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61  7.1 General A numerical modeling program starts with a preparation process in which (i) the dimension- ality of the simulations (1D, 2D, 3D, or some combination thereof) is chosen, (ii) the software is chosen, (iii) CMs are selected, and (iv) the manner in which the results of SRA will be evaluated is identified. The results may be evaluated by comparison of calculated spectra to the code- mandated minimum values, by evaluating case histories (e.g., replicate case history, then use the same modeling approach for design evaluations), or by using engineering judgment. The numerical modeling program is typically based on a prioriâestablished protocols. Sample protocols for the calibration of constitutive models (i.e., for calibration at the soil element level) and for calibration at the system level (i.e., calibration at the soil profile level) are presented in Sections 5.3.2 and 5.3.3, respectively. The numerical modeling program presented herein has been performed following the pro- tocols outlined in Sections 5.3.2 and 5.3.3. It has been undertaken on case histories that were either identified by screening or created (and amended) by centrifuge modeling. Three case histories have been updated to reflect the results of site-specific investigation and testing at the WLA site and to include supplemental relevant information for the Treasure Island site. The protocols outlined in Sections 5.3.2 and 5.3.3 (as further developed and explained in Sec- tions 7.2.2 and 7.2.3) and the results of the numerical modeling program presented herein are an element used to develop the guidelines presented in Chapter 8. 7.2 Preparation 7.2.1 Updated Case Histories The numerical modeling program included seven case histories identified by screening or generated herein to fill in data gaps. The screening process and selections are explained in Chapter 4. A summary of case histories identified by screening is presented in Table 7-1 (case histories 1, 2, and 4 through 6). The selected case histories include six field case histories (i.e., case histories 1 through 6; see Table 7-1 and Figure 7-1) and one case history generated by physical modeling (i.e., the centrifuge experiment referred to as case history No. 7 in Table 7-1 and in Figure 7-1). Collectively, these case histories encompass a breadth of site and record- ing conditions. As schematically presented in Figure 7-1, soils are horizontally stratified, silty sands are liquefiable (including those that liquefied in the past), and a variety of other soils such as silts and clays are present in the profile. Predominant periods of 1D columns (Ts) shown in Figure 7-1 range from approximately 0.2 s to 1.4 s and, as such, are representative of both short- and long-period soil sites. C H A P T E R 7 Numerical Modeling Program
62 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines The first (i.e., leftmost) soil column shown in Figure 7-1 was evaluated as two case histories, each with a different set of recorded acceleration histories. The second column represents the WLA site at its re-instrumented location nearby. The profile differs from the original WLA profile due to its slightly different location (north versus south end of the site) and includes the results of additional investigation conducted as part of the re-instrumentation effort and this study. The third and fourth columns are the Owi and Port Island man-made sites in Japan. No updated information was available for these two case histories. The fifth soil column is representative of the Treasure Island case history. The last (i.e., seventh) column is a replica of the WLA site con- structed for this project in a laminar box. The Treasure Island site is the only screened effective-stress case history with input motion recorded at a nearby rock outcrop (see definition of rock outcrop in Figure 2-1). For numerical modeling purposes, this motion was applied as an âoutcropâ motion. Motions at other field case histories were recorded in-hole and were therefore applied at the base of SRA models as âwithinâ motions. The centrifuge experiment resembles a field case history with an in-hole motion. There- fore, selected motion was applied as a within motion at the location within the modeled profile that corresponds to the base of laminar box. A summary of information used to update, develop, and interpret calculated responses of selected case histories to applied ground motions is provided in Table 7-1. This information is No. Case History Updated Summary of Key Items 1 WLA site â 1987 M 6.2 Elmore Ranch earthquake Ts = 0.29 s Strong-motion case history without PWP measurements. Did not liquefy. This case history is used to test its counterpart in the Superstition Hills earthquake (given that everything else is the same, 1D model with the Elmore Ranch record should not liquefy and should liquefy when subjected to the Superstition Hills record). ru = not recorded in 1987, but replicated in the centrifuge experiment. 2 WLA site â 1987 M 6.6 Superstition Hills earthquake (occurred 7 hrs after the Elmore Ranch earthquake). Ts = 0.29 s Still the most complete SM case history with PWP measurements. Widespread liquefaction. An abundance of observational data, and a controversy about the accuracy of PWP records. ru = 0.95+ (recorded). 3 Re-instrumented WLA site â 2012 M 4.9 Hovley earthquake Ts = 0.63 s Instrumentation originally installed at the wildlife site in 1981 was abandoned. New, modern instrumentation was installed in 2004 at a site nearby. Significant site characterization/material testing was performed immediately prior to re-instrumentation. ru = 0.65 (recorded). 4 Owi Island No. 1 - 1985 M 6.2 Chiba-Ibaragi, Japan, earthquake Ts = 0.25 s Well-instrumented hydraulic fill site in Tokyo Bay. Ground surface (0.072 g) and in-hole (0.043 g) SM records and a PWP record at depth. Site did not liquefy. ru = 0.02 (recorded). 5 Port Island â 1995 M 6.9 Hyogo-Ken Nanbu (Kobe), Japan, earthquake Ts = 0.38 s Instrument array extends through hydraulic fill known to have liquefied in the 1995 Hyogo-Ken Nanbu (Kobe), Japan, earthquake into the native marine sediments but does not include pore-pressure transducers. This is the effective-stress case history with the highest intensity of ground motion (0.58 g recorded in-hole at a depth of 16 m) and hence exhibits nonlinear effects. ru = 0.95+ (inferred from the observational data). 6 Treasure Island â 1989 M 6.9 Loma Prieta earthquake Ts = 1.38 s Well-known case history and the only effective-stress case history for which both bedrock outcrop and ground surface records are available. (This is important because design is performed with bedrock outcrop motions.) Unfortunately, no PWP records are available. However, the site liquefied as numerous sand boils were observed in 1989. ru = 0.95+ (inferred from the observational data). 7 Centrifuge experiment â 1949 M 7.1 Western Washington earthquake Ts = 0.22 s Experiment designed to fill in a void within the suite of case histories available. (Strong excitation at sites with PWP instrumentation is lacking.) Resembles, as close as possible, the upper 7.5 meters of the wildlife site. Western Washington earthquake (Olympia) WHTL record scaled to 0.68 g/ 0.57 g (applied/achieved at the base of the laminar box). This motion liquefied the model. ru ⥠0.95. Notes: ru = PWP ratio (PWP normalized by the initial vertical effective-stress; ru ⥠0.95 indicates full liquefaction); Ts = site period (herein calculated above the elevation where input motion is applied). Table 7-1. Summary of case histories.
Figure 7-1. Schematic representation of case histories evaluated in this study.
64 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines supplemented with grain size distributions for the liquefiable sands shown in Figure 4-2, and information for the WLA site shown in Figure 4-4 (PWP response in the 1987 Superstition Hills earthquake), Figure 6-3 (updated soil profile at the WLA site), and Figure 6-4 (revised modulus reduction curves for the silty sand from the WLA site). The processed and synthesized information about the seven case histories is voluminous. Therefore, this information, including a summary of relevant information from past studies, information about the characteristics of input motions and records of excess PWP, and informa- tion related to available observational data, is presented in Appendices B-1 through B-4. Addi- tional information, mostly related to the characteristics of input motions recorded at the WLA site, is provided in Appendices E-1 through E-3. 7.2.2 Element Tests (Calibration at the Soil Element Level) As explained in Section 5.3.2, element tests are essentially numerical simulations of advanced laboratory tests. Fitting of modulus reduction and damping curves is the first step in element testing. It is performed using a set of equations that are referred to as a sub-CMs. Sub-CMs are applied to either generic MRD curves or to the project-specific curves that were developed from the results of advanced laboratory or in-situ testing performed under, preferably, drained condi- tions (e.g., see list of tests in the legend of Figure 6-4). Other examples of element testing include fitting of excess PWP with semi-empirical CMs (see, e.g., Figure 5-2) and simultaneous fitting of the stressâstrain and excess PWP response with advanced CMs (see, e.g., Figure 5-3). An element test is performed at the onset of the numerical modeling process, typically as soon as results of advanced laboratory testing become available, and as such is a part of preparation. Besides generating input for numerical modeling, the purpose of an element test may be to dem- onstrate that the combination of the modelerâs knowledge and experience, software, constitutive model, and input parameters for site response analysis can adequately reproduce soil behavior under well-controlled conditions. The element tests utilize either a single finite element (e.g., OpenSeesPL and D-MOD2000), two triangular finite elements (e.g., PLAXIS33), or a single zone (e.g., FLAC). A single constitutive model is assigned to a finite element/grid zone. Vertical or radial loading is applied to consolidate the soil, and cyclic loading is applied under drained (fitting of MRD curves) or undrained (fit- ting of stressâstrain and excess PWP responses) conditions. The parameters for CMs are selected following the protocol outlined in Section 3.6. The process is iterative. The results are monitored at nodes/grid points (displacements) and Gauss points/zone values (stresses and strains). The element test is successful if, for a given confining stress, the agreement between measured and calculated outputs is relatively close (as subjectively assessed by the modeler or reviewer). Several element tests undertaken for this study are presented in Section 5.3.2 (Figures 5-1 through 5-3). Additional tests are presented here. Collectively, they are representative of broad testing conditions (drained and undrained strain- and stress-controlled CyDSS testing) and material conditions (loose to medium-dense silty sand from the WLA site Unit B and medium- dense to dense silty sand representative of select site conditions at the Treasure Island site). Detailed information about these element tests and testing software is presented in Appendix D-1 (Treasure Island site; two CMs), Appendix D-2 (WLA site; one CM), and Appendix D-3 (two CMs that are used in this study to model soils above the groundwater table as well as models used to simulate the cyclic response of saturated silt, clay, and gravel). In Figure 7-2, selected results of a representative stress-controlled CyDSS test on loose to medium-dense silty sand from the WLA site are compared to the results of numerical modeling in an element test with an advanced CM (UCSDSAND3). The discrepancy between measured and calculated stressâstrain response is notable, while the match between measured and calculated
Numerical Modeling Program 65  excess PWP response is very good. This mismatch in agreements is typical. The CM parameters can be adjusted to match the stressâstrain response, but the match of measured and calculated excess PWP would be adversely affected. For many soils, numerous iterations on material param- eters may be required for matching, and sometimes matching is not possible. Examples include anomalous advanced laboratory test results. Such test results may be difficult to identify in a for- mulaic way (see Section 6.3.2.3) due to the limitations of CMs considered herein. Most CMs in use today, including those considered herein, offer a choice of several generic material parameter sets. These sets typically include sets for loose sand (LS), medium-dense sand (MDS), dense sand (DS), and very dense sand (VDS). In many cases, a numerical modeler can select an appropriate generic set of CM parameters based on the interpretation of the results of in-situ testing in terms of density. The TI case history provides an opportunity to validate this approach because, for a deep layer of silty sand, both results of in-situ and advanced laboratory testing are available (for details, see discussion in Appendix D-1). Figure 7-3 compares element test calculations for MDS, DS, and VDS with results of CyDSS testing of the TI silty sand. The limiting shear strain of 9% (i.e., equipment limitation) was reached after 15 cycles for MDS, after 27 cycles for DS, and never for VDS. By inspection, the generic set of parameters corresponding to DS was selected for further adjustment. (a) (b) Figure 7-2. WLA site silty sand â comparison of measured and calculated: (a) normalized excess PWP (ru) histories; (b) normalized stressâstrain loops for cycles N 5 1 and N 5 2. Figure 7-3. Comparison of measured and calculated ru for the TI sand. MDS, DS, and VDS correspond to generic sets of parameters for medium-dense, dense, and very dense sand.
66 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines After adjusting several parameters of the generic DS set in a trial-and-error process, relatively good agreement between measured and calculated excess PWP was achieved. This is shown in Figure 7-4, which compares recorded and calculated excess PWP response for the subject TI silty sand. However, relatively good agreement between measured and calculated ru does not neces- sarily result in a comparably good stressâstrain response during the entire duration of shaking. This is illustrated in Figure 7-5 for the same TI silty sand and the same set of CM parameters used to fit the excess PWP response. Figure 7-5 shows relatively good agreement between measured and calculated stressâstrain response for the first 10 cycles of the subject CyDSS test. However, as cycling progressed, the dif- ference between measured and calculated response increased. The calculated response, as shown in Figure 7-5, is significantly overdamped after the 50th cycle. 7.2.3 System Tests (Calibration at the Soil Profile Level) 7.2.3.1 General A âsystem testâ is calibration at the soil profile level. It is performed after element tests have been completed and the SRA model has been assembled. For this exercise, required element test- ing includes the fitting of CM sub-models (i.e., the fitting of modulus reduction and damping curves, which are usually available from literature). Recommended element testing includes both the fitting of the results of drained testing (i.e., to develop site-specific modulus reduction and damping curves) and the results of undrained cyclic testing. Preference should be given to the fit of undrained stressâstrain response. The simultaneous good fit of both stressâstrain and excess PWP response is desirable but may be difficult to achieve for silty and clayey sands. Calibration at the system level is coupled with validation.34 As noted in Section 5.3.3, there are several options for both calibration and validation at the system level, but the reference model (i.e., the reference analysis, reference case) method is the most common and is used herein. The reference model is usually an SRA model developed for use with a commonly used in practice and verified SRA software such as frequency-domain software based on the equivalent-linear model (e.g., SHAKE, STRATA; see Appendix A-1 and discussion in Section 3.2). Such a software is also preferred as no element testing is required to develop parameters of the S-I CM. (Modulus reduction and damping curves are directly input into the program.) After the reference model is assembled, validation is performed. If the model response matches the spectral response of its reference model, then no adjustments are required, and analysis Figure 7-4. Comparison of measured and calculated ru for the TI silty sand. Generic parameters for the DS were modified to achieve good agreement.
Numerical Modeling Program 67Â Â (a) (c) (e) (b) (d) (f) Figure 7-5. Comparison of measured and calculated stressâstrain response for the TI silty sand. CM parameters were adjusted to fit the excess PWP response.
68 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines proceeds with the next calibration/validation step, as explained in the next subsection. If the spectral responses do not match, then additional review of the model, with adjustments and elimi- nation of errors, is required. For example, static initialization of normal and shear stress may be in error,35 subroutine coding errors36 may exist, or boundary conditions37 and ground motion input38 may be assigned incorrectly. Required adjustments may include (re)selection of constitu- tive model(s), adjustment of damping, selection of a different integration scheme, improvement in sub-model and Rayleigh damping model fits, and so forth. The calibration/validation process followed in this study is explained in the next subsection. 7.2.3.2 Initial Calibration The initial calibration may be organized in steps. Up to four steps may be required, as explained in the following. Step 1 â Develop a Reference Model In this study, a 1D equivalent-linear model is considered for the reference model because it is well known, well established, easy to use, does not require element testing, and is easy to convert into a nonlinear model. Furthermore, as explained in Section 3.2, when an equivalent-linear model is subject to a low-intensity motion39 (i.e., a motion that induces small strains within the profile), the calculated site response corresponds to a calculation with correct equivalent viscous damping (ξtar). Most published damping curves do not include information for strains less than 0.001% (see, e.g., Figure 3-1). Vucetic et al. (1998) provide information on low-strain damping (typically ranging between 0.5% and 5%). The same range (0.5% and 5%) is also found in the Darendeli (2001) and Menq (2003) models. Step 2 â Develop a Nonlinear SRA Model Development of both reference and nonlinear SRA models follows completion of site explora- tion and characterization efforts, including review of previous studies and completion of stan- dard and advanced laboratory testing. Element testing at a sub-CM level, and preferably also at the CM level, should be completed before assembling the nonlinear SRA model. Following completion of element testing, a 1D, 2D, or 3D SRA model is selected considering the required attributes presented in this study and is created following the recommendations and guidelines provided herein and by the software developer. The nonlinear SRA model is then ready for vali- dation and, if required, for calibration. Step 3 â Validate Nonlinear SRA Model This step is required to demonstrate that the modeler correctly processed and applied input motion and assigned the proper boundary conditions. If 2D or 3D software is used in 1D mode, the choice of damping type, side boundary conditions, or selected element aspect ratios might be required. The modeler should be cognizant of the limitations of the equivalent-linear analy- sis, such as the maximum strain that can be accommodated (typically less than 1%; see discus- sion in Section 3.2). Validation is performed, at a minimum,40 by comparing spectra from the nonlinear SRA analysis to their counterpart from the simulation with the reference model. For design, validation with a single motion from a suite of design motions will typically suffice. An example of a close match is presented in Figure 5-4. An example of trends to observe, including the characteristic shift of spectral ordinates toward longer periods that occurs at deep soft soil sites, is presented on Figure 4-1. Step 4 â Calibrate SRA Mode (if Required) Upon completion of Step 3, if the difference in spectral ordinates of nonlinear SRA model spectra and reference model spectra is relatively large (e.g., notably larger than the difference between blue and red spectra shown in Figure 5-4), modelers may opt for calibration41 of the nonlinear
Numerical Modeling Program 69  SRA model(s). The calibration process, if required, typically boils down to the fine-tuning of CM sub-model fit(s), which is performed (i) at the design peak ground acceleration level (modeler should be cognizant of the limitations of the equivalent-linear analysis, which include maximum calculated shear strain of approximately 1.0%; see modulus reduction and damping curves in figures across this study, which are limited to 1%), and (ii) at a reduced peak ground acceleration level (typically with PGA = 0.05 g) to adjust the Rayleigh damping model parameters. To adjust the Rayleigh damping model parameters, the modified procedure by Kwok et al. (2007) is followed. This is an iterative procedure, with the final selection of model parameters based on engineering judgment. Table 7-2 presents a calibration matrix (i.e., a matrix of parameters typically used to evaluate Rayleigh damping coefficients αR and βR). In the simplified Rayleigh damping formulation, the model parameter n = 0. In this study, it was assumed that ξtar does not vary within the profile. Case histories were run with parameters listed in Table 7-2. Input motion was scaled down to 0.05 g to allow for calculations in a nearly linear-elastic range. In this study, most of the best matches were obtained with n = 5 and ξtar = 0.5%. Figure 5-4 shows an example of a nearly perfect match between measured and calculated spectra, which is not always achieved. Evaluations completed in this study confirm that, in gen- eral, Rayleigh damping model parameters are not software dependent. They are, however, input- motion dependent. The parametric studies completed herein reveal that, for practical purposes, calibration with a single accelerogram and viscous damping assigned uniformly with depth is sufficient. 7.2.3.3 Subsequent Calibration(s) Subsequent calibrations follow the initial calibration. As with the initial calibration, they may be organized in steps, as follows. Step 1 â Establish a Total Stress Nonlinear Reference Model The total stress nonlinear model is typically the same model that was calibrated and validated in Steps 2 through 4 in Section 7.2.3.2 but run at the design acceleration level or levels. The ground surface acceleration response spectrum (or spectra, if several columns are evaluated) thus become the reference spectrum (or spectra) for ESA. Step 2 â Run ESA Without Excess PWP Dissipation ESA without PWP dissipation (but with PWP generation) is performed first. The results of this evaluation are compared to the results of the reference model established in Step 1. This allows for the identification of errors (i.e., the inadequate assignment of boundary conditions for PWP generation). The comparison also provides insight into the effects of excess PWP genera- tion on calculated site response. These effects, including the base isolation effect42 (lengthening of period of ground motion above the liquefiable layer; e.g., see Figure 7-8), are discussed in greater detail in Sections 7.3.2 and 7.3.3. Simplified Rayleigh Damping Full Rayleigh Damping n = 0; ξtar = 0.5% n = 3; ξtar = 0.5% n = 5; ξtar = 0.5% n = 0; ξtar = 2.5% n = 3; ξtar = 2.5% n = 5; ξtar = 2.5% n = 0; ξtar = 5.0% n = 3; ξtar = 5.0% n = 5; ξtar = 5.0% Notes: n = an odd integer (1, 3, 5, â¦, 7); ξtar is the target viscous damping ratio. Rayleigh damping coefficients are calculated using Equations 6 and 7, which are provided in Section 3.3. Table 7-2. Calibration matrix â Rayleigh damping model parameters.
70 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines Step 3 â Run ESA with Excess PWP Dissipation If the expected trends in the results of the ESA are identifiable, ESA is valid and ready for the next step (i.e., for this step). In this step, dissipation of excess PWP is allowed. Expected effects of excess PWP dissipation include a drop in excess PWP with time (e.g., see Figures 4-6 and 4-7 and the corresponding results of calculations shown in Figure 7-10). The results of effective- stress nonlinear SRA model reruns with PWP dissipation may be an important consideration for design (excess PWP buildup softens the profile; relief of excess PWP through dissipation is representative of a stiffer profile with a larger surface acceleration response). 7.2.3.4 Validation for Research Purposes As the name of this section implies, supplemental validations may be performed to evaluate whether the site has been sufficiently explored and characterized and whether the capabilities of software and CMs are adequate, as well as to evaluate the modelerâs ability to perform this type of analysis. This type of validation calls for a direct comparison between recorded and calcu- lated values. This includes direct comparisons of acceleration response spectra, excess PWP, and acceleration histories. Additional comparisons of recorded and calculated acceleration response spectra, excess PWP, and acceleration histories are also possible. Examples include comparisons of recorded and calculated peak values of ground acceleration and maximum PWP within the profile, which are shown in Figures 7-11 and 7-12. Indirect comparisons (i.e., validations) are possible as well. For example, one can compare back-calculated and interpreted stressâstrain responses. Examples of this type of validation, where in-situ stressâstrain response is evaluated from the results of field measurements, are shown in Figure 6-5. For sites where only observational data about soil liquefaction exist (e.g., there is evidence of sand boils or lateral spreading, but there are no actual PWP records), results of calculations can be qualitatively evaluated (e.g., do calculations show a lengthening of periods of soils within and above liquefiable layers as would be expected?). Additional validations, such as comparisons of recorded and calculated lateral displacement, are possible, to an extent in 1D and especially in 2D nonlinear SRA. 7.3 Summary and Interpretation of the Results 7.3.1 General Case histories evaluated herein are schematically presented in Figure 7-1, outlined in Table 7-1, and explained in detail in Appendices E-1 through E-5. The information in these appendices references the results of previous investigations and evaluations and includes processed detailed descriptions of case histories, including site conditions, recorded events, soil profiles with the location of geotechnical instrumentation, assumed groundwater elevations, results of material testing, key information about seismic events and parameters of recorded motions, and where available, a summary of relevant observational data (e.g., sand boils, lateral spreading, settle- ment). Only select information could be reproduced here from the appendices. Also included in Appendices E-1 through E-5 is information relevant for the performance of numerical modeling and for interpretation of the results. This includes tabulation of profile parameters used to assemble SRA models, tabulation of CM parameters as evaluated by ele- ment testing, and the results of calculations. The results are presented for each step outlined in Section 7.2.3. To facilitate review and minimize repetition of definitions and explanations, case histories are presented in a uniform format (i.e., the same site characterization data format, data input format, and style of presentation of the results were followed).
Numerical Modeling Program 71  7.3.2 Ground Surface Response The results of numerical modeling with multiple software programs and CMs are presented in Appendices E-1 through E-5. Review of this information indicates that a relatively good agree- ment between recorded and calculated response has been achieved for all software and CMs considered, at least in terms of acceleration response at the ground surface. For the sake of clear presentation, only the best matches between recorded and calculated acceleration spectra and acceleration histories are shown herein. For the same reason (i.e., clarity of presentation), plots of recorded and calculated acceleration responses are shortened at both ends. The shortened plots of acceleration response are referred to herein as âwindowsâ and were selected to show the strongest parts of ground shaking. References to software (computer programs) were omitted for administrative reasons. Figure 7-6 compares recorded and calculated ground surface response for the six field case histories and the centrifuge experiment. The corresponding earthquake information is presented (a) Wildlife Liquefaction Array Site (Original) (b) Wildlife Liquefaction Array Site (Original) (c) Wildlife Liquefaction Array Site (Re-Instrumented) Figure 7-6. Windows of acceleration histories â recorded at ground surface (target) and calculated. (Only the best match is shown.) (continued on next page)
72 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines (e) Port Island, Japan (f) Treasure Island (g) Centrifuge Experiment (This Study) (d) Owi Island, Japan Figure 7-6. (Continued).
Numerical Modeling Program 73  in an abbreviated form in the figure insets. The response presentation is in the form of recorded and calculated acceleration histories. Recorded quantities are shown in red, while the best cal- culated matches are shown in blue. This type of presentation of ground surface response may not be necessary for engineering evaluations but provides valuable insight into the ESA analysis and facilitates interpretation of the results. For example, the base insolation effect (i.e., lengthening of motion periods) is observ- able in field acceleration histories that are recorded above liquefied soil. This includes the WLA site in the Superstition Hills event [Figure 7-6(b)], where lengthening of motion periods starts at approximately 13 s, Port Island [Figure 7-6(e)], where lengthening also starts at approximately 13 s, and Treasure Island [Figure 7-6(f)], where lengthening starts at approximately 11 s. The base isolation effect was replicated by numerical simulations in all three cases evaluated. Remolded silty sand from the WLA site liquefied in the centrifuge experiment (at a depth of 4.2 m). However, the base isolation effects (base isolation effects occur in limited cases where soils are either very loose or are not shaken strongly post-liquefaction) are not readily observable in Figure 7-6(g). Information presented in Figure 7-6(d) for the Owi Island case history may be misleading. As shown, it looks like motion periods are lengthened and that the cause of length- ening may be soil liquefaction. However, this is a short acceleration record, and the abscissa scale is stretched to facilitate comparison of recorded and calculated response; hence, the appearance of lengthening is deceiving. Figure 7-6 further shows that the agreement between recorded and calculated ground motion is the best at the onset of ground shaking. As ground shaking progresses, PWP builds up and affects the results of calculations. Ultimately, soil liquefies, and soil liquefactionârelated phenomena such as sand boils (sudden PWP relief) and lateral spreading affect the results. These phenomena cannot be simulated by the software considered herein. For example, Figure 4-5(a) shows that the onset of soil liquefaction does not coincide with the peak in the acceleration history. Sudden drops in P5 [piezometer closest to the ground surface; see Figures 4-5(a) and 4-5(b)] likely reflect the occurrence of sand boils observed in the 1987 M 6.6 Superstition Hills event. Although data presentation in the acceleration windows (e.g., Figure 7-6) may point to certain phenomena and help with the associated interpretation of numerical modeling results, this type of presentation is limited. As pointed out previously, this type of presentation can also be deceiv- ing (e.g., see discussion on the response of Owi Island site, Japan), and it may be difficult to assess whether the PGA values have been matched by calculations. Finally, this type of presentation is neither convenient nor suitable for practical use. Therefore, the most common way to present the results of SRA, including results of the effective-stress SRA, is in the form of acceleration response spectra. Figure 7-7 is a presentation of the ground surface response of case histories considered herein in the form of acceleration response spectra. All spectra shown are 5% damped. Recorded spectra (i.e., spectra calculated from ground surface acceleration records) are shown in red. Calculated spectra are shown in gray, with the best match in blue. Information presented in Figure 7-7 shows that, consistent with the matching of acceleration records, the acceleration response spectra can be matched as well if the model parameters are chosen appropriately. The agreement between recorded and calculated motions is closer for the low-intensity motion case histories [see Figure 7-7 (a), (c), and (d)]âin other words, for sites con- sidered herein that did not liquefy. The agreement is also relatively good for the centrifuge experi- ment, which is well constrained by controlled testing conditions and is supported by the results of advanced laboratory testing. The range of calculated values is relatively large for the WLA site in the 1987 M 6.6 Superstition Hills earthquake. Unlike the response in the 1987 M 6.2 Elmore Ranch event, the response in the Superstition Hills event may have been affected by ground sur- face cracking (manifested by observed sand boiling) and by observed lateral spreading.
74 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines (a) WLA Site (Original) (Elmore Ranch Eq.) (Ts = 0.29 s) Ts = 0.29 s)(b) WLA Site (Org.) (Superstition Hills Eq.) ( (c) WLA Site (Re-Instr.) (Hovley Eq.) (Ts = 0.63 s) (d) Owi Island, Japan (Chiba-Ibaragi Eq.) (Ts = 0.25 s) (e) Port Island, JP (Hyogo-Ken Nanbu Eq.) (Ts = 0.38 s) (f) Treasure Island (Loma Prieta Eq.) (Ts = 1.38 s) Figure 7-7. Recorded (target) and calculated (ESA) acceleration response spectra.
Numerical Modeling Program 75  The impacts of sand boiling and ground surface cracking on site response are especially nota- ble at the WLA site in the 1987 M 6.6 Superstition Hills earthquake. Sudden drops in the normal- ized PWP history of piezometer P5 (the piezometer closest to the ground surface, just below the WLA site clay crust) are visible in Figure 4-5(a). These drops can be explained by the opening of cracks in the clay crust (Unit A). Onset of cracking likely started between seconds 13 and 14 and coincides with the largest excursions of surface acceleration in the record (PGA in Figure 7-8). Note how the match between recorded and calculated motions becomes progressively poorer beyond 14 s. Note also that the occurrence of the PGA at about 14 s and the onset of soil lique- faction at approximately 60 s (see Figure 4-5) do not coincide. As shaking progresses, generation of PWP continues, and the period in recorded ground motion lengthens. At approximately 21 s, the soil is softened enough for the initiation of lateral spreading. Both the Port Island site in the M 6.9 Hyogo-Ken Nanbu earthquake and the Treasure Island site in the M 6.9 Loma Prieta earthquake were affected by ground surface cracking and associated sand boiling. However, no lateral spreading was observed at either site. At the ground surface, recorded and calculated motions are relatively close at both sites [see Figures 7-6(e) and 7-6(f), respectively]. The results of calculations for these sites are affected by a lack of results from advanced laboratory testing of liquefied silty sand. (g) Centrifuge Experiment (This Study) (Western Washington Eq.) (Ts = 0.22 s) Figure 7-7. (Continued). Figure 7-8. Annotated window of recorded and calculated response of WLA site at ground surface. (Only the best match is shown.)
76 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines In all cases, recorded and calculated spectra agree the best43 at spectral periods beyond 3.0 s. However, agreement at periods longer than 3.0 s, which typically corresponds to 1.5 times the softened site period (Stewart, 2022b), might be deceiving. This is because 1D analysis calculates no appreciable site response effects beyond approximately 4.0 s. Beyond approxi- mately 4.0 s, calculated spectral acceleration mostly reflects the input ground motion (Stewart, 2022b; see the limitations of this study outlined in Section 1.3). The agreement for the PGA (i.e., at spectral periods of 0.01 s and below) is important as PGA is used for calculations of liquefaction triggering. Figure 7-9 compares ground surface response in terms of acceleration response spectra cal- culated by TSA and ESA using the same software and CM. For clarity of presentation, only the best ESA matches, as identified in Figure 7-7, are shown. As a reference, the corresponding peak PWP ratios (ru) are provided in the figure captions. As expected, for small-peak PWP ratios, the results of TSA and ESA coincide [Figures 7-9(a) and (d)]. The difference between TSA and ESA is, with one exception, the most pronounced at sites that liquefied in the past [Figures 7-9(b) and (e)] or came close to liquefaction in a centrifuge experiment [Figure 7-9(g)]. At these sites, peak spectral ordinates are reduced relative to TSA by as much as approximately 30% at the WLA site in the M 6.6 Superstition Hills earthquake, (a) WLA Site (Original) (Elmore Ranch Eq.) (ru â 0.025) (b) WLA Site (Org.) (Superstition Hills Eq.) (ru â 0.95) (c) WLA Site (Re-Instr.) (Hovley Eq.) (ru â 0.6) (d) Owi Island, Japan (Chiba-Ibaragi Eq.) (ru â 0.025) Figure 7-9. Comparison of the best match ESA acceleration response spectra and the corresponding TSA spectra. ESA herein includes excess PWP dissipation.
Numerical Modeling Program 77  by approximately 50% at the Port Island site in the M 6.9 Hyogo-Ken Nanbu earthquake, and by approximately 50% in the centrifuge experiment. The difference between TSA and ESA spectral response is also notable in the response of the WLA site in the M 4.9 Hovley earthquake (peak ru = 0.6). Reduction in the ESA peak spectral ordinates relative to their TSA counterparts is approximately 30%. 7.3.3 Response Within Soil Profile Figure 7-10 is a presentation of PWP response within a series of soil profiles. It is represen- tative of the field and centrifuge experiment case histories considered herein. Presentations are for critical layers within the profiles considered; results of calculations are reported for the mid-height of the layer. Normalization of excess PWP is with the initial vertical effec- tive stress Ïâ²v. Therefore, the shown plots may be viewed as a representation of PWP ratio ru development with time. Recorded histories of ru are shown in red. Calculated counterparts are shown in gray, with the best matches in blue. These best matches do not always correspond to their surface response counterparts shown in Figure 7-7. In other words, some simulations may result in a good match of ground surface response and in a relatively poor match of excess PWP response. (g) Centrifuge Experiment (This Study) (Western Washington Eq.) (max ru â 0.95 at 4.2 m b.g.s.) (e) Port Island, Japan (Hyogo-Ken Nanbu Eq.) (ru â 0.95) (f) Treasure Island (Loma Prieta Eq.) (ru â 0.95) Figure 7-9. (Continued).
78 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines Initially, no excess PWP record was available for the WLA site in the 1987 M 6.2 Elmore Ranch earthquake. However, as shown in Figure 6-14, for this case history, there is relatively good agree- ment between recorded ground surface spectrum and its centrifuge experiment counterpart. Therefore, it is reasonable to assume that the excess PWP record from the subject centrifuge experiment is representative of its missing 1987 Elmore Ranch earthquake counterpart. The excess PWP record from the centrifuge experiment is included in Figure 7-10(a). The Port Island site is known to have liquefied in the M 6.9 Hyogo-Ken Nanbu (Kobe) earthquake. Similarly, the Treasure Island site is known to have liquefied in the M 6.9 Loma Prieta earthquakes. Therefore, the excess PWP response was inferred (ru = 0.95) and is, as such, represented by dashed red lines in Figure 7-10(f) and 7-10(g). (a) WLA Site (Original) (max ru â 0.025) (b) WLA Site (Original) (max ru â 0.95) (c) WLA Site (Re-Instrumented) (max ru â 0.6) (d) Owi Island, Japan (max ru â 0.025) (e) Port Island, Japan (max ru â 0.95) (f) Treasure Island (max ru â 0.95) Figure 7-10. Recorded (target) and calculated PWP histories.
Numerical Modeling Program 79  As discussed in Section 4.4.7 and further in Section 7.2.1, field case histories with excess PWP recorded within soil profile are rare. PWP records from the only case that liquefied (i.e., WLA site in the 1987 M 6.6 Superstition Hills earthquake) are questioned by some (see discussion in Section 4.4.3). Nevertheless, as shown in Figure 7-10(b), the history of excess PWP recorded in this event can be matched reasonably well by effective-stress numerical modeling. For the other two field case histories for which PWP records are available, a match between recorded and calculated excess PWP was achieved in two simulations (the WLA site in the 2012 M 4.9 Hovley earthquake and the Owi Island site in the 1985 M 6.2 Chiba-Ibaragi earthquake). However, as shown in Figure 4-6, there is a wide range in excess PWP response recorded in the WLA site critical layer in the Hovley earthquake. The WLA site response in the M 4.9 Hovley earthquake is relatively significant. This is because (i) this is the only field case history where excess PWP was recorded at the same depth and further at multiple depths, and (ii) unlike at the WLA site in the Superstition Hills earthquake, recording of excess PWP is complete. (It was not affected by the limitation of data acquisition system storage.) As shown in Figure 4-6(a), in the Hovley earthquake, the excess PWP was recorded well beyond cessation of strong ground shaking (i.e., for up to 230 s as opposed to a 95-second-long excess PWP record from the Superstition Hills event). The results of the simula- tions shown in Figure 7-10(c) reveal that only three out of five ESA models matched PWP over the entire duration of the Hovley record, which is approximately 5 s (see Figure 7-6(c) and Ds in Table 4-8). However, when acceleration response spectra from the same simulations are com- pared to the recorded spectrum [see Figure 7-7(c)], the match is reasonable by all five models. This is consistent with the pulse nature of this motion (i.e., most of the energy from this motion is delivered in a relatively short time at the beginning of shaking). A very close match between recorded and calculated excess PWP is also achieved for the very low PWP response (ru = 0.02) of the Owi Island site in the 1985 M 6.2 Chiba-Ibaragi, Japan, earthquake. In the simulation of the Port Island response to the 1995 M 6.9 Hyogo-Ken Nanbu (Kobe), Japan, earthquake, soil liquefaction is triggered in all simulations. On the other hand, the peak calculated PWP response for the Treasure Island liquefaction site in the 1989 M 6.9 Loma Prieta earthquake was matched in only one simulation. Similarly, the PWP response in the centrifuge experiment was matched by only one of the simulations. [Due to a large file size, only the first 250 s could be plotted in Figure 7-10(g).] An additional comparison of recorded and calculated response to strong ground shaking within the soil profile is presented in Figure 7-11 for peak ground acceleration, in Figure 7-12 for peak excess PWP ratio, and in Figures 7-13 and 7-14 for stressâstrain response. As with the presentation of ground surface response in the form of (window) acceleration histories, (g) Centrifuge Experiment (This Study; max ru â 0.95) Figure 7-10. (Continued).
80 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines (a) M 6.6 Superstition Hills Earthquake (b) M 4.9 Hovley Earthquake Figure 7-12. Recorded and calculated ru profiles at the WLA site in two earthquakes. (a) M 6.6 Superstition Hills Earthquake (b) M 4.9 Hovley Earthquake Figure 7-11. Recorded and calculated PGA profiles at the WLA site in two earthquakes.
Numerical Modeling Program 81  (c) Program 3 (UBCSAND) (f) Program 5 (UBCSAND) (i) Inferred from SM Records (a) Program 3 (PM4SAND) (d) Program 4 (PM4SAND) (g) Program 5 (PM4SAND) (b) Program 3 (UCSDSAND3) (e) Program 4 (UCSDSAND3) (h) Program 2 (MKZ) Figure 7-13. Calculated stressâstrain response to the M 6.6 Superstition Hills earthquake in the middle of the WLA site critical layer. this type of presentation is not necessary for engineering evaluations. However, it may provide a valuable insight into site response to strong ground shaking with PWP generation and may facilitate validation of the results. Information presented in Figure 7-12(a) indicates that the critical layer liquefied over its entire height (ru ⥠0.95 over the entire layer height). This is consistent with post-earthquake observa- tion of extensive sand boiling, settlement, and lateral spreading reported by Youd et al. (2004) and with the results of four simulations shown herein and presented in detail in Appendix E-2. Figure 7-12(b) shows significantly higher excess PWP response in the upper half of the critical
82 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines layer. In the 1987 Superstition Hills event, the WLA site liquefied for the first time in its history. Soil was first suspended, then settled, resulting in looser silty sand in the upper half of the critical layer that existed at the time of the 2012 Hovley earthquake (compare pre- and post-liquefaction results of in-situ testing in Figure 6-1). The observed trend in excess PWP response has been matched herein in three out of eight simulations. Figure 7-12(a) shows significant excess PWP recorded in lean clay (Unit C). The information presented in Appendix B-1, including evaluation of soil liquefaction potential by the Bray and Sancio (2006) method, indicates that lean clay (Unit C) is not liquefiable. Therefore, recorded excess PWP that plots below the silty sand and lean clay interface in Figure 7-12(a) is likely within silty sand (Unit B). See discussion about the variability in layer thickness presented in Section 6.2.3 and in Appendix B-1. Figure 7-13 shows stressâstrain response approximately in the middle of the WLA site critical layer (i.e., silty sand layer liquefied in the 1987 M 6.6 Superstition Hills event). This type of pre- sentation is not necessary for engineering evaluations; nonetheless, it may provide a valuable insight into site response to strong ground shaking and may facilitate validation of the results. Differences in the results can be explained by the different software and CMs used, as well as varying discretization within the soil profile as chosen by different modelers. Figure 7-13(b), for example, is typical of a stressâstrain response in a liquefied layer. At the end of shaking, soil strength approaches its residual value, calculated shear strain is relatively larger (approximately 1.3%), and loops do not exhibit stress- or strain-dominated (or controlled) behavior. The same trend can be seen, to an extent, in Figure 7-13(h) where calculated peak shear (a) Normalized Peak Shear Stress (b) Peak Shear Strain Figure 7-14. Inferred and calculated peak shear stress and strain profiles at the WLA site in the 1987 M 6.6 Superstition Hills earthquake (calculated closest to the inferred are shown in blue; other calculations are in gray; normalization is with the initial vertical effective stress).
Numerical Modeling Program 83  strain reaches a similar value. While the stressâstrain loops shown in Figures 7-13(b), (f), and (h) are suggestive of soil liquefaction, in general, stressâstrain loops in the other plots are not. The previously noted phenomenon of apparently conflicting calculated stressâstrain response is common when different software programs and CMs are used in calculations. This is because, for analysis purposes, the critical layer is typically subdivided in sub-layers (see example of sub- divided critical layer in Appendix E-2). Although the occurrence of liquefaction may be cal- culated by different models, it may occur slightly shallower in one model and slightly deeper in another. For this reason, stressâstrain loops plotted for the same depth, as presented in Fig- ure 7-13, may not be appropriate for comparison across models. A better approach is to plot profiles of calculated peak shear strain and normalized peak shear stress (normalization with the initial vertical effective stress), and then, for each model considered, present the calculated stressâstrain response for the sub-layer in which the largest peak shear strain was calculated. Figure 7-13(i) shows stressâstrain loops as inferred using Newtonâs second law (i.e., force equals mass times acceleration), closely spaced SM records, and unit weight of soil between the SM instruments (i.e., a proxy for mass density). Figure 7-13(i) has been reproduced herein from Section 6.2.5 to facilitate the comparison of calculated stressâstrain loops with the inferred data. This information can be further used for validation of site response within the profile, as shown in Figure 7-14(a) for normalized peak shear stress and in Figure 7-14(b) for peak shear strain. Calculated values are representative of the 1987 M 6.6 Superstition Hills earthquake and agree relatively well with peak (i.e., maximum) values inferred for the same event in Figure 7-13(i). 7.3.4 Discussion The numerical modeling program presented herein and presented in detail in Appendix D (element tests) and Appendix E (case histories) has been performed in accordance with the research approach presented in Chapter 5 and the specific calibration protocols outlined in Sec- tion 7.2. These protocols are supported by research presented herein. They include calibration at the element level (i.e., element test), as presented in Section 7.2.2, and calibration at the soil pro- file (i.e., system) level, as presented in Section 7.2.3. Validation is provided by comparing results of calculations against well-known solutions (such as a case history or information inferred from a case history), simple SRA model results, or results of advanced laboratory testing. A general observation is that the match between recorded and calculated response to strong ground shaking is very good when monitored at the ground surface, both in terms of accel- eration histories and acceleration response spectra. Almost all software (and CMs) considered herein can match recorded excess PWP response within the profile, but not consistently. The match in excess PWP development can be improved by extensive element testing. A poor match in excess PWP response does not necessarily translate to a poor match in acceleration response. At liquefiable sites (i.e., in liquefiable layers), the peak in acceleration history typically occurs before the peak in excess PWP (see, e.g., Figure 4-5), and that explains inconsistencies between good spectra matches and erratic PWP matches. However, for large-magnitude/long-duration design events, the peak in spectral acceleration may approach the peak in excess PWP [compare Figures 7-6 (g) and 7-10 (g)]. Element testing with advanced CMs is desirable but should be performed with caution. A good match of stressâstrain response may not result in a good match of excess PWP response, especially when the element test is performed on silty sands (see discussion and simulations in Sections 5.3 and 7.2.2). Adjusting the parameters of an advanced CM to match excess PWP response often results in a poor match of stressâstrain response, especially at larger strains. This mismatch is not an issue when simple CMs are used and, in many cases, compensates for the inability of simple CMs to simulate dilation.
84 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines Two field case histories at the original WLA site were considered. They are both based on the same soil profile and the same sets of material properties but are shaken by different motions representative of different earthquakes in the vicinity of the site. The WLA site did not liquefy in the first event (i.e., in the M 6.2 Elmore Ranch event), but did in the subsequent M 6.6 Supersti- tion Hills event. Successful combination of a CM and nonlinear SRA model should be able to replicate this sequence of events (i.e., not to trigger liquefaction in the first event and to do so in the second one). Overall, all software considered herein passed this trigger/no trigger test. Excess PWP response was, however, overestimated in all of the five simulations. The ability to simulate soil dilation has been identified as an attribute that can only be captured by advanced CMs (see Table 4-3). When medium relative density soils (40 ⤠Dr < 60) liquefy and experience strong shaking after triggering, dilation spikes can be expected. This is shown in Figure 6-5, which presents processed strong-motion records from the WLA site in the M 6.6 Superstition Hills earthquake. Dilative behavior of silty sand after liquefaction can be seen along the horizontal axis, from a shear strain of 0.75% to approximately 7%. Effects of soil dilation may be observed in Figure 6-10(b) within the similar strain range in the results of the advanced laboratory testing44 of silty sand (note the banana-shaped stressâstrain response). The closest match between recorded and calculated WLA site surface response in the 1987 M 6.6 Superstition Hills earthquake is calculated by the UCSDSAND3 CM. This CM has been specifically designed to simulate soil dilation effects. However, for the same event, a good match was calculated with other CMs, including with the relatively simple MKZ model, which cannot simulate dilation.