 crustal ground motions (G1–G14) spectrally-matched to theUHS of Vancouver. . . . . . . . . . . . . . . . . . . . . . . . 138Figure 5.41 The resultant maximum drift ratios and the corresponding av-erage and average ± one standard deviation of the 4-level and6-level basement walls designed for different fractions of theNBCC (2010) code PGA, founded on Case I and Case II soilprofiles and subjected to 14 crustal ground motions spectrally-matched to the UHS of Vancouver. . . . . . . . . . . . . . . . 139Figure 6.1 Tectonic plates in west coast of Canada and the United States(Natural Resources Canada, 2012) . . . . . . . . . . . . . . . 142Figure 6.2 Tectonic setting of south-western British Columbia showingthe oceanic Juan de Fuca plate is subducting beneath the con-tinental crust of North America plate along the Cascadia sub-duction zone (Natural Resources Canada, 2012) . . . . . . . 143Figure 6.3 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Figure 6.3 Acceleration time histories of the selected 14 crustal groundmotions linearly scaled to the NBCC (2010) UHS of Vancou-ver using PGA scaling method. . . . . . . . . . . . . . . . . . 153Figure 6.4 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 154Figure 6.4 Acceleration time histories of the selected 14 crustal groundmotions linearly scaled to the NBCC (2010) UHS of Vancou-ver using Sa(T1) scaling method. . . . . . . . . . . . . . . . . 155Figure 6.5 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 155xxiiiFigure 6.5 Acceleration time histories of the selected 14 crustal groundmotions linearly scaled to the NBCC (2010) UHS of Vancou-ver using ASCE scaling method. . . . . . . . . . . . . . . . . 156Figure 6.6 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Figure 6.6 Acceleration time histories of the selected 14 crustal groundmotions linearly scaled to the NBCC (2010) UHS of Vancou-ver using SIa scaling method. . . . . . . . . . . . . . . . . . 158Figure 6.7 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Figure 6.7 Acceleration time histories of the selected 14 crustal groundmotions linearly scaled to the NBCC (2010) UHS of Vancou-ver using MSE scaling method. . . . . . . . . . . . . . . . . 159Figure 6.8 The 5% damped acceleration response spectra of the selected14 crustal ground motions and their corresponding mean re-sponse using different methods of scaling/matching with re-spect to the target NBCC (2010) UHS of Vancouver. Dashed-green lines show the single period or the period range at whichthe motions are scaled. . . . . . . . . . . . . . . . . . . . . . 160Figure 6.9 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 162Figure 6.9 Acceleration time histories of the selected 14 subcrustal groundmotions linearly scaled to the NBCC (2010) UHS of Vancou-ver using MSE scaling method. . . . . . . . . . . . . . . . . 163Figure 6.10 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Figure 6.10 Acceleration time histories of the selected 14 subcrustal groundmotions spectrally matched to the NBCC (2010) UHS of Van-couver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Figure 6.11 The 5% damped acceleration spectra of the selected 14 sub-crustal ground motions and the corresponding mean responseusing MSE linear scaling and spectral matching methods withrespect to the target NBCC (2010) UHS of Vancouver. Dashed-green lines show the period range at which the motions are scaled.165xxivFigure 6.12 The 2% in 50 year robust probabilistic hazard design valuesfrom the NBCC (2010) in comparison with the hazard valuesfrom deterministic Cascadia subduction earthquake scenariofor Vancouver. . . . . . . . . . . . . . . . . . . . . . . . . . 166Figure 6.13 The 5% damped acceleration response spectra of 14 subduc-tion records scaled to hazard values for Cascadia subductionearthquake scenario proposed by the NBCC (2010) for Van-couver. Dashed-green lines show the period range at whichthe motions are scaled. . . . . . . . . . . . . . . . . . . . . . 167Figure 6.14 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 168Figure 6.14 Acceleration time histories of the selected Cascadia subduc-tion ground motions. . . . . . . . . . . . . . . . . . . . . . . 169Figure 6.15 The 5% damped acceleration spectra of the selected 14 near-fault pulse-like ground motions and the corresponding meanresponse using MSE linear scaling method with respect to thetarget NBCC (2010) UHS of Vancouver. . . . . . . . . . . . . 171Figure 6.16 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Figure 6.16 Acceleration time histories of the selected 14 near-fault groundmotions linearly scaled to the NBCC (2010) UHS of Vancou-ver using MSE scaling method. . . . . . . . . . . . . . . . . 173Figure 6.17 Continued. . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Figure 6.17 Velocity time histories of the selected 14 near-fault ground mo-tions linearly scaled to the NBCC (2010) UHS of Vancouverusing MSE scaling method. . . . . . . . . . . . . . . . . . . 174Figure 6.18 Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the heightof the walls designed for 50% of the code PGA subjected to asuite of crustal ground motions scaled/matched using variousmethods outlined in this study. . . . . . . . . . . . . . . . . . 177xxvFigure 6.19 Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the heightof the walls designed for 60% of the code PGA subjected to asuite of crustal ground motions scaled/matched using variousmethods outlined in this study. . . . . . . . . . . . . . . . . . 178Figure 6.20 Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the heightof the walls designed for 70% of the code PGA subjected to asuite of crustal ground motions scaled/matched using variousmethods outlined in this study. . . . . . . . . . . . . . . . . . 179Figure 6.21 Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the heightof the walls designed for 100% of the code PGA subjected to asuite of crustal ground motions scaled/matched using variousmethods outlined in this study. . . . . . . . . . . . . . . . . . 180Figure 6.22 The resultant maximum drift ratios and the corresponding meanand mean± one standard deviation along the height of the walldesigned for different fractions of the code PGA subjected tocrustal ground motions (G1–G14) scaled/matched using vari-ous methods outlined in this study. . . . . . . . . . . . . . . . 181Figure 6.23 The resultant maximum drift ratios and the corresponding meanand mean ± one standard deviation along the height of the 4-level and 6-level basement walls designed for different frac-tions of the NBCC (2010) code PGA subjected to 14 crustalground motions scaled/matched using MSE linear scaling andspectral matching methods. . . . . . . . . . . . . . . . . . . . 184Figure 6.24 Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the heightof the wall designed for 50% and 6% of the code PGA sub-jected to 14 subcrustal ground motions (a) linearly scaled and(b) spectrally matched to the NBCC (2010) UHS of Vancouver. 185xxviFigure 6.25 Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the heightof the wall designed for 50% of the code PGA subjected to14 Cascadia subduction ground motions linearly scaled to theNBCC (2010) subduction hazard values for Vancouver. . . . . 186Figure 6.26 Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the heightof the wall designed for 50% of the code PGA subjected to 14pulse-like ground motions linearly scaled to the NBCC (2010)UHS of Vancouver. . . . . . . . . . . . . . . . . . . . . . . . 187Figure 7.1 Summary of the resultant maximum drift ratio of the basementwalls designed for 50% and 60% of the NBCC (2010) PGA fordifferent cases outlined in Table 7.2. . . . . . . . . . . . . . . 194Figure A.1 The structural details of the model basement wall . . . . . . . 215Figure A.2 Calculated θ capacity at governing section of the wall . . . . 222xxviiAcknowledgmentsThough only my name appears on the cover of this dissertation, a great many peo-ple have contributed to its production. I owe my gratitude to all those people whohave made this dissertation possible and because of whom my graduate experiencehas been one that I will cherish forever.Firstly, I would like to express my deepest gratitude to my research supervisorProf. W.D. Liam Finn for his continuous support, patience, motivation, and im-mense knowledge. I have been amazingly fortunate to have an advisor who gaveme the freedom to explore on my own, and at the same time the guidance to re-cover when my steps faltered. I could not have imagined having a better advisorand mentor and he is the one teacher who truly made a difference in my life.I take this opportunity to sincerely acknowledge the support of Dr. John Howiefor providing necessary infrastructure and resources to accomplish my researchwork. I am very much thankful to him for picking me up as a student at the criticalstage of my Ph.D. program.Besides my supervisor, I would like to thank the members of my thesis advisorycommittee: Dr. Ronald H. DeVall from Read Jones Christoffersen Consultants Ltd.and Prof. Carlos Ventura for their deep interest, support, dedication, passion, andinsightful comments and encouragement, but also for the questions which incentedme to widen my research from various perspectives. I am honored of having theopportunity of working with them. I would like to thank Prof. Geoffrey R. Mar-tin from the Faculty of Civil and Environmental Engineering at the University ofSouthern California, Dr. Gregory A. Lawrence, from the Faculty of Civil Engineer-ing at the University of British Columbia and Dr. Davide Elmo from the NormanB. Keevil Institute of Mining Engineering at the University of British Columbia forxxviiitaking time out from their busy schedule to serve as my examiners.Dr. Taiebat’s insightful comments and constructive criticisms at different stagesof my research were thought-provoking and they helped me focus my ideas. I amgrateful to him for holding me to a high research standard and enforcing strictvalidations for each research result.Most of the results described in this thesis would not have been obtained with-out a close collaboration with some people from early days of my research. Mythanks go in particular to Dr. Ernest Naesgaard and Dr. Ali Amini from Naesgaard-Amini Geotechnical Ltd., Prof. Donald Anderson, and Prof. Peter Byrne withwhom I started this work and many rounds of discussions on my project with themhelped me a lot. I owe a great deal of appreciation and gratitude to Mr. Doug Wallisfrom Levelton Consultants Ltd. for his suggestions and guidance in geotechnicalaspects of the project. Thanks also goes out to Dr. Armin Bebamzadeh for sharinghis knowledge and experience.I am ever indebted to Prof. Perry Adebar, Head of the Civil Engineering De-partment at the University of British Columbia, who helped me at the time of crit-ical need and his moral support. Appreciation also goes out to Ms. Glenda Levinsand Ms. Sylvia Margraff for all the instances in which their assistance helped mealong the way.My appreciation extends to all of my colleagues and friends who helped meimmensely during the four-year Ph.D. journey. I am very grateful to my office-mates: Amin Rahmani, Sajjad Fayyazi, Speideh Ashtari, Gaziz Seidalinov, AndresBarrero, and Boris Kolev for our exchanges of knowledge, skills, and venting offrustration during my graduate program, which helped enrich the experience.Most importantly, none of this would have been possible without the love andpatience of my family. My family to whom this dissertation is dedicated to, hasbeen a constant source of love, concern, support and strength all these years. Iwould like to express my heart-felt gratitude to my parents and my brother fortheir unconditional trust, timely encouragement, and endless patience and theirgenerosity with their love and support despite the long distance between us. Lastbut not least, my loving, supportive, encouraging, and patient husband, Hessam,whose faithful support during the different stages of this Ph.D. is so appreciated.Finally, I recognize that this research would not have been possible withoutxxixthe financial assistance of the Natural Sciences and Engineering Research Councilof Canada (NSERC- PGS D and NSERC- CGS M), the Office of Graduate andPostdoctoral Studies at the University of British Columbia (Four Year DoctoralFellowship), and the Department of Civil Engineering at the University of BritishColumbia (teaching assistantships, research assistantships, and Thurber Engineer-ing Graduate Scholarship in Civil Engineering), and express my gratitude to thoseagencies.xxxChapter 1IntroductionDesign is not just what it looks like and feels like. Design is how itworks.— Steve Jobs (1955-2011)1.1 OverviewDeep basement walls constructed to utilize the underground parking, constitute anessential part of buildings and should be designed to resist the static and seismicinduced lateral earth pressures during earthquakes. The seismic performance ofbasement walls is a complex soil–structure interaction problem that depends onmany different parameters such as the nature of the earthquake ground motion,dynamic response of the backfill soil, and the flexural response of the wall.The current state of practice for seismic design of basement walls in the UnitedStates (Lew, 2012; Lew et al., 2010b; Psarropoulos et al., 2005) as well as in BritishColumbia, Canada (DeVall et al., 2010) is generally based on the studies of Ok-abe (1924) and Mononobe and Matsuo (1929) known as the Mononobe-Okabe(M-O) method and incorporating the modification suggested by Seed and Whit-man (1970) for estimating seismic pressures on the walls. In this limit-equilibriumforce method, the earthquake thrust acting on the wall is a function of the PeakGround Acceleration (PGA). The Mononobe-Okabe method is simple to use, butthe validity and applicability of the method and its limiting assumptions have been1questioned by researchers. Despite the limitations and uncertainties of the M-Omethod, it has been and continues to be widely used in practice for designing base-ment walls.The seismic hazard level for design of buildings in an earlier version of theNational Building Code of Canada (NBCC, 1995) had a probability of exceedanceof 10% in 50 years (the 475 year earthquake), resulting in a PGA of 0.24 g forVancouver. The more recent editions of the NBCC (2005, 2010) mandate a con-siderably different seismic hazard level with the probability of exceedance of 2%in 50 years (the 2475 year earthquake). Under the current code, the design PGA isabout 0.46 g, almost double that of NBCC (1995). Adopting higher PGA leads thedesigners who have been using the M-O method for estimating the seismic lateralpressures to very large seismic forces that make the resulting structures expensive.Lew et al. (2010a) and Sitar et al. (2012) reported on the performance of base-ment walls during past earthquake events inside and outside the United States andshow that the failure is rare even though no particular seismic design was imple-mented. Based on their research no report of any damage to building basementwalls has been found for the San Fernando (1971), Whittier Narrows (1987), LomaPrieta (1989), and Northridge (1994) earthquakes in the United States.Due to the fact that there is no reported damage to the basement walls duringthe recent major earthquake events, the Structural Engineers Association of BritishColumbia (SEABC) became concerned about whether basement walls are beingover-designed against the NBCC (2010) seismic hazard with the present designprocedure. This led the SEABC to set up a task force to review current seismicdesign procedures for deep basement walls and the University of British Columbiawas asked to carry out this research. This study was initiated in response to theSEABC request. The main purpose of this study is to capture the essential featuresof the seismic behavior of the basement wall systems and determine an appropriatefraction of PGA for Vancouver to be used in the M-O analysis to ensure a satisfac-tory performance in terms of moment and shear capacity and drift ratio along theheight of the wall.Various researchers have proposed the use of a reduced seismic coefficient lessthan the peak ground acceleration for the design of basement walls (Arulmoli,2001; Lew et al., 2010b; Seed and Whitman, 1970; Sitar et al., 2012). Recent2centrifuge modeling work by Al Atik (2008); Al-Atik and Sitar (2007, 2009) onmodel cantilever walls showed that estimating seismic lateral pressures utilizingthe full peak ground acceleration overestimates the seismic earth pressure on can-tilever retaining walls. To expand upon the work by Al-Atik and Sitar, additionalcentrifuge experiments were reported by Geraili Mikola (2012) at the Universityof California, Berkeley on non-displacing cross-braced basement wall structuresfounded on dry medium-dense sand. These results also confirm that the M-O pres-sures calculating using PGA are considerably higher than measured pressures andusing the full PGA leads to very large seismic forces and very conservative design.1.2 Objectives and scopeThe first objective of this study is to develop a full-scale two-dimensional contin-uum model of soil–basement wall system, in which the walls are designed usingthe M-O procedure for various fractions of the NBCC (2010) PGA. The goal is toprovide benchmark data for evaluating the state of practice for dynamic analysisof braced basement walls and to provide a basis for recommending an acceptablefraction of PGA for their seismic design. To this aim, a series of plane-strain non-linear dynamic analyses have been conducted, taking into an account the flexibilityand potential yielding of the wall components, to study the seismic performance ofthe basement walls designed for different fractions of PGA. This requires a com-prehensive understanding of the interaction between the basement wall structureand the surrounding soil.More specific components and features of this study are as follows:• A 4-level basement wall structure is designed by members of the SEABCcommittee following the state of practice for six different values of the pseudo-static horizontal seismic coefficient varying from 100% down to 50% of theNBCC (2010) PGA (=0.46g). This results in a total of six walls.• The designed walls and the surrounding soil domain are modeled in a fullycoupled manner using a finite difference code, FLAC 7.0 (Itasca, 2012). Dy-namic nonlinear soil–structure interaction analyses are then conducted oncomputational models of these basement walls to explore the capacity of the3walls under seismic demand corresponding to an exceedance rate of 2% in50 years for Vancouver.• The soil layers of the computational model are simulated using the Mohr–Coulomb material model with non-associated flow rule. With insight fromequivalent linear analyses of the soil system in the far field, degraded elas-tic modulus and equivalent damping ratios are also employed for a betterrepresentation of the soil system response in seismic loading.• A suite of crustal ground motions are selected and the spectral matchingmethod is used to modify the earthquake time histories to become compati-ble with the NBCC (2010) uniform hazard spectrum for Vancouver. In thisfashion the variance of the structural responses is reduced and a platformto estimate the robust mean value of the response with fewer numbers ofanalyses is provided. Later on, the results will be compared with additionalsensitivity analyses conducted using different linear scaling methods. Theresults show that spectral matching gives good estimates of the mean values.• The seismic performance of the basement walls is presented in terms of thetime history and envelope of lateral earth pressures along the height of thewalls, lateral earth forces on the walls, envelopes of the bending momentsand shear forces, and envelopes of lateral displacements and drift ratios. Theresults indicate that flexibility and deflection of the wall have important ef-fects on the distribution of the seismic lateral pressures on the wall. Theresults of these analyses are used to evaluate an appropriate fraction of PGAto be used in the M-O analysis to have a satisfactory performance in termsof the resulting drift ratio along the height of the wall.• A number of sensitivity analyses on different input parameters are also con-ducted, and the results are presented and discussed.The second objective of this thesis is to provide additional analyses for furtherevidence to evaluate the recommended fraction of code mandated PGA that may beused with the M-O method for acceptable seismic performance of basement walls.To this end the following specific components and features are investigated:4• A more advanced constitutive model is used instead of a simple Mohr–Coulomb, to simulate nonlinear behavior of soils undergoing time-varyingdeformations caused by earthquake ground motions.• Dynamic soil–structure interaction effects in the form of local site conditionand the corresponding local amplification of strong ground motions due toshallow soft soil layers are investigated. The importance of the impedancecontrast of underlying soil deposits and the depth of the underlying stiff soillayers on the seismic performance of the embedded structures are studied.• The effect of geometric parameters of the basement wall structures on theirseismic performance is investigated. To this aim two new sets of deep base-ment walls with different heights, thickness and configurations are designedfor different fractions of code PGA and their performance under the full seis-mic demand in Vancouver are evaluated.• In addition to shallow crustal earthquakes, deep subcrustal earthquakes andinterface earthquakes from the Cascadia subduction event are added to thedatabase to reflect three dominant seismic mechanisms in the Lower Main-land, Vancouver. Also the effect of near-fault pulse-like ground motions,which contain a short-duration pulse with high amplitude is investigated.• In addition to the spectrally matched accelerograms used in benchmark anal-yses to estimate the robust mean values of the seismic response, differentlinear scaling methods are adopted to capture the inherent motion-to-motionvariability of the basement wall responses subjected to a suites of earthquakeground motions under the seismic demand adopted by NBCC (2010) forVancouver. The seismic performance of the basement walls in the form ofdrift ratio are evaluated and the level of variability of the response, quantifiedby a standard deviation, are presented. The results of these analyses usingdifferent scaling/matching techniques are compared to facilitate a decisionon the more reliable scaling/matching technique to use for this problem.51.3 Organization of dissertationThis dissertation consists of seven Chapters. Chapters two, three and four addressthe first aforementioned objective and Chapters five and six cover the second objec-tive discussed in the previous section. The organization of the thesis for fulfillingthe research objectives are as follows:Chapter 2, The state-of-the-art for seismic design of the basement walls based onthe current state of practice in British Columbia is presented in this chapter.The performance of basement walls during past major earthquake events aswell as a summary of the building code provisions requirements for seismicdesign of basement walls are discussed. Also the assumptions and limita-tions of the M-O method are reviewed.Chapter 3, A seismic design of a typical 4-level basement wall structure accord-ing to the state of practice in Vancouver for different fractions of the codePGA is described in this chapter. In order to assess the seismic performanceof these walls, a series of two-dimensional nonlinear dynamic analyses havebeen set up using a finite difference platform, FLAC 7.0 (Itasca, 2012). Ele-ments of the computational model, including the model building procedure,boundary conditions, interface elements, applied ground motions, and soilproperties used in these analyses are described.Chapter 4, The seismic performance of the 4-level basement walls described inChapter 3 are evaluated using nonlinear dynamic analyses and are set asbenchmark analyses. Typical results such as the time history and envelope oflateral earth pressures and lateral earth forces along the height of the walls,envelope of the bending moments, shear forces, lateral displacements anddrift ratios are presented and discussed. Based on the results of these anal-yses, an appropriate fraction of PGA to be used in the M-O analysis is rec-ommended to ensure a satisfactory cost-effective performance based on thelimiting drift ratio along the height of the wall. In addition, the sensitivity ofthe findings to variations of adopted system parameters is evaluated.Chapter 5, The 4-level basement wall described in Chapter 4 is analyzed usinga more sophisticated and representative constitutive model than the simple6Mohr–Coulomb model which was used initially. Also this chapter providesan insight into dynamic soil–structure interaction effects as well as the localsite effects on the seismic performance of basement walls. The effect of localsite conditions defined by various shear wave velocity profiles on the seismicperformance of the designed basement walls is investigated. This chapteralso offers an evaluation on the influence of the wall geometry in terms ofthe wall’s height, thickness and configuration on the seismic performance ofbasement walls by investigating a 4-level basement wall with a higher toplevel and a 6-level basement wall.Chapter 6, This chapter provides an insight into the selection and scaling of asuite of earthquake accelerograms for time history analyses. This is one ofthe most important steps in any nonlinear dynamic history analysis and gov-erns the result and amount of uncertainty in seismic design. Five intensity-based linear scaling methods, which preserve the variety of each ground mo-tion are introduced and the full distribution of the structural responses in theform of standard deviation are presented. In this chapter four ground mo-tion ensembles are considered; shallow crustal earthquakes, deep subcrustalearthquakes, interface earthquakes from a Cascadia subduction event and thenear-fault pulse-like ground motions. The result of this study indicates thatthe spectrum matched results compare well (both mean and scatter) with rea-sonable and established linear scaling methods. The results also indicate thatseveral other linear scaling methods introduce amounts of scatter viewed asunreasonable.Chapter 7, A summary of key results and conclusions drawn from this researchare presented in this chapter. Suggestions for future research are also pro-vided.7Chapter 2Literature reviewIf I have seen further it is by standing on the shoulders of Giants.— Isaac Newton (1643–1727)2.1 IntroductionThe problem of evaluating seismically induced lateral earth pressures on retainingstructures was first addressed in Japan after the Great Kanto Earthquake (1923) byOkabe (1926) and followed by Mononobe and Matsuo (1929). The Mononobe-Okabe (M-O) method is based on Mononobe and Matsuo’s experimental studieson a small scale cantilever wall with a dry, medium dense cohesionless granularbackfill excited by a one gravity (1g) sinusoidal excitation on a shaking table.The M-O computational method was originally developed for gravity non-yielding walls retaining cohesionless backfill materials. It follows the proceduredeveloped by the Coulomb (1776) theory of static soil pressures and is today, themost common approach in determining seismically induced lateral earth pressuresdue to its simplicity. Despite the uncertainties associated with this method, thecurrent state of practice in British Columbia (DeVall et al., 2010) as well as in theUnited States (Lew, 2012; Lew et al., 2010b; Psarropoulos et al., 2005) is to usethe M-O method incorporating the modification suggested by Seed and Whitman(1970) for estimating seismic pressures on the walls.8This Chapter summarizes the performance of basement walls during past ma-jor earthquake events in Section 2.2. A summary of the building code provisionsin Canada as well as the United States for seismic design of basement walls arereported in Section 2.3. The state of practice in British Columbia for evaluationof seismic earth pressures on building basement walls as well as the applicabil-ity of the M-O method are discussed in Section 2.4. The areas of confusion anddeficiency of the M-O method is covered in Section 2.5.2.2 Performance of basement walls during pastearthquake eventsAn extensive summary of reports on basement wall behavior under recent majorearthquakes inside and outside the United States is presented in Lew et al. (2010a)and Sitar et al. (2012). The performance of basement walls during past earthquakeevents shows that the failure is rare even if the structures were not explicitly de-signed for earthquake loading.Based on a search of literature by Lew et al. (2010a) and Sitar et al. (2012),the engineered building basement walls did not experience any damage in the ma-jor recent United States earthquakes. No reports of any damage to building base-ment walls have been found for the San Fernando (1971), Whittier Narrows (1987),Loma Prieta (1989), and Northridge (1994) earthquakes in the United States basedon the documents published by Benuska (1990); Hall (1995); Holmes and Somers(1996); Lew et al. (1995); Murphy (1973); Stewart et al. (1994); Whitman (1991).During the magnitude 7.0 Kobe earthquake (1995) in Japan no evidence ofdamage to building basement walls was reported (Lew et al., 2010a). Also dam-age to building basement walls were not reported during Kocaeli, Turkey (1999)earthquake by Youd et al. (2000). Huang (2000), Tokida et al. (2001) and Abra-hamson et al. (1999) reported different types of retaining structures (gravity-typewalls, geosynthetics-reinforced retaining walls, cantilever walls) damages duringChi-Chi, Taiwan (1999) earthquakes, but there is no report of failure or damage ofbuilding basement walls. As reported by Sitar et al. (2012), no significant dam-ages or failures of retaining structures occurred in the Wenchuan earthquake inChina (1998), or in the recent great subduction zone generated earthquakes in Chile9(2010) and Japan (2011).2.3 Building code provisions requirementThe current edition of the National Building Code of Canada (NBCC, 2010), In-ternational Building Code (IBC, 2009) and the Minimum Design Loads for Build-ing and Other Structures (ASCE/SEI 7-05, 2005; ASCE/SEI 7-10, 2010) requirethat basement walls be designed to resist increased lateral pressure associated withearthquake ground motions and the geotechnical investigation report shall includethe determination of lateral pressures on basement walls due to earthquake mo-tions.The National Cooperative Highway Research Program (NCHRP) report (An-derson et al., 2008), European Standards for Design of Structures for EarthquakeResistance (Eurocode8-EN1998-5, 2004) and Canadian Highway Bridge DesignCode (CAN/CSA-S6-06, 2014) refer to the work of Mononobe and Matsuo (1929)and Okabe (1924) for the design of cantilever walls. Also the current edition ofthe American Association of State Highway Officials for the Load and ResistanceFactor Design for bridges (AASHTO LRFD, 2012) suggests allowing reduction inthe seismic coefficient by 50% in the design of cantilever walls.The NBCC (2010) Commentary J recommended the use of the M-O methodfor the design of basement walls and stated that these walls are normally con-sidered non-yielding due to the restraints at the top and bottom of these walls,which prevent the small amount of movement required to develop minimum activeearth pressures. NBCC (2010) refers to the National Earthquake Hazards Reduc-tion Program report (NEHRP, 2000) for the seismic design of the basement walls.The latest editions of NEHRP Recommended Provisions for Seismic Regulationsfor New Buildings and Other Structures, NEHRP (2003) and NEHRP (2009) alsoknown as FEMA 450 and FEMA 750 reports, respectively, provide a discussion ofthe seismic earth pressures on retaining structures for two main categories of walls:• Yielding walls, which can move sufficiently to develop minimum active earthpressures. The amount of 0.002 times the wall height movement at the topof the wall is typically sufficient to develop the minimum active earth pres-sure. The simplified Mononobe-Okabe seismic coefficient analysis reason-10ably represents the dynamic lateral earth pressure increment for yielding re-taining walls (Mononobe and Matsuo, 1929; Okabe, 1924).• Non-yielding walls are rigid, fixed at the base and do not satisfy the move-ment condition. For these walls, NEHRP Recommended Seismic Provi-sions presents an elastic solution developed by Wood (1973) for a rigid non-yielding wall retaining a homogeneous linear elastic soil and connected to arigid base. The dynamic thrust, ∆PE , is calculated using the following equa-tion with the point of application at a height of 0.6H above the base of thewall:∆PE = khγH2 (2.1)where γ is the unit weight of soil , H is the retaining wall height, and kh in thehorizontal ground acceleration divided by gravitational accelaration.The two aforementioned methods cover two extreme cases. One is the limit-equilibrium method assumes rigid plastic behavior, while the other one is the elasticapproach that treats the soil as a visco-elastic continuum. NEHRP RecommendedSeismic Provisions refers to the work of Ostadan (2005) and suggests that dynamicearth pressure solutions would lead to the results that correspond in magnitude tothe Mononobe-Okabe solution as a lower bound and the Wood (1973) solution asan upper bound, which is as much as 2 to 2.5 times greater than the M-O approach.The earlier versions of the National Earthquake Hazards Reduction Program(NEHRP, 2000, 2003) and the more recent edition (NEHRP, 2009) refer to theworks of Lam and Martin (1986), Veletsos and Younan (1994a), Veletsos andYounan (1994b), and Ostadan (2005) among others, which argue that the earthpressures acting on the walls of partially embedded structures (e.g., basementwalls) during earthquakes are primarily governed by soil–structure interaction, andthus these walls should not be treated as non-yielding. Sitar et al. (2012) arguedthat deep basement walls constructed in open excavations that are generally shored,cause the retained backfill soil to be in a yielded (active) condition already. In ad-dition centrifuge tests of Sitar et al. (2012) confirm that the solutions provided fornon-yielding walls, such as the one by Wood (1973), grossly overestimate the seis-11mic pressures on basement-type walls and would result in wall designs that aremuch thicker with more steel reinforcement than those commonly used.Veletsos and Younan (1997) and Younan and Veletsos (2000) conducted a studyon dynamic response of flexible cantilever retaining walls and state that the flexi-bility of the wall and the rotational compliance at its base are the main reasons fora substantial drop of resultant force from a rigid solution. Gazetas et al. (2004) ad-dressed a couple of other phenomena which lead to a further reduction of dynamicthrust acting on several types of flexible retaining systems. One is the elastic non-homogeneity of the backfill soil which results in a reduction of soil stiffness due toits softening in large shearing and the nonlinear soil–wall interface behavior. In-elastic soil behavior and the frequency content of the ground motion are anotherreasons for a further reduction of dynamic wall pressure to the values which mayonly be a fraction of the M-O. For all these reasons along with its simplicity, theM-O method became the most widely used method of analysis of seismic earthpressure in practice.In the light of the fact that there is no evidence of basement wall failure dur-ing the recent major earthquake events, the review of literature suggest that usingPGA as a seismic coefficient in the M-O method is overly conservative. Howevercodes have not recommended values less than PGA. This maybe because most ofthe researches which support the reduction by using fraction of PGA are fairlyrecent and have not been generally embraced by practice yet. For example theFEMA 450 and FEMA 750 limited the M-O method to yielding walls and suggestusing Wood (1973) formula for calculating pressures against non-yielding wallssuch as basement walls, but neither one of them suggest reducing seismic pressureby reducing PGA. The present study, which is conducted using nonlinear dynamicanalyses, examines the seismic resistance of basement walls designed according tocurrent practice in British Columbia, but using fractions of the code PGA (100% to50%) as a seismic coefficient. The seismic response of all these walls are all eval-uated by subjecting them to ensembles of earthquake motions comprise of crustal,subcrustal, subduction and near-fault earthquake ground motions that match thehazard intensity of the current Building Code (NBCC, 2010). The prime objectiveof this study is to provide solid bases for designing the basement walls using anappropriate fraction of the code PGA in the M-O analyses.122.4 State of practice in British ColumbiaThe current state of practice for the seismic design of basement walls in BritishColumbia is generally based on the M-O method but incorporating the modificationadvanced by Seed and Whitman (1970), which is referred to as ”the modified M-Omethod” in this study.The M-O method is a limit-equilibrium force approach, developed by includingthe inertial forces due to ground motions into the Coulomb (1776) theory of staticearth pressure on retaining walls. This method was developed for dry cohesionlessmaterials. It is assumed that a rigid wall moves sufficiently to produce minimumactive (or maximum passive) pressures. The M-O method does not consider thekinematic and dynamic behavior of the structure, backfill and foundation soil dueto the earthquake excitation and instead the complex transient ground shaking isrepresented by pseudo-static accelerations in horizontal and vertical directions. Itis assumed that the soil behind the wall behaves as a rigid body so the pseudo-staticacceleration can be applied uniformly throughout the mass. Therefore, in additionto the forces that exist under static conditions, the wedge is also acted upon byhorizontal and vertical pseudo-static forces whose magnitudes are related to themass of the wedge by the pseudo-static accelerations: ah = khg and av = kvg, wherekh and kv are the horizontal and vertical components of an earthquake excitation,respectively.The forces acting on an active wedge in a dry, cohesionless backfill are shownin Figure 2.1. By applying pseudo-static accelerations to a Coulomb active wedge,the pseudo-static soil thrust is calculated from force equilibrium of the wedge. Thetotal (static + dynamic) active lateral force during earthquake, PAE , is expressed as:PAE = 0.5γH2KAE(1− kv) (2.2)where γ is the unit weight of soil and H is the retaining wall height. The dy-namic active earth pressure coefficient, KAE , is given in textbooks on soil dynamics(Kramer, 1996; Prakash, 1981; Towhata, 2008) as:13H Walli !W kvW khW"Cohesionless soilPAEFigure 2.1: Forces considered in the Mononobe-Okabe analysis.KAE =cos2 (φ −ψ−β )cos2β cosψ cos(δ +β +ψ)(1+√sin(δ+φ)sin(φ−ψ−i)cos(δ+β+ψ)cos(i−β ))2 (2.3)In this equation φ and δ represent the angle of internal friction of the backfillsoil and the angle of interface friction between the wall and the soil, respectively. iis the slope of the ground surface behind wall and β is the slope of the back of thewall with respect to vertical alignment. ψ is calculated as ψ = arctan [kh/(1− kv)]with the limitation of φ −β ≥ ψ . In this equation kh and kv are the horizontal andvertical ground acceleration divided by gravitational acceleration, respectively. Ifthe pseudo-static accelerations are set to zero, Equations 2.2 and 2.3 will give theCoulomb static active lateral force, PA, and the static active earth coefficient, KA,respectively.The M-O method provides only the magnitude of the total lateral force dur-ing an earthquake, PAE . This method does not give the distribution of lateralearth pressure and the point of application of the seismic force. Several analyti-cal and experimental studies have been conducted to investigate the distribution ofthe lateral earth pressures and its corresponding point of application due to earth-14quake loading. (Al Atik, 2008; Bolton and Steedman, 1985; Gazetas et al., 2004;Geraili Mikola, 2012; Ichihara and Matsuzawa, 1973; Lam and Martin, 1986; Or-tiz et al., 1983; Prakash and Basavanna, 1969; Seed and Whitman, 1970; Sherifand Fang, 1984; Sherif et al., 1982; Sitar et al., 2012; Stadler, 1996; Steedman andZeng, 1990; Whitman, 1991).For practical purposes, Seed and Whitman (1970) proposed to separate the total(static + dynamic) active lateral force, PAE , into two components: the initial activestatic component, PA, and the dynamic increment due to the base motion, ∆PAE ,where PAE = PA +∆PAE as illustrated in Figure 2.2. The static thrust calculatedfrom the Coulomb theory is applied at H/3 from the base of the wall, resulting in atriangular distribution of pressure. As Seed and Whitman (1970) stated, most of theinvestigators agree that the increase in lateral pressure due to the shaking, ∆pAE(z),is greater near the top of the wall and the resultant increment in force acts at aheight varying from H/2 to 2H/3 above the base of the wall. Seed and Whitman(1970) in particular recommended that the resultant dynamic thrust be applied at0.6H above the base of the wall (i.e., inverted triangular pressure distribution).It is worth to mention that in this approach dry cohesionless backfill material isassumed.Static Seismic Total+ =+ =H/3PA PAE2H/3PAEhFigure 2.2: State of practice for seismic design of the basement walls inBritish Columbia using the modified M-O method.15The state of practice in British Columbia (DeVall et al., 2010) is to apply the∆PAE at height 2H/3 above the base of the wall, resulting in an inverted triangulardistribution of pressure. On this basis, the total thrust will act at a height h =[PA(H/3)+∆PAE(2H/3)]/PAE above the base of the wall. The value of h dependson the relative magnitudes of PA and ∆PAE , and it often ends up near the mid-heightof the wall. This method as presented in Figure 2.2 hereinafter will be referred toas ”the modified M-O method”.As presented in Equations 2.2 and 2.3, the earthquake thrust acting on the wallis a function of the horizontal and vertical ground seismic coefficients. The M-Oanalyses show that kv, when taken as one-half to two-thirds the value of kh, affectsPAE by less than 10% (Kramer, 1996). As stated by Seed and Whitman (1970),for most earthquakes ”the horizontal acceleration components are considerablygreater than the vertical acceleration components”, thus the vertical component(kv) could be neglected for practical purposes. Another reason for neglecting verti-cal loading is attributed to the fact that the ”higher frequency vertical accelerationswill be out of phase with the horizontal accelerations and will have positive andnegative contributions to wall pressures, which on average can reasonably be ne-glected for design” as stated in the National Cooperative Highway Research Pro-gram (NCHRP) report (Anderson et al., 2008). Gazetas et al. (2004) concluded thateven simultaneous vertical acceleration does not have any noticeable effect on thedistribution of the dynamic pressure and consequently the resultant deformation onthe wall. Due to all these facts the current state of practice in British Columbia isto use the PGA as the horizontal acceleration and ignore the vertical accelerationin the M-O method.Finally it should be noted that consideration of a passive pressure cut–off wouldchange the design pressure distribution on the wall near the ground surface. How-ever, according to the Structural Engineers Association of British Columbia (SEABC)pressure cut–off is not being used among practitioners in current design practice ofbasement walls in British Columbia. As this study is focused on the evaluation ofbasement walls designed based on the current practice, pressure cut–off is ignoredin their seismic design.The M-O method is a simple and powerful tool for evaluating the seismic earthpressure, but it is based on an experimental study of a small scale cantilever wall16with a dry, medium dense cohesionless granular backfill excited by 1g sinusoidalexcitation on shaking table and does not scale very well with the size of actualwalls. Numerical studies conducted by Green et al. (2003) on cantilever retainingwall-soil system using the FLAC modeling tool showed that at very low levels ofacceleration, the seismic earth pressures are in agreement with the M-O predic-tions, whereas at high levels of acceleration the M-O method may lead to uncon-servative estimates of the dynamic earth pressures. On the other hand, Gazetaset al. (2004) performed a series of finite element analyses on different types offlexible retaining walls subjected to earthquake motions of either high or moder-ately low dominant frequencies with PGA of 0.40 g and relatively short duration.They analytical studies and field observations suggested that the M-O method isconservative, if not overly conservative. Brandenberg et al. (2015) addressed theseconflicting findings based on different approaches and assumptions regarding sys-tem behavior and conducted a kinematic soil–structure interaction using springmodels for evaluating seismic earth pressures on buried rigid U-shaped structure.There are number of concerns associated with the M-O approach which raisequestions about the applicability of this method for evaluating the seismic earthpressures on the basement walls (Lew, 2012; NEHRP, 2009; Ostadan and White,1998). For instance, in basement walls the horizontal movements are often limiteddue to the presence of floor slabs and the fact that the development of limit-statecondition is unlikely. Besides since most deep basement walls are not cantileveredbut braced, the applicability of the M-O method can be questioned. In this methodthe PGA is the only representative of the frequency content of the ground motion,which is not a good indicator of the characteristics and energy content of the motionespecially at important frequencies. Arulmoli (2001) recommended the use of theM-O method and stated its unrealistic seismic earth pressure estimation in the caseof large ground acceleration. In addition, in this method the dynamic nonlinearbehavior of the soil undergoing time-varying deformations caused by earthquakeground motions are not considered and appropriate dynamic properties of the soil,such as the shear wave velocity, are not taken into an account.Another major area of deficiency in the M-O method is that it is just applicableto the cohesionless soils. The National Cooperative Highway Research Program(NCHRP) report (Anderson et al., 2008) provides design charts and guidelines to17account for cohesion in practical design problems. Candia (2013) conducted scaledcentrifuge tests on braced U-shaped wall or basement-type wall and a freestandingcantilever wall founded in low plasticity cohesive soils. It was concluded that evena small amount of cohesion can reduce the seismic pressure acting on the wallsignificantly and proposed that the horizontal ground acceleration can be reducedby one-half to two-third of the PGA, depending on the different wall configuration.Despite all these concerns about the M-O method, this approach has been usedwidely in practice and has been recommended by documents such as the NEHRP(2000, 2003, 2009).2.5 Seismic coefficient in basement wall designThe M-O equation is used by practitioners for a pseudo-static analysis of all typesof retaining walls including basement walls. Despite the recent advances in com-putational technology, sophisticated and time consuming dynamic analysis maynot be feasible for routine design practice and professionals may continue to usethe simple M-O approach for seismic design of basement structures. Hence the keyquestion to be addressed is: what seismic coefficient kh should be used in the M-Omethod to obtain a reasonable and acceptable performance.Over time there have been studies suggesting that the M-O method may leadto conservative estimates of the dynamic earth pressures (Al Atik, 2008; Cloughand Fragaszy, 1977; Gazetas et al., 2004; Koseki et al., 1998; Lew et al., 2010b).By increasing the awareness of seismic risks and moving towards the performance-based design, the practitioners found that designing the walls using the M-O seis-mic forces would result in an expensive and over-conservative design. There aresome well-documented case histories that confirm retaining structures designedonly for static loading can stand remarkably well under seismic loading with PGAup to 0.5 g (Clough and Fragaszy, 1977; Gazetas et al., 2004). Similar conclusionwere made by Seed and Whitman (1970) that the wall designed to a reasonablestatic factor of safety (e.g. 1.5) should be able to resist seismic loads up to 0.3 g.They observed that the peak ground acceleration occurs for only one instant oftime and does not have sufficient duration to cause significant wall movements.Therefore an effective acceleration equal to 85% of the peak value was suggested18to be used in wall design. Seed and Whitman (1970) also stated that “many wallsadequately designed for static earth pressures will automatically have the capacityto withstand earthquake ground motions of substantial magnitudes and in manycases, special seismic earth pressure provisions may not be needed.”The major challenge for design is to select an appropriate seismic coefficient.Based on the evidence from shaking table and centrifuge tests reported by Whitman(1991) and subsequent regulatory guidance from documents such as the NEHRP(2000, 2003, 2009), it is recommended that except where structures were foundedat a sharp interface between soil and rock, the M–O method should be used with anactual expected PGA that is consistent with the design earthquake ground motions.NEHRP (2009) states that “... In the past, it was common practice for geotech-nical engineers to reduce the instantaneous peak by a factor from 0.5 to 0.7 torepresent an average seismic coefficient for determining the seismic earth pressureon a wall. The reduction factor was introduced in a manner similar to the methodused in a simplified liquefaction analyses to convert a random acceleration recordto an equivalent average series of cyclic loads. This approach can result in con-fusion on the magnitude of the seismic active earth pressure and, therefore, is notrecommended. Any further reduction to represent average rather than instanta-neous peak loads is a structural decision and must be an informed decision madeby the structural designer...”.Further justification for the use of a reduced seismic coefficient comes from theFederal Highway Administration (FHWA) (1997) for the design of highway struc-tures. This document states that “...for retaining walls wherein limited amounts ofseismic deformation are acceptable, use of a seismic coefficient between one-half totwo-thirds of the peak horizontal ground acceleration divided by gravity would ap-pear to provide a wall design that will limit deformations in the design earthquaketo small values...”. Arulmoli (2001) commented on the use of the M-O methodand stated that the M-O method “blows up” for cases of large ground acceleration.Lew et al. (2010b) in his report mentioned that “... in practice, many geotechnicalengineers have been using a seismic coefficient that is less than the expected peakground acceleration for the design of building basement walls and other walls...”.Seed and Whitman (1970) suggested 0.85 PGA as an effective acceleration in theirpaper.19In practice many geotechnical engineers have been using a horizontal acceler-ation less than the PGA for the design of basement walls. The seismic coefficientof one-half and 0.67 of the horizontal peak ground acceleration are used by practi-tioners for designing the walls with limited deformations as reported by Lew et al.(2010b) and Sitar et al. (2012), respectively. Lew et al. (2010b) associated the re-duction to the fact that the M-O method is a pseudo-static approach of analysis thatuses a pseudo-static coefficient to represent earthquake loading. Also in order totake into an account the repeatable nature of ground motions, Lew et al. (2010b)suggested a reduction based upon the use of an effective ground acceleration ratherthan an isolated peak ground acceleration. They also proposed to take into an effecta reduction to account for the averaging of the lateral forces on the retaining wallover the height of the wall.The M-O method was originally developed for a medium dense cohesionlessbackfill soil. As in the real world even the most natural cohesionless soils havesome fine content that often contributes to cohesion (Anderson et al., 2008) whichwould have a significant effect in reducing the dynamic active pressure for design.The results of the dynamic centrifuge tests conducted over the past decadeson model retaining walls with dry cohesionless backfills were compared with theresults of the original M-O method by Bolton and Steedman (1985); Conti et al.(2012); Dewoolkar et al. (2001); Ortiz et al. (1983); Stadler (1996); Steedman andZeng (1991). Most of these researchers concluded that the earth pressure deter-mined by the M-O method gives adequate results, whereas the point of applica-tion of the dynamic thrust has been the subject of a continuing discussion. Stadler(1996) concluded that the incremental dynamic lateral earth pressure profile rangesbetween triangular and rectangular and suggested using a modified magnitude ofseismic coefficient by reducing them to magnitudes ranging from 20% to 75% ofthe M-O method.Recent centrifuge modeling works by Al Atik (2008) and Al-Atik and Sitar(2007) on stiff and flexible model cantilever walls with medium dense dry sandbackfill suggested that estimating seismic lateral pressures using the M-O methodand utilizing the full peak ground acceleration overestimates the seismic earth pres-sure forces for some structures. Later on Al-Atik and Sitar (2009, 2010) developedrelationships for the dynamic increment in earth pressure coefficient (∆Kae) com-20puted from the dynamic earth pressures at the time of maximum wall moments.Their experimental data suggest that seismic loads higher than 0.4 g could be re-sisted by cantilever walls designed to an adequate factor of safety and the dynamicearth pressures are insignificant for low levels of shaking (PGA less than 0.4 g).This observation is consistent with the observations and analyses performed byClough and Fragaszy (1977) who concluded that conventionally designed can-tilever walls with granular backfill could be reasonably expected to resist seis-mic loads at accelerations up to 0.5 g. Lew et al. (2010b) also reported on thework of Al-Atik and Sitar (2009) and proposed a horizontal ground accelerationof 25% PGA, 50% PGA and 67% PGA for cohesionless backfill soil with peakground accelerations of 0.4 g, 0.6 g and 1.0 g, respectively.To expand upon the work by Al Atik (2008); Al-Atik and Sitar (2007, 2009,2010), additional centrifuge experiments. The experiments were conducted on twostiff and flexible U-shaped structures with two levels of internal struts to modelbasement type rigid structures founded on dry medium-dense sand (Geraili Mikola,2012; Sitar et al., 2012). The resultant incremental dynamic earth pressure datashow that the Seed and Whitman (1970) approximation using the PGA, representsa reasonable upper bound for the value of the seismic earth pressure incrementfor cross-braced basement type walls. The use of 0.85 PGA in the same analysisproduces values very close to the mean of the experimental data. However, theM-O solution is considerably higher than measured values at accelerations above0.4 g. Also it was concluded from these centrifuge tests that the seismic earthpressure increments exerted on the basement walls do not support the use of Wood(1973) solution for rigid or non-yielding walls as suggested by documents such asNEHRP (2000, 2003, 2009).It is important to note that the proposed reduction factors by the researchersin the United States (Al-Atik and Sitar, 2009, 2010; Geraili Mikola, 2012; Lewet al., 2010b; Sitar et al., 2012) are applicable to the walls designed using the In-ternational Building Code (IBC, 2009) load combinations, where the tests wereconducted (Lew et al., 2010b; SEAOC, 2013). Considering the load combinationsin IBC (2009), it appears that the basement walls in California are designed usingat rest pressures with a 1.6 loading factor in static design, which seems adequatefor even seismic earth pressure loading. For seismic design, if the M-O analysis is21used to determine the seismic loads, the total lateral seismic pressure should con-sist of the static active earth pressure and the dynamic increment of earth pressurewith a load factor of 1.6 and 1.0, respectively. This is while the National BuildingCode of Canada (NBCC, 2010) proposed lower lateral pressures which are beingused by practitioners for seismic design of walls in British Columbia. This rec-ommendation prescribed 1.5 times an active Coulomb pressure for static designand the lateral total seismic pressure consists of the static active earth pressure andthe dynamic increment of earth pressure, each with a loading factor of 1.0 for theseismic design.Based on aforementioned facts it can be concluded that walls designed inthe United States following the IBC (2009) load combinations are considerablystronger both in static and dynamic than the similar structures designed in BritishColumbia using the NBCC (2010) load factors. Therefore, the reduction factorsproposed by researchers in United States might not be applicable for the case ofbasement walls designed in British Columbia and a separate study is required,which is a prime objective of this dissertation.22Chapter 3Development of thecomputational model of abasement wallSoftware is a great combination between artistry and engineering.— Bill Gates3.1 IntroductionThis chapter introduces the methodologies used to better approximate the interac-tions between the basement wall structure and the surrounding soil. First a 4-levelbasement wall structure is designed following the state of practice for differentfractions of the pseudo-static horizontal seismic coefficient as presented in Sec-tion 3.2. A commercially available, two-dimensional, finite difference program,FLAC 2D (Itasca, 2012), is used for the analysis in Section 3.3. The interactionof the basement wall and the adjoining soil is treated as a plane-strain problem,which is the condition associated with long structures perpendicular to the analysisplane (e.g., retaining wall systems). Elements of the computational model such asboundary conditions, interface elements, structural and soil properties and appliedground motions are described in detail in this Chapter.233.2 Seismic design of the typical 4-level basement wallThe prototype model of the 4-level basement wall with a total height of 11.7 m isdesigned according to the state of practice in Vancouver (see Section 2.4) by theSEABC structural engineers. To determine an appropriate value of the horizontalseismic coefficient to be used in the M-O method, six basement walls are designedfor different values of khg varying from 100% down to 50% of the NBCC (2010)PGA (= 0.46g). Each wall is subjected to the dynamic analyses using groundmotions corresponding to 1/2475 hazard levels of NBCC (2010).Following the state of practice in British Columbia, the structural engineersused two load combinations prescribed by the National Building Code of Canada(NBCC, 2010), for seismic designing the basement walls:(1) 1.5pA(z), which pA(z) is not less than 20 kPa compaction/surcharge pressure.(2) pAE(z) = pA(z)+∆pAE(z)where pAE(z) is the total active lateral pressure consists of pA(z), the staticlateral active pressure and ∆pAE(z), the dynamic increment of the lateral earthpressure acting on the wall.Figure 3.1 depicts the distribution of the pressure along the height of the 11.7 mwall based on the factored static load, which comprises 1.5 times static activeCoulomb pressure plus compaction pressure at the top. The construction pro-cess has a considerable impact on earth pressure distribution of the backfill soil.Therefore the induced lateral earth pressures due to compaction of soil in lay-ers can be significantly higher than those predicted by conventional earth pres-sure theory. Large number of laboratory and full scale tests (Clayton and Symons,1992; Duncan and Seed, 1986) have been conducted to investigate the compaction-induced lateral earth pressures on the wall. Clayton and Symons (1992) suggestedthat in the case of granular backfill, compaction-induced pressures do not nor-mally exceed 20-30 kPa and the effective depth to which compaction pressures aresignificant will not exceed 3-4 m. The Canadian Highway Bridge Design Code(CAN/CSA-S6-06, 2014) Clause 6.9.3 also provides rough estimations for the lat-eral force caused by compaction for retained backfill placed and compacted inlayers. Based on this recommendation a lateral pressure varying linearly from24minimum of 12 kPa at the fill surface to 0 kPa at a depth of 1.7 to 2.0 m below thesurface, depending on the internal friction angle of the soil, shall be added to thelateral earth pressure.(a) (b)2.7 m2.7 m2.7 m3.6 mGround LevelLevel !1Level !2Level !3Level !48.1 m5.4 m2.7 m0.0 m11.7 m67.6 x 1.5 = 101.4 kPa20 x 1.5 = 30 kPaFigure 3.1: (a) Floor heights in the 4-level basement wall and (b) the calcu-lated lateral earth pressure distributions from the first load combination.(a) (b) (c) (d) (e) (f) (g)67.6 kPa36.1 kPa67.6 kPa45.4 kPa95.4 kPa67.6 kPa 67.6 kPa 67.6 kPa67.6 kPa55.9 kPa67.4 kPa80.5 kPa2.7 m2.7 m2.7 m3.6 mGround LevelLevel !1Level !2Level !3Level !48.1 m5.4 m2.7 m0.0 m11.7 mFigure 3.2: (a) Floor heights in the 4-level basement wall and the calculatedlateral earth pressure distributions from the second load combinationusing the modified M-O method with (b) 100% PGA, (c) 90% PGA,(d) 80% PGA, (e) 70% PGA, (f) 60% PGA, and (g) 50% PGA, wherePGA=0.46g, based on the NBCC (2010) for Vancouver.25Figure 3.2 presents the distribution of the lateral earth pressure along the heightof the basement walls designed for different fractions of the NBCC (2010) PGA,based on the second load combination. This figure shows the linear triangular dis-tribution of the static active component of pressure, pA(z), with the highest pressureat the base of the wall. The value of PGA/g is used as the pseudo-static horizon-tal seismic coefficient (kh) in the calculation of the dynamic increments, ∆pAE(z)distributed in an inverted triangular with the highest pressure at the top of the wall,following the modified M-O method described in Section 2.4. The basement wallis designed for the conditions of horizontal backfill without any surcharge load orwater pressure.The design moment considered at each depth of the wall is the maximum ofthe calculated moments from the aforementioned load combinations (1) and (2)defined previously . This design moment must be less than or equal to the factoredmoment resistance, Mr (See Appendix A). The wall is designed to the CanadianConcrete Design Code (CAN/CSA-A23.3-04, 2004) by SEABC structural engi-neers (DeVall, 2011). The nominal moment capacity of the wall, approximated asMn(z) = 1.3 Mr(z), is used in the computational model for evaluating the responseof the walls to a suite of ground motions. Note that the member over-strength fac-tor of 1.3, calculated as 1/0.85×1.1 following NBCC (2010), is used to estimatethe ”nominal” bending strength of the wall. This assumes the bending strengthfor lightly reinforced wall sections is governed by the yield strength of the steel.The factor of 1/0.85 removes the resistance factor from the yield strength, and thefactor of 1.1 approximates the over strength of the steel.Consistent with the six scenarios of lateral earth pressures shown in Figure3.2, six levels of yielding moment are calculated for the walls based on differentfractions of the code-mandated PGA. The calculated moment from the first and thesecond load combinations are compared and the maximum value at each depth ischosen. The values of the nominal moment capacity, Mn(z), along the height of thewalls designed for different fractions of PGA are illustrated in Figure 3.3.The moment capacity of all six walls end up to be different only from the heightof 7.2 m to 11.7 m from the base of the wall, where the second load case governsthe design moment. The moment capacity of these six walls appear to be the samefrom height of 0.0 to 3.6 m from the base, where the static load case governs260 20 40 60 80 100 120 14002.75.48.111.7Moment (kN−m/m)Height (m)  100% PGA90% PGA80% PGA70% PGA60% PGA50% PGAFigure 3.3: Moment capacity distribution along the height of the 4-level base-ment walls designed for various fractions of the code PGA.the design moment, and from height of 3.6 m to 7.2 m from the base, where theconcrete code minimum reinforcement requirement governs the moment capacity.The responses of these basement walls to the actual expected code demand havethen been evaluated using a series of nonlinear dynamic computational analyses,as will be described in the next chapter.The factored shear resistance based on the unreinforced concrete section aloneand using the Canadian Concrete Design Standard (CAN/CSA-A23.3-04, 2004) iscalculated as 134.6 kN/m by DeVall (2011). The material resistance factor (φc) is0.65 and this gives a nominal resistance of Vn(z) = 134.6/0.65 = 207 kN/m. Anintermediate shear value that reflects a common code elastic response cut-off ofRd .Ro = 1.3 force level is 134.6×1.3= 175 kN/m (note that it also corresponds tothe flexural over-strength factor of 1.3). However, this value is for information onlyas there currently is no code provision for using Rd .Ro = 1.3 force level cut-off forretaining walls.The walls in this study have been kept relatively thin (thickness = 250 mm)and based on current design practice require shear ”stirrup/tie” reinforcement inportions of the wall height when the shear in the wall due to either the static orearthquake load case generate shears greater than the factored shear capacity of theconcrete section alone. Details of the basement wall designs prepared by DeVall(2011) are presented in Appendix A. Note that for even designs less than PGA, thewalls are designed for full PGA for shear.273.3 Description of the computational modelA series of two-dimensional nonlinear dynamic analyses have been conducted us-ing the finite difference computer program FLAC 2D (Itasca, 2012) to assess theseismic performance of the basement walls.FLAC (Fast Lagrangian Analysis of Continua) is an explicit finite differenceprogram for conducting the soil–structure interaction analysis under static and seis-mic loading. FLAC has been used widely as a design tool by geotechnical, civil,and mining engineers for modeling geomechanical problems. This program simu-lates the behavior of structures built of different materials that may undergo plasticflow when their yield limits are reached. FLAC provides a range of constitutivemodels from linearly elastic models to highly nonlinear plastic models. In addi-tion, it allows user-defined models to be incorporated. The null model is com-monly used in simulating excavations or construction, where the finite differencezones are assigned no mechanical properties for a portion of the analysis. Alsothis program has interface element feature, which facilitates the simulation of theinteraction between the backfill soil and the concrete basement wall.A finite difference model of the typical basement wall is developed consistingof two-dimensional plane-strain quadrilateral elements to model the soil medium,structural elements to model structural components, and interface elements to sim-ulate frictional contact between the structure and the surrounding soil. Details ofthe computational model, including the model building procedure, boundary con-ditions, applied ground motions, and soil properties used in these analyses, aredescribed in this section.3.3.1 Modeling the construction sequenceIt is important to model the construction sequence of the basement wall as closelyas possible in order to provide a reasonable representation of the initial, static shearstresses in the structure. So in order to ensure the proper initial stress distributionon the basement structure, the actual construction sequence is modeled in stagesto simulate the actual sequence of excavation. The basement wall model is nu-merically constructed in FLAC similar to the way an actual wall would be con-structed. As each stage is excavated, the excavation support is installed and later28on removed. Under this condition the soil pressures applied to the wall are repre-sentative of the actual pressures. FLAC model can incorporate interaction of thesoil and the structure using interface elements and provides direct information onthe ground movements outside of and inside the excavation.Layer 1Layer 224.3 m150 m(a)12.15 m12.15 m60 m 30 m 60 m(b)Gap(c).2/Figure 3.4: Different stages of the computational model building procedure.The analysis is started by carrying out a set of initial stage analyses to simulateinitial geostatic stresses followed by the construction of the basement wall and thebackfill soil. First, a 24.3 m deep and 150 m wide layer of soil is created. Figure3.4(a) shows the mesh adopted to carry out the analyses. The model consists of twosoil layers that will be discussed further in this Chapter. The horizontal and verticalstresses are initialized based on self-weight of the soil and a coefficient of at restearth pressure K0 from Jaky’s equation (Jaky, 1948). A first approximation of thestresses in soil-wall system are estimated using an elastic analysis and the model is29brought to equilibrium under gravity forces. Then these stresses are corrected byre-analyzing the system using Mohr–Coulomb model. This procedure is adoptedto speed up the analyses.In the next stage, a part of the upper soil layer is excavated in lifts to a depth of11.7 m and a width of 30.0 m. As each lift is excavated, lateral pressures (shoring)equal to the corresponding active pressure are applied to retain the soil (Figure3.4(b)). This is because deep building basement walls are constructed in open ex-cavations are generally shored, which cause the retained soils to be in a yielded(active) conditions already (Lew et al., 2010b). Then the basement wall is con-structed, leaving a gap between the soil and the structure, and the static analysis isrepeated to establish the equilibrium static stress condition (Figure 3.4(c)). Finally,the gap between the basement wall and the backfill soil is filled, and the shoringpressures are removed in stages, allowing the load from the soil to transfer to thebasement wall (Figure 3.4(d)). Note that following the current state of practice inBritish Columbia, in the present study the building above the ground level is notconsidered and inertial loading of the surface structures on basement wall pressuresare not taken into an account.The following sections outline the procedures used to determine the variousmodel parameters.3.3.2 Input ground motions characterizationIn performance-based seismic design of structures, it is critical to develop a crite-ria for selecting an appropriate number of acceleration time histories in which themean acceleration response spectrum of the selected ground motions provides agood match to the target spectrum over the period range of interest. In practice asuite of input motions is used to capture the motion-to-motion variability present inearthquake ground motions as each ground motion has its unique detailed charac-teristics, such as frequency content and duration that influence the induced dynamicresponse differently.There are two main methods of scaling/matching the input ground motion toinsure that the input motion match the code specified intensity of the seismic haz-ard which is typically specified by the Uniform Hazard Spectrum (UHS). The first30method is to linearly scaled the ground motions, which each accelerogram is mul-tiplied by a scalar coefficient to become more compatible with the target spectrum.In this method the average spectrum of the scaled motions matches the UHS overthe period range of interest. This approach has an advantage of preserving the fre-quency content and characteristics of each ground motion record and ensures thatthe variability between earthquake ground motions is reflected in the analyses.The second approach is spectral matching where each input motion by itself ismatched to the UHS in the period range of interest. Spectrum-compatible groundmotions greatly reduce the dispersion in the elastic response spectra of the inputground motion and enhance the variability of the output of nonlinear response his-tory analyses. Spectral matching is popular in engineering practice because it re-duces the variance of the structural responses due to motion-to-motion variabilityand provides a platform to estimate the mean value of the engineering demandparameter with fewer number of analyses (Seifried and Baker, 2014).In this chapter the spectral matching method is used to modify earthquake timehistories to become compatible with the NBCC (2010) UHS for Vancouver. Asit is generally considered desirable to maintain the measure of variability betweenthe ground motions, other than spectral matching, different intensity-based linearscaling methods are discussed in Chapter 6 to capture motion-to-motion variability.The results of these analyses are compared with the corresponding average valueand scatter of the demand concluded from spectrally-matched motions.Selection of ground motion records:Regarding to the number of ground motions, following the recommendation ofNEHRP (2011), ASCE/SEI 7-05 (2005) and ASCE/SEI 7-10 (2010) for selectingand scaling earthquake ground motions in response-history analyses, by selectingseven or more ground motions an arithmetic mean of the peak response can beused for performance checking. However this rule does not have any technicalbasis and is strongly depends on the goodness of the fit of the scaled motion tothe target spectrum (NEHRP, 2011). Increased number of time histories result in acloser average match to the target and higher confidence in determining the meanresponse and its variability to the design-level motions. The appropriate number of31motions, which is dependent on the application, is still a topic of needed research(Buratti et al., 2010; Hancock et al., 2008; Heo et al., 2010; Kalkan and Chopra,2010; Michaud and Le´ger, 2014; NEHRP, 2011; Reyes and Kalkan, 2011).In this study a suit of seven crustal ground motions, each consists of two hori-zontal components (total of 14 ground motion records), are selected. The recordsare selected to cover the inherent uncertainties associated with earthquake motionssuch as amplitude, frequency content and duration of ground excitation.The main considerations in selecting ground motion records are earthquakemagnitude, site-to-source distance and local site condition. Appropriate ranges ofmagnitudes and distances to earthquake sources, which contribute most stronglyto the hazard at the site in question, are determined based on the de-aggregationof the current seismic hazard. Based on the results of de-aggregation of the UHSfor Vancouver (Pina et al., 2010), searching criteria for the crustal ground motionsis set as the magnitude range of 6.5 to 7.5, with the closest distance of 10-30 kmof the causative fault plane from the earthquake sites. The reference soil classifi-cation, site class C, proposed by the National Building Code of Canada (NBCC,2010) is selected as the site condition at the point of application of ground motions.According to the NBCC (2010), site class C is defined by a time-averaged shearwave velocity in the upper 30 m (Vs30) between 360 m/s and 760 m/s, which isconsidered as a dense soil or soft rock.The spectral shape of the ground motion in comparison with the target spec-trum over the period range of interest is a parameter that plays an important rolein the selection process of ground motion records. Selecting the motions whosespectral shapes are similar to the target spectrum minimizes the need for spectralmodification.Based on aforementioned selection criteria, time histories are selected from thePacific Earthquake Engineering Research Center (PEER) ground motion database(Chiou et al., 2008; PEER, accessed on January 2013). In order to take into anaccount the spectral shape of the ground motions, the candidate records are chosenbased on the best linearly scaled motions to the UHS of Vancouver in the periodrange of 0.02-1.7 sec. The Mean Squared Error (MSE) of the difference betweenthe spectral acceleration of the record and the target spectrum is chosen as a cri-terion for selecting the best linear-scaled records. In addition, in order to elimi-32nate the potential bias towards one specific event, no more than two out of sevenrecords are selected from a single seismic event. Table 3.1 listed the selected sevencrustal ground motions. For each record, the PEER-NGA database provides twohorizontal components of acceleration time histories, which have been rotated toFault-Normal (FN) and Fault-Parallel (FP) directions. The use of rotated time his-tories does not imply that they are only for use in time history analyses in FN andFP directions, whereas they can be used in any other direction (Wang et al., 2013).Both components of the selected records are decided to be used which leads to atotal of 14 crustal ground motions (G1–G14).Table 3.1: List of the selected crustal ground motions.No. Event Name Year Station Magnitude Vs30 (m/s) DirectionG1Friuli- Italy 1976 Tolmezzo 6.5 424.8FNG2 FPG3Tabas- Iran 1978 Dayhook 7.35 659.6FNG4 FPG5New Zealand 1987 Matahina Dam 6.6 424.8FNG6 FPG7Loma Prieta 1989Coyote Lake Dam (SW Abut)6.93597.1FNG8 FPG9San Jose - Santa Teresa Hills 671.8FNG10 FPG11Northridge 1994 LA - UCLA Grounds 6.69 398.4FNG12 FPG13Hector Mine 1999 Hector 7.13 684.9FNG14 FPSpectral matching the selected ground motion records:The computer program, SeismoMatch (Seismosoft, 2009a) has been used to spec-trally match the ground motions to the target UHS in the period range of 0.02–1.7 sec. Grant and Diaferia (2013) investigated the period range for spectral match-ing and concluded that matching up to three times the fundamental period is bene-ficial in reducing dispersion in the results.33SeismoMatch is an application uses the wavelet algorithm proposed by Abra-hamson N.A. (1992) and Hancock et al. (2006) to adjust earthquake ground mo-tions and obtain a response spectrum with a close match to the target spectrum in aperiod range of interest. The basic characteristic of the original record with respectto the amplitude and frequency content of the record over the time history durationis preserved and a developed design time histories have a spectra similar to the adesign spectrum (NEHRP, 2011).The spectrally matched ground motions are baseline corrected with a linearfunction and filtered with a bandpass Butterworth filter with cut-off frequencies of0.1 Hz and 25 Hz, using the computer program SeismoSignal (Seismosoft, 2009b).ith GM mean UHS Vancouver0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)Spectrally matchedFigure 3.5: The 5% damped acceleration response spectra of the selected 14crustal input ground motions, all spectrally matched to the target NBCC(2010) UHS of Vancouver in the period range of 0.02-1.7 sec.The 5% damped acceleration response spectra of suite of ground motions G1–G14 in comparison with the target NBCC (2010) UHS for Vancouver is presentedin Figure 3.5. Also the acceleration time histories of the spectrally matched groundmotions corresponding to the 2% in 50 year hazard level specified in the NBCC(2010) are presented in Figure 3.6.340 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G20 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G30 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G40 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G50 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G60 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G70 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G80 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G90 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10Figure 3.6: Continued.350 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G110 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G120 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G130 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 3.6: Acceleration time histories of the selected 14 crustal ground mo-tions spectrally matched to the NBCC (2010) UHS of Vancouver.3.3.3 Structural elementsStructural elements of the model including basement walls, interior walls, con-crete floor slabs, foundation and braces are modeled using beam elements in FLAC(Itasca, 2012). Beam elements are two-dimensional elements with three degrees offreedom (x–translation, y–translation and rotation) at each end node. The beam isassumed to behave as a linearly elastic material with no failure limit. However ifdesired, a plastic moment may also be specified to model inelastic behavior of thestructure (FLAC User’s guide).The flexural behavior of the basement walls is simulated by elastic-perfectlyplastic beam elements with uniform properties of E = 2.74×107 kPa, A= 0.25 m2/m,and Icr = 0.00104 m4/m, and with varying yield moments along the height of thewalls, as obtained for different designed walls in the previous section and presentedin Figure 3.3.Based on recommendation of the NBCC (2010) Commentary J, the effects ofcracked sections must be taken into consideration in determining the stiffness and36strength of reinforced concrete elements. For this purpose the moment of inertia ofthe cracked concrete section (Icr) is used for the basement walls. The Los AngelesTall Buildings Structural Design Council (LATBSDC, 2014) recommended to useIcr = 0.8Ig for the reinforced concrete basement walls under earthquakes eventshaving 2% probability of being exceeded in 50 years (2475 year return period).An additional analyses conduced on cracked section with Icr = 0.5Ig show that theseismic response of the basement wall is not significantly sensitive to the choice ofreduction factors applied to the stiffness of the uncracked cross section.The basement wall nodes are created at the same geometric location as the soilnodes along the height of the wall and the interface elements maintain the nodalconnectivity between the soil and the wall. The basement walls are braced byconcrete floor slabs, which are pinned at the wall and take no moment. The actualmodel is for a below grade structure that is basically a box of walls with internalfloor diaphragms that span horizontally to the end walls by acting as horizontalbeams as they support the retaining wall being loaded by the soil and earthquakeactions. This is a complicated model and the effects of the supporting floor slabsand walls are reduced to a series of stiffnesses supporting the retaining wall beinganalysed. A sensitivity analysis using various stiffnesses was performed in theinitial stages to study the effects. The results were not very sensitive to the variousassumptions and the one giving the most conservative results were used to proceedwith the rest of the work.3.3.4 Representative soil propertiesSoil medium beneath and around the basement wall in this soil-structure modelis simulated by using finite difference mesh composed of quadrilateral elements.These two-dimensional plane-strain soil elements behave in accordance with a pre-scribed constitutive model in response to applied loads and boundary conditions.The elastic-perfectly plastic Mohr–Coulomb model with non-associated flowrule is adopted as the soil constitutive model for the sake of simplicity and itspopularity among local practitioners. This model has been employed by many re-searchers to simulate nonlinear behavior of the soil domain under seismic loading.A typical and simplified stratigraphy of an underlying soil layers are recom-37mended by practitioners in Vancouver. In consultation with the geotechnical en-gineers and the members of the SEABC Task Force (DeVall et al., 2010, 2014),the soil properties listed in Table 3.2 are proposed for the two soil layers in Figure3.4, representing the site condition relevant for high-rise construction, especiallyin downtown Vancouver.Table 3.2: Soil layer material properties.Soil Density Vs1 Poisson’s Cohesion Friction Dilationlayer (kg/m3) (m/s) ratio (kPa) angle (◦) angle (◦)1 1950 200 0.28 0 33 02 1950 400 0.28 20 40 0The shear wave velocity (Vs) is known to be a function of an effective over-burden stress σ ′0 and based on the suggestion of Robertson et al. (1992), can bepresented in the form of a normalized shear wave velocity:Vs1 =Vs(pat/σ ′0)0.25 (3.1)where pat is the reference atmospheric pressure. Normalized shear wave veloc-ities (Vs1) of 200 and 400 m/s are assigned to soil layers 1 and 2, respectively. Thesevalues result in a shear wave velocity profile, which varies along the depth of themodel due to the change of confining pressure (Figure 3.7). The small strain shearwave velocity is directly related to the small strain shear modulus via Gmax = ρV 2s ,where ρ is the mass density of the soil medium.In order to more appropriately simulate the nonlinear response of soil in thelinear elastic range of the Mohr–Coulomb model in a nonlinear analyses, it is nec-essary to incorporate shear modulus reduction and additional material dampingto account for stiffness reduction and cyclic energy dissipation during the elasticrange of the response. This approximate method is recommended by FLAC User’sGuideline (Itasca, 2012) when Mohr–Coulomb material model is employed forrepresenting the soil response in the full soil-structure system. Similar approachwas adopted by other researches (Argyroudis et al., 2013; Gazetas et al., 2005; Gilet al., 2001; Hashash et al., 2001) for the analysis of buried structures. It is worth38mentioning that the equivalent linear methods are more reliable only for low-strainlevels. For higher strain levels the effect of nonlinearity is captured through theMohr–Coulomb yield criterion used for modeling stress–strain response of the soilmedium in the 2D model. To this aim a site response analyses are conducted inthe free-field to determine depth-varying parameters such as shear modulus anddamping ratio of soil at different soil layers through-out the model in an absenceof the wall structure.The state of practice for site response analysis is to use the computer pro-gram SHAKE (EduPro Civil Systems Inc., 2003; Schnabel et al., 1972), in whichan equivalent linear approach is utilized to obtain reasonable estimates of groundnonlinear response. SHAKE is a widely used one-dimensional linear-elastic wavepropagation code for site response analysis in the frequency domain using transferfunctions. In this code the vertical shear waves propagate through a semi-infinitehorizontally-layered soil deposit overlying a uniform half-space. The method in-corporates soil nonlinearity through the use of strain-compatible soil properties foreach soil layer. This code is based on the multiple reflection theory and within eachlayer, the wave equation can be expressed as the sum of an upward-propagatingmotion and a downward-propagating motion following the general approach ofKramer (1996). The equivalent linear method has the advantage of short computa-tional time and few input parameters.A series of equivalent linear analyses are conducted on the two-layered soil pro-file subjected to the selected spectrally matched earthquake ground motions (G1–G14). Each soil layer is divided into number of sublayers with almost the sameheight. A constant density of 1950 kg/m3 is assigned to all sublayers throughoutthe model. The assigned shear wave velocity to each sublayer is reported in Fig-ure 3.7. The dynamic characteristics of the sublayers are assumed to be governedby the shear modulus degradation and damping ratio curves as a function of shearstrain. Following the recommendation of Task Force Report (2007) for geotechni-cal design in Greater Vancouver region, the upper-bound modulus reduction curveand the lower-bound damping curve of Seed et al. (1986) are selected for repre-senting the cyclic response of the sandy soil in the equivalent linear analyses.The profiles of the shear modulus reduction and damping ratios through-out thefree-field soil column are presented in Figure 3.8. Average values of damping ratios39Sub layer 1Sub layer 2Sub layer 3Sub layer 4Sub layer 5Sub layer 6Sub layer 7Sub layer 8Sub layer 9Sub layer 10Sub layer 11Sub layer 12Sub layer 13Sub layer 14Sub layer 15Sub layer 16Sub layer 17Sub layer 18Sub layer 19Sub layer 20Sub layer 21Sub layer 22Halfspace layer0 200 400 600 800Shear wave velocity (m/s)114.1150.1170.6185.6197.6207.8216.6224.5231.6238.2244.3500.1510.6520.5529.9538.8547.2555.3563.1570.5577.7584.7Soil layer 112.15 mSoil layer 212.15 m584.7Figure 3.7: Schematic sketch of the SHAKE model reporting on the numberof sublayers, the assigned shear wave velocities at each sublayer and thedepth at which the ground motions are applied.and shear modulus reduction factors are estimated for each layer and incorporatedinto the FLAC model. The results of the equivalent linear analyses of the free-fieldsoil column presented in Figure 3.8(a) suggest an equivalent G/Gmax of 0.41 and0.81 for the first and the second soil layers, respectively. These average equivalentmodulus reduction values are used for modifying the Gmax to G, at different depthsof the FLAC model. Similarly, Figure 3.8(b) suggests the equivalent damping400 0.25 0.5 0.75 1−24.3−12.150G/GmaxDepth of the model (m)Layer 1Layer 2(a)0 3 6 9 12−24.3−12.150Damping Ratio (%)Layer 1Layer 2(b)Figure 3.8: Resulting (a) G/Gmax and (b) damping ratios along the depth ofthe model from the equivalent linear analyses of the free-field column ofsoil subjected to G1–G14. The red solid lines show the average valuesof G/Gmax and damping ratio in the first and the second soil layers usedin the subsequent nonlinear analyses in FLAC.ratios of 8% and 3% for the first and the second soil layers, respectively. Thesedamping ratios are added to the nonlinear analyses of the soil-structure systemin the form of Rayleigh damping. The only draw back of using high values ofdamping ratio is that it causes the reduction in time step of the explicit solution andconsequently increases calculation time.Although Rayleigh damping is frequency-dependent, it is commonly used toprovide frequency-independent damping over a restricted range of frequencies.Therefore, selection of an appropriate range of frequencies is essential to obtainproper results. Velocity response spectrum of any input record has a flat region thatspans about a 3:1 frequency range. Thus, by applying constant Rayleigh dampingover a span of roughly 3:1 (or one-third) of the frequency range, the damping canbe considered frequency independent. This flat region in velocity response con-tains most of the dynamic energy in the spectrum and is centered at the dominantfrequency. The idea in dynamic analyses is to adjust a center frequency of theRayleigh damping, fmin, so that its 3:1 range coincides with the range of predom-inant frequencies in the problem, in order to provide the right amount of damping41at the important frequencies (FLAC User’s Guide).The center frequency of Rayleigh damping is set to the dominant frequencyof the input records, 1 Hz, which is basically calculated using velocity responsespectrum of the selected input records in logarithmic space. As is shown in Figure3.9, the velocity spectrums of all motions have an almost flat region of 3:1 over afrequency range of 0.5 Hz to 1.5 Hz.ith GM mean100 1010306090120Frequency (Hz)Velocity spectrum (cm/s)Figure 3.9: Velocity response spectrum versus frequency of the selected 14crustal ground motions (G1–G14).The small strain natural period of the basement wall-soil system in the FLACmodel is estimated to be approximately 0.4 sec, as determined by the peak of thetransfer function from the base of the model to the top of the backfill. The predomi-nant period of the system can also be calculated by applying a constant shear stressat the base of the model for a short time and then allow the whole system vibrateunder the damped free vibration condition till the initial displacement decays withtime. Comparing the results of these two studies confirm that natural period of thesoil–basement wall system is about 0.4 second. At higher strains, it is expectedthat the natural period of the system to be higher due to yielding.423.3.5 Mesh refinement of the soil domainProper dimensioning of the finite difference zones is required to avoid numericaldistortion of propagating ground motions and preparing an acceptable wave trans-mission through-out the model. Based on the work of Kuhlemeyer and Lysmer(1973), the FLAC User’s guide recommends to restrict the length of the element(∆l) to one-tenth or one-eight of the shortest wavelength (λ =Vs/ fmax) associatedwith the fundamental frequency of the input motion and velocity of propagation inthe soil media, i.e.,∆l ≤ Vs10. fmax(3.2)From this equation, the finite difference zone with the lowest Vs and a given∆l limits the highest frequency that can pass through the zones without numericaldistortion. After conducting number of trial dynamic analyses on the model withdifferent levels of mesh refinement, a relatively fine mesh size with the length of0.45 m is selected to be used at both sides of the basement wall structure. Theelement size increases gradually toward the left-side and right-side boundaries asis shown in Figure 3.4. Using Equation 3.2 and ∆l = 0.45 m as a finest meshsize used in the simulation, one can concluded that the assigned mesh size canadequately propagate shear waves having frequencies up to 40 Hz. This value iswell above the 25 Hz cut-off frequency used in the preparation of ground motions inSection 3.3.2 and well above the estimated fundamental frequency of the basementwall–soil system.Figure 3.10 shows the cumulative power spectral densities of the ground mo-tions G1–G14 and presents information about input energy and frequency contentof each record. As is shown in this figure, more than 99% of the earthquakespower are concentrated within frequency range of 0.1 to 25 Hz, which were set asthe corners of bandpass filtering process described in Section 3.3.2. Thus, it canbe concluded that filtering frequencies greater than 25 Hz and lower than 0.1 Hz inorder to avoid any numerical distortion due to wave propagation process, does notaffect the original characteristics of the input ground motions.4310−1 100 101 10200.20.40.60.81Frequency (Hz)Cumulative Power Density  G1G210−1 100 101 10200.20.40.60.81Frequency (Hz)Cumulative Power Density  G3G410−1 100 101 10200.20.40.60.81Frequency (Hz)Cumulative Power Density  G5G610−1 100 101 10200.20.40.60.81Frequency (Hz)Cumulative Power Density  G7G810−1 100 101 10200.20.40.60.81Frequency (Hz)Cumulative Power Density  G9G1010−1 100 101 10200.20.40.60.81Frequency (Hz)Cumulative Power Density  G11G1210−1 100 101 10200.20.40.60.81Frequency (Hz)Cumulative Power Density  G13G14Figure 3.10: Cumulative power densities of the unfiltered selected 14 crustalground motions spectrally matched to the NBCC (2010) UHS for Van-couver.443.3.6 Modeling soil–wall interaction using an interface elementsSimulating the interaction between the backfill soil and the concrete basement wallplays an important role in modeling the soil–structure interaction. To simulate slid-ing and loss of contact at the soil–wall interfaces, nulled zones with zero thicknesscontaining interface elements are employed in FLAC. Without an interface elementthe structure and the soil are tied together and no relative displacement (slipping/-gapping) is allowed between them. By using an interface element, node pairs arecreated at the interface of the structure and the soil. From a node pair, one nodebelongs to the structure and the other node belongs to the soil. The interactionbetween these two nodes consists of two elastic-perfectly plastic shear and normalsprings, which allow modeling of opening (separation) and slippage between thesoil and the wall in normal and shear directions, respectively.A simple elastic-perfectly plastic response consisting of constant values forboth shear and normal stiffnesses (ks and kn) is used for modeling the interfacecontact in FLAC. The shear response of the interface element is controlled byCoulomb shear strength criterion, which limits the shear force to the maximumshear strength defined as a function of cohesion and friction angle of the interfaceelement, i.e.,Fs max = cA+ tanφFn (3.3)where Fs max is the maximum shear strength, c and φ are the cohesion andfriction angle of the interface and Fn is the normal force. Equation 3.3 assumesabsence of pore water pressure.The yield relationship in the normal direction is controlled by the (positive)normal tensile strength (σt):Fn max = σt (3.4)At every time step in FLAC calculation, the normal compression/tension force(Fn) and shear force (Fs) of interface nodes are compared to the normal tensilestrength (σt) and maximum shear strength (Fs max), respectively, which leads to thefollowing three cases:45• If Fn < σt and Fs < Fs max, the interface node remains in the elastic range.In this case the interfaces are declared glued and no slippage or opening isallowed.• If Fn < σt and Fs > Fs max, the interface node falls into Coulomb sliding stateand the shear force is corrected as Fs = Fs max. The interface may dilate at theonset of slip and causes an increase in effective normal force on the targetface after the shear-strength is reached. In this case the normal force will becorrected as:Fn = Fn+(|FS|0−Fs max)L kstanψ kn (3.5)where |FS|0 is the magnitude of shear force before the correction and ψ isthe dilation angle of the interface.• If Fn > σt , the bond breaks for the segment and the segment behaves there-after as un-bonded and the separation and slip are allowed.In these analyses, a friction angle of δ = 10◦ equal to one-third of the angle ofinternal friction of backfill soil (φ ) and a dilation and tensile strength of zero areassigned to the interface element.The values of the interface stiffnesses (kn and ks) in comparison with the sur-rounding soil should be high enough in order to minimize the contribution of in-terface elements to the accumulated displacements (Comodromos and Pitilakis,2005). In addition, kn should be greater than or equal to ks, otherwise penetra-tion will occur between the soil and the wall faces, which does not correspond toactual condition. To satisfy the above requirement, the FLAC guideline proposesvalues for kn and ks in the order of ten times the equivalent stiffness of the stiffestneighbouring zone:kn = ks = 10 max[K+4/3G∆zmin] (3.6)In this equation, ∆zmin is the smallest width of the adjoining zones on both sidesof the interface and K and G are the bulk and shear modulus of the neighbouringzone, respectively. The max[ ] notation indicates that the maximum value over allzones adjacent to the interface is to be used. The FLAC manual warns against46using arbitrarily large values for stiffnesses, as is commonly done in finite elementanalyses, which leads to a very small time step and therefore long computationaltimes. Using Equation 3.6, a value of 9× 106 kPa/m is assigned for kn and ks inthese analyses.3.3.7 Boundary conditionsSimulation of dynamic soil–structure interaction problem requires appropriate con-ditions to be enforced at the computational model boundaries. Boundary conditionsof the 2D finite difference mesh comprise:• The lateral boundaries of the model should be placed at a location whichthe presence of the structure does not have any influence on the free-fieldconditions at the lateral boundaries of the mesh. Studies of Rayhani et al.(2008) based on computational modeling and centrifuge testing showed thatin dynamic analysis, the horizontal distance of the lateral boundaries shouldbe at least five times the width of the structure. As illustrated in Figure3.4, horizontal distance of the lateral boundaries of the model is assumedto be 150 m, which is five times the 30 m width of the structure and is farenough to avoid boundary effects. A series of an additional sensitivity analy-ses conducted on the continuum model with various soil domain dimensionsconfirmed that the proposed dimensions are appropriate for the analyses anda free-field condition at the lateral boundaries are properly captured.• A free-field boundaries are applied to the lateral boundaries which accountfor the existence of the free-field condition in an absence of the structure(Kramer, 1996). Free-field boundaries consists of a one-dimensional col-umn of unit width, simulating the behavior of the extended media. Theseboundaries are placed at distances far enough to minimize wave reflectionback to the model and simulate the free-field condition on both sides.• The velocity of the base nodes of the soil continuum model are fixed andprevented from changing in the horizontal and vertical directions. The lateralboundary nodes are fixed in a vertical direction, while they can move freelyin the horizontal direction.47• Lateral boundary conditions are imposed to slave the displacement degreesof freedom of the nodes across the soil continuum. Each grid point on theleft-side boundary (e.g., i = 1, j = n) is attached to its corresponding gridpoint at the same height on the right-side boundary (e.g., i = k, j = n). Thisensures that the lateral boundaries of the mesh move simultaneously.• Since the mesh cannot extended infinitely, there is a need for some sort of ab-sorbing boundaries in order to simulate the radiation of energy at the base ofthe model. This is achieved by using a compliant boundary condition alongthe base of the FLAC mesh, which means no large dynamic impedance con-trast is meant to be simulated at the base of the model. A quiet (absorbing)boundary (Lysmer and Kuhlemeyer, 1969), consisting of two sets of dash-pots attached independently to the mesh in the normal and shear directions,are applied along the base of the model to minimize the effect of the reflectedwaves. The viscous dashpots of the quiet boundary absorb downward prop-agating waves so that they are not reflected back into the model.For the compliant-base boundary, the input motion is the upward-propagatingmotion, which is half of the outcrop target motion (Mejia and Dawson,2006). At a quiet boundary, an acceleration time history cannot be input di-rectly because the boundary must be able to move freely to absorb incomingwaves. To this end first the acceleration-time history is integrated to obtainthe velocity time history, and then the following equation is used to convertthe velocity time history to shear stress time history that can be applied atthe base of the model:τs = 2ρVbvsu (3.7)In this equation ρ and Vb are the density and shear wave velocity of the basematerial, and vsu is the particle velocity of the upward propagating motion.A factor of two is added to the calculation of the shear stress time historybecause half of the stress is absorbed by the viscous dashpots of the quietbase (Mejia and Dawson, 2006). Figure 3.11 illustrates the shear stress timehistories of the selected 14 crustal ground motions (G1–G14), which are480 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G10 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G20 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G30 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G40 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G50 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G60 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G70 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G80 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G90 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G10Figure 3.11: Continued.490 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G110 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G120 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G130 10 20 30 40 50 60−500−2500250500Time (sec)Shear Stress (kPa)G14Figure 3.11: Shear stress time histories of the selected 14 crustal ground mo-tions applied at the base of the FLAC model.applied at the compliant-base of the FLAC model as an input motion.• The comprehensive study of Roesset and Ettouney (1977) on the effect ofdifferent types of boundary condition on structural response shows that ap-plying quiet (viscous) boundaries at lateral boundaries can significantly re-duce the reflection of the waves produced by lateral boundaries back to themodel. The sensitivity analyses in this study showed that due to a sufficienthorizontal distance of the lateral boundaries, the presence of viscous dash-pots at lateral boundaries do not have any effect on dynamic response of thestructure under study. Therefore, no viscous dashpots are assigned at thelateral boundaries of the soil model.50Chapter 4Seismic performance of a typical4-level basement wallThe most important thing is to keep the most important thing the mostimportant thing.— From the book ”Foundation design”, by Donald P. Coduto (1994)4.1 IntroductionThe seismic performance of the 4-level basement wall designed for six differentfractions of the NBCC (2010) PGA as discussed in Chapter 3, are numericallyanalyzed. Each wall is subjected to 14 crustal ground motions spectrally matchedto represent the seismic hazard level enforced by the NBCC (2010) in Vancouver.The seismic response of the basement walls are obtained from the nonlineardynamic analyses and presented in the form of the time histories and envelopesof the lateral earth pressures along the height of the walls, lateral earth forces onthe walls, envelopes of the bending moments, shear forces, lateral deformationsand drift ratios in Sections 4.2 to 4.4. The results indicate that flexibility of thewall has significant effect on the distribution of the seismic lateral earth pressureson the wall and consequently its seismic performance. Based on the results of theanalyses, recommendations for an appropriate fraction of NBCC (2010) PGA to51be used in the M-O analysis to have a satisfactory performance, in terms of theresulting drift ratio along the height of the wall are made. In addition, number ofsensitivity analyses on different input parameters are conducted, and the results arepresented and discussed in Section 4.5.Sections 4.2 to 4.4 presents the seismic response of the left-side walls, whilethe response of the right-side walls are found to be very similar to the left-sidewalls.4.2 Lateral earth forces and pressures on the wallDistribution and magnitude of the seismically induced lateral earth pressure on abasement walls are important issues to address since they directly affect the appliedtotal forces on the wall and consequently influence the magnitude of the imposedshear and moment forces in structural elements. Figure 4.1 shows the distributionof the lateral pressure at different heights of the basement wall designed for 100%of the code PGA subjected to earthquake ground motion G1. As shown in thisfigure each element of the wall undergoes a different regime of lateral pressure,which varies by time and height of the wall.During an earthquake event, the stress distribution is nonlinear and changes asa function of wall deflection. Figure 4.2 shows the time histories of lateral earthpressure at different levels along the height of the 4-level basement wall designedfor 100% PGA subjected to earthquake G1. At all elevations of the wall, the initialstatic lateral pressures before the earthquake is lower than the residual static lateralpressures after the earthquake. In addition, during the seismic loading the lateralpressure at each level increases gradually from its initial value to the higher finalvalue. The trend of this increase is slightly different at various locations. In par-ticular, more seismic lateral pressure is absorbed at floor levels with larger lateralsupport from the structure, than at the mid-height of the floor levels where the wallis not directly supported by the slabs.The resultant lateral earth force at a specific time can be calculated by inte-grating the induced lateral earth pressures along the height of the wall at that time.Figure 4.3 shows the time histories of resultant lateral earth force on the wall de-signed for 100% of the code PGA subjected to 14 ground motions (G1-G14). As5205101505010015020025030002.75.48.111.7Height of the wall (m)Pressure (kPa) Time (sec)Figure 4.1: Lateral earth pressure distribution along the height of the base-ment wall designed for 100% code PGA subjected to ground motion G1(only the first 15 sec response is illustrated).shown in this figure the lateral earth force starts from the static active thrust, os-cillates at different levels during the application of the ground motion, and finallystabilizes at a higher level than was initially, indicating an increase in the residualstatic earth force at the end of shaking. The M-O method for the same level ofPGA (= 0.46g) gives an almost similar peak resultant lateral earth force (PAE), asplotted by the dot-dashed line.Figure 4.4 illustrates the time histories of the corresponding height of applica-tion of the resultant lateral earth force measured from the base of the wall normal-ized with respect to the height of the wall, H. The height of the resultant lateralearth force starts from about 0.33H prior to shaking, i.e., the level suggested byCoulomb’s theory for static lateral earth pressure distribution. Then it oscillates atdifferent levels during the application of the ground motion. As illustrated in thisfigure, the M-O method using the same level of PGA results in a similar height53Ground levelLevel !1Level !2Level !3Level !48.1 m5.4 m2.7 m0.0 m11.7 mL4L5L2L1L30 5 10 15 20 25050100150200Pressure (kPa)Time (sec)  L1L2L3L4L5Ground levelLevel !1Level !2Level !3Level !48.1 m5.4 m2.7 m0.0 mM111.7 mM2M3M40 5 10 15 20 25050100150200Pressure (kPa)Time (sec)  M1M2M3M4Figure 4.2: The lateral earth pressure time histories at floor levels and mid-height of the floor slab levels along the 4-level basement wall designedfor 100% PGA subjected to ground motion G1.of application of the resultant lateral earth force at the instance of peak resultantlateral earth force.Figures 4.5 and 4.6 show the dynamic analysis results for ground motions G1–G14 in terms of the maximum resultant lateral earth forces and their correspondingnormalized heights of application from the base of the wall designed for 100%of the code PGA. These figures also present the maximum resultant forces andtheir corresponding normalized heights of application from the M-O method using100% PGA for comparison. As illustrated in Figure 4.5, the maximum resultantforces from dynamic analyses are in an approximate range of ±10% of the cal-culated maximum resultant force using the M-O method with 100% PGA. Figure4.6 shows that the corresponding heights of application of the maximum resul-tant forces on all the walls subjected to 14 ground motions are consistently aroundmid-height of the wall.540 10 20 30 40 50 6020040060080010001200Time (sec)Resultant Force (kN)modified M−O, 100% PGAG1100% PGA0 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG20 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG30 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG40 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG50 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG60 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG70 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG80 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG90 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG10Figure 4.3: Continued.550 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG110 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG120 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG130 10 20 30 40 50 6020040060080010001200Time (sec)Res. Force (kN)modified M−O, 100% PGA100% PGAG14Figure 4.3: Time histories of the resultant lateral earth force of the wall de-signed for 100% PGA subjected to 14 ground motions, compared withthe corresponding PAE calculated from the modified M-O method.0 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGAG1100% PGA0 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG20 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG30 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG40 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG50 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG6Figure 4.4: Continued.560 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG70 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG80 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG90 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG100 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG110 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG120 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG130 10 20 30 40 50 600.20.30.40.50.6Time (sec)Center of Res. Forcemodified M−O, 100% PGA100% PGAG14Figure 4.4: Time histories of the normalized height of application of the lat-eral earth force from the base of the wall designed for 100% PGA sub-jected to 14 ground motions, compared with the corresponding PAE cal-culated from the modified M-O method.57G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12 G13 G1440060080010001200  Max res. force (kN) 100% PGAmodified M−O, 100% PGAFigure 4.5: Maximum resultant lateral earth forces on the walls designed for100% PGA subjected to 14 ground motions, compared with the corre-sponding PAE values calculated from the modified M-O method usingthe same fraction of PGA.G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12 G13 G140.20.30.40.50.6   Center of res. force 100% PGA modified M−O, 100% PGAFigure 4.6: The normalized heights of application of the maximum resultantlateral earth forces from the base of the wall designed for 100% PGAsubjected to 14 ground motions, compared with the corresponding nor-malized heights of application of PAE from base of the wall calculatedfrom the modified M-O method using the same fraction of PGA.Figure 4.7 shows the distribution of the maximum lateral earth pressures alongthe height of the wall at different times during ground motion excitation. Themaximum value of the lateral earth pressure that each element located at specificheight of the wall is experienced during the ground motion shaking in this study is5805101505010015020025030002.75.48.111.7 Time (sec)Pressure (kPa) Height of the wall (m)20406080100120140160180Figure 4.7: Distribution of the maximum envelope of the lateral earth pres-sure along the height of the basement wall designed for 100% codePGA subjected to earthquake ground motion G1 (only the first 15 secresponse is illustrated).referred to as the “maximum envelope” of earth pressure. Similarly the minimumlateral earth pressure along the height of the wall during excitation is referred to asthe “minimum envelope”. The distribution of the pressure at the end of excitationis known as the “residual”.Figure 4.8 shows the average of the maximum envelopes, average of the min-imum envelopes, and the residual lateral earth pressures along the height of thebasement walls designed for different factions of code PGA and subjected to groundmotions G1–G14. The instantaneous distributions of earth pressure at differenttimes during the shaking event fall between the maximum and the minimum en-velopes. Three particular cases of these instantaneous distributions of earth pres-59sure are: (1) the residual pressures at the end of shaking as is shown in Figure 4.8,(2) the static lateral pressure at the beginning of the dynamic analysis as illustratedin Figure 4.9 and (3) the pressures at the instance of occurrence of the maximumresultant lateral earth force shown in Figure 4.10.Figure 4.9 shows the averages of pressure distribution at the beginning of dy-namic analysis of the walls designed for different fractions of code PGA subjectedto ground motions G1–G14. In this figure the averages of pressure distributionis compared with the suggested distribution of lateral pressures from Coulomb’sstatic theory (black dashed line). It can be concluded from this figure that the com-putational analyses results at t = 0 sec adequately match those obtained from theCoulomb’s theory for static lateral earth pressure distribution and distributed ap-proximately linearly with depth prior to earthquake and the computational modelsimulates the static condition properly.The averages of pressure distribution patterns at the instance of occurrence ofmaximum resultant lateral force for ground motions G1–G14 are shown in Fig-ure 4.10. The corresponding linear distributions of the total active lateral pres-sure (pAE) used in seismic design of the walls, calculated from the modified M-Omethod using the same fraction of PGA (Figure 3.2), are also plotted for compar-ison. In case of the weaker walls designed for 50% to 60% of the code PGA, thedynamic pressure distributions at the instance of maximum resultant force are dif-ferent from the pressure distributions calculated from the modified M-O methodused in the design of the walls. In these walls the distributed pressures on the wallsat the instance of occurrence of the maximum resultant lateral earth force are moreconcentrated at the floor levels than between the floor levels. The flexibility andyielding of these weaker walls at different locations along their height result in avery different displacement pattern compare to the stronger ones (90% and 100%PGA).Figure 4.10 shows that when the wall is designed for any fraction less that100% PGA based on the modified M–O procedure but still subjected to groundmotions corresponding to the full current seismic demand, the design pressure un-derestimates the average of the actual soil pressure acting on the wall. The per-formance of the basement walls depend on what happens between floor levels andthe dynamic pressures on the more flexible walls do not violate the performance60Avg. of Max. EnvelopesAvg. of Min. EnvelopesAvg. of ResidualsModified M-O method0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)50% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)60% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)70% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)80% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)90% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)100% PGAFigure 4.8: Average of maximum envelopes, average of minimum envelopes,and residual lateral earth pressures for ground motions G1–G14, alongthe height of the walls designed for different fractions of the code PGA,compared with the corresponding pAE calculated from the M-O methodfor the same fraction of PGA used for design of each wall.61Numerical simulation Coulomb method0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)50% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)60% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)70% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)80% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)90% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)100% PGAFigure 4.9: Average of static pressures prior to the dynamic analysis forground motions G1–G14, along the height of the walls designed fordifferent fractions of the code PGA, compared with the correspondingpA calculated from the Coulomb static theory.62Numerical simulation Modified M-O method0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)50% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)60% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)70% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)80% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)90% PGA0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)100% PGAFigure 4.10: Average of pressure patterns at the instance of occurrence ofmaximum resultant lateral earth force for ground motions G1–G14,along the height of the walls designed for different fractions of thecode PGA, compared with the corresponding pAE calculated from theM-O method for the same fraction of PGA used for design of eachwall.630 10 20 30 40 50 60−600−3000300600Time (sec)Shear stress (kPa) t=4.15 sect=5.37 sec(a)0 40 80 120 160 20002.75.48.111.7Pressure (kPa)Height (m)  t=4.15 sect=5.37 sec(b)Figure 4.11: (a) Shear stress time history corresponding to earthquake groundinput motion G1 and (b) the lateral earth pressure distributions at theinstances of the maximum shear stress along the height of the basementwall designed for 50% PGA; black-dashed lines represent the averageof the maximum and minimum envelopes of the lateral earth pressuresfor ground motions G1–G14.criteria, which is related to the mid-level deflections between floors as will be pre-sented and discussed later on. The results also show that near the base of the wallsthe pressures are generally higher than the corresponding modified M–O pressures,and that might be attributed the higher lateral restraint at the base and the fact thatthe foundation of the wall is embedded in the second stiffer layer, which signifi-cantly affects the displacement pattern on the wall.There might be a hypothesis that the maximum pressure on the wall occurs atthe time of the maximum shear stress applied at the base of the model. Figure 4.11illustrates the earth pressure distribution along the height of the wall subjected toground motion G1 at t = 4.15 sec and t = 5.37 sec, which the shear stress time his-tory reaches its maximum values at different directions. It can be concluded fromthis figure that the maximum shear base and the maximum pressure on the wall donot happen simultaneously. Besides, the size and the shape of the earth pressuredistribution change over time, which is in contrast with hypothetical condition ofthe Mononobe-Okabe method that assumes the earth pressure distribution does notchange with time.644.3 Bending moments and shear forces on the wallFigures 4.12 and 4.13 show the average of the maximum and minimum bendingmoment and shear force envelopes, and the residual bending moments and shearforces, for ground motions G1–G14. In both of these figures the results are shownfor the wall designed for six different fractions of the code PGA. The correspond-ing profiles of nominal moment capacity Mn(z) and shear capacity Vn(z) for eachwall as discussed and calculated in Section 3.2 are illustrated in these figures forcomparison.Yielding occurs where the seismic moment or shear envelopes reach the mo-ment or shear capacities, respectively. Figure 4.12 shows that the strong walls,designed for 100% down to 80% of the code PGA, almost remain elastic at allbasement wall levels. They barely yield in moment at the mid-height of the base-ment level -4 and at the floor of basement levels -3 and -2 (basement level No. is inaccordance with Figures 3.1 and 3.2). However, the walls designed for lower per-centages of PGA (70% to 50%) show more significant signs of yielding in momentat different elevations. The weakest wall, designed for 50% PGA, shows significantyielding at the mid-height of the basement level -1. It also shows signs of yieldingat the mid-height of the basement level -4 and at the floor of basement levels -1, -2,and -3.The shear envelopes in Figure 4.13 show that in all cases the shear demand isconsiderably less than the shear capacity along the height of the wall.4.4 Displacements and drift ratios on the wallGiven that the weaker walls yield in moment in various elevations along theirheight, from the engineering performance-based design standpoint it is very im-portant to monitor the resulting deformations and drift ratios of the walls, whichcan be considered as representative parameters for assessing the performance of astructure.The deformations are calculated as displacements of the wall at each eleva-tion relative to the base of the wall. To the best knowledge of the author, exceptfor a recommendation by the ASCE Task Committee on Design of Blast-ResistantBuildings in Petrochemical Facilities (ASCE-TCBRD, 2010), there is no other sig-65Avg. of Max. EnvelopesAvg. of Min. EnvelopesAvg. of ResidualsMoment Capacity−150 −100 −50 0 50 100 15002.75.48.111.7Moment (kN−m/m)Height (m)50% PGA−150 −100 −50 0 50 100 15002.75.48.111.7Moment (kN−m/m)Height (m)60% PGA−150 −100 −50 0 50 100 15002.75.48.111.7Moment (kN−m/m)Height (m)70% PGA−150 −100 −50 0 50 100 15002.75.48.111.7Moment (kN−m/m)Height (m)80% PGA−150 −100 −50 0 50 100 15002.75.48.111.7Moment (kN−m/m)Height (m)90% PGA−150 −100 −50 0 50 100 15002.75.48.111.7Moment (kN−m/m)Height (m)100% PGAFigure 4.12: Average of maximum envelopes, average of minimum en-velopes, and residual bending moments for ground motions G1–G14,along the height of the walls designed for different fractions of thecode PGA, compared with the corresponding nominal moment capac-ity, Mn(z), of each wall.66Avg. of Max. EnvelopesAvg. of Min. EnvelopesAvg. of ResidualsShear Capacity−200 −100 0 100 20002.75.48.111.7Shear (kN/m)Height (m)50% PGA−200 −100 0 100 20002.75.48.111.7Shear (kN/m)Height (m)60% PGA−200 −100 0 100 20002.75.48.111.7Shear (kN/m)Height (m)70% PGA−200 −100 0 100 20002.75.48.111.7Shear (kN/m)Height (m)80% PGA−200 −100 0 100 20002.75.48.111.7Shear (kN/m)Height (m)90% PGA−200 −100 0 100 20002.75.48.111.7Shear (kN/m)Height (m)100% PGAFigure 4.13: Average of maximum envelopes, average of minimum en-velopes, and residual shear forces for ground motions G1–G14, alongthe height of the walls designed for different fractions of the codePGA, compared with the corresponding nominal shear capacity, Vn(z),of each wall.67nificant report presented in the literature on the acceptable drift ratios for con-strained walls with distributed lateral loading.The ASCE-TCBRD (2010) introduced hinge rotation at support of beams,slabs, and panels as a measure of member response that indicates the degree ofinstability present in critical areas of the member. In the search for an appropriateperformance level, and in the absence of any other reported criteria, the recom-mendations of the ASCE task committee is adopted as the performance standardfor the walls. To this end, and consistent with the concept of hinge rotation at sup-port, the drift ratio of a basement wall at the middle of each storey is calculated asthe difference between the displacement of the wall at that level and the averagedisplacements of the wall at the top and bottom of the storey divided by half ofthe storey height, as illustrated in Figure 4.14. In this figure, h is the floor height,ufloor,top and ufloor,bottom are the wall deformations at the floor levels, and uwall is thewall deformation at the mid-height of the storey.ufloor,topufloor,bottomuwallh Drift ratio =2uwall − (ufloor,top + ufloor,bottom)hFigure 4.14: Definition of drift ratio for each level of the basement wall.The ASCE committee specified two performance categories that may apply tobasement walls: low and medium response categories. The Low Response Cate-gory is defined as: “Localized component damage. Building can be used, howeverrepairs are required to restore integrity of structural envelope. Total cost of re-pairs is moderate”. The Medium Response Category is defined as: “Widespreadcomponent damage. Building should not be occupied until repaired. Total costof repairs is significant.” The response limits associated with these two responsestates for “reinforced concrete wall panels (with no shear reinforcement)” are 1◦hinge rotation at support (hence 1.7% drift ratio) and 2◦ hinge rotation at support68(hence 3.5% drift ratio). The Low Response Category defined above is used as theperformance criterion in the present study. Separate calculations were also con-ducted using standard procedure for calculating curvature demand in reinforcedconcrete (Park and Pauly, 1975) by SEABC structural Engineers (Appendix A).The results suggested that even a slightly greater drift ratio could be adopted as theperformance criterion safely (DeVall and Adebar, 2011).Profiles of wall deformations (displacements relative to the base of the wall)and the associated drift ratios are shown in Figures 4.15 and 4.16, respectively.These figures show the average of maximum envelopes, average of minimum en-velopes, and the residual lateral deformations and drift ratios for ground motionsG1–G14, along the height of the 4-level basement wall designed for different frac-tions of the code PGA. The relative displacements are larger between the floorsand are smaller at each floor level. According to the adopted performance crite-rion for drift ratio, only the response of the top level of the basement wall in thepresent problem needs careful consideration. Figure 4.16 shows that for the wallsdesigned for 60% and 50% of the code PGA, the average of maximum envelopes ofdrift ratios in the top basement level for ground motions G1–G14 are about 0.5%and 1.1%, respectively, which fall into the low response category (< 1.7%). Atother levels of the basement wall the drift ratios are insignificant. These resultssuggest that the performance of the wall designed for even 50% of the code PGAfor Vancouver seems adequate.All the results presented so far were based on information regarding to the left-side walls. The right-side walls undergo almost the same performance as the left-side walls. The average of the maximum envelopes of drift ratios along the heightof the both right-side and the left-side walls designed for different fractions of thecode PGA, are presented in the left-hand-side column of Figure 4.17. In theseplots the solid line corresponds to the average of the maximum drift ratio alongthe height of the both right-side and left-side walls subjected to 14 crustal groundmotions (G1–G14) spectrally matched to the NBCC (2010) hazard level. By as-suming normally distributed drift ratios, average ±1σ represents the first standarddeviation with a 68% chance that the mean falls within the range of standard error.Right-hand-side column of Figures 4.17 illustrates a detailed information re-garding to the distribution of the maximum drift ratios along the height of the wall69Avg. of Max. EnvelopesAvg. of Min. EnvelopesAvg. of Residuals0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)60% PGA0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)70% PGA0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)80% PGA0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)90% PGA0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)100% PGAFigure 4.15: Average of maximum envelopes, average of minimum en-velopes, and residual lateral deformations (displacements relative tothe base of the basement wall) for ground motions G1–G14, along theheight of the walls designed for different fractions of the code PGA.70Avg. of Max. Drift ratioAvg. of Min. Drift ratioAvg. of Residual Drift ratio−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)80% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)90% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGAFigure 4.16: Average of maximum envelopes, average of minimum en-velopes, and residual drift ratios for ground motions G1–G14, alongthe height of the walls designed for different fractions of the code PGA.71in the form of exceedance probability. Each point in these plots corresponds tothe maximum drift ratio of the right-side and the left-side walls subjected to oneground motion. Exceedance probability presented in the y-axis is the probabilityof an event being greater than or equal to a given value; e.g., in the case of thewall designed for 50% PGA, there is a 40% chance that the maximum drift ratioexceeds 1.2%. In these figures the value of the center of the distribution is the driftratio at which the curve crosses the 50% line from the vertical axis and representsan average value of the response.4.5 Sensitivity analysesA series of sensitivity analyses are conducted to identify sensitive or important in-put parameters and study their effects on the seismic performance of the basementwall. The nonlinear dynamic response of the wall in the present soil-structure sys-tem can be assessed in many ways. As it is not possible to cover all aspects of theseismic performance results, it is decided to only focus on the maximum drift ratioof the wall, which has the greatest significance for engineering design and can beevaluated based on an adopted performance criterion.The results presented in this section cover the sensitivity analyses on the em-ployed shear wave velocity, friction and dilation angles of the backfill soil, themodulus reduction factor (G/Gmax), the Rayleigh damping ratio (D) for the topsoil layer, applied shoring pressure during excavation process and also the prop-erties of the interface element between soil and the basement wall. In all theseanalyses, the wall is designed for 50% of the code PGA and is subjected to theselected 14 crustal ground motions spectrally matched to NBCC (2010) UHS forVancouver (G1–G14). Based on these sensitivity analyses, the parameters whichhave more effect on the seismic performance of the basement walls are determinedand discussed in more detail in Chapter 5.4.5.1 Soil–wall interface elementWall response is found to be sensitive to the interface friction angle, as shownin Figure 4.18. In all the analyses presented so far, an interface friction angle ofδ = 10◦ (' φ/3) based on a judgment of local consultants is used. Two additional72Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)60% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)70% PGAFigure 4.17: Continued.73−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)80% PGA0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)80% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)90% PGA0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)90% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGA0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)100% PGAFigure 4.17: (Left-hand-side column) Average of maximum envelopes ofdrift ratios and the corresponding average ± one standard deviationalong the height of the wall;(right-hand-side column) distribution ofthe maximum drift ratios in the form of exceedance probability of thewalls designed for different fractions of the code PGA, subjected toground motions G1–G14 spectrally matched to NBCC (2010) UHSfor Vancouver.74sets of analyses are conducted, with δ = 5◦ and 15◦, to check the sensitivity of wallresponse to interface friction angle. As expected higher values of interface frictionangle lead to smaller wall drift ratios. An additional analyses are conducted tocheck the importance of allowing soil–wall slippage and separation. To this aim aseries of analyses are conducted in which opposite nodes are not allowed to sepa-rate from each other and consequently no slippage or opening is allowed along theinterface element. The results of these simulation show that considering interfaceslippage and separation is crucial for realistic evaluation of wall performance.No Interface No slip/opening δ=5° δ=10° δ=15°−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)Figure 4.18: Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50% the codePGA, subjected to ground motions G1–G14 showing the sensitivity ofresponse to variation of the friction angle of the soil–wall interface ele-ment, including the case where no slippage and/or opening is allowed.Sensitivity analyses show that the drift ratios are not sensitive to elastic normaland shear stiffnesses of the interface element (kn and ks), even if these values areincreased or decreased by ten times as illustrated in Figure 4.19. This is consistentwith the conclusion of Day and Potts (1998).75kn=9x105 kPa/m kn=9x106 kPa/m kn=9x107 kPa/m−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)ks=9x105 kPa/m ks=9x106 kPa/m ks=9x107 kPa/m−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(c)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(d)Figure 4.19: Average of maximum envelopes of (a,c) lateral deformationsand (b,d) drift ratios along the height of the wall designed for 50% thecode PGA subjected to ground motions G1–G14, showing the lack ofsensitivity of response to variation of the normal and shear stiffnessesof the soil–wall interface element.4.5.2 Dilation angle of the backfill soilThe angle of dilation controls an amount of plastic volume change over plasticshear strain. The soil in the current study is modeled using the non-associativeflow rule by adopting a dilation angle of ψ = 0◦ in the Mohr–Coulomb model,76which corresponds to the volume preserving deformation in shear. For soils thedilatancy angle is known to be significantly smaller than the friction angle.In this section the importance of the soil dilation angle and its influence onthe seismic performance of the basement walls are examined. The importance ofdilation angle is determined by examining two additional dilation angles of ψ = 5◦and ψ = 10◦.A series of sensitivity analyses are conducted on the 4-level basement walldesigned for 50% PGA and subjected to ground motions G1–G14. The result ofthese analyses presented in Figure 4.20 show the lack of sensitivity of the walldisplacements and drift ratios to the change in the dilation angle of the top soillayer between zero and 10◦. =0! =5! =10!−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)Figure 4.20: Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50% the codePGA subjected to ground motions G1–G14, showing the lack of sen-sitivity of the response to variation of top soil dilation angle.4.5.3 Friction angle of the backfill soilThis section evaluate the effect of slightly change (± 5◦) in the friction angle of thebackfill soil, which was assumed as 33◦ in the benchmark analyses. The results of77this study presented in Figure 4.21 confirm that there is not a considerable effecton the performance of the structure if the wall is embedded in a backfill soil withslightly higher or lower friction angles of 28◦ and 38◦. =28! =33! =38!−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)Figure 4.21: Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50% the codePGA subjected to ground motions G1–G14, showing the lack of sen-sitivity of the response to variation of top soil friction angle.4.5.4 Shear wave velocity of the backfill soilThe normalized shear wave velocity (Vs1) of the top soil layer was assumed to be200 m/s in the benchmark analyses. The value of Vs1 = 200 m/s was recommendedby the geotechnical engineers in practice for Vancouver. In order to study the effectof the top soil layer stiffness, the performance of the basement wall embedded intwo other soil profiles with the normalized shear wave velocities of 150 m/s and250 m/s at their top soil layer are studied. The resulting two different profiles ofthe shear wave velocity in the first soil layer as well as the shear wave velocityprofile of the second layer corresponding to Vs1 = 400 m/s are presented in Fig-ure 4.22. Following the procedure described in Section 3.3.4 for calculating theequivalent modulus reduction and damping ratios from the SHAKE analyses, Ta-ble 4.1 presents the calculated G/Gmax and damping ratios correspond to two new78soil profiles. It is worth to mention that the values of interface stiffnesses which arethe function of the stiffness of the stiffest neighbouring zones (See Equation 3.6)along the interface elements are also modified accordingly in these analyses.Vs1=150 m/s Vs1=200 m/s Vs1=250 m/s0 200 400 600 800−24.3−12.150Shear wave velocity (m/s)Depth of the model (m)Layer 1Layer 2Vs1=400 m/sFigure 4.22: Different scenarios of the shear wave velocity profiles of the soilalong the depth of the model.Table 4.1: Soil modulus reduction and damping ratios obtained from SHAKEanalyses for different normalized shear wave velocities of top soil layer.Vs1 (m/s) Modulus reduction, G/Gmax Damping ratio, D (%)Layer 1 Layer 1 Layer 2 Layer 1 Layer 2150 0.25 0.84 11.5 2.5200∗ 0.41 0.81 8.0 3.0250 0.60 0.79 6.0 3.3∗ Calcultaed from Figure 3.8 and used for the benchmark analyses.Simulations are conducted based on the corresponding elastic shear modulusand the Rayleigh damping ratios applied to two levels of Vs1 at the top soil layerfor the wall designed for 50% of the code PGA excited by ground motions G1–G14. The resultant average of the maximum envelopes of lateral deformationsand drift ratios for each value of Vs1 are presented in Figure 4.23. The results ofthe benchmark analyses with Vs1 = 200 m/s are also added for comparison. This79figure suggests considerable sensitivity of the results to the shear wave velocity ofthe top soil layer, based on the adopted method of analysis. As illustrated in thisfigure, increasing the shear wave velocity in the top soil layer decreases the driftratio of the wall. The sensitivity analysis shows that a Vs1 = 150 m/s, which mightbe a bit low for the high-rise construction sites in Vancouver, results in a maximumdrift ratio of about 2.5% in the basement wall. This is still in the lower range of themedium response category, as defined by ASCE-TCBRD (2010).Vs1=150 m/s Vs1=200 m/s Vs1=250 m/s−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)Figure 4.23: Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50% the codePGA subjected to ground motions G1–G14, showing the sensitivity ofresponse to variation in the normalized shear wave velocity of the topsoil layer.Due to the considerable amount of sensitivity of the resultant maximum driftratio of the basement wall to the shear wave velocity profile of the site, an extensivestudy on the effect of underlying soil stiffness is conducted in Chapter 5.4.5.5 Modulus reduction and Rayleigh dampingIn the benchmark analyses presented in Sections 4.2 to 4.4, the top soil layer wasmodeled using an average value of G/Gmax = 0.41 and D = 8%. Additional anal-yses are conducted on two additional modulus ratios, G/Gmax = 0.3 and 0.5 both80with D = 8%, and with two additional levels of damping D = 6% and 10% bothwith G/Gmax = 0.41, on the weakest wall designed for 50% of the code PGA andsubjected to 14 ground motions (G1–G14).G/Gmax=0.3 G/Gmax=0.41 G/Gmax=0.5−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)Figure 4.24: Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50% the codePGA subjected to ground motions G1–G14, showing the sensitivity ofthe response to variation in the modulus reduction of the top soil layer.Figures 4.24 and 4.25 show the sensitivity of the maximum envelope of lateraldeformations and drift ratios to variations of the modulus reduction and dampingratios of the first soil layer, respectively. These results suggest that lower values ofG/Gmax and damping result in higher wall drift ratios.The fact that the results produced using Mohr–Coulomb model with an addi-tional modulus reduction factor and Rayleigh damping are sensitive to the selectionof G/Gmax and damping values suggests that the seismic performance of the base-ment walls may be dependent on the nature of the stress–strain response of the soilmaterial and using more representative constitutive model could be helpful. Theinfluence of more advanced nonlinear constitutive model with hysteresis dampingon seismic performance of the embedded basement walls is examined in Chapter 5.81D=6% D=8% D=10%−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)Figure 4.25: Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50% the codePGA subjected to ground motions G1–G14, showing the sensitivity ofthe response to variation in the damping ratio of the top soil layer.4.5.6 Shoring pressure during excavation stageIn most cases deep building basement walls are constructed in open excavationsthat are generally shored, which cause the retained soils to be in a yielded (active)conditions already. For this reason in all the results presented so far it was assumedthat during excavation stage of analysis the wall is free to move outward and thesoil mass moves sufficiently to mobilize its shear strength. Therefore, in modelingthe construction sequence of the basement walls in benchmark analyses, the ac-tive earth pressure coefficient (KA) has been used to calculate the applied shoringpressure to restrain the soil during excavation.In some cases where surface settlements adjacent to the excavation are of con-cern, a shoring system providing restraint equivalent to at-rest earth pressure (Ko)rather the active earth pressure (KA) could be appropriate. For this purpose an ad-ditional analyses are conducted using at rest shoring pressures, which causes thewall to experience no lateral movement during the excavation stage of analyses.This typically occurs when the wall is restrained from movement, such as along a82basement wall that is restrained at the bottom by a slab and at the top by a floorframing system prior to placing soil backfill against the wall. Geotechnical practi-tioners have traditionally calculated the at-rest earth pressure coefficient, Ko againstnon-yielding walls using Jaky (1944) equation:Ko = 1−Sin(φ) (4.1)Where Ko is the at-rest earth pressure coefficient and φ is the angle of internalfriction of the soil. Result of the analyses presented in Figure 4.26 suggests that thedisplacement and drift response of the wall in the present problem are not sensitiveto the applied shoring pressures during the excavation stage of analysis, being setto either the active or the at-rest pressures.k0kA−0.02 0 0.02 0.04 0.06 0.0802.75.48.111.7Deformation (m)Height (m)50% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b)Figure 4.26: Average of maximum envelopes of (a) lateral deformations and(b) drift ratios along the height of the wall designed for 50% the codePGA subjected to ground motions G1–G14, showing that the resultsare not sensitive to the initial shoring pressure during excavation stage.83Chapter 5Additional studies on soilproperties and wall geometriesNo amount of experimentation can ever prove me right; a singleexperiment can prove me wrong.— Albert Einstein (1879–1955)5.1 IntroductionThe importance of Soil–Structure Interaction (SSI) in dynamic analysis has beenwell known and well established during the past decades and several literaturescovered the computational and analytical approaches to solve these problems. Thedynamic response of structures supported on soft soil deposits are completely dif-ferent than the response of a similarly excited, identical structures supported onstiff ground due to their different dynamic characteristics.In this Chapter the effects of dynamic soil–structure interaction on seismic per-formance of the basement walls and the resultant lateral structural response arestudied in order to provide guidance on the selection of an appropriate fraction ofthe NBCC (2010) PGA to be used in the M-O analysis. The maximum resultantdrift ratio of the basement wall is selected as a parameter for evaluating the seismicperformance of the basement walls due to its greatest significance for engineer-ing design. The seismic performance of the basement walls are re-evaluated using84more representative constitutive model instead of the simple elastic–perfectly plas-tic Mohr–Coulomb model. Two additional wall geometries including (1) a 4-levelbasement wall with a higher 5.0 m top storey (instead of the 3.6 m height whichwas used in benchmark analyses in Chapters 3 and 4) with a total height of 13.1 mand (2) a 6-level basement wall with a total height of 17.1 m are selected. Eachwall is founded on various NBCC (2010) site class D soil profiles. The nonlineardynamic response of the basement walls have been compared and discussed andfurther evidences for evaluating the recommended fraction of the code mandatedPGA used in the M–O method in order to achieve an acceptable seismic perfor-mance of basement walls are presented.5.2 Nonlinear stress-strain characteristics of soilIt is now standard practice in seismic engineering to take into consideration thenonlinear behavior of soils undergoing time-varying deformations caused by earth-quake ground motions. Among different soil models that could be used in the firstset of analyses, the linear elastic–perfectly plastic Mohr–Coulomb model was cho-sen because it is simple and has been widely used locally by practitioners. Theaforementioned procedure conducted in SHAKE for estimating a modulus reduc-tion factor (G/Gmax) and damping ratio (D) used in the elastic range of Mohr–Coulomb model in FLAC analysis is normally followed by the prominent geotech-nical analyst in Vancouver.In this procedure as outlined in Section 3.3.4, the upper-bound modulus reduc-tion curve and the lower-bound damping curve of Seed et al. (1986) were used todevelop the strain–compatible shear modulus reduction and Rayleigh damping val-ues, which were used in the elastic portion of the Mohr–Coulomb model. For thispurpose the equivalent linear analyses of the free-field soil column were conductedin SHAKE to calculate the equivalent G/Gmax and damping ratio for each soil lay-ers. These average equivalent modulus reduction values were used for modifyingthe Gmax to G, at different depths of the model in the elastic range of the elastic-plastic Mohr–Coulomb model. Similarly, the equivalent damping ratios for eachlayer were added to the nonlinear analyses of the soil-structure system in the formof Rayleigh damping.85This approach is an attempt to approximate the actual stress–strain response ofthe soil material, following the current state of practice, and is crude, especiallywhen there are significant nonlinearity effects. In this section the seismic perfor-mance of the basement walls using the more representative advanced nonlinearconstitutive model, UBCHYST (Naesgaard, 2011), are examined.5.2.1 Description of the UBCHYST soil modelThe behavior of soil material under seismic loading is nonlinear and depends onseveral factors such as intensity of loading, duration of loading, soil type, and in-situ soil condition. Soil constitutive models have been used to characterize thenonlinear hysteretic soil behavior by linking the strain and stress increments. Con-stitutive models are used to simplify the description of the material response whilestill being representative of the real behavior of the soil. In most of these modelsthe equivalent secant shear modulus and viscous damping are the parameters whichhave been used for characterization. Secant shear modulus normalized by maxi-mum shear modulus decreases by increasing the cyclic shear strain, whereas theamount of damping, which is a measure of the energy dissipation in one loadingcycle, increases with increasing magnitude of shear strain.The relatively simple total stress model, UBCHYST, was developed at the Uni-versity of British Columbia (UBC) for dynamic analyses of soil subjected to earth-quake loading. This model was implemented in the two-dimensional finite dif-ference program FLAC (Itasca, 2012) as a FISH source by Naesgaard and Byrne(Naesgaard, 2011). Later on, in order to speed up the computations time, the FISHsource code was converted to C++ and compiled as a DLL file by a group of re-searchers at UC–Berkeley (Geraili Mikola, 2012). In the current study the DLL fileis used for conducting the nonlinear simulations in FLAC, which is provided bythe Itasca website (User Defined constitutive Models (UDM) for the Itasca codes,2015).The UBCHYST model is intended to be used with undrained strength param-eters in low permeability clayey and silty soils, or in highly permeable granularsoils, where excess pore water could dissipate as generated (Naesgaard, 2011).This model simulates non-linear cyclic behavior including shear modulus degra-86Figure 5.1: UBCHYST model (Naesgaard, 2011).dation with shear strain and strain-dependent damping ratio. The tangent shearmodulus (Gt) is a function of the peak shear modulus, Gmax, times reduction fac-tors, which are a function of the developed stress ratio and the change in stressratio to reach failure as are shown in Figure 5.1 and Equation 5.1. In this equationthe tangent shear modulus varies through-out the loading cycle to give hystereticstress–strain loops of varying amplitude and area (damping) through-out the earth-quake excitation.Gt = Gmax× (1− ( η1η1 f )n1×R f )n×mod1×mod2 (5.1)where,η = stress ratio (τxy/σ ′v),η1 = change in stress ratio η since last reversal (η−ηmax),ηmax = maximum stress ratio (η) at last reversal,η1 f = change in stress ratio to reach failure envelope in direction of loading (η f −ηmax),η f = sin(φ f )+ cohesion× cos(φ f )/σ ′v,τxy = developed shear stress in horizontal plane,σ ′v = vertical effective stress,φ f = peak friction angle,87n1, R f and n = calibration parameters,mod1 = a reduction factor for first-time or virgin loading which typically has avalue between 0.6 to 0.8,mod2 = optional function to account for “permanent” modulus reduction with largestrain which is defined as (1− ( η1η1 f )rm)×d f ac≥ 0.2.In this model the stress reversals occur when the absolute value of the devel-oped stress ratio (η) is less than the previous value and a cross-over occurs if τxychanges sign. A stress reversal causes η1 to be reset to 0 and η1 f to be re-calculated.The UBCHYST model has been combined with the Mohr–Coulomb failurecriteria and incorporated into FLAC as a user defined constitutive model. In thismodel the magnitude of the stress ratio is limited by a Mohr–Coulomb failure enve-lope in high shear strains as such the shear strength of the soil materials estimatedby UBCHYST model is consistent with estimates using Mohr–Coulomb model asis shown in Figure 5.2. This figure shows typical responses of the Mohr–Coulomband UBCHYST models in a cycles of simple shear test.The Mohr–Coulomb model captures hysteretic load-unload behavior if plas-ticity occurs. The advantage of UBCHYST model over a simpler Mohr–Coulombmodel is the nonlinear hysteretic loops developed by varying the tangent shearmodulus during loading and unloading. This model replicates the behavior of realsoil and reduces the necessity of defining G/Gmax and Rayleigh damping as withthe simple Mohr–Coulomb model.5.2.2 Calibration of UBCHYST input parametersNumber of empirical relations (i.e., shear modulus reduction and damping ratiovariation with cyclic shear strain) have been published by several researches for awide range of soils in order to estimate seismic site response in soil deposits. Dif-ferent soil parameters such as strain amplitude, mean effective confining pressure,soil type, plasticity, and void ratio influence the dynamic properties of the soil. Forcohesionless soils, which is the focus of this study, the variation of dynamic curveswith change in soil properties is small and therefore, it is assumed that modulusdegradation and damping curves fall within a narrow range for most cohesionless88−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−300−200−1000100200300Shear Strain (%)Shear Stress (kPa)(a)−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−300−200−1000100200300Shear Strain (%)Shear Stress (kPa)(b)−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−300−200−1000100200300Shear Strain (%)Shear Stress (kPa)(c)−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−300−200−1000100200300Shear Strain (%)Shear Stress (kPa)(d)Figure 5.2: Typical schematic stress–strain response of (a,c) Mohr–Coulomband (b,d) UBCHYST soil materials in a cyclic direct shear test in a caseof 0.2% and 1% maximum shear strains.soils (Hashash and Park, 2001; Seed and Idriss, 1970).The UBCHYST model was calibrated against modulus degradation and damp-ing curves published by Darendeli (2001). Figure 5.3 shows Darendeli (2001)normalized shear modulus and material damping curves corresponding to the co-hesionless sandy soils (PI=0) at different confining pressures (0.25 atm, 1 atm,4 atm, and 16 atm). In this figure both shear modulus and material damping varywith shear strain amplitude. The shape of the shear modulus reduction curve im-89Darendeli  !o=0.25 atmDarendeli  !o=1 atmDarendeli  !o=4 atmDarendeli  !o=16 atm10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)Figure 5.3: Normalized modulus reduction and material damping curves rec-ommended by Darendeli (2001) for different confining pressures for co-hesionless sandy soils with PI=0.parts valuable information regarding to the behavior of a soil, while the dampingcurve provides a complimentary plot of the rate of damping increases with shearstrain.Darendeli (2001) concluded that shear modulus and damping values are stress-dependent and lead to changes in shear modulus reduction and the material damp-ing curves. This effect had been also recognized by other researchers (Hardin andDrnevich, 1972; Hardin et al., 1994; Ishibashi and Zhang, 1993; Iwasaki et al.,1978; Kokusho, 1980; Laird and Stokoe, 1993). Figure 5.3 shows that increasingthe confining pressure results in a lower shear modulus degradation and dampingratio at a given cyclic shear strain.In calibration process, an initial estimate of each parameter is made at eachsoil layer based on a sensitivity analysis that has been computed. An elementcyclic simple shear test (CSS) using UBCHYST constitutive model is conductedin FLAC at different depth of the model over a range of strain levels, in order togenerate shear modulus and material damping curves corresponding to that specificconfining pressure.90Xvel XvelTop nodesconstrained to move together in X direction( x!,! y)Figure 5.4: Element cyclic simple shear (CSS) test in FLAC.As illustrated in Figure 5.4, an element cyclic simple shear test is simulated inFLAC by applying a constant x-velocity at the top nodes of an element while thebase nodes are fixed in both x and y directions. The total displacement resultingfrom applied x-velocity is limited by shear strain value. The top nodes are allowedto deform laterally until the developed shear strain at the top nodes become equalto the specified maximum value. Then, the x-velocity is reversed until the abso-lute value of shear strain is achieved in the opposite direction. This generates thefamiliar hysteresis loop associated with cyclic simple shear laboratory tests.The nonlinear shear stress versus shear strain response of soil under cyclicloading results in a hysteresis loop as illustrated in Figure 5.5(a). The tips of thehysteresis loops at different cyclic shear strain amplitudes create a locus of pointsforming the backbone curve. The hysteresis loop at different levels of shear straincan be characterized by its inclination and its breadth. The inclination of hysteresisloop depends on the soil stiffness, which is characterized by the secant shear mod-ulus as illustrated in Figure 5.5(a) at three different shear strain levels (G1, G2 andG3). The breadth of the hysteresis loop is related to the area inside the loop whichis a measure of energy dissipation in one cycle of oscillation and is described bythe damping ratio (D1, D2 and D3) in Equation 5.2:D =WD4piWs=12piAloopGγ2max(5.2)In this equation WD is the dissipated energy, Ws is the maximum strain energy91−0.3 −0.2 −0.1 0 0.1 0.2 0.3−300−200−1000100200300Shear Strain (%)Shear Stress (kPa)D2D3G1 G2 G3(a)10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/GmaxG1/GmaxG2/GmaxG3/Gmax(b)10−4 10−3 10−2 10−1 100051015202530Shear strain (%)Damping Ratio (%)D3D2D1(c)Figure 5.5: (a) The typical nonlinear shear stress versus shear strain responseof soil under cyclic loading for three different levels of shear strain,(b,c) shear modulus reduction and damping curves that characterize thenonlinear response of soil.92and Aloop is the area of the hysteresis loop.To relate a nonlinear stress–strain model to a measured modulus reduction anddamping curves, the nonlinear behavior of the soil in the form of hysteresis loopsat different strain levels are converted into the equivalent G/Gmax and dampingcurves. The slope of the backbone curve at the origin corresponds to the maxi-mum tangent shear modulus (Gmax) but at greater cyclic shear strain amplitudesthe modulus ratio (G/Gmax) will drop to values less than one. The variation ofshear modulus ratio with shear strain, which is represented by a modulus reductioncurve provides the same information as the backbone curve. As shown in Figures5.5(b,c) by increasing the shear strain, the modulus reduction (G/Gmax) decreasesand damping (D) increases.The values of normalized shear modulus and material damping are plotted ver-sus shear strain for 15 strain levels, ranging from 0.0001% to 1% shear strain.The nonlinear fitting parameters of UBCHYST soil model are selected such thatthe resultant equivalent modulus reduction and damping curves from the nonlin-ear model match the Darendeli (2001) laboratory test curves at different confiningpressures (Geraili Mikola, 2012; Jones, 2013).Input parameters for the UBCHYST model include the maximum shear mod-ulus (Gmax), bulk modulus (K), Mohr–Coulomb failure criteria parameters such ascohesion, friction angle, dilation angle and tensile strength and also a set of cali-bration parameters, which control the shape and the size of the stress–strain loops.The list of the parameters used in UBCHYST model are presented in Table 5.1.Figures 5.6 and 5.7 show a comparison of modulus reduction and dampingcurves from the empirical model of Darendeli (2001) with those from the UBCHYSTmodel at different depths of the first and the second layers. As illustrated inthese figures, the model overestimates the damping response at medium to large(> 0.1%) shear strains. This issue is common with nonlinear models and the rea-son for this overestimation of damping factor appears to be due to the shape ofthe modified stress–strain curve at large strains and has been pointed out beforeby many researchers (Callisto et al., 2013; Cundall, 2006; Geraili Mikola, 2012;Jones, 2013; Kottke, 2010; Ma´nica et al., 2014; Naesgaard, 2011).The UBCHYST model provides almost no energy dissipation at very low cyclicstrain levels, which may be unrealistic. In this study a small amount of Rayleigh93Table 5.1: Soil parameters of the UBCHYST constitutive model used inFLAC analyses.Parameter description Parameters Layer 1 Layer 2Unit weight (kN/m3) γ 19.5 19.5Cohesion (kPa) c 0 20Peak friction angle (deg) φ 33 40Dilation angle (deg) ψ 0 0Small strain shear modulus (MPa) Gmax 17-143 580-885Poisson’s ratio ν 0.28 0.28Stress rate factor R f 0.98 0.85Stress rate exponent n 3.3 2.0Stress rate exponent n1 1.0 1.5First cycle factor mod1 0.75 0.75Large strain exponent rm 0.5 0.5Large strain factor d f ac 0 0 !"#"$ !%&'(!)"*+#, )"#"$ !%&'(-'"*+#, .'"#"$ !%&.(!"*+#, .)"#"$ !%&.(/'"*+#,0*1234256  !%&'(!)"*+#0*1234256  !%&."*+#0*1234256  !%&7"*+#0*1234256  !%&.-"*+#10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)Figure 5.6: Variation of shear modulus and damping ratio with cyclic shearstrain amplitude at different depths of the first soil layer estimated byFLAC using UBCHYST model.94 !"#$#% !&'!(!"#)*$+ !,#$#% !&'!(-"#)*$+ ."#$#% !&'.(.,#)*$+ .,#$#% !&'.(/"#)*$+ 0"#$#% !&'0(,"#)*$+1)2345367  !&'"(!,#)*$1)2345367  !&'8#)*$1)2345367  !&'0#)*$1)2345367  !&'89#)*$10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)Figure 5.7: Variation of shear modulus and damping ratio with cyclic shearstrain amplitude at different depths of the second soil layer estimated byFLAC using UBCHYST model.damping (e.g., 0.5%) is used to provide damping in the analysis at very smallstrains and avoid low-level oscillation, where the hysteretic damping from the non-linear soil models is nearly zero.5.2.3 Simulation resultsA series of dynamic computational analyses are conducted to study the effect ofusing more representative constitutive model in seismic response of the basementwalls, in order to more appropriately simulate nonlinear stress–strain response ofthe soil medium.Figure 5.8 shows the maximum drift ratios along the height of the 4-level base-ment walls, designed for different fractions of code PGA and subjected to 14 crustalearthquake ground motions (G1–G14) spectrally matched to the hazard level inVancouver. In these analysis the UBCHYST soil model is used instead of the95Avg. of Max. Drift ratio Avg. ± 1σ−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGAFigure 5.8: Average of maximum envelopes of drift ratios ± one standarddeviation along the height of the 4-level basement wall, designed forfour different fractions of the code PGA subjected to 14 spectrallymatched crustal ground motions (G1–G14), using UBCHYST consti-tutive model.simple Mohr–Coulomb model for simulating the stress–strain response of the soilmedia. The red solid lines in these plots represent an average of the maximumdrift ratio of the both right-side and left-side walls subjected to 14 seismic events.Assuming normally distributed drift ratios, average ± one standard deviation (σ )shown by blue dashed lines represent the first standard deviation with a 68% chancethat the average value of response falls within the range of standard error.The exceedance probability of drift ratios for the basement walls designed for96different fractions of code PGA are presented in Figure 5.9. This figure illustratesa detailed information about the distribution of the resultant maximum drift ratioof the walls designed for different fractions of code PGA subjected to 14 crustalground motions in the form of exceedance probability. Each point represents themaximum value of the resultant drift along the height of the left-side and the right-side walls subjected to one out of 14 ground motions. As mentioned in Chapter4, the acceptance criterion for the basement walls is a drift ratio not larger than1.7% at any point along the height of the wall. Results shown in Figure 5.9 suggestthat even in the case of the weakest wall (designed for 50% PGA) none of the 14scenarios results in a drift ratio higher than acceptance criterion.The result of the analyses using more sophisticated and more representativeconstitutive model confirms the conclusion made based on using simple Mohr–Coulomb model (Figure 4.17) that the performance of the basement walls designedfor 50% to 60% of the code PGA for Vancouver and founded on relatively densesandy soil seem adequate. Also it can be concluded that for a hazard level of 2% in50 years in Vancouver, design to the associated PGA= 0.46 g may not be warrantedand leads to an over-conservative performance.0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)  50% PGA60% PGA70% PGA100% PGAFigure 5.9: Exceedance probability of drift ratio for 4-level basement wallsdesigned for different fractions of the code PGA subjected to 14 spec-trally matched crustal ground motions (G1–G14), using UBCHYSTconstitutive model.975.3 Local site conditionDuring an earthquake event, local amplification of strong ground motion by shal-low soft soil layers can have a large impact on the intensity of ground shakingaround the structure and consequently dynamic behavior of the soil–wall system.The site conditions in terms of geometrical and geological structures of the softersurface deposits affect the waves from the underlying stiff soil during wave trans-mission to the surface, so a structure supported on soft ground can have a com-pletely different behavior from the same structure supported on stiff soil or rocksubjected to an identical earthquake motion. Therefore, neither the structure norits underlying soil can act independently. This phenomenon is referred to as Soil–Structure Interaction (SSI) effect.Site amplification in some cases causes a bedrock outcrop motion to be am-plified about five times (Finn and Wightman, 2003) and can have devastating ef-fects on structures with periods close to the site period. Damage patterns in someearthquakes, such as the Mexico City, Mexico (1985), and Loma Prieta, California(1989) confirm the significant effect of site amplification on earthquake-induceddamages (Anderson et al., 1986; Holzer, 1994). The study by Holzer et al. (1999)of ground failure observations during the Northridge, California earthquake (1994)showed that the local subsurface conditions affect the overall dynamic response ofthe ground and may also help to explain localized variations in recorded groundmotions. Therefore, site condition and soil profile play important roles in estab-lishing seismic performance of basement walls and deserve an extra attention.As described in the geotechnical earthquake engineering literature (Das, 1992;Kramer, 1996; Towhata, 2008), local site conditions can affect a number of impor-tant characteristics of strong ground motions, such as an amplitude and a frequencycontent of a record. Ground motion amplification is mainly controlled by few pa-rameters such as:• the ratio of the predominant period of the applied motions to the fundamentalperiod of the system,• the relative stiffness between different soil layers characterized by the impedanceratio, α . The impedance of a soil layer is the mass density multiplied by the98shear-wave velocity of the material. Therefore, the impedance ratio is de-fined as α = ρtVst/ρbVsb, where ρ is the mass density, Vs is the shear wavevelocity and t and b refer to the top surface layer and bottom underlyinglayer, respectively, and• the strain amplitude level reached during a seismic event, which has a directimpact on the amount of modulus reduction and damping ratio.The local site condition has been addressed in the seismic provisions of mostbuilding codes (NBCC, 2005, 2010; NEHRP, 2003, 2009), and the average shearwave velocity of the top 30 m is recommended for site characterization. Recent edi-tions of the National Building Code of Canada (NBCC, 2005, 2010) quantified theamplification potential of site conditions by the use of foundation factors. As siteclassification is critical for seismic hazard assessment of underground structures,the NBCC (2005, 2010) categorizes site conditions into five major soil types, siteclass A (hard rock) to site class E (soft soil), based on time-averaged shear wavevelocity in the upper 30 m of a site (V s30). This classification scheme follows thatdeveloped by the National Earthquake Hazards Reduction Program provisions inthe United States (NEHRP, 2000, 2003, 2009). Its application to the NBCC isdescribed by Finn and Wightman (2003).A time-averaged shear wave velocity is calculated as the time for a shear waveto travel from a depth of 30 m to the ground surface. As shown in Equation 5.3, thetime-averaged V s30 is calculated as 30 m divided by the sum of the travel times forshear waves to travel through each layer. The travel time for each layer is calculatedas the layer thickness (hi) divided by the shear wave velocity associated with eachlayer, (Vs,i):V s30 =30∑i hi/Vs,i(5.3)In the benchmark analyses presented in Chapter 4, the chosen soil profile wassuggested by a group of geotechnical engineers as representative of the site con-dition relevant for high-rise construction in downtown Vancouver. In this sectionthe 4-level basement wall is founded on different soil profiles, with variation of theground shear wave velocities differentiating the cases. Seismic performance of the99basement wall in terms of drift ratio is evaluated. The selected soil profiles are in-tended to capture a range of practical scenarios, which address the effect of the soilprofiles with various stiffnesses and amplification factors as a result. This sectionis an attempt to account for two influential factors affecting seismic site response:• Depth to a stiff soil layer with a significant impedance contrast.• Stiffness of the soil layers underneath the structure and their correspondingimpedance contrast. A time-averaged shear wave velocity is adopted as ameasure of the overall site stiffness.11.7 m0.0 m!12.15 m0 200 400 600 800Shear wave velocity (m/s)Layer 1Vs1=200 m/sc=0 kPa"=33°Layer 2Vs1=400 m/sc=20 kPa"=40°11.7 m0.0 m 0 200 400 600 800Vb=670 m/sShear wave velocity (m/s)Layer 1Vs1=200 m/sc=0 kPa"=33°Layer 2Vs1=400 m/sc=20 kPa"=40°!24.3 m!12.15 m!40.0 mVb=590 m/sFigure 5.10: Schematic of the 4-level basement wall model with differentmodel depths (dimensions are not to scale).To simulate the top 30 m of the soil profile, the original depth of the modelin the benchmark analyses (24.3 m) is extended to 40.0 m, as illustrated in Figure5.10. A series of sensitivity analyses are conducted on the effect of the depth of themodel on the seismic performance of the embedded basement wall. By increasingthe depth of the model from 24.3 to 40.0 m, the shear wave velocity at the base ofthe model (Vb), which has been used for calculation of shear stress time histories(see Equation 3.7), increases from 590 to 670 m/s. Therefore, the applied shearstress time histories at the base of the 40.0 m model are about 13% stronger thanthose of a model with 24.3 m depth. The results of these tests, shown in Figure1005.11, suggest that depth of the model does not a have significant effect on theseismic performance of the embedded structures. Hereafter, the depth of 40.0 mwill be used in all the analyses.Avg. (24.3 m model)Avg.   1!Avg. (40.0 m model)Avg.   1!−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGAFigure 5.11: Average of maximum envelopes of drift ratios ± one standarddeviation along the height of the 4-level basement wall, designed for50% of the code PGA embedded in 24.3 and 40.0 m soil deposits,subjected to 14 spectrally matched crustal ground motions.5.3.1 General subsurface conditions in VancouverThe soil condition in parts of Vancouver can be represented using a number of mainstratigraphic sections (Atukorala et al., 2008; Hunter and Christian, 2001; Hunteret al., 1999; Monahan, 2005). In the order of increasing depth, these are:Deltaic sediments: These sediments consist of silts, fine sands and silty clay. De-spite the different sand–silt–clay ratios of the sediments, the average shearwave velocity of these materials can be characterized by the empirical curvefitted to the data Vs = 71.22+ 35.26 Z 0.4632± 2σ m/s as a function of thedepth, as proposed by Hunter and Christian (2001).Glaciomarine and glacial deposits: Underlying the marine sediments is a thicklayer of till-like sediments deposited during glacial and interglacial periods.101These deposits occur at or near the surface in much of the city of Vancou-ver (Monahan, 2005). While the shear wave velocity of 400 to 1100 m/sis proposed by Hunter and Christian (2001) with a poorly defined depthdependency for these materials, Atukorala et al. (2008) reported a depth–dependent maximum shear modulus as 169(σ´m/Pa)0.5 (MPa).Bedrock: Britton et al. (1995) developed a map of bedrock surface beneath theFraser River Delta consists of sandstone, shales and coal beds (i.e., sedimen-tary rocks). The geotechnical investigation conducted in downtown Vancou-ver and presented by Atukorala et al. (2008) found that bedrock exists atdepths ranging from 10 to 45 m below ground surface, is in various states ofsignificantly weathered to slightly weathered, and is generally classified asvery weak to weak. The average shear wave velocity at the bedrock bound-ary of 1200 to 1500 m/s is proposed by Atukorala et al. (2008) and Hunterand Christian (2001).Figure 5.12: Soil type map for the Greater Regional District of Vancouver(Monahan, 2005).Figure 5.12 shows the soil hazard map for the Greater Regional District of Van-couver for assessing the earthquake hazard due to lateral ground shaking presentedby Monahan (2005). This map reflects surface geological conditions in the formof the NBCC site classes. As previously mentioned, the shear wave velocity–depth102function of the top 30 m of the soil profile can be used to determine the soil classi-fication of the site under study.The City of Vancouver is mainly constructed on the NBCC site class C andD soil deposits (Monahan, 2005; White et al., 2008). As in general, the intensityof ground shaking increases from site class C (360 m/s < V s30 < 760 m/s) to thesofter site class D (180 m/s<V s30 < 360 m/s), it is conservative to study a seismicresponse of the basement walls founded on site class D soil profiles. In order toinvestigate the effect of geometrical and geological structure of underlying soildeposits on wave transmission to the surface, a series of analyses are carried out onthe various NBCC (2010) site class D soil deposits in the following sections.5.3.2 Depth to the significant impedance contrastIn this section as illustrated in Figure 5.13 two soil profiles, Case I and Case II,are considered. Case I is the benchmark soil geometry that has been studied so farin Chapters 3 and 4. It has a 12.15 m thickness of the first layer and by consider-ing a 11.7 m height for the 4-level basement wall results in the foundations beingembedded in the second stiff soil layer. Case II as illustrated in Figure 5.13(b) isanother variation derived from Case I soil profile with an overall lower soil stiff-ness in order to highlight the influence of the depth to the second stiff soil layer.In Case II, the first soil layer is 17.1 m deep, which results in the foundation ofthe basement wall to be embedded in this layer. Both soil profiles have the samesoil properties as described in Table 5.1. Their only difference is the depth to thesecond layer, which leads to different shear wave velocity profiles along the heightof the model. Both soil profiles can be categorized in the NBCC (2010) site classD based on their average shear wave velocities in the top 30 m (V s30,I = 310 m/sand V s30,II = 282 m/s).A series of dynamic nonlinear soil–structure interaction analyses are conductedto explore the effect of the first soil layer thickness on the seismic performance ofthe basement walls designed for different fractions of NBCC (2010) PGA (50%PGA, 60% PGA, 70% PGA, and 100% PGA). Figure 5.14 shows the finite differ-ence grid and soil layer geometries together with the layouts of the basement wallstructures founded on Case I and Case II soil deposits. Details of the boundary con-10311.7 m0.0 m!12.15 m!40.0 m0 200 400 600 800Shear wave velocity (m/s)Layer 1Vs1=200 m/sc=0 kPa"=33°Layer 2Vs1=400 m/sc=20 kPa"=40°(a) Case I11.7 m0.0 m!17.1 m!40.0 m0 200 400 600 800Layer 1Vs1=200 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=400 m/sc=20 kPa"=40°(b) Case IIFigure 5.13: Schematic of the 4-level basement walls supported on (a) CaseI and (b) Case II soil profiles (dimensions are not to scale).Layer 1Layer 212.15 m27.85 m60 m 30 m 60 m11.7 m(a) Case ILayer 1Layer 217.1 m22.9 m60 m 30 m 60 m11.7 m5.4 m(b) Case IIFigure 5.14: FLAC models of the 4-level basement walls with a total heightof 11.7 m founded on Case I and Case II soil profiles.104ditions, construction simulation, and structural and interface elements are similarto those described in Chapter 3. The analyses are conducted using the UBCHYSTconstitutive model. These soil–basement wall systems are subjected to a suite of14 crustal ground motions (G1–G14) spectrally matched to the NBCC (2010) UHSof Vancouver, as outlined in Chapter 3.Avg. of Max. Drift ratio Avg. ± 1σ−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGAFigure 5.15: Average of maximum envelopes of drift ratios ± one standarddeviation along the height of the 4-level basement wall embedded inCase I soil profile, designed for four different fractions of the codePGA subjected to 14 spectrally matched crustal ground motions.Results of the computational study are presented in the form of the envelopeof the maximum drift ratios along the height of the walls. Figures 5.15 and 5.16confirm that all the basement walls founded on the Case I soil profile have a critical105behavior just at the top basement level (similar to the conclusion drawn in chapter4), whereas if the same walls are embedded in the Case II soil profile, the perfor-mance of the bottom basement levels also become critical. In both soil profilesthe drifts at the bottom level vary with different earthquakes but they do not varymuch with changing the percentage of PGA used in the design. This is attributedto the fact that the assigned moment capacity in the design of the walls is the sameat lower levels. In these levels of the walls the static Coulomb pressure (with thefactor of 1.5) governs the moment capacity (see Figure 3.3).Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGAFigure 5.16: Average of the maximum envelopes of drift ratios ± one stan-dard deviation along the height of the 4-level basement wall embeddedin Case II soil profile, designed for four different fractions of the codePGA subjected to 14 spectrally matched crustal ground motions.106The probabilities of drift ratio exceedance of the basement walls founded onthe Case I and Case II soil profiles are presented in Figure 5.17. As shown in thisfigure, the probability curves of the walls designed for different fractions of thecode PGA founded on the Case II soil profile are closer to each other compared tothe similar curves corresponding to the soil Case I. The walls designed for 70% and100% PGA founded on the Case II soil profile have almost the same probabilitiesof drift exceedance rates. This attributed to the fact that in the Case II soil profile, asshown in Figure 5.16, the performance of the lowest basement levels designed for0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)  50% PGA60% PGA70% PGA100% PGA(a) Case I0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)  50% PGA60% PGA70% PGA100% PGA(b) Case IIFigure 5.17: Exceedance probability of drift ratio of the 4-level basementwall designed for different fractions of code PGA founded on (a) CaseI and (b) Case II soil profiles and subjected to 14 crustal ground mo-tions spectrally-matched to the UHS of Vancouver.10770% and 100% PGA dominant the response, and the top basement levels basicallyundergo very small drift ratios compared to the bottom levels. Whereas, in the CaseI soil profile, the bottom basement level experiences very small drift ratio with anaverage value of 0.2% and the top level results in a considerably higher drift andconsequently dominates the response.Thus, it can be concluded from Figures 5.15 to 5.17 that the performance ofthe 4-level basement wall designed for a specific fraction of PGA (e.g., 50%) ishighly sensitive to the stiffness and strength of a soil layer that the foundation ofthe basement wall is embedded in. In addition, the resultant drift ratios along theheight of the basement walls vary dramatically with the percentage of PGA used fortheir design, which provide valuable information for determining what percentageof PGA is a reasonable engineering value to be used for seismic design of thebasement walls. The results presented in these figures confirm that a basementwall designed for 50% to 60% PGA would result in a satisfactory performance interm of resultant drift ratio, even if the foundation of the wall is founded on a softersandy soil with lower shear wave velocity.The reason for different patterns of resultant drift ratios along the height of thebasement walls founded on two different soil profiles is attributed to the local soilcondition and dynamic soil–structure interaction effects. For this purpose it is ofinterest to calculate the spectral acceleration at the surface of the soil deposits orat the foundation level of the walls in an absence of the basement wall structure,which in this study is referred to as the free-field condition. Presence of the struc-ture can significantly affect the motion at the base of the structure and results in itsdeviation from the free-field condition. Therefore, nonlinear site response analyseson the free-field column of the Case I and Case II soil profiles are conducted inFLAC using UBCHYST constitutive model with the properties presented in Table5.1. Each soil column is subjected to a suite of 14 crustal ground motions (G1–G14) spectrally matched to the NBCC (2010) UHS of Vancouver, as described inChapter 3.The influence of the soft soil layer at the foundation of the wall in the Case IIsoil profile results in increasing the fundamental period of the system as well as theamplification level and leads to higher drift ratios at the bottom basement level un-der seismic loading. To evaluate the amplification ratio at different locations along108the height of the model, the 5% damped spectral acceleration at various locationsthrough-out the model is normalized with respect to the 5% damped spectral accel-eration of the applied motion at the base of the model. Figure 5.18 illustrates theamplification ratios at the foundation level of the wall as well as the ground surfacewith respect to the base of the model for both Cases I and II. The location of thesurface level, foundation level, and base of model are indicated in Figure 5.13 byred circles. As expected, the Case II soil profile, which has a lower average shearwave velocity (V s30,II = 282 m/s) compared to Case I (V s30,I = 310 m/s), resultsin a softer site with longer fundamental period and larger amplification ratio.10−1 10002468Period (sec)Amplification ratiofoundation level/model base  Case ICase II(a)10−1 10002468Period (sec)Amplification ratiosurface/model base  Case ICase II(b)Figure 5.18: Results of the nonlinear site response analyses conducted inFLAC in the form of amplification ratio at the (a) foundation level and(b) ground surface with respect to the base of the free-field column ofsoil subjected to 14 ground motions (G1–G14), the solid red and bluelines show the mean value of the response for each case.Figure 5.19 shows the amplification ratio along the depth of the model at thefundamental period of the Case I and Case II soil profiles. Each ground motionamplifies as it propagates vertically through–out the model but with different rates.As expected, the rate of amplification of ground motions in the stiffer second layeris lower than that in the softer first layer. By comparing the results of the nonlinearsite response analyses presented in Figures 5.18 and 5.19, one can conclude thatthe mean values of amplification ratios at ground surface in both Cases I and IIsoil profiles are almost the same, whereas there is a significant difference between1090 1 2 3 4 5 6−40−12.150Layer 1Layer 2Amplification ratioDepth (m)(a) Case I0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)(b) Case IIFigure 5.19: Results of the nonlinear site response analyses conducted inFLAC in the form of amplification ratio at the fundamental period ofthe systems along the depth of the free-field column of soil subjected to14 ground motions (G1–G14), the solid red lines show the mean valueof the response. The sketch of the location of the 4-level basement wallwith respect to the soil geometry is added for comparison.the amplification ratios at the foundation level. This fact justifies the differencebetween the performances of the bottom level of the basement walls founded onCases I and II soil profiles and demonstrates the importance of the underlying foun-dation soil stiffness on the seismic performance of the basement walls.5.3.3 Shear wave velocity and impedance contrast of the soil depositsThe analyses presented in Section 4.5.4 suggested considerable sensitivity of theresultant drift ratio of the basement wall to the shear wave velocity of the top soillayer, using a simple Mohr–Coulomb model. In order to investigate the effect of thelocal site conditions on the dynamic response of the 4-level basement wall usinga more representative UBCHYST model, ten soil profiles are selected and theircorresponding free-field two-dimensional models are developed in FLAC (Itasca,2012) following the same procedure outlined in the previous section.The same soil domain geometry as the Case II soil profile is used for the sub-sequent case studies, which are delineated by different material stiffnesses of thefirst and the second soil layers. The goal of this study is to highlight the potential110influence of the underlying soil stiffness on the earthquake motion amplificationand consequently the drift ratio of the wall elements at different locations alongthe height of the basement wall. The descriptions of the proposed ten soil profilesin terms of shear wave velocity of the first and the second soil layers are summa-rized in Table 5.2, and their corresponding geometries are shown in Figure 5.20.Different combinations of shear wave velocities for the first and the second soillayers are considered, which leads to two uniform (U) and eight non-uniform (N)soil profiles. All these sites are classified as the NBCC (2010) site class D soilmaterials with an average shear wave velocity in the upper 30 m (Vs30) between180 and 360 m/s, as reported in Table 5.2.In Table 5.2 ”Nx-y” represent a non-uniform soil profile with normalized shearwave velocities of Vs1 = x m/s and Vs1 = y m/s at the first and the second soillayers, respectively, while in all cases a significant impedance contrast lies at 17.1m depth. For instance, normalized shear wave velocities of Vs1 = 150 m/s andVs1 = 250 m/s are assigned to the model N150-250. This site has an average shearwave velocity of V s30 = 203 m/s in the upper 30 m of the soil deposit and basedTable 5.2: Shear wave velocities of the first and the second soil layers corre-sponding to ten proposed soil profiles. The numbers in the parenthesisrepresent the average shear wave velocities of the top 30 m of the soil(Vs30) used for NBCC (2010) site classification.FirstlayerV s1Second Layer Vs1250 m/s 300 m/s 400 m/s150 m/sNa150-250 N150-300 N150-400(Vs30 = 203 m/s) (Vs30 = 211 m/s) (Vs30 = 223 m/s)N200-250 N200-300 N200-400200 m/s(Vs30 = 250 m/s) (Vs30 = 263 m/s) (Vs30 = 282 m/s)250 m/sUb250 N250-300 N250-400(Vs30 = 291 m/s) (Vs30 = 309 m/s) (Vs30 = 335 m/s)300 m/s -U300-(Vs30 = 349 m/s)aN=Non-uniform soil profilebU=Uniform soil profile11111.7 m0.0 m!40.0 m0 200 400 600 800Layer 1Vs1=150 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=250 m/sc=0 kPa"=33°!17.1 m0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N150-25011.7 m0.0 m!40.0 m0 200 400 600 800Layer 1Vs1=150 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=300 m/sc=0 kPa"=33°!17.1 m0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N150-30011.7 m0.0 m!40.0 m0 200 400 600 800Layer 1Vs1=150 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=400 m/sc=20 kPa"=40°!17.1 m0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N150-400Figure 5.20: Continued.11211.7 m0.0 m!40.0 m0 200 400 600 800Layer 1Vs1=200 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=250 m/sc=0 kPa"=33°!17.1 m0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N200-25011.7 m0.0 m!40.0 m0 200 400 600 800Layer 1Vs1=200 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=300 m/sc=0 kPa"=33°!17.1 m0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N200-30011.7 m0.0 m!17.1 m!40.0 m0 200 400 600 800Layer 1Vs1=200 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=400 m/sc=20 kPa"=40°0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N200-400Figure 5.20: Continued.11311.7 m0.0 m!40.0 m0 200 400 600 800Shear wave velocity (m/s)Layer 1Vs1=250 m/sc=0 kPa"=33°0 1 2 3 4 5 6−400Amplification ratioDepth (m)U25011.7 m0.0 m!40.0 m0 200 400 600 800Layer 1Vs1=250 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=300 m/sc=0 kPa"=33°!17.1 m0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N250-30011.7 m0.0 m!40.0 m0 200 400 600 800Layer 1Vs1=250 m/sc=0 kPa"=33°Shear wave velocity (m/s)Layer 2Vs1=400 m/sc=20 kPa"=40°!17.1 m0 1 2 3 4 5 6−40−17.10Layer 1Layer 2Amplification ratioDepth (m)N250-400Figure 5.20: Continued.11411.7 m0.0 m!40.0 m0 200 400 600 800Vs1=300 m/sc=0 kPa"=33°Shear wave velocity (m/s)0 1 2 3 4 5 6−400Amplification ratioDepth (m)U300Figure 5.20: Left-hand-side column: schematic of the 4-level basement wallssupported on 11 different soil profiles (dimensions are not to scale);Right-hand-side column: results of the nonlinear site response analy-ses conducted in FLAC in the form of amplification ratio at the fun-damental period of the systems along the depth of the far-field columnof soil subjected to 14 crustal ground motions (G1–G14) spectrally-matched to the UHS of Vancouver. The solid red lines show the meanvalue of the response. The sketch of the location of the 4-level base-ment wall with respect to the soil geometry is added for comparison.on the NBCC (2010) is categorized in site class D. Likewise, model N200-400 hasnormalized shear wave velocities of Vs1 = 200 m/s and Vs1 = 400 m/s at its firstand second soil layers, respectively, which corresponds to the soil properties usedin the benchmark scenario and has been used so far in this study. The N200-400 soilprofile is equal to the Case II soil profile presented in Section 5.3.2. Two uniformsoil profiles, U250 and U300, have uniform parabolic distributions of shear wavevelocities corresponding to Vs1 = 250 m/s and Vs1 = 300 m/s, respectively through-out the depth of the model. The list of the parameters corresponding to each shearwave velocity used in UBCHYST model is presented in Table 5.3. In the caseof Vs1 = 200 m/s and Vs1 = 400 m/s, the same selected parameters are used asdescribed in Table 5.1 .Figures 5.21 and 5.22 show the modulus reduction and damping curves at dif-ferent depths of the first and the second soil layers computed by FLAC following11510−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)(a) Vs1 = 150 m/s10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)(b) Vs1 = 250 m/s10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)(c) Vs1 = 300 m/sFigure 5.21: Modulus reduction and damping curves at different depths ofthe first soil layers with normalized shear wave velocities of (a) Vs1 =150 m/s, (b) Vs1 = 250 m/s and (c) Vs1 = 300 m/s estimated by FLACusing UBCHYST model.116 !"#$#% !&'!(!"#)*$+ !,#$#% !&'!(-"#)*$+ ."#$#% !&'.(.,#)*$+ .,#$#% !&'.(/"#)*$+ 0"#$#% !&'0(,"#)*$+1)2345367  !&'"(!,#)*$1)2345367  !&'8#)*$1)2345367  !&'0#)*$1)2345367  !&'89#)*$10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)(a) Vs1 = 250 m/s10−4 10−3 10−2 10−1 10000.20.40.60.81Shear strain (%)G/Gmax10−4 10−3 10−2 10−1 1000510152025Shear strain (%)Damping Ratio (%)(b) Vs1 = 300 m/sFigure 5.22: Modulus reduction and damping curves at different depths of thesecond soil layers with normalized shear wave velocities of (a) Vs1 =250 m/s and (b) Vs1 = 300 m/s estimated by FLAC using UBCHYSTmodel.117Table 5.3: Soil parameters of the UBCHYST constitutive model used inFLAC analyses.Parameter description ParametersVs1 (m/s)150 250 300Unit weight (kN/m3) γ 19.5 19.5 19.5Cohesion (kPa) c 0 0 0Peak friction angle (deg) φ 33 33 33Dilation angle (deg) ψ 0 0 0Small strain shear modulus (MPa) Gmax 10-124 25-345 38-500Poisson’s ratio ν 0.28 0.28 0.28Stress rate factor R f 0.98 0.98 0.98Stress rate exponent n 6.0 2.5 1.8Stress rate exponent n1 1.0 1.1 1.1First cycle factor mod1 0.75 0.75 0.75Large strain exponent rm 0.5 0.5 0.5Large strain factor d f ac 0 0 0the procedure outlined in Section 5.2.2 using UBCHYST model parameters listedin Table 5.3. The Darendeli (2001) curves for different confining pressures are alsoadded for comparison. Generally there is a good agreement between the resultantmodulus reduction and damping curves calculated by FLAC using UBCHYST soilmodel and the curves of Darendeli (2001), except that the UBCHYST dampingcurves are higher at strains greater than approximately 0.1%, as discussed previ-ously.The nonlinear site response analyses of ten free-field soil columns are evaluatedusing FLAC (Itasca, 2012). Plots of the amplification ratios at the fundamentalperiod of each site versus depth of the model are presented in the right-hand-sidecolumn of Figure 5.20. Even though all these soil profiles are categorized as NBCC(2010) site class D materials and their Vs30 are almost in the same range, there is asignificant difference in the level of shaking experienced at the foundation level aswell as at the surface among these cases. It can be concluded from this figure thatthe stiffness of the soil profile in term of shear wave velocity of each soil layer andthe level of impedance contrast between soil layers are two main parameters thataffect the nonlinear site response of a site in question.118The presence of a relatively soft soil layer either underneath the basement wallfoundation or far below the foundation level substantially affects the amplificationof the ground acceleration and consequently the seismic response of the embeddedbasement wall in terms of the resultant drift ratio. Figure 5.23 shows the ampli-fication ratio of the 5% damped acceleration response spectra at the foundationlevel and at the surface with respect to the base of the model for four differentcases (N150-300, N200-300, N250-300, and U300). All these cases, as high-lighted in Table 5.2, have the same shear wave velocity at their second soil layer(Vs1 = 300 m/s), and are differentiated by the shear wave velocity of their first soillayer, which varies between Vs1 = 150 m/s to Vs1 = 300 m/s. This figure confirmsthat for the range of stiffnesses shown, a change in the stiffness of the top soillayer can significantly affect the overall site response in terms of spectral accelera-tions and consequently impact the seismic performance of the basement wall if thefoundation of the structure is embedded in top soil layer.Moreover, in order to investigate the effect of the second layer stiffness onnonlinear site response of the free-field soil column and accordingly the seismicperformance of the embedded basement wall, three different cases shown in thehighlighted row in Table 5.2 (N200-250, N200-300, and N200-400) are investi-gated. As shown in Figure 5.24, the stiffness of an underlying second soil layeralso has a significant effect on the nonlinear seismic response of the site in theform of amplification level and frequency content of the ground motion at the sur-face and the foundation level of the basement wall structure.It is evident from Figures 5.23 and 5.24 that increasing the shear wave veloci-ties of either the first or the second soil layers increases the overall stiffness of thesystem and as a result decreases the fundamental period of the soil column. Asshown in Figure 5.23, increasing the shear wave velocity of the first layer, resultsin a site with higher overall stiffness and drops the amplification ratio at the sur-face significantly. In contrast as illustrated in Figure 5.24, a stiffer site results ina higher amplification ratio. This phenomenon can be justified by the impedancecontrast between soil layers, which plays an important role in the nonlinear seismicresponse of the site. For the aforementioned reasons there is no doubt that Vs30 byitself is not a good indicator of the overall stiffness of the site and the impedancecontrast among soil layers should also be considered as a key parameter.11910−1 10002468Period (sec)Amplification ratiofoundation level/model base  N150−300N200−300N250−300U300(a)10−1 10002468Period (sec)Amplification ratiosurface/model base  N150−300N200−300N250−300U300(b)Figure 5.23: Effect of the shear wave velocity of the first soil layer and thecorresponding impedance contrast among different soil layers on am-plification ratio at the (a) foundation level and (b) ground surface withrespect to the base of the model. Each model is subjected to 14 crustalground motions (G1–G14) spectrally-matched to the UHS of Vancou-ver. The mean values of the response are presented in solid lines.10−1 10002468Period (sec)Amplification ratiofoundation level/model base  N200−250N200−300N200−400(a)10−1 10002468Period (sec)Amplification ratiosurface/model base  N200−250N200−300N200−400(b)Figure 5.24: Effect of the shear wave velocity of the second soil layer andthe corresponding impedance contrast among different soil layers onamplification ratio at the (a) foundation level and (b) ground surfacewith respect to the base of the model. Each model is subjected to 14crustal ground motions (G1–G14) spectrally-matched to the UHS ofVancouver. The mean values of the response are presented in solidlines.120A series of nonlinear two-dimensional finite difference analyses using FLAC(Itasca, 2012) are conducted to model the seismic behavior of the 4-level basementwall designed for 50% and 60% of the NBCC (2010) PGA and founded on ten siteclass D soil profiles presented in Table 5.2. Each wall is subjected to 14 crustalground motions (G1-G14) spectrally matched to NBCC (2010) UHS of Vancou-ver, as described in Chapter 3. The finite difference grid, the soil layer geometries,boundary conditions, construction simulation, and structural and interface elementsare the same as the Case II model described in Section 5.3.2. The soil properties ofthe first and second layers in conjunction with the UBCHYST constitutive modelused to model the soil media are reported in Tables 5.1 and 5.3. The values of in-terface stiffnesses (kn and ks), which are the function of the stiffness of the stiffestneighbouring zones (See Equation 3.6) along the interface elements, are also mod-ified based on the stiffness of the soil zones around the structure.Similar to previous sections the average of the maximum envelopes of the re-sultant drift ratio along the height of the basement wall (both right-side and left-sidewalls) is selected as a parameter to be evaluated in this section. For almost all thesimulations, the basic shape (distribution) of the drift ratio of the wall along theheight of the wall does not change significantly, and the magnitude of the resultsare the only parameter that varies. The average of the maximum envelopes of driftratios along the height of the wall designed for 50% and 60% PGA founded ondifferenet soil profiles highlighted in Table 5.2 are plotted in Figure 5.25.Figure 5.25 suggests considerable sensitivity of the results to the normalizedshear wave velocities of the first and the second soil layers. By comparing theseismic performance of the walls in the form of drift ratio with the results of thenonlinear site response analyses of the corresponding sites presented in Figures5.23 and 5.24, one can conclude that the level of amplification of the ground mo-tion at the foundation and surface levels has a direct impact on the resultant driftratios at the bottom and top basement levels. The uniform soil layer (U300), whichcauses a minimum amplification ratio among all the other cases, results in a verynegligible amount of drift ratio along the height of the wall, whereas soil pro-file N150-300 amplifies the ground motions the most and consequently, the wallfounded on this soil profile experiences the largest amount of drift ratio at the topand bottom basement levels.121−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)  N150−300N200−300N250−300U30050% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)  N150−300N200−300N250−300U30060% PGA(a)−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)  N200−250N200−300N200−40050% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)  N200−250N200−300N200−40060% PGA(b)Figure 5.25: Average of the maximum envelopes of drift ratios along theheight of the walls designed for 50% and 60% of the code PGA sub-jected to 14 crustal ground motions spectrally-matched to UHS of Van-couver (G1–G14) and founded on different soil profiles, showing thesensitivity of response to variation in the normalized shear wave ve-locities of (a) the first and (b) the second soil layers.Figure 5.26 provides detailed information regarding to the distribution of themaximum drift ratios of the walls presented in Figure 5.25. Each blue circle onthis figure corresponds to the maximum value of the drift ratio along the height ofthe right-side and left-side walls subjected to one out of 14 ground motion. Theaverage resultant maximum drift ratios along the height of the walls are shown byred solid circles that are comparable with the mean value of the response presented122Max. Drift Ratio from ith GM Avg. Avg.   1!N150−300 N200−300 N250−300 U300    01234  Drift (%)50% PGAN150−300 N200−300 N250−300 U300    01234  Drift (%)60% PGA(a)N200−250 N200−300 N200−40001234  Drift (%)50% PGAN200−250 N200−300 N200−40001234  Drift (%)60% PGA(b)Figure 5.26: Sensitivity of the resultant maximum drift ratios and the corre-sponding average ± one standard deviation of the 4-level basementwall designed for 50% and 60% PGA to variation of the normalizedshear wave velocities of (a) the first and (b) the second soil layers. Thewalls are subjected to 14 crustal ground motion spectrally-matched tothe UHS of Vancouver.123in Figure 5.25. For instance, as illustrated in Figure 5.25, an average of the resultantmaximum drift ratio of the basement wall founded on N150-300 soil profile andsubjected to ground motions G1–G14 has a maximum value of 1.77% at the topbasement level, which is consistent with an average value plotted by the red circlein Figure 5.26.In addition, Figure 5.26 quantifies the amount of variation and dispersion ofthe maximum drift ratios resulting from the basement wall founded on certain soilprofile excited by 14 spectrally-matched ground motions. The standard deviationmeasures the spread of the data about an average value. A lower standard deviationindicates that the maximum resultant drift ratios tend to be very close to an averagevalue from 14 ground motions, while a high standard deviation shows that themaximum drift ratios spread out over a wider range of values. In this figure, ifone assumes normally distributed drift ratios, the red dashted-lines represent anaverage± one standard deviation with a 68% chance that the mean falls within arange of standard error.According to the adopted performance criterion for drift ratio (ASCE-TCBRD,2010), Figure 5.26 shows that except for the case of N150-300, the resultant av-erage ± one standard deviation of all basement walls designed for even 50% and60% PGA falls within an acceptance range (< 1.7%) when subjected to the currentseismic hazard level in Vancouver, with a 2% chance of being exceeded in 50 years.It is worth mentioning that there are some concerns about using Vs1 = 150 m/s asthe normalized shear wave velocity of the first soil layer because according to prac-titioners (DeVall et al., 2010, 2014) it might be a bit low for high-rise constructionin Vancouver. Even in the case of constructing the 4-level basement wall on theN150-300 soil profile, the analyses show that the resultant maximum drift ratiofalls within a range of 1.77%±0.52% and 1.41%±0.49% for the basement wallsdesigned for 50% and 60% code PGA, respectively. These are in the lower rangeof the medium response category (< 3.5%) defined by ASCE-TCBRD (2010).Figure 5.27 is an extended version of Figure 5.26, which summarizes the max-imum values of drift ratios along the height of the walls designed for 50% and60% PGA and founded on ten soil profiles outlined in this section. In these three-dimensional figures, horizontal axes represent the normalized shear wave veloci-ties of the first and the second soil layers, as described in Table 5.2. The vertical124250 30040015020025030001234 Second Soil Layer Vs1 (m/s)First Soil Layer Vs1 (m/s) Drift Ratio (%)Avg. of Max. Envelopes+1 Standard Deviation50% PGA250 30040015020025030001234 Second Soil Layer Vs1 (m/s)First Soil Layer Vs1 (m/s) Drift Ratio (%)Avg. of Max. Envelopes+1 Standard Deviation60% PGAFigure 5.27: Average of the maximum drift ratios and the corresponding onestandard deviation of the 4-level basement wall designed for differ-ent fractions of the code PGA and founded on ten different soil pro-files. Each wall is subjected to 14 crustal ground motions (G1–G14)spectrally-matched to the UHS of Vancouver.125axis presents the mean of the maximum drift ratios along the height of the 4-levelbasement walls and the corresponding mean + one standard deviation. It can beconcluded from this figure that decreasing the shear wave velocity of the first soillayer increases the resultant drift ratio along the height of the basement wall. Incontrast, decreasing the shear wave velocity of the second soil layer decreases thedrift ratio. Moreover, two uniform soil profiles (U250 and U300) result the min-imum value of the resultant drift ratios compare to the non-uniform soil profiles.In fact, the mean value of the maximum drift ratio increases proportionally to theincrease of the impedance ratio between two soil layers.According to the performance criterion adopted for drift ratio (1.7%), exceptfor the cases in which Vs1 = 150 m/s is assigned for the first soil layer, the wall de-signed for 50% PGA using modified M-O method, performs adequately under fullseismic demand driven from the NBCC (2010). The resultant drift ratios of the walldesigned for 60% PGA confirm that the walls founded on a soil profile with a veryloose first soil layer (Vs1 = 150 m/s) and with relatively high impedance contrastwith the second soil layer (N150-250 and N150-300) would perform adequatelyunder the demand corresponding to an exceedance rate of 2% in 50 years. It isworth mentioning that the case in which the basement wall is founded on a softsoil with a very high impedance contrast with the second soil layer (N150-400)needs an extra attention. In this case as is illustrated in Figure 5.27, the seismicresponse would fall in the lower range of the medium response (< 3.5%) categorydefined by ASCE-TCBRD (2010).5.4 Effect of basement wall geometryIn an expensive and congested urban area of downtown Vancouver, deep basementwalls have been constructed extensively to allow for underground parking and otherusages. Deep excavations induce significant changes in both stress and strain of thesurrounding soil and, therefore, generate permanent displacements and potentiallymore severe damages.This section investigates the effect of the geometric parameters of the base-ment walls (e.g., total height and top storey height) on the seismic performance ofthe structure and is considered as an extension of the study on the 11.7 m 4-level126basement wall described earlier in Chapter 4. The result of the analyses presentedin Chapters 4 and 5 showed that the performance of the top and bottom basementlevels are critical. As it is common in design practice to allow higher height tothe top basement storey a set of sensitivity analyses are conducted in this sectionto study the effect of the higher top basement height (e.g. 5.0 m instead of 3.6 m,which has been used so far in this study). In addition to the 4-level basement wall,deeper basement structures with higher number of underground levels and deeperdepths are studied in this section.Therefore, two very common configurations in practice of deep basement wallsare designed by SEABC structural engineers (DeVall, 2011) for various fractionsof the NBCC (2010) PGA:• 4-level basement wall with 5.0 m top storey and a total height of 13.1 m, asshown in Figures 5.28 and 5.30,• 6-level basement wall with a total height of 17.1 m, as illustrated in Figures5.29 and 5.31.In order to take into an account the effect of soil stiffness at the foundationlevel, each wall is founded on Case I and Case II soil profiles outlined in Section5.3.2.5.4.1 Seismic design of a 4-level basement wall with higher top storeyheight and a 6-level basement wallAs discussed previously in Section 3.2, the state of practice for seismic design ofbasement walls is to use two load combinations prescribed by the National Build-ing Code of Canada (NBCC, 2010): (1) 1.5 times an active lateral pressure, pA(z),which pA(z) is not less than 20 kPa compaction/surcharge pressure as illustratedin Figures 5.28 and 5.29, and (2) pAE(z) = pA(z)+∆pAE(z) where pAE(z) is thetotal active lateral pressure consists of pA(z), the static lateral active pressure and∆pAE(z), the dynamic increment of the lateral earth pressure acting on the wall.Each basement wall is designed for four fractions of the code PGA (=0.46 g) fol-lowing the state of practice in British Columbia using the modified M-O methodas illustrated in Figures 5.30 and 5.31.127(a) (b)20 x 1.5=30 kPaGround LevelLevel !1Level !2Level !3Level !40.0 m2.7 m5.4 m8.1 m2.7 m2.7 m2.7 m5.0 m13.1 m72.8 x 1.5=109.2 kPaFigure 5.28: (a) Floor heights in the 4-level basement wall with 5 m topstorey and (b) the calculated lateral earth pressure distributions fromthe first load combination.(a) (b)Ground LevelLevel !1Level !2Level !3Level !4Level !5Level !60.0 m2.7 m5.4 m8.1 m10.8 m13.5 m17.1 m 20 x 1.5=30 kPa95.0 x 1.5=142.5 kPaFigure 5.29: (a) Floor heights in the 6-level basement wall and (b) the cal-culated lateral earth pressure distributions from the first load combina-tion.128(a) (b) (c) (d) (e)fGround LevelLevel !1Level !2Level !3Level !40.0 m2.7 m5.4 m2.7 m2.7 m2.7 m5.0 m8.1 m13.1 m72.8 kPa 72.8 kPa 72.8 kPa 72.8 kPa38.9 kPa49.0 kPa60.2 kPa102.8 kPaFigure 5.30: (a) Floor heights in the 4-level basement wall with 5 m topstorey and the calculated lateral earth pressure distributions from thesecond load combination using the M-O method with (b) 100% PGA,(c) 70% PGA, (d) 60% PGA, and (e) 50% PGA, where PGA=0.46g.(a) (b) (c) (d) (e)f fGround LevelLevel !1Level !2Level !3Level !4Level !5Level !60.0 m2.7 m5.4 m8.1 m10.8 m13.5 m2.7 m2.7 m2.7 m2.7 m2.7 m3.6 m17.1 m134.2 kPa 78.5 kPa 63.9 kPa 50.8 kPa95.0 kPa 95.0 kPa 95.0 kPa 95.0 kPaFigure 5.31: (a) Floor heights in the 6-level basement wall and the calculatedlateral earth pressure distributions from the second load combinationusing the M-O method with (b) 100% PGA, (c) 70% PGA, (d) 60%PGA, and (e) 50% PGA, where PGA=0.46g.129For each wall consistent with four scenarios of lateral earth pressure corre-sponding to four different fractions of PGA (50%, 60%, 70% and 100%), fourlevels of yielding moments are calculated and presented in Figure 5.32. Detailsabout the calculation of moment capacities at different elevations along the heightof the walls are discussed in Appendix A.100% PGA 70% PGA 60% PGA 50% PGA0 50 100 150 200 25002.75.48.113.1Moment (kN−m/m)Height (m)(a)0 50 100 150 200 25002.75.48.110.813.517.1Moment (kN−m/m)Height (m)(b)Figure 5.32: Moment capacity distribution along height of (a) the 4-levelbasement wall with 5.0 m top storey and (b) the 6-level basement walldesigned for different fractions of the NBCC (2010) PGA for Vancou-ver (= 0.46 g).5.4.2 Simulation resultsA series of nonlinear two-dimensional finite difference analyses using FLAC 2Dare conducted to model the seismic behavior of the 4-level and 6-level basementwalls designed for various fractions of the NBCC (2010) PGA for Vancouver. Thedescription of the boundary conditions, construction simulation, and structural andinterface elements can be found in Chapter 3. Each basement wall is founded ontwo different soil profiles, Cases I and II, as described in Section 5.3.2. Figures5.33 and 5.34 show the finite difference grids and the soil geometries together with13013.1 m13.55 m26.45 m60 m 30 m 60 mLayer 1Layer 260 m 30 m 60 m17.55 m22.45 m17.1 mLayer 1Layer 2Figure 5.33: (a) 4-level basement wall with 5.0 m top storey and total heightof 13.1 m and (b) 6-level basement walls with a total height of 17.1 mfounded on Case I soil profile.5.4 m13.1 m18.5 m21.5 m60 m 30 m 60 mLayer 1Layer 260 m 30 m 60 m22.5 m17.5 m17.1 m5.4 mLayer 1Layer 2Figure 5.34: (a) 4-level basement wall with 5.0 m top storey and total heightof 13.1 m and (b) 6-level basement walls with a total height of 17.1 mfounded on Case II soil profile.131a layout of the 4-level and 6-level basement walls founded on Case I and Case IIsoil profiles. In each case the depth from the foundation level of the basement wallto the second stiff soil layer is constant. The soil properties of the first and thesecond soil layers in Cases I and II soil profiles are as reported in Table 5.1 and aremodeled using the UBCHYST constitutive model.The average of the maximum envelopes of drift ratios along the height of thewalls designed for different fractions of the code PGA subjected to 14 crustalground motion records spectrally-matched to the UHS of Vancouver (G1–G14) andembedded in Case I and II soil profiles are presented in Figures 5.35 to 5.38. Inthese plots an average value corresponds to the average of the maximum envelopesof drift ratio along the height of the both right-side and left-side walls subjected to14 ground motions. If normally distributed drift ratios are assumed, average±1σrepresents the one standard deviation with a 68% chance that the mean falls withinthe range of standard error.From these figures one can conclude that the walls embedded in Case II soilprofile result in slightly higher drift ratios compared with the ones founded onCase I site. For instance, the 13.1 m 4-level basement wall designed for 50% PGAfounded on Case I soil profile results in an average of the maximum drift ratioof 0.80%±0.15%, whereas the same wall embedded in the Case II soil profileundergoes the maximum drift ratios in a range of 0.88%±0.25%. The results of thisstudy confirm that the response of both the top and bottom levels of either 4-leveland 6-level basement walls are critical and need careful consideration. Accordingto the adopted performance criterion for drift ratio (1.7%), the maximum resultantdrift ratios along the height of the 4-level and 6-level basement walls (with totalhight of 13.1 m and 17.1 m) designed for 50% to 60% code PGA, founded onsandy soil materials and subjected to the full seismic hazard level in Vancouverwith a 2% chance of being exceeded in 50 years, fall into the acceptance criterion.Figures 5.39 and 5.40 illustrate a probability of the maximum drift ratio ex-ceedance. As discussed previously, exceedance probability is the probability of anevent being greater than or equal to a given value. These figures describe detailedinformation regarding the distribution of the maximum resultant drift ratio of thebasement walls subjected to 14 ground motions spectrally matched to the NBCC(2010) seismic hazard in Vancouver.132Avg. of Max. Drift ratio Avg. ± 1σ−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)100% PGAFigure 5.35: Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 13.1 m 4-level basementwalls designed for different fractions of the code PGA, founded onCase I soil profile subjected to 14 crustal ground motions (G1–G14)spectrally-matched to the UHS of Vancouver.133Avg. of Max. Drift ratio Avg. ± 1σ−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.113.1Drift (%)Height (m)100% PGAFigure 5.36: Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 13.1 m 4-level basementwalls designed for different fractions of the code PGA, founded onCase II soil profile subjected to 14 crustal ground motions (G1–G14)spectrally-matched to the UHS of Vancouver.134Avg. of Max. Drift ratio Avg. ± 1σ−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)100% PGAFigure 5.37: Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 17.1 m 6-level basementwalls designed for different fractions of the code PGA, founded onCase I soil profile subjected to 14 crustal ground motions (G1–G14)spectrally-matched to the UHS of Vancouver.135Avg. of Max. Drift ratio Avg. ± 1σ−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)60% PGA−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)70% PGA−1 0 1 2 3 402.75.48.110.813.517.1Drift (%)Height (m)100% PGAFigure 5.38: Average of the maximum envelopes of drift ratios and ± onestandard deviation along the height of the 17.1 m 6-level basementwalls designed for different fractions of the code PGA, founded onCase II soil profile subjected to 14 crustal ground motions (G1–G14)spectrally-matched to the UHS of Vancouver.1360 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)  50% PGA60% PGA70% PGA100% PGA(a) Case I0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)  50% PGA60% PGA70% PGA100% PGA(b) Case IIFigure 5.39: Probability of drift ratio exceedance of the 13.1 m 4-level base-ment walls designed for 50%, 60%, 70% and 100% of the code PGA,founded on Case I and II soil profiles subjected to 14 crustal groundmotions (G1–G14) spectrally-matched to the UHS of Vancouver.Figure 5.41 summarizes and compares the resultant maximum drift ratios ofthe 11.7 m, 13.1 m and 17.1 m basement walls founded on both Case I and CaseII soil profiles according to the adopted performance criterion for drift ratio in thisstudy (< 1.7%). It can be concluded that the behavior of the basement walls de-signed for 50% to 60% PGA, founded on relatively dense or loose sandy materialsare satisfactory when subjected to the current seismic hazard level in Vancouverwith a 2% chance of being exceeded in 50 years. Within a significant range of1370 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)  50% PGA60% PGA70% PGA100% PGA(a) Case I0 0.5 1 1.5 2020406080100Drift (%)Probability of Drift Exceedance (%)  50% PGA60% PGA70% PGA100% PGA(b) Case IIFigure 5.40: Probability of the maximum drift ratio exceedance of the 17.1 m6-level basement walls designed for different fractions of the codePGA, founded on Case I and II soil profiles subjected to 14 crustalground motions (G1–G14) spectrally-matched to the UHS of Vancou-ver.variations, the conclusion still stands that the basement walls can be safely de-signed with 50–60% NBCC (2010) PGA using the modified M-O method. Thepresent design procedure in Vancouver using 100% PGA leads to very expensiveand overly-conservative structures and the findings of this research can have con-siderable impact on cost effectiveness of the design of the basement walls.138Max. Drift Ratio from ith GM Avg. Avg.   1!Case I Case II Case I Case II Case I Case II0123  Drift (%)50% PGA13.1 m basementwall11.7 m basementwall17.1 m basementwallCase I Case II Case I Case II Case I Case II0123  Drift (%)60% PGA13.1 m basementwall11.7 m basementwall17.1 m basementwallCase I Case II Case I Case II Case I Case II0123  Drift (%)70% PGA13.1 m basementwall11.7 m basementwall17.1 m basementwallCase I Case II Case I Case II Case I Case II0123  Drift (%)100% PGA13.1 m basementwall11.7 m basementwall17.1 m basementwallFigure 5.41: The resultant maximum drift ratios and the corresponding av-erage and average ± one standard deviation of the 4-level and 6-levelbasement walls designed for different fractions of the NBCC (2010)code PGA, founded on Case I and Case II soil profiles and subjectedto 14 crustal ground motions spectrally-matched to the UHS of Van-couver.139Chapter 6Selection and modification of timehistories for VancouverMake things as simple as possible, but not simpler.— Albert Einstein (1879–1955)6.1 IntroductionThe goal of ground motion selection and scaling is to develop a suite of accelera-tion time histories representative of the seismic demand anticipated for the analysisof a structure at a specific site. The absence of recordings at the site forces prac-titioners to modify the existing time histories to match the target spectrum at thesite. Selected ground motions are scaled to match the Uniform Hazard Spectrum(UHS) for the site within a period range of interest.The objective of scaling the ground motions is to get reliable estimate of themean response of a structure and an adequate assessment of its variation about themean (Baker and Allin Cornell, 2006; Hancock et al., 2006; Shome et al., 1998).For this purpose, an appropriate number of ground motions are selected and theircorresponding structural responses are estimated by subjecting the soil–structuresystem to acceleration time histories that are compatible with the scenario in ques-tion.140As discussed previously in Chapter 3, a spectrally matched ground motions,due to the nature of the method, result in lower variance of the structural responseand consequently provide a robust value of the mean response with lower numberof motions. The mean value of the structural response is used for design basis,however estimating the probability of collapse requires the estimation of the po-tential variability of a basement wall response. Therefore, the intensity-based lin-ear scaling methods, which preserve the motion-to-motion variability are preferredover spectral matching techniques, which modify the frequency content and phas-ing of the record to match its response spectrum to the target spectrum (Kalkan andChopra, 2010).So far the conclusion drawn on the seismic performance of the basement wallsdesigned for different fractions of the NBCC (2010) PGA was on the basis ofone type of ground motions: crustal earthquakes. Besides, in order to expediteextensive parametric analyses, the mean value of the structural response establishedby spectrally matched ground motion records to the target spectrum were reported.In this Chapter the seismic performance of the designed basement walls will be re-evaluated by subjecting them to motions from other dominant types of earthquakesources in British Columbia.The seismicity of the south-western British Columbia and the dominant typesof earthquake sources in the area are discussed in Section 6.2. Various options forscaling and matching earthquake records to be representative of the seismic hazard(NBCC, 2010) are studied in Section 6.3. Comprehensive procedures for selectionand modification of strong ground motions for the seismic assessment of basementwalls in Vancouver are presented in Section 6.4. The the maximum resultant driftratio of the basement wall designed for different fractions of NBCC (2010) PGAusing modified M-O method, subjected to linearly scaled ground motions are pre-sented in Section 6.5. Based on these results an appropriate fraction of the codePGA for design of the basement walls using the modified M-O method is evaluated.6.2 Seismicity of south-western British ColumbiaEach year, seismologists with the Geological Survey of Canada (Natural ResourcesCanada, 2012) record and locate more than 1000 earthquakes in Pacific Coast,141which is the most seismically active regions of Canada. Ten moderate to large(M6–7) earthquakes have occurred within 250 km of Vancouver and Victoria dur-ing the last 130 years (Clague, 2002; Rogers, 1998).Four tectonic plates meet and interact in south-western British Columbia andthree different types of plate movements take place, resulting in significant earth-quake activities. Plates move towards each other at converging, apart at divergingand past each other at transform (strike-slip) boundaries as illustrated in Figure 6.1.Figure 6.1: Tectonic plates in west coast of Canada and the United States(Natural Resources Canada, 2012)The tectonic setting of south-western British Columbia is mainly influenced bythe subduction of the oceanic Juan de Fuca plate beneath the North America conti-nental plate as shown in Figure 6.2. This region is called the Cascadia subduction142zone, which is located about 50 km beneath Vancouver and extends along the coastfrom northern California to central Vancouver Island. Another small plate, the Ex-plorer, is also sliding underneath the North American plate, and at the same timethe Juan de Fuca plate is sliding along the Nootka fault. In the north, there is a ma-jor strike-slip fault boundary between the Pacific plate moving northwest and theNorth American plate moving southeast relative to one another, called the QueenCharlotte fault. This fault was the site, in 1949, of the largest earthquake recordedin Canada (M8.1).Given these facts, the seismicity of the west coast of British Columbia has sig-nificant hazard contributions from shallow crustal earthquakes in the North Amer-ica plate, deeper subcrustal earthquakes in the subducting Juan de Fuca plate, andvery large (M8+) Cascadia subduction earthquakes at the interface of the two platesextended beneath Vancouver (Finn et al., 2000; Levson et al., 2003; Onur, 2001;Pina, 2010). The crustal and subcrustal ground motions have the major contribu-Figure 6.2: Tectonic setting of south-western British Columbia showing theoceanic Juan de Fuca plate is subducting beneath the continental crust ofNorth America plate along the Cascadia subduction zone (Natural Re-sources Canada, 2012)143tions to hazard at small periods, whereas at long periods, the potential for greatmegathrust earthquakes on the Cascadia subduction zone is the main concern. Amajor earthquake associated with either one of these sources could have devastat-ing effects in Vancouver.The hazard contributions from each scenario is reflected in a calculation of theUniform Hazard Spectrum (UHS), which is referred as a target response spectrumin the National Building Code of Canada (NBCC, 1995, 2005, 2010). The UHSenvelopes the maximum response of a single-degree-of-freedom oscillator with5% damping and provides the design response spectrum corresponding to differentperiods.The probability level used in 1995 edition of the National Building Code ofCanada (NBCC, 1995) was 0.0021 per year and had a 10% chance of exceedence in50 years (a 475-year return period earthquake), whereas the recent versions of thecode (NBCC, 2005, 2010) provide the 2% chance of exceedence in 50 years equiv-alent to an annual probability of 0.000404 (a 2475-year return period earthquake).In computation of the 2% in 50 years robust probabilistic hazard values for Vancou-ver, the hazard due to shallow crustal and deeper subcrustal earthquakes and alsoa great earthquake along the Cascadia subduction zone are included. According toNBCC (2010), for the western Canadian cities the crustal and subcrustal data hasbeen treated probabilistically and subduction data deterministically (Adams andHalchuk, 2003).The corresponding hazard values for different cities (e.g., Vancouver) are re-ported in the NBCC (2010). The proposed design UHS also depends on the lo-cation of the site and its local soil condition (Finn and Wightman, 2003). Basedon the NBCC (2010), soil condition is classified into different categories accord-ing to the time-averaged shear wave velocity in the top 30 m of the soil deposit(Vs30). The site conditions range from class A: hard rock (Vs30 > 1500 m/s),Class B: rock (760 m/s < Vs30 < 1500 m/s), class C: very dense soil and softrock (360 m/s < Vs30 < 760 m/s), class D: stiff soil (180 m/s < Vs30 < 360 m/s),and Class E: soft soil (Vs30 < 180 m/s).The rate of occurrences of crustal, subcrustal and subduction earthquakes aredifferent and so are their effects on seismic hazard. Therefore, for nonlinear dy-namic time history analyses of basement walls, it is necessary to explore ground144motions representative of different types of expected earthquake motions, and matcheach record to the NBCC (2010) target UHS over the period range of interest.There are number of acceptable methods for obtaining UHS-compatible time his-tories which will be outlined in the next section.6.3 Ground motion scaling methodsScaling/matching ground motions plays an important role in engineering perfor-mance design and enables determination of the structural response with higherconfidence and through fewer number of analyses compare to using unscaled ac-celerograms. The premise to verify is to modify a time history so that its responsespectrum matches within a prescribed tolerance level the target response spectrum(Finn, 2000). Reducing the dispersion in the elastic response spectra of the inputground motion reduces the variability in the output of nonlinear response historyanalyses.For conducting nonlinear dynamic analyses of basement walls, several methodsof scaling/matching the input ground motions are chosen to modify accelerogramsto become representative of the site-specific hazard level (e.g., the uniform hazardspectrum) at the site. Scaling the ground motions is necessary in evaluating theperformance of the basement walls in order to expose the structure to the level ofground motion corresponds to the probability of exceedance adopted in the NBCC(2010).As mentioned previously in Chapter 3, there are two main options for scaling/-matching the ground motions:(1) adding wavelets in the time domain and modifying the spectral shape of theresponse spectrum to match the target demand, which is known as spectralmatching; and(2) linear scaling of accelerograms without affecting frequency content or phasingby minimizing the difference between a target spectrum and the spectrum ofa scaled ground motion, either at a single period or over a period range.The spectral matching method was used in Chapter 3 to modify the selected14 crustal earthquake time histories to become compatible with the NBCC (2010)145hazard level in Vancouver. This method is popular in engineering practice, becauseit reduces the variance of the structural responses and provides a platform to esti-mate the mean response with fewer numbers of analyses (Carballo and Cornell,2000; Seifried and Baker, 2014); thereby the computational cost is significantlyreduced. A gross rule of thumb is that one spectrum compatible time series isworth three scaled time series in terms of the variability of the mean of the non-linear response of structures (Al Atik and Abrahamson, 2010; Bazzurro and Luco,2006). For example, if it takes engineering analyses of 12 scaled time series to get20% accuracy in the mean structural response, then it takes only analyses of fourspectrum compatible time series to get the same accuracy. In addition, the spectralmatching technique has an advantage of meeting the target spectrum requirementsadequately. In this method, the frequency content and phasing of actual record ismanipulated to match a smooth target spectrum (Bolt and Gregor, 1993; Carballoand Cornell, 2000; Hancock et al., 2006; Heo et al., 2010; Lilhanand and Tseng,1989). The only argument can be made is that the spectral matching process ar-tificially smooth out the natural peaks and troughs of the original record responsespectra and may obscure somewhat the potential variability of the response (Atkin-son, 2009; Luco and Cornell, 2007).On the other hand, in linear scaling methods the whole accelerogram time his-tory is multiplied by a scalar coefficient to become more compatible with the targetspectrum. In these methods the deviation from the target is measured by variousparameters. To keep the records realistic, it is recommended to scale the recordswith required scaling factors in the range from 0.5 to 2.0 (approximately). Al-though there will be some occasions later on in this chapter that due to the absenceof the recordings with the desired characteristics, higher values of scaling factorsare used. An additional ground motion criteria proposed by Pina et al. (2010) isconsidered in this study in scaling process of ground motions as an average of ac-celeration response spectrum of a selected suite of ground motion must be abovethe 90% the target spectrum within the period range of interest.Five ground motion scaling methods are investigated as follows:1466.3.1 PGA scalingIn this method, the selected record is multiplied by a scalar coefficient in a way thatthe PGA of the scaled record becomes equal to the PGA of the target spectrum,which based on the NBCC (2010) for Vancouver is 0.46 g. The drawback of thismethod is the fact that the frequency content and spectral shape of the accelerogramover a range of periods are not taken into consideration. Even though all scaledground motions have the same PGA, their response spectrum fall in a very widerange through-out the different periods and produce inaccurate estimates with largedispersion of an engineering demand parameter (Miranda, 1993; Nau and Hall,1984; Shome and Cornell, 1998; Vidic et al., 1994).6.3.2 Sa(T1) scalingAccounting for the vibration properties of the structure led to an improved methodof scaling based on an elastic spectral acceleration at the fundamental vibrationperiod of the structure, T1, which provides improved results for structures whoseresponse are dominated by their first-mode (Shome et al., 1998). The objective ofthis method is to use a multiplier to scale the records so that the spectral acceler-ation at a fundamental period of the system, also called as the spectral intensity,Sa(T1), matches the target spectral acceleration at that period, i.e.,f =Satarget(T1)Sarecord(T1)(6.1)This method provides a set of scaled time histories, whose spectral accelerationof all are equal to the target spectrum at the fundamental period of the system.Shome and Cornell (1998) demonstrated that in the cases of SDOF and MDOFstructures, the seismic demand estimates are strongly correlated with the linear-elastic spectral response acceleration at the fundamental period of the structureand the scatter in the demand can be significantly reduced.One of the main concerns in using this methodology in the complex basementwall model is losing accuracy and efficiency at higher modes of vibration and farinto the inelastic range due to yielding and nonlinear behavior, which elongatesthe vibration periods (Kurama and Farrow, 2003; Mehanny and Deierlein, 1999).Moreover, scaling a record just based on one specific period is not a good indicator147of the strength and frequency content of the ground motion and the first-modeperiod does not necessarily dictate the response of the system (Huang et al., 2011).6.3.3 ASCE scalingThe procedures and criteria in International Building Code (IBC, 2009) and Cal-ifornia Building Code (CBC, 2010) for selection and scaling ground motions innonlinear response history analyses of structures are based on the recommendationof the American Society of Civil Engineering (ASCE/SEI 7-05, 2005; ASCE/SEI7-10, 2010). It recommends intensity-based scaling of ground motion records suchthat the average value of the 5% damped response spectra for the suites of scaledmotions is not less than the design response spectrum over the period range of 0.2T1to 1.5T1, where T1 is the first mode natural vibration period of the system. The up-per limit on the period range of 1.5T1 is intended to account for period elongationdue to inelastic action, and 0.2T1 is intended to capture higher modes of response.The ASCE scaling procedure does not insure a unique scaling factor for eachrecord. Obviously, various combinations of scaling factors can be defined to insurethat the average spectrum of the scaled records remains above the design spectrum.In this study the procedure recommended by Reyes and Kalkan (2011) has beenused for scaling the suite of selected records in order to utilize a minimum scalingfactor closest to unity for each record.6.3.4 SIa scalingIn this method, the multiplier is applied to each accelerogram in a way that the areaunder the response spectrum becomes equal to the integration of spectral accelera-tion in the period range of interest 0.2T1 to 1.5T1 (Michaud and Leger, 2014).6.3.5 MSE scalingIn this method a quantitative measure of the overall fit of the record to a targetspectrum is the Mean Squared Error (MSE) of the difference between the spectralaccelerations of the record and the target spectrum, computed using the logarithmsof the spectral acceleration. For this purpose a period range of interest is subdividedinto a large number of points equally-spaced and the target and the record response148spectra are interpolated to provide spectral acceleration at each period, respectively.The MSE is then computed using the following equation over the selected periodrange as:MSE =∑w(Ti){ln[Satarget(Ti)]− ln[ f ×Sarecord(Ti)]}2∑w(Ti)(6.2)In this equation, Satarget(Ti) is the spectral acceleration of the target spectrum,Sarecord(Ti) is the spectral acceleration of the scaled ground motion, and w(Ti) is aweight function that allows the user to assign relative weights to different periodsover the period range of interest. In this study an equal weight is assigned to allperiods (i.e., w(Ti) = 1). Parameter f is a linear scaling factor applied to the entireresponse spectrum of the record in order to minimize MSE between the targetspectrum and the response spectrum of the record.The U.S. Army Corps of Engineers (USACE) (2009) recommends a criteria forthe fit of an average spectrum of the scaled time histories to the design spectrumin seismic analyses, design, and evaluation of civil works structures. Based onthis recommendation the mean spectrum should not be below the design responsespectrum by more than 10% at any spectral period over the period range of interestand the average of the ratios of the mean spectrum to the design spectrum over thesame period range should not be less than 1.0.6.4 Selection of ground motion recordsCommonly, a suite of input motions is used to capture the inherent motion-to-motion variability of the earthquake ground motions. A suite of earthquake recordsis required due to the fact that unique characteristics of each input motion influencethe induced dynamic response differently. The selection procedure considers theimportant characteristics of the ground motions (magnitude, distance, site condi-tion and etc.) consistent with the hazard conditions. Selecting records by takinginto an account the hazard demand for a given site, increases accuracy in deter-mining the mean value of the structural response by reducing the dispersion of theresults.As stated by Finn (2000), determining appropriate scenario earthquakes for se-149lecting appropriate recorded ground motions for nonlinear analyses is one of thedifficulties in design based on spectra. The probabilistic response spectrum repre-sents the aggregated contribution of a range of earthquake magnitudes on differentfaults and seismic zones at various distances from the site, and also includes theeffect of random variability for a given magnitude and distance. Appropriate earth-quakes can be determined using a procedure proposed by McGuire (1995), whichdeaggregates the contributions to the spectrum by magnitude and distance. As out-lined previously in Chapter 3, Pina et al. (2010) determined appropriate rangesof magnitudes and (closest) source-to-site distance by de-aggregating the seismichazard in Vancouver and selected the values that contribute most strongly to thehazard for different earthquake scenarios. In addition, in this study the referencesoil classification, site class C, adopted by the NBCC (2010) is selected as a sitecondition, which is consistent with the site condition at the depth of earthquakemotion application in the FLAC model.In this study, four ground motion ensembles representative of the dominantseismic mechanisms in the Greater Vancouver region are investigated. Differencesamongst these ensembles can be observed in terms of spectral shapes and frequencycontent. Each ensembles affect the structure in a different way and therefore, thevalue of the engineering demand parameter (e.g. drift ratio) substantially variesamongst these types of earthquakes.The first and the second ensembles each includes a total of 14 records repre-sentative of crustal and subcrustal seismic events, respectively. All these accelero-grams are linearly scaled to the proposed NBCC (2010) uniform hazard spectrumusing different methods of scaling outlined in Section 6.3.The third ensemble comprises a total of 14 ground motions representative ofthe Cascadia subduction events. All these records are scaled to the correspondinghazard values of Cascadia subduction earthquake scenario derived from the deter-ministic (Cascadia) model for a probability of 2% in 50 years presented in Adamsand Halchuk (2003) and are representative of the NBCC (2010) hazard level.The forth ensemble covers 14 near-fault ground motions. These are assumedto occur within a distance of 20 km from the causative fault and contain distinctpulses either in the acceleration, velocity or displacement time histories. Scalingis also necessary for these records in order to expose the structures to the level of150ground motion that corresponds to the probability of exceedance adopted by theNBCC (2010).The records in the Pacific Earthquake Engineering Research Center (PEER)ground motion database (Chiou et al., 2008) have been processed for instrumentcorrection, bandpass filtering (removal of unwanted noise), and baseline correc-tion, as described in Darragh et al. (2004). However, time histories selected fromother databases require to be checked for their need to further data processing be-fore ground motion scaling. Each of the selected ground motions is baseline cor-rected with a linear function and filtered with a bandpass Butterworth filter withcut-off frequencies of 0.1 Hz and 25 Hz, using the computer program SeismoSig-nal (Seismosoft, 2009b). Once it processed, the 5% damped acceleration responsespectrum is obtained and used in linear scaling process of ground motions.6.4.1 Crustal earthquakesIn south-western British Columbia region most crustal earthquakes occur withinapproximately 20 to 30 km of the surface. These crustal earthquakes usually havea magnitude less than 7.5 and a typical duration of less than one minute.Fourteen selected crustal ground motions presented in Table 3.1 in Chapter 3are linearly scaled in this section. Different methods of linear scaling outlined inSection 6.3 are conducted to modify the time histories to become compatible withthe target demand. Each selected record is scaled using a constant factor based ondifferent methods of linear scaling. The scaling factors are reported in Table 6.1.Figures 6.3 to 6.7 illustrate the acceleration time histories of the 14 selectedcrustal ground motions, linearly scaled to the NBCC (2010) UHS for Vancouverusing different linear scaling techniques.Figure 6.8 shows the 5% damped acceleration response spectrum of each groundmotion linearly scaled to the NBCC (2010) UHS for Vancouver, and their corre-sponding mean spectrum with respect to the target spectrum. The response spec-trum of the spectrally matched ground motions is also included for comparison.151Table 6.1: Scaling factors calculated for the selected crustal ground motionsusing different linear scaling methods.No. Event Name Station DirectionPGA Sa(T1) ASCE SIa MSEscaling scaling scaling scaling scaling1Friuli- Italy TolmezzoFN 1.19 0.90 1.07 0.98 1.02 FP 1.40 1.05 0.95 0.97 0.993Tabas- Iran DayhookFN 1.46 1.41 1.40 1.14 1.184 FP 1.28 0.62 1.25 0.94 0.975New Zealand Matahina DamFN 1.52 0.93 1.61 1.17 1.196 FP 1.79 0.82 1.47 1.27 1.317Loma PrietaCoyote Lake Dam (SW Abut)FN 2.88 1.83 1.99 2.06 1.998 FP 1.02 0.95 0.94 0.94 0.969Centerville Beach Naval FacFN 1.74 1.15 1.86 1.26 1.3310 FP 1.99 1.70 1.63 1.40 1.4211Northridge LA - UCLA GroundsFN 1.41 1.72 1.76 1.42 1.4712 FP 1.06 1.63 1.50 1.04 1.1013Hector Mine HectorFN 1.27 0.97 0.98 0.90 0.9514 FP 1.59 1.83 1.49 1.36 1.430 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G20 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G30 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G4Figure 6.3: Continued.1520 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G50 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G60 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G70 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G80 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G90 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G100 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G110 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G120 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G130 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.3: Acceleration time histories of the selected 14 crustal ground mo-tions linearly scaled to the NBCC (2010) UHS of Vancouver using PGAscaling method.1530 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G20 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G30 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G40 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G50 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G60 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G70 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G80 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G90 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10Figure 6.4: Continued.1540 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G110 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G120 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G130 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.4: Acceleration time histories of the selected 14 crustal ground mo-tions linearly scaled to the NBCC (2010) UHS of Vancouver usingSa(T1) scaling method.0 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G20 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G30 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G4Figure 6.5: Continued.1550 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G50 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G60 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G70 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G80 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G90 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G100 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G110 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G120 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G130 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.5: Acceleration time histories of the selected 14 crustal ground mo-tions linearly scaled to the NBCC (2010) UHS of Vancouver usingASCE scaling method.1560 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G20 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G30 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G40 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G50 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G60 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G70 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G80 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G90 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10Figure 6.6: Continued.1570 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G110 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G120 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G130 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.6: Acceleration time histories of the selected 14 crustal ground mo-tions linearly scaled to the NBCC (2010) UHS of Vancouver using SIascaling method.0 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G20 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G30 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G4Figure 6.7: Continued.1580 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G50 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G60 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G70 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G80 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G90 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G100 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G110 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G120 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G130 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.7: Acceleration time histories of the selected 14 crustal ground mo-tions linearly scaled to the NBCC (2010) UHS of Vancouver using MSEscaling method.159ith GM mean UHS Vancouver0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)PGA scaling0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)Sa(T1) scaling0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)ASCE scaling0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)SIa scaling0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)MSE scaling0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)Spectrally matchedFigure 6.8: The 5% damped acceleration response spectra of the selected 14crustal ground motions and their corresponding mean response usingdifferent methods of scaling/matching with respect to the target NBCC(2010) UHS of Vancouver. Dashed-green lines show the single periodor the period range at which the motions are scaled.1606.4.2 Subcrustal earthquakesDeeper subcrustal earthquakes typically occur between 30 to 45 km depth. Likethe crustal earthquakes, these motions usually have a magnitude less than 7.5 withshaking duration of less than a minute.Searching for the subcrustal records are conducted using S2GM (accessed onMarch 2015), which is a web-based tool used to facilitate the selection, scaling,and downloading of ground motion time history records and data. Subcrustalearthquakes are mostly downloaded from the COSMOS database (Archuleta et al.,2006). Japanese earthquakes are directly downloaded from the K-NET (Kinoshita,1998) and KiK-net (Aoi et al., 2000) databases.The criteria for selection of the subcrustal ground motions are set as the mag-nitude range of 6.5 to 7.5, with the closest distance of 30 to150 km of the causativefault plane from the earthquake sites. Also the reference site class C is adopted asthe fundamental site condition. Selection of the candidate records are conductedbased on the best linearly scaled motions to the UHS of Vancouver in the periodrange of 0.02 to 0.8 sec, which covers slightly higher range than 0.2T1 to 1.5T1.Based on aforementioned criteria, the list of the selected 14 subcrustal ground mo-tions are presented in Table 6.2. Both components of E-W and N-S of each groundmotion are used in this study.Table 6.2: List of the selected subcrustal ground motions.No. Event Name Year Station Magnitude Vs30 (m/s) Direction SF1Miyagi Oki, Japan 2005MYG0167.2580.0E-W 2.642 N-S 2.783MY6014 706.2E-W 2.224 N-S 2.665FKS010 585.9E-W 1.566 N-S 1.637MYG013 535.5E-W 1.168 N-S 1.639IWT011 565.3E-W 2.4110 N-S 1.9511Nisqually, WA 2001 Olympia Residence 6.8 -E-W 2.8812 N-S 3.0913Michoacan, Mexico 1997 Villita Margen Derecha (VILE) 7.3 -E-W 3.1014 N-S 3.84Among five linear scaling methods, the MSE method which is the commonly1610 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G10 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G20 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G30 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G40 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G50 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G60 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G70 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G80 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G90 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G10Figure 6.9: Continued.1620 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G110 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G120 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G130 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.9: Acceleration time histories of the selected 14 subcrustal groundmotions linearly scaled to the NBCC (2010) UHS of Vancouver usingMSE scaling method.0 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G10 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G20 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G30 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G4Figure 6.10: Continued.1630 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G50 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G60 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G70 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G80 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G90 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G100 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G110 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G120 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G130 20 40 60 80 100−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.10: Acceleration time histories of the selected 14 subcrustal groundmotions spectrally matched to the NBCC (2010) UHS of Vancouver.164ith GM mean UHS Vancouver0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)MSE scaling0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)Spectrally matchedFigure 6.11: The 5% damped acceleration spectra of the selected 14 sub-crustal ground motions and the corresponding mean response usingMSE linear scaling and spectral matching methods with respect to thetarget NBCC (2010) UHS of Vancouver. Dashed-green lines show theperiod range at which the motions are scaled.used method in practice for scaling the earthquake records and provides a resean-able match to the target UHS (Figure 6.8), is used to linearly scaled the subcrustalground motions to the UHS of Vancouver. In addition the motions are spectrallymatched to the target spectrum in order to evaluate the mean value of the struc-tural response and provide the basis for comparison the seismic performance of thebasement walls. The calculated scaling factors from MSE method are reported inTable 6.2.6.4.3 Subduction earthquakesThe largest earthquakes recorded around the world are subduction interface earth-quakes, sometimes called megathrust events. These events are typically greaterthan M8+ and are associated with shaking in excess of two or three minutes.Searching criteria for the subduction ground motions is set as the magnituderange of 8.0 to 9.0, with the closest distance of 30 to 150 km of the causative faultfrom the earthquake sites. Site class C soil is adopted for selecting subduction mo-tion records. Also the spectral shape of the records are compared with the hazardvalues corresponding to the subduction events presented in NBCC (2010).Seismic hazard values intended for the NBCC (2010) design data for subduc-165tion scenario in Vancouver proposed by Adams and Halchuk (2003) are illustratedin Figure 6.12. These values are determined for firm ground (site class C - averageshear wave velocity of 360 to 760 m/s) with the probability of an exceedence of2% in 50 years. In this figure the solid line corresponds to the hazard values ofCascadia subduction earthquake scenario derived from the deterministic (Casca-dia) model for a probability of 2% in 50 years; whereas the dashed line representsthe spectral values corresponds to the median spectral ordinates obtained from theprobabilistic model for crustal and subcrustal events that has been used so far asthe target spectrum in this study.0 1 2 3 400.30.60.91.21.5Period (sec)ARS (g)  UHS corresponding to 2%/50 yearCascadia subduction hazard valuesFigure 6.12: The 2% in 50 year robust probabilistic hazard design valuesfrom the NBCC (2010) in comparison with the hazard values fromdeterministic Cascadia subduction earthquake scenario for Vancouver.Table 6.3 presents the selected Cascadia subduction events and the magnitudeand the hypocentral distance of each record. Same as subcrustal ground motions,S2GM (accessed on March 2015) search engine is used for selecting subductionearthquakes records.Scaling is also necessary for subduction ground motions in order to expose thestructures to the level of ground motion that corresponds to the seismic demandadopted by the NBCC (2010) for Vancouver. All the selected subduction groundmotions are linearly scaled to match the proposed design spectra for Cascadia sub-duction event over the period range of 0.02 to 0.8 sec (≈ 0.2T1 to 1.5T1) using thescaling factors presented in Table 6.3.The 5% damped elastic response spectra of the scaled Cascadia subduction166Table 6.3: List of the selected subduction ground motions.No. Event Name Year Station MagnitudeClosest distance Vs30 SF(m) (m/s)1Tokachi-Oki, Japan 2003Noya (HKD107)8.0126.4 1.652 Obihiro (HKD095) 132.2 1.033 Futamata (HKD087) 148.7 0.844 Tsurui (HKD083) 163.4 0.975Michoacan, Mexico 1985Caleta De Campos (CALE)8.138.3 0.916 Villita (VILE) 47.8 1.297 La Union (UNIO) 83.9 0.758 Zihuatanejo (AZIH) 132.6 1.289Hokkaido, Japan 1952HKD0818.1148.4 410 1.8210 HKD093 123.3 512 1.4211 HKD094 110.8 381 1.4912Tohoku, Japan 2011FKS0159.095.3 706 0.7413 TCG015 137.7 464 0.8514 YMT007 148.9 371 0.83ground motions with respect to the NBCC (2010) subduction hazard values areshown in Figure 6.13. Unlike crustal and subcrustal earthquake records which havea clear short-period spectral content, in subduction motions the major contributionsto hazard is focused on large periods. Acceleration time histories of the linearlyscaled subduction ground motion are presented in Figure 6.14.ith GM mean Cascadia suduction hazard values0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)Figure 6.13: The 5% damped acceleration response spectra of 14 subductionrecords scaled to hazard values for Cascadia subduction earthquakescenario proposed by the NBCC (2010) for Vancouver. Dashed-greenlines show the period range at which the motions are scaled.1670 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G10 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G20 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G30 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G40 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G50 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G60 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G70 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G80 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G90 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G10Figure 6.14: Continued.1680 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G110 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G120 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G130 50 100 150 200 250 300−0.4−0.200.20.4Time (sec)Acceleration (g)G14Figure 6.14: Acceleration time histories of the selected Cascadia subductionground motions.6.4.4 Near-fault pulse-like earthquakesAs discussed in Section 6.2, there are major faults near British Columbia, whichcause earthquakes. It is highly probable that the interaction between tectonic platesgenerate long-duration pulse-like motions especially in the direction of fault planerupture. These pulse-like ground motions affect the seismic response of the struc-tures in a different manner than the far-fault ground records and can impose asevere demand on structures to an extent not predicted by typical measures suchas response spectra (Alavi and Krawinkler, 2001; Bertero et al., 1978; Bray andRodriguez-Marek, 2004; Kalkan and Kunnath, 2006; Luco and Cornell, 2007;Makris and Black, 2003).The response spectrum alone does not adequately characterize near-fault groundmotion (Finn, 2000). The pulse-like ground motion is mainly considered to con-tain a short-duration pulse with high amplitude that occurs early in the velocitytime history. One cause of these velocity pulses is the forward directivity effectof the near-fault region. Forward directivity occurs when both the rupture and thedirection of slip on the fault are towards the site. This conditions are usually met169in strike-slip faulting, where the fault slip direction is oriented horizontally in thedirection along the strike of the fault, and rupture propagates horizontally alongstrike. In addition, the conditions required for forward directivity can be met indip-slip faulting, including both reverse and normal faults (Somerville et al., 1997).Another near-fault effect is fling step which is mentioned for completeness but isexcluded from this study.Search for the pulse-like ground motions is conducted using PEER-NGA database(Chiou et al., 2008; PEER, accessed on November 2014). In this database pulse-like ground motion records have been identified following the criteria proposed byBaker (2007). The pulse-like ground motions are selected based on moment mag-nitude of 6.5 to 7.5, occurred within a distance of 20 km from the causative faultand they all belong to the NBCC (2010) site class C. For selection of the near-faultground motions other than aforementioned criteria, the presence of a short-durationpulse with high amplitude is necessary. It is worth to mention that without a de-tailed seismological study on individual records, there is no assurance that velocitypulses of the pulse-like records in PEER-NGA database are all due to directivityeffect. Although it is likely that other factors may have caused or contributed tothe velocity pulses of some records, but it is expected that the pulses are similar tothose caused by directivity effect and therefore can be used in modeling the effectsof directivity pulses on structures.Table 6.4 lists the selected 14 near-fault motions. The table provides eventname, year, station magnitude, shear wave velocity of the top 30 m of the recordedsite, ground motion component and scaling factor. All selected ground motions arelinearly scaled to the target UHS of Vancouver in the period range of 0.02–0.8 sec,using MSE linear scaling method. Figure 6.15 illustrates the 5% damped accel-eration response spectra of the scaled ground motions with respect to the NBCC(2010) UHS of Vancouver. Acceleration and velocity time histories of the selectednear-fault motions are presented in Figures 6.16 and 6.17, respectively.170Table 6.4: List of the selected pulse-like ground motions.No. Event Name Year Station Magnitude Vs30 (m/s) Comp. SF1Irpinia Italy-01 1980 Sturno (STN) 6.9 382.0000 1.262 270 1.083Loma Prieta 1989 Saratoga - Aloha Ave 6.93 380.9000 1.034 090 1.175Cape Mendocino 1992 Centerville Beach Naval Fac 7.01 459.0270 1.096 360 0.717Northridge-01 1994 Sylmar - Converter Sta East 6.69 370.5011 1.098 281 0.799Bam Iran 2003 Bam 6.6 487.4L 0.5610 T 0.6711Niigata Japan 2004 NIGH11 6.63 375.0E-W 0.6612 N-S 0.8413Chuetsu-oki Japan 2007 Joetsu Kakizakiku Kakizaki 6.8 383.4E-W 0.9214 N-S 1.20ith GM mean UHS Vancouver0 0.5 1 1.5 200.40.81.21.62Period (sec)ARS (g)Figure 6.15: The 5% damped acceleration spectra of the selected 14 near-fault pulse-like ground motions and the corresponding mean responseusing MSE linear scaling method with respect to the target NBCC(2010) UHS of Vancouver.1710 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G20 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G30 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G40 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G50 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G60 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G70 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G80 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G90 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G10Figure 6.16: Continued.1720 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G110 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G120 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G130 10 20 30 40 50 60−0.8−0.400.40.8Time (sec)Acceleration (g)G14Figure 6.16: Acceleration time histories of the selected 14 near-fault groundmotions linearly scaled to the NBCC (2010) UHS of Vancouver usingMSE scaling method.0 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G10 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G20 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G30 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G4Figure 6.17: Continued.1730 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G50 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G60 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G70 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G80 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G90 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G100 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G110 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G120 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G130 10 20 30 40 50 60−60−40−200204060Time (sec)Velocity (cm/s)G14Figure 6.17: Velocity time histories of the selected 14 near-fault ground mo-tions linearly scaled to the NBCC (2010) UHS of Vancouver usingMSE scaling method.1746.5 Simulation resultsThis section presents a distillation of the results of more than 600 nonlinear dy-namic analyses performed on basement walls designed for different fractions ofthe code PGA, subjected to ensembles of dominant seismic mechanisms in south-western BC comprise of shallow crustal, deep subcrustal, interface earthquakesfrom a Cascadia subduction events and near-fault earthquake motions. Two mainmethods of spectral matching and linear scaling are used to ensure that the inputmotions match the NBCC (2010) specified UHS for Vancouver.All the basement walls presented in this section are founded on Case I soilprofile, which result in the foundation of the basement walls be embedded in thesecond stiff soil layer (Figure 5.13). The normalized shear wave velocities ofVs1 = 200 m/s and Vs1 = 400 m/s are assigned to the first and the second soillayers, respectively. The UBCHYST soil model with the calibrated set of param-eters presented in Table 5.1 are used. The maximum resultant drift ratio along theheight of the basement wall is a parameter which is used to compare the nonlinearseismic response of the walls.Crustal ground motionsThe first set of calculations is conducted using the 4-level basement wall with thetotal height of 11.7 m, designed for different fractions of the code PGA as de-scribed in Chapter 3. The main objective of this section is to evaluate the effect ofvarious methods of scaling/matching ground motions on seismic performance ofthe basement walls. Also the variation of the resultant maximum drift ratios in theform of standard deviation using different scaling/matching techniques is studied.Figures 6.18 to 6.21 provide comparisons of the envelopes of the maximumdrift ratio along the height of the 4-level basement wall designed for different frac-tions of the NBCC (2010) code PGA, subjected to the suite of 14 crustal groundmotions scaled/matched according to the various methods outlined in this thesis. Inthese plots, the average value corresponds to the mean of the maximum envelopesof the drift ratios resulting from 14 crustal seismic events. Assuming normally dis-tributed drift ratios, average ± 1σ represents the first standard deviation with a68% chance that the mean falls within the range of standard error.175In order to evaluate the performance of the basement walls using different scal-ing techniques, one must first establish a basis for comparison. The true distri-bution of drift response corresponding to the suite of crustal records is unknown,so a reference distribution is adopted as a substitute for the true, but ultimatelyunknowable distribution of drift. It is legitimate to assume that the resultant driftratio of the system subjected to the spectrally matched ground motions presentedin Chapter 4 is an unbiased estimate of the mean response and is defined as a “ref-erence” value (Figures 6.18(f) to 6.21(f)), to provide a basis for comparing theperformance of the system subjected to the various scaling methods. As previouslymentioned spectral matching reduces spectral variability within a suite of groundmotions at a period range of interest and provide an estimation of mean responsewith a reasonable standard deviation.Figures 6.18(a,b) to 6.21(a,b) show that scaling the crustal ground motionsbased on the peak ground acceleration (PGA scaling) and spectral acceleration atthe fundamental period of the system (Sa(T1) scaling), introduce a large scatterin the resultant maximum drift ratio at the top and bottom basement levels. Fromthese figures one can concluded that there is a more pronounced scatter in nonlinearseismic response of basement walls using scaling method based on scalar intensitymeasures such as PGA and Sa(T1) than other scaling techniques. These techniquesare considered non-efficient and estimation of seismic performance based on themare not accurate. Miranda (1993) and Shome et al. (1998) performed similar stud-ies and observed that using acceleration parameters (such as PGA or Sa(T1)) forscaling ground motions increases the scatter in the nonlinear response of the struc-tures.As shown in Figures 6.18(a) to 6.21(a), the PGA scaling method leads to de-signs with significant uncertainty and unknown margins of safety. This is due tothe importance of spectral shape of an accelerogram in nonlinear response, as PGAis not a good indicator of the strength and frequency content of the ground motion.Shome and Cornell (1998) and Shome et al. (1998) found that seismic demandestimates are strongly correlated with the linear-elastic spectral response acceler-ation at the structure fundamental period, T1 and by using this method the scatterin the demand estimates can be significantly reduced compared with PGA scalingmethod. Although Sa(T1) scaling method substantially reduces the scatter in the176Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(a) PGA scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(b) Sa(T1) scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(c) ASCE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(d) SIa scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(e) MSE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA(f) Spectral matchingFigure 6.18: Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the height of thewalls designed for 50% of the code PGA subjected to a suite of crustalground motions scaled/matched using various methods outlined in thisstudy.177Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(a) PGA scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(b) Sa(T1) scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(c) ASCE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(d) SIa scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(e) MSE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(f) Spectral matchingFigure 6.19: Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the height of thewalls designed for 60% of the code PGA subjected to a suite of crustalground motions scaled/matched using various methods outlined in thisstudy.178Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA(a) PGA scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA(b) Sa(T1) scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA(c) ASCE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA(d) SIa scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA(e) MSE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)70% PGA(f) Spectral matchingFigure 6.20: Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the height of thewalls designed for 70% of the code PGA subjected to a suite of crustalground motions scaled/matched using various methods outlined in thisstudy.179Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGA(a) PGA scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGA(b) Sa(T1) scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGA(c) ASCE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGA(d) SIa scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGA(e) MSE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)100% PGA(f) Spectral matchingFigure 6.21: Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the height of thewalls designed for 100% of the code PGA subjected to a suite of crustalground motions scaled/matched using various methods outlined in thisstudy.180Max. Drift Ratio from ith GM Avg. Avg.   1!Scaled at PGA    Scaled at T=Ts   SIa 0.2T−1.5T    MSE 0.2T−1.5T    ASCE 0.2T−1.5T   Spectral Matching01234  Drift (%)50% PGAScaled at PGA    Scaled at T=Ts   SIa 0.2T−1.5T    MSE 0.2T−1.5T    ASCE 0.2T−1.5T   Spectral Matching01234  Drift (%)60% PGAScaled at PGA    Scaled at T=Ts   SIa 0.2T−1.5T    MSE 0.2T−1.5T    ASCE 0.2T−1.5T   Spectral Matching01234  Drift (%)70% PGAScaled at PGA    Scaled at T=Ts   SIa 0.2T−1.5T    MSE 0.2T−1.5T    ASCE 0.2T−1.5T   Spectral Matching01234  Drift (%)100% PGAFigure 6.22: The resultant maximum drift ratios and the corresponding meanand mean ± one standard deviation along the height of the wall de-signed for different fractions of the code PGA subjected to crustalground motions (G1–G14) scaled/matched using various methods out-lined in this study.181demand, but as illustrated in Figures 6.18(b) to 6.21(b) still there is a unacceptableamount of uncertainty and dispersion due to lengthening the apparent period ofvibration becuase of yielding compared to other methods of scaling.Figure 6.22 summarizes the maximum value of drift ratio along the height ofthe basement walls designed for different fractions of the code PGA, subjectedto 14 crustal ground motions all scaled/matched using various methods outlined inthis chapter. Within the limitation of the sample size used in this study, discrepancyimplies that the use of either linear-scaled records in a period range (SIa, MSE andASCE methods) or spectrum-compatible records (Spectral matching) introduces acertain degree of bias in the computed structural response. In contrast, the highdispersion calculated as the standard deviation of the resultant maximum drift ratiofor a sample size of 14 crustal ground motions scaled to a constant PGA, impliesthat the demand estimates are subject to significant uncertainty and the results arenot suggested to be considered.As depicted in Figure 6.22, scatter in dynamic response can be reduced byscaling the suites of ground motions over a range of periods instead of a singleperiod, which results in a more reasonable estimate of the mean resultant drift ratio(Martinez-Rueda, 1998; Shome and Cornell, 1998; Shome et al., 1998). This isdue to consideration of the spectral shape and frequency content of each groundmotion in the scaling factor calculation process. Three different methods of linearscaling over the period range have been evaluated in this study: SIa scaling, MSEscaling, and ASCE scaling methods. Results of the analyses show that using SIaand MSE linear scaling methods lead to a mean drift ratio similar to the referenceexpected mean value of the response, whereas ASCE scaling generates larger driftratios. As was illustrated earlier in Figure 6.8 scaling the suites of ground motionsbased on SIa and MSE scaling methods result in a mean spectrum with an overallgood match with respect to the seismic demand in a period range of interest. Con-sequently, these motions result in a mean drift ratio in agreement with the referencemean value. In contrast, ASCE scaling method generates stronger motions and asa result found to be conservative and generally overestimates the mean value ofdeformation by 20% in the case of the wall designed for 50% PGA.The data gathered in this study suggest that although most of the scaling andmatching techniques adopted herein are able to adequately capture the expected182response of the structure, the level of variability of the response in the form ofthe standard deviation of the resultant drift ratios are reduced significantly as onemoves from:(1) linear scaling the records to match the target spectrum at PGA or the naturalperiod of the system Sa(T1), to(2) linear scaling the records to match the target spectrum over the period rangeusing different methods such as ASCE, MSE and SIa scaling, to(3) spectrally matching the records in a time domain using the wavelet algorithmproposed by Abrahamson N.A. (1992) and Hancock et al. (2006).By assuming 1.7% drift ratio as an acceptance criterion, one can concluded thatwithin a significant range of variation, the conclusion still stands that the basementwall founded on dense soil can be safely designed using the M-O method with50% and 60% PGA and result in a satisfactory performance in a term of drift ratioif subjected to the linear scaled crustal ground motions regardless of the techniqueused for scaling the records to the target demand.In addition to the 11.7 m 4-level basement wall, the effect of linearly scaledmotions on the walls with deeper depths are also checked. To this aim, a seriesof analyses are conducted on the 4-level and 6-level basement walls with a totalheight of 13.1 m and 17.1 m, respectively, subjected to 14 crustal ground motionslinearly scaled to UHS of Vancouver. These walls are embedded in Case I soilprofiles as shown in Figure 5.33. The results of these analyses in form of themaximum resultant drift ratio are illustrated in Figure 6.23. In this figure MSEscaling method is chosen as a linear scaling method. The resultant drift ratios ofthe spectrally matched motions, as discussed earlier in Section 5.4, are also plottedfor comparison. The results confirm that the maximum resultant drift ratios alongthe height of the 4-level basement walls with 5.0 m top storey and the 6-levelbasement walls designed for 50% of the code PGA fall within an acceptable range.Subcrustal ground motionsFigure 6.24 shows the envelope of the maximum drift ratios along the height ofthe 4-level basement wall designed for 50% and 60% PGA subjected to a suite of183Max. Drift Ratio from ith GM Avg. Avg.   1!Spectral match MSE scaling   Spectral match MSE scaling   Spectral match MSE scaling   01234  Drift (%)50% PGA13.1 m basement11.7 m basement 17.1 m basementSpectral match MSE scaling   Spectral match MSE scaling   Spectral match MSE scaling   01234  Drift (%)60% PGA13.1 m basement11.7 m basement 17.1 m basementSpectral match MSE scaling   Spectral match MSE scaling   Spectral match MSE scaling   01234  Drift (%)70% PGA13.1 m basement11.7 m basement 17.1 m basementFigure 6.23: The resultant maximum drift ratios and the corresponding meanand mean ± one standard deviation along the height of the 4-level and6-level basement walls designed for different fractions of the NBCC(2010) code PGA subjected to 14 crustal ground motions scaled/-matched using MSE linear scaling and spectral matching methods.18414 subcrustal ground motions linearly scaled and spectrally matched to the UHSof Vancouver. The resultant drift ratio at the top floor levels of the wall designedfor 50% PGA have the maximum values of 1.24%±0.38% and 1.11%±0.23% incase the walls subjected to linear scaled and spectrally matched ground motions,respectively which in both cases fall within an acceptable range (< 1.7%).Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(a) MSE scaling−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGA(b) Spectral matchingFigure 6.24: Average of the maximum envelopes of drift ratios and the cor-responding average ± one standard deviation along the height of thewall designed for 50% and 6% of the code PGA subjected to 14 sub-crustal ground motions (a) linearly scaled and (b) spectrally matchedto the NBCC (2010) UHS of Vancouver.185Cascadia subduction ground motionsFigure 6.25 shows that the Cascadia subduction motions have no significant effecton the basement walls and result in very low drift ratios (< 0.2%) even on theweakest wall designed for 50% PGA.Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGAFigure 6.25: Average of the maximum envelopes of drift ratios and the corre-sponding average± one standard deviation along the height of the walldesigned for 50% of the code PGA subjected to 14 Cascadia subduc-tion ground motions linearly scaled to the NBCC (2010) subductionhazard values for Vancouver.Near-fault pulse-like ground motionsFigure 6.26 demonstrate the performance of the 4-level basement walls designedfor 50% and 60% of the code PGA, subjected to a suite of 14 near-fault pulse-likeground motions. These motions cause the performance of the bottom basementlevel become more critical and in some cases dominant, but still in an acceptablerange.The presented results suggest that the basement walls designed for 50% to60% NBCC (2010) PGA using the modified M-O method and founded on sandysoil would result in satisfactory performance when subjected to ground motionsreflecting three dominant seismic mechanism (crustal, subcrustal and Cascadia186Avg. of Max. Drift Ratio Avg.   1!.−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)50% PGA−1 0 1 2 3 402.75.48.111.7Drift (%)Height (m)60% PGAFigure 6.26: Average of the maximum envelopes of drift ratios and the corre-sponding average± one standard deviation along the height of the walldesigned for 50% of the code PGA subjected to 14 pulse-like groundmotions linearly scaled to the NBCC (2010) UHS of Vancouver.subduction) and pulse-like near-fault records in Vancouver and matching the codespecified intensity of the seismic hazard,which has an exceedance rate of 2% in 50years.187Chapter 7Summary and future researchScience never solves a problem without creating ten more.— George B. Shaw (1856–1950)7.1 SummaryA comprehensive study of the current seismic design procedure of deep basementwalls during earthquake events and the seismic pressures for which they should bedesigned for is being conducted at the University of British Columbia at the requestof the Structural Engineers Association of British Columbia (SEABC).The current state of practice for seismic design of basement walls in BritishColumbia is based on the studies of Okabe (1924) and Mononobe and Matsuo(1929) by incorporating the modification suggested by Seed and Whitman (1970)which is referred to as the Mononobe-Okabe (M-O) method. In this method theearthquake thrust acting on the wall is a function of the Peak Ground Acceleration(PGA), which is representative of the seismic demand anticipated for the subjectstructure at the site in question.The seismic hazard level in the National Building Code of Canada (NBCC,2010) for design of buildings has a probability of exceedance of 2% in 50 yearsand the related PGA hazard of 0.46 g for Vancouver. For designers who have beenusing the M-O method for estimating the seismic lateral pressures and eventually188designing the basement walls, using the full PGA leads to very large seismic forcesthat make the resulting structures expensive and over-designed. Because there hasbeen no reports of damage to building basement walls as a result of seismic earthpressures in recent United States earthquakes including the San Fernando (1971),Whittier Narrows (1987), Loma Prieta (1989), and Northridge (1994) earthquakes,SEABC became interested in designing the walls under the new code mandatedPGA and set up a task force to review the current seismic design procedure ofbasement walls in British Columbia.The seismic performance of the typical basement wall designed according tothe state of practice in Vancouver was examined. It is important to point out thatin this practice the building above the ground level is not considered and inertialloading of the surface structures on basement wall pressures are not taken into anaccount. In the benchmark analyses, the typical 4-level basement wall structurewith a total height of 11.7 m, was designed by SEABC structural engineers fordifferent fractions of the NBCC (2010) PGA for Vancouver.An enhanced dynamic nonlinear soil–structure interaction analyses were thenconducted on computational model of these basement walls to capture the essentialfeatures and response characteristics of the basement wall-backfill system underseismic loading and explore the capacity of the walls to absorb demand correspond-ing to NBCC (2010) with an exceedance rate of 2% in 50 years. For this purposeeach wall was subjected to the full demand imposed by a suite of 14 crustal groundmotions spectrally matched to the UHS of Vancouver. The soil–structure modelemployed elastic-plastic beam elements to model all structural components of themodel including basement walls. The soil layers consisted of two-dimensionalplane-strain quadrilateral elements simulated using the simple Mohr-Coulomb ma-terial model. With an insight from equivalent linear analyses, degraded elasticmodulus and equivalent damping ratio in the form of Rayleigh damping were em-ployed for closer representation of nonlinear soil system response in seismic load-ing. Interface elements represented by two elastic-perfectly plastic normal andshear springs between the soil and the structure were utilized to simulate inter-action between the concrete basement structure and surrounding soil and facilitatemodeling opening (separation) and slippage. In order to avoid reflection of outwardpropagating waves back into the model, quiet (viscous) boundaries, comprising in-189dependent dashpots in the normal and shear directions, were placed at the baseof the soil medium. The lateral boundaries of the soil grid were coupled to thefree-field boundaries at the sides of the model to simulate the free-field condition,which would exist in the absence of the structure.The results of the computational benchmark study were presented in the formof typical time histories of the lateral earth pressure, resultant lateral earth force andthe corresponding normalized height of application from the base of the wall. Also,envelopes of bending moments, shear forces, lateral deformations, and drift ratiosalong the height of the walls were presented and discussed. In an absence of anyreport on the acceptable drift ratios for constrained walls with distributed lateralloading, the ASCE-TCBRD (2010) was selected as the performance standard. Theresults of the benchmark analyses suggested that the walls designed for 100% PGAwere over conservative and the behavior of the basement wall designed for 50%to 60% PGA resulted in satisfactory performance when subjected to the currentseismic hazard for Vancouver with an exceedance rate of 2% in 50 years.A series of sensitivity analyses were conducted to identify the impact of variousparameters on the seismic performance of the basement wall. Table 7.1 lists theevaluated parameters, a range of variation and the sensitivity of the resultant driftratio along the height of the wall to the variation:Table 7.1: Summary of the sensitivity analyses conducted in this study.Parameter description Parameter Range of sensitivitySensitivityhigh a low bFriction angle of the interface element δ 5◦−15◦ XNormal stiffness of the interface element kn 9×105−9×107 kPa/m XShear stiffness of the interface element ks 9×105−9×107 kPa/m XDilation angle of the backfill soil ψ 0◦−10◦ XFriction angle of the backfill soil φ 28◦−38◦ XShear wave velocity of the backfill soil Vs1 150−250 m/s XModulus reduction in Mohr-Coulomb model G/Gmax 0.3−0.5 XDamping ratio in Mohr-Coulomb model D 6%−10% XShoring pressure during excavation KA−Ko 0.3−0.5 XaGreater than 25% change.bEqual or less than 25% change.190The benchmark analyses were conducted on a specific basement depth, foundedon dense soil deposit modeled using a simple Mohr-Coulomb model. Because ofthe radical shift in design practice suggested by these findings, extensive studieswere conducted to more fully validate the major conclusion regarding design andanalyses presented. In order to have a clear and comprehensible conclusion re-garding the effects of the structural height, subsoil stiffness, and ground motioncharacteristics on seismic response of the basement walls under the influence ofSSI, a comprehensive computational investigation has been conducted. A series ofanalyses were carried out on number of primary soil–structure interaction param-eters in order to assess the effect of input parameters’ uncertainties on proposeddesign seismic coefficient of basement walls and the robustness of the results. Tothis aim the seismic performance of the basement walls designed for different frac-tions of the NBCC (2010) PGA were re-calculated under alternative assumptionslisted in Table 7.2 to determine their impact on the conclusion drawn from thebenchmark analyses. The effect was measured by monitoring changes in the re-sultant maximum drift ratios along the height of the wall as summerized in Figure7.1.Table 7.2, Case 2: Adopting more representative constitutive model for simulat-ing nonlinear stress–strain response of the soil medium to obtain realisticestimates of an interaction between the basement wall and the surroundingsoil. For this purpose the relatively simple total stress UBCHYST modelwas used, which replicates the behavior of real soil and reduces the essenceof defining modulus reduction and Rayleigh damping with the simple Mohr–Coulomb model. The results of the analyses show that changing soil consti-tutive model does not have a considerable effect on the seismic performanceof the basement wall.Table 7.2, Cases 3–12: Evaluate the effect of local site condition in terms of ge-ometrical and geological structure of soft soil deposits underneath the base-ment wall, which cause a huge impact on the intensity and frequency con-tent of ground shaking around the structure. The seismic performance ofthe basement wall founded on various soil deposits that the variation of theshear wave velocity profiles and the depth to an impendence contrast be-191tween soil layers differentiating the cases were evaluated. The importanceof the impedance contrast and stiffness of soil layers on characterizing thesite response were assessed in terms of amplitude and frequency content andeventually the response of the embedded basement wall was evaluated.According to the results of the nonlinear site response analyses, it was ob-served that the presence of a relatively soft soil layer underneath the base-ment wall structure and the impendence contrast between various soil lay-ers, substantially affect the rate of ground motion amplification at differentbasement wall levels and consequently the resultant seismic deformation atvarious basement levels.Figure 7.1 shows that except for the cases 5 and 6, the resultant average± one standard deviation of all basement walls designed for even 50% and60% PGA falls within an acceptance range (< 1.7%) when subjected to thecurrent seismic hazard level in Vancouver, with a 2% chance of being ex-ceeded in 50 years. Eventhough according to practitioners (DeVall et al.,2010, 2014) using Vs1 = 150 m/s as the normalized shear wave velocity ofthe first soil layer is a bit low for high-rise construction in Vancouver, but theperformance of the basement walls designed for 50% and 60% PGA foundedon these soil layers would still fall in the lower range of the medium response(< 3.5%) category defined by ASCE-TCBRD (2010).Table 7.2, Cases 13–16: Assess the effect of wall geometry in the form of eitherincreasing a number of basement levels or assigning the higher top storey.To this aim the 4-level basement wall with 5.0 m top storey and total heightof 13.1 m, and the 6-level basement wall with total height of 17.1 m weredesigned by SEABC structural engineers following the state of practice inVancouver and were subjected to the full demand imposed by NBCC (2010).Figure 7.1 compares the resultant maximum drift ratios of the 4-level (H =13.1 m) and 6-level basement walls (H = 17.1 m) basement walls foundedon two different soil profiles and confirms that within a significant range ofvariations, the conclusion still stands that the basement walls can be safelydesigned with 50–60% NBCC (2010) PGA using the modified M-O method.192Table 7.2: Summary of analyses.Soil profileCase Basement wall Input Method of Constitutive Normalized Vs Depth toNo. geometry motion scaling/matching model top layer bottom layer impedance contrast(m/s) (m/s) (m)1 4-level (11.7 m) crustal spectral matching Mohr-Coulomb 200 400 12.152 4-level (11.7 m) crustal spectral matching UBCHYST 200 400 12.153 4-level (11.7 m) crustal spectral matching UBCHYST 200 400 17.14 4-level (11.7 m) crustal spectral matching UBCHYST 150 250 17.15 4-level (11.7 m) crustal spectral matching UBCHYST 150 300 17.16 4-level (11.7 m) crustal spectral matching UBCHYST 150 400 17.17 4-level (11.7 m) crustal spectral matching UBCHYST 200 250 17.18 4-level (11.7 m) crustal spectral matching UBCHYST 200 300 17.19 4-level (11.7 m) crustal spectral matching UBCHYST 250 250 -10 4-level (11.7 m) crustal spectral matching UBCHYST 250 300 17.111 4-level (11.7 m) crustal spectral matching UBCHYST 250 400 17.112 4-level (11.7 m) crustal spectral matching UBCHYST 300 300 -13 4-level (13.1 m) crustal spectral matching UBCHYST 200 400 13.5514 4-level (13.1 m) crustal spectral matching UBCHYST 200 400 17.5515 6-level (17.1 m) crustal spectral matching UBCHYST 200 400 18.516 6-level (17.1 m) crustal spectral matching UBCHYST 200 400 22.517 4-level (11.7 m) crustal PGA linear scaling UBCHYST 200 400 12.1518 4-level (11.7 m) crustal Sa(T1) linear scaling UBCHYST 200 400 12.1519 4-level (11.7 m) crustal ASCE linear scaling UBCHYST 200 400 12.1520 4-level (11.7 m) crustal SIa linear scaling UBCHYST 200 400 12.1521 4-level (11.7 m) crustal MSE linear scaling UBCHYST 200 400 12.1522 4-level (13.1 m) crustal MSE linear scaling UBCHYST 200 400 13.5523 6-level (17.1 m) crustal MSE linear scaling UBCHYST 200 400 18.524 4-level (11.7 m) subcrustal spectral matching UBCHYST 200 400 12.1525 4-level (11.7 m) subcrustal MSE linear scaling UBCHYST 200 400 12.1526 4-level (11.7 m) subduction MSE linear scaling UBCHYST 200 400 12.1527 4-level (11.7 m) near-fault MSE linear scaling UBCHYST 200 400 12.15193Max. Drift Ratio from ith GM Avg. Avg.   1!1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 2701234Case No.Drift (%)50% PGA1.7% acceptance criteria1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 2701234Case No.Drift (%)60% PGA1.7% acceptance criteriaFigure 7.1: Summary of the resultant maximum drift ratio of the basement walls designed for 50% and 60% of theNBCC (2010) PGA for different cases outlined in Table 7.2.194Table 7.2, Cases 17–23: In addition to the spectrally matched accelerograms usedin benchmark analyses to estimate the robust mean values of the seismicresponse, five linear scaling methods were adopted to capture the inherentmotion-to-motion variability of the basement wall responses subjected to asuites of earthquake ground motions under the seismic demand adopted byNBCC (2010) for Vancouver. Most of the adopted linear scaling techniqueswere able to adequately capture the expected response of the basement wall,but the level of variability of the response in the form of the standard de-viation of the resultant maximum drift ratios were reduced significantly asone moves from: (1) linear scaling the records to match the target spectrumat PGA or the natural period of the system Sa(T1); to (2) linear scaling therecords to match the target spectrum over the period range using differentmethods such as ASCE, MSE and SIa scaling; to (3) spectrally matching therecords in a time domain using the wavelet algorithm proposed by Abraham-son N.A. (1992) and Hancock et al. (2006).Within the limitation of the sample size used in this study, discrepancy im-plies that the use of either linear-scaled records over a period range (SIa,MSE and ASCE methods) or spectrum-compatible records (Spectral match-ing) introduces a certain degree of bias in the computed structural response.Results of the analyses show that using SIa and MSE linear scaling methodslead to a mean drift ratio similar to the reference expected mean value of theresponse, calculated by using spectrally-matched motions, whereas ASCEscaling technique generates larger drift ratios.Table 7.2, Cases 24–27: In order to assess the seismic performance of the base-ment walls in Vancouver, the input motions for these analyses should re-flect three dominant seismic sources in the south-western British Columbia:shallow crustal earthquakes, deep subcrustal earthquakes and interface earth-quakes from a Cascadia event. Also the effect of pulse-like near-fault groundmotions which contain a short-duration pulse with high amplitude in theirvelocity time histories, and consequently affect the structure in a differentmanner than far-field records were evaluated. Therefore, in addition to theselected 14 crustal ground motions, 14 subcrustal, 14 Cascadia subduction,195and 14 near-fault pulse-like records were selected and each scaled to the haz-ard levels proposed by NBCC (2010) using the MSE linear scaling method.As illustrated in Figure 7.1, the Cascadia subduction motions have no signif-icant effect on the basement walls and the performance of the 4-level base-ment wall designed for 50% and 60% PGA subjected to subcrustal and near-fault pulse like ground motions fall into an acceptable range.In conclusion the result of these analyses show that the behavior of the topand bottom basement levels are critical and the resultant drift ratios at these lev-els are significantly higher than the drift ratio of the other levels. The results asare presented in Figure 7.1 confirm that within a significant range of variations, theconclusion still stands that the basement wall founded on dry cohesionless mediumdense soil can be safely designed using the modified M-O method as presently usedin Vancouver but with an acceleration of 50–60% PGA instead of 100% PGA,which results in an over-designed structures. As noted in literature review (Ander-son et al., 2008; Candia, 2013; Lew, 2012), even a small amount of cohesion canreduce the seismic pressure acting on the wall significantly.7.2 Recommendations for future researchSince the purpose of this research work was to determine the seismic response ofthe basement walls resting on dry sandy soil deposits, further studies and somerefinements are recommended to make this research work more comprehensive forpractical applications. Future research work may be carried out in the followingareas:• The results presented herein are limited to the basement wall structures em-bedded in a dry medium dense sandy backfill soils. Fine-grained soils com-prising silt and clay with substantial amount of cohesion behave differentlyfrom soils containing clean sands and can be investigated in future studies.• There are many cities and districts exposed to seismic risk in south-westernBritish Columbia. This study was focused on the city of Vancouver. Othercities such as Victoria and Nanaimo with high seismicity require similar as-sessment of seismic performances of the basement walls196• The study can be expanded to the three-dimensional (3D) analyses becauseof significant site economic savings that can be achieved by reducing thePGA to lower fractions. In these analyses the basement walls will be sub-jected to the 3D earthquake ground motions, consist of two horizontal com-ponents and a vertical component, which has generally been neglected in thedesign process. It has been observed in recent earthquakes that the verticalcomponent of the ground motions may be equal or even in some cases signif-icantly exceed the local horizontal ground motion and can have an importanteffect on the seismic performance of the subjected basement wall.• This study is based on the walls meeting the safety criteria. By consideringthe possibility of collapse/failure for the walls, ground motions should ex-ceed the design ground motion and therefore analyzing the basement wallsusing Incremental Dynamic Analysis (IDA) is recommended. IDA is a state-of-the-art method for determining the effect of increasing earthquake groundmotion intensity on structural response up to collapse, following the pro-cedure introduced by the U.S. Federal Emergency Management Agency,FEMA P695 (2009) guideline.• Nonlinear continuum dynamic analyses of basement walls can be complexand is not a routine process. Therefore some engineers like to investigate theinteraction between the wall and the backfill using p-y springs. Very littlehas been done to evaluate the effect of this spring approach compare to thecontinuum approach. 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Earthquake case: active pressure without compaction load + appropriate%PGA earthquake load. Load factor=1.02143. Design case (CAN/CSA-A23.3-04, 2004): the wall is designed for whicheverof the above cases governs at any point in the wall. The governing case maychange along the wall height. In no case is the flexural capacity lass than thatprovided by minimum reinforcement.Stucture Model Reinforcementt+M1+M2+M3+MNLVL 1LVL 2LVL 3LVL NM=0-M1-M2-M3M=0+A1+A2+A3+AN-A1-A2-A3200 mmsoilFigure A.1: The structural details of the model basement wallIn Figure A.1:• Wall is continuous.• Floors are 200 mm slabs, 3 m long, pinned at the end, f ′c = 25 MPa providesonly ”nominal” fixity at wall to approximate pinned condition.215• 200 mm slab used to adjust wall ”centre line” moments at slab/wall joint towall ”design” negative moments near top and bottom face of slab.• Actual floor slab thickness and span lengths will vary from project to project,but for common conditions will only have a small effect on results.• floor slabs are pinned at their ends but are fixed laterally.• All results are for a 1 m length horizontally along the wall.• The non-linear model that includes soil is not fixed laterally at the floors.• The lower levels were modeled as a ”box” and the floor slabs and end wallswere modeled with shear and flexural stiffnesses. Various stiffnesses wereassumed to develop supports for the support stiffnesses was undertaken earlyin this project. The effect on the foundation wall results was small and thestiffness that gave the most conservative result was used in the remainder ofthe study.A.3 Moment capacity• Calculated factored moments from governing load case ×1.3 ∼= ”nominal”flexural capacity.• In no case are the moments less than the ”nominal” flexural capacity basedon minimum reinforcement requirements.216Table A.2: Nominal moment capacity (kN−m/m) in W1W1 Height Static 50% 60% 70% 80% 90% 100%(m) No EQ. PGA PGA PGA PGA PGA PGALVL 1 3.60.0 0.0 0.0 0.0 0.0 0.0 0.0+44.5 +48.8 +59.0 +70.6 +82.6 +96.8 +113.2-44.5 -59.9 -70.6 -82.1 -95.5 -109.7 -126.2LVL 2 2.7-44.5 -59.9 -70.6 -82.1 -95.5 -109.7 -126.2+44.5 +44.5 +44.5 +44.5 +44.5 +44.5 +44.5-44.5 -44.5 -44.5 -44.5 -44.5 -44.5 -44.5LVL 3 2.7-44.5 -44.5 -44.5 -44.5 -44.5 -44.5 -44.5+44.5 +44.5 +44.5 +44.5 +44.5 +44.5 +44.5-70.3 -70.3 -70.3 -70.3 -70.3 -70.3 -70.3LVL 4 2.7-70.3 -70.3 -70.3 -70.3 -70.3 -70.3 -70.3+63.2 +63.2 +63.2 +63.2 +63.2 +63.2 +63.20.0 0.0 0.0 0.0 0.0 0.0 0.0Table A.3: As(mm2/m) in W1W1 Height Static 50% 60% 70% 80% 90% 100%(m) No EQ. PGA PGA PGA PGA PGA PGALVL 1 3.60.0 0.0 0.0 0.0 0.0 0.0 0.0+500 +529 +635 +762 +909 +1015 +1248-500 -698 -825 -952 -1121 -1311 -1524LVL 2 2.7-500 -698 -825 -952 -1121 -1311 -1524+500 +500 +500 +500 +500 +500 +500-500 -500 -500 -500 -500 -500 -500LVL 3 2.7-500 -500 -500 -500 -500 -500 -500+500 +500 +500 +500 +500 +500 +500-825 -825 -825 -825 -825 -825 -825LVL 4 2.7-825 -825 -825 -825 -825 -825 -825+677 +677 +677 +677 +677 +677 +6770.0 0.0 0.0 0.0 0.0 0.0 0.0217Table A.4: Nominal moment capacity (kN−m/m) in W2W2 Height Static 50% 60% 70% 100%(m) No EQ. PGA PGA PGA PGALVL 1 5.00.0 0.0 0.0 0.0 0.0+66.6 +99.3 +118.0 +138.8 +218.0-83.8 -119.0 -139.0 -161.0 -245.6LVL 2 2.7-83.8 -119.0 -139.0 -161.0 -245.6+65.0 +65.0 +65.0 +65.0 +65.0-65.0 -65.0 -65.0 -65.0 -65.0LVL 3 2.7-65.0 -65.0 -65.0 -65.0 -65.0+65.0 +65.0 +65.0 +65.0 +65.0-77.0 -77.0 -77.0 -77.0 -77.0LVL 4 2.7-77.0 -77.0 -77.0 -77.0 -77.0+66.0 +66.0 +66.0 +66.0 +66.00.0 0.0 0.0 0.0 0.0Table A.5: As(mm2/m) in W2W2 Height Static 50% 60% 70% 100%(m) No EQ. PGA PGA PGA PGALVL 1 5.00.0 0.0 0.0 0.0 0.0+615 +927 +1109 +1314 +2122-779 -1119 -1316 -1537 -2414LVL 2 2.7-779 -1119 -1316 -1537 -2414+600 +600 +600 +600 +600-600 -600 -600 -600 -600LVL 3 2.7-600 -600 -600 -600 -600+600 +600 +600 +600 +600-711 -711 -711 -711 -711LVL 4 2.7-711 -711 -711 -711 -711+611 +611 +611 +611 +6110.0 0.0 0.0 0.0 0.0218Table A.6: Nominal moment capacity (kN−m/m) in W3W3 Height Static 50% 60% 70% 100%(m) No EQ. PGA PGA PGA PGALVL 1 3.60.0 0.0 0.0 0.0 0.0+65.0 +65.0 +78.9 +103.0 +155.0-65.0 -68.0 -93.0 -115.0 -174.0LVL 2 2.7-65.0 -68.0 -93.0 -115.0 -174.0+65.0 +65.0 +65.0 +65.0 +65.0-65.0 -65.0 -65.0 -65.0 -65.0LVL 3 2.7-65.0 -65.0 -65.0 -65.0 -65.0+65.0 +65.0 +65.0 +65.0 +65.0-65.0 -65.0 -67.3 -73.8 -97.6LVL 4 2.7-65.0 -65.0 -67.3 -73.8 -97.6+65.0 +65.0 +65.0 +65.0 +65.0-65.0 -65.0 -65.0 -65.0 -65.0LVL 5 2.7-65.0 -65.0 -65.0 -65.0 -65.0+65.0 +65.0 +65.0 +65.0 +65.0-104.8 -104.8 -104.8 -104.8 -104.8LVL 6 2.7-104.8 -104.8 -104.8 -104.8 -104.8+88.5 +88.3 +88.3 +88.3 +88.30.0 0.0 0.0 0.0 0.0219Table A.7: As(mm2/m) in W3W3 Height Static 50% 60% 70% 100%(m) No EQ. PGA PGA PGA PGALVL 1 3.60.0 0.0 0.0 0.0 0.0+600 +600 +726 +957 +1470-600 -624 -860 -1071 -1665LVL 2 2.7-600 -624 -860 -1071 -1665+600 +600 +600 +600 +600-600 -600 -600 -600 -969LVL 3 2.7-600 -600 -600 -600 -969+600 +600 +600 +600 +600-600 -600 -617 -679 -903LVL 4 2.7-600 -600 -617 -679 -903+600 +600 +600 +600 +600-600 -600 -600 -600 -600LVL 5 2.7-600 -600 -600 -600 -600+600 +600 +600 +600 +600-972 -972 -972 -972 -972LVL 6 2.7-972 -972 -972 -972 -972+816 +816 +816 +816 +8160.0 0.0 0.0 0.0 0.0220A.4 Shear capacity - CAN/CSA-A23.3-04 (2004)Factored shear resistance at supports:Vf =Vc = φcλβ√f ′c b dv (A.1)where, λ = 1.0, φc = 0.65, b = 1.0, and β = 0.21• For t = 250 mmdv = 0.9× (250−50) = 180 mmf ′c = 30 MpaVf =Vc = 0.65×0.21×√30×180 = 134.6 kN/m• For t = 300 mmdv = 0.9× (300−50) = 225 mmf ′c = 40 MpaVf =Vc = 0.65×0.21×√40×225 = 194.2 kN/mTable A.8: Nominal shear capacityWallFactor Resistance ×1.3 Nominal (×1/0.65 = 1.54)(kN/m) (kN/m) (kN/m)250 mm 134.6 175 207300 mm 194.2 252 299• Walls designed for 100% PGA loading for shear.• Shear at 50%, 60%, 70% PGA close to 100% PGA load.• Shear reinforcement would be applied to wall to maintain thin wall thick-nesses, if required.A.5 Wall curvature and rotation capacityDrift defined as: δ/(L/2)≡ θ in radians.221LVL 1 L !Critical hingeFigure A.2: Calculated θ capacity at governing section of the wallAssumptions:• εc maximum strain = 0.004.• εs maximum strain = 0.05.• φc taken as 1.0 (nominal concrete strength).• fy taken as 1.2× 400 to approximate actual yield strength and some strainhardening.• length of plastic hinges taken as 0.67×d.• Non-linear curve taken as elastic-perfectly plastic.Table A.9: Drift limitWall 50% PGA 60% PGA 70% PGA 100% PGAW1 0.033 0.027 0.023 0.014W2 0.032 0.027 0.023 0.014W3 0.035 0.035 0.034 0.020222Note:• The recommendation by the ASCE Task Committee on Design of Blast-Resistant Buildings in Petrochemical Facilities (ASCE-TCBRD, 2010) fordrift limit is 0.017 used as upper limit, which governs all of the above exceptfor 100% PGA loads. However actual drifts for this case are very small andwell within limits.• εs ≤ 0.05 cuts θ off at 0.035.223

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