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Suggested Citation:"Chapter 5 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27536.
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Suggested Citation:"Chapter 5 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27536.
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Suggested Citation:"Chapter 5 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27536.
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Suggested Citation:"Chapter 5 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27536.
×
Page 40
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Suggested Citation:"Chapter 5 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27536.
×
Page 41
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Suggested Citation:"Chapter 5 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27536.
×
Page 42
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Suggested Citation:"Chapter 5 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27536.
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Page 43

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37   5.1 General For simulations of site response to be reliable, clear and consistent protocols are required. These protocols include (i) protocols for specifying how input motions are applied to the model, (ii) protocols for model development, including discretization22 of soil profile, (iii) protocols for parameter selection, and (iv) protocols for the interpretation of results. Once these protocols are in place, the software (including CMs) should be verified and validated. Verification is the pro- cess of checking that the software meets specifications (e.g., the requirements set in this study). Software is verified against other software. Validation is the process of checking that software achieves its goal (i.e., “validation” refers herein to a comparison of a user’s model against a well- known solution, such as a simple SRA model, a case history, or the results of advanced laboratory testing, all as provided in this study). Verification of software and CMs used in this study has been completed in the past, as explained in Chapter 4. Protocols for specifying how input motions are applied at the base of 1D models are addressed and explained elsewhere (e.g., Kwok et al., 2007; Mejia and Dawson, 2006). One of the approaches for validation of effective-stress SRA includes a demonstration that (i) selected CMs can replicate material behavior observed/recorded in an advanced cyclic test or in a physical model,23 (ii) the SRA model can replicate the results obtained using equivalent- linear representations of soil properties when the site is subject to low-intensity motion, and (iii) in a separate analysis performed using selected site response and constitutive models, the model can replicate a field case history or representative results of physical modeling. The research presented follows the approaches for validation of effective-stress SRA outlined previously. In accordance with the constraints of this study, focus was on closing the data gaps identified. This called for site-specific investigation at the broader WLA site that included in-situ testing and sampling, as well as routine and advanced laboratory testing of intact specimens of liquefiable silty sand. Remolded samples of silty sand and clay soil recovered during this explora- tion were tested as a part of a centrifuge experiment. 5.2 Required Input and Required Attributes There are three general categories of information needed for development of a nonlinear effective-stress SRA model of a site. These general categories are (i) seismic loading, (ii) site characterization, and (iii) material behavior. The categories are interrelated. For example, based on site characterization information, one needs to determine the appropriate depth at which to replace the rest of the profile with a half-space. In code-based design (e.g., see ASCE 7-22 and its C H A P T E R 5 Research Approach

38 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines commentary), shear wave velocity assigned to a half-space is used as an input into the seismic hazard analysis. The acceleration response spectrum corresponding to that shear wave velocity is assumed to be representative of an outcrop and is used to develop design ground motions (accelerograms) for use in SRA. General categories of information needed to develop a nonlinear effective-stress SRA model representative of a site are outlined in Table 5-1. As explained in Chapter 2, evaluation of seismic loading conditions (i.e., seismic hazard analysis and development of design ground motions considering source and path parameters) in most cases requires specialty expertise. For design purposes, this task is commonly performed by engineering seismologists or by professionals with background in geotechnical earthquake engi- neering. For evaluation of case histories and design of centrifuge experiments, ground motions are available (or may be selected from pool of available records for use in centrifuge modeling), and specialty expertise for developing the relevant ground motion(s) is not required. Site characterization is one of the most important tasks, not only in the context of site response analysis, but also for foundation design and evaluation of the overall stability of the site. How- ever, with the exception of sampling and specification of advanced laboratory testing, it does not require specialized expertise or experience. Seasoned geotechnical engineers and engineering geologists can, based on the results of a carefully planned and executed site exploration program, characterize the site without having knowledge of advanced numerical modeling. The results of site characterization efforts serve as a basis for development of the dataset required to develop a model of the site, and further for development of the SRA model. Basic information required to model nonlinear hysteretic material behavior with PWP gen- eration and dissipation is discussed in Section 3.4.2.2 (for simple constitutive models) and in Section 3.4.2.3 (for advanced constitutive models). This information is further summarized and organized for quick reference in Table 5-2. The information required to model nonlinear hysteretic material behavior with PWP genera- tion and dissipation differs for different applications. For most practical applications, the infor- mation listed in Table 5-2, in some form or another, will suffice. Additional options, too many to list here, are available for selection of modulus reduction and damping curves in cohesive soils, gravels, peat, and municipal solid waste. (i) Seismic Loading (ii) Site Characterization (iii) Material Behavior Acceleration record(s)(1) (either outcrop or in- profile motions) • Stratification (including depth to significant impedance contrast) • Depth to groundwater • Shear wave velocity (profile) • Mass density (profile) • Compression wave velocity (profile)(2) • Hydraulic conductivity of soil layers below groundwater level (profile) Each layer in the profile can be characterized by a variety of material parameters defining shear and volumetric behavior of the soil with depth (Section 3.6). Notes: (1) Only a single record may be required for back analysis. For design, depending on the code requirements, 5, 7, or more acceleration records may be required. In some situations, a deconvolution of recorded surface motion(s) to bedrock might be required. (2) Required only when 2D or 3D models are run in 1D mode, but this is not necessarily critical information (i.e., of secondary importance compared with shear wave velocity; also, water compressibility, not soil skeleton compressibility, may control compression wave velocity in saturated soils). Table 5-1. Input information required to develop 1D nonlinear effective-stress SRA model.

Research Approach 39   5.3 Calibration of Constitutive and Site Response Models 5.3.1 General 1D nonlinear ESA requires, at a minimum, two types of calibration: (i) calibration at the soil element level (i.e., element test), and (ii) calibration at the soil profile level (i.e., system test). While it is desirable that calibration at the soil element level be performed for every layer in the profile and that calibration at the soil profile level be performed for multiple motions, neither is commonly, if ever, performed. Instead, element tests are performed for critical layers (i.e., for critical FEM or FDM model grid elements) as identified by the design engineer. System tests are commonly performed for an accelerogram randomly selected from a suite of design accelerograms. 5.3.2 Calibration of Constitutive Models (Element Test) Figure 5-1 is representative of the simplest element test—a CM-sub-model test. It shows test results (i.e., modulus reduction and damping curves) obtained by advanced laboratory testing (red line) and their counterparts matched (i.e., fitted) with a constitutive model (black line). This is a total-stress exercise performed to evaluate parameters of nonlinear constitutive models that Correlation-Based Option Material-Specific Option • Index properties of soils (PI, grain size distribution, OCR, void ratio, and Dr) and, in sand, vertical effective stress (for evaluation of MRD) • SPT blow counts [N1, better (N1)60] to their clean sand equivalent (N1)60–CS and then using correlations between the necessary properties and (N1)60–CS • CPT normalized tip resistance can be correlated to SPT (N1)60 or Dr and then used for evaluation of the advanced CM parameters. • Results of undrained cyclic testing (CyDSS or CyTX with excess pore water measurements) for evaluation the advanced CM parameters • Hydraulic conductivity and results of consolidation test might be required to calibrate PWP dissipation models. • Location (depth) and extent (layer thickness) of soil liquefaction, as evaluated by screening (by means of the most recent updates of the simplified method) Notes: Dr = relative density; N1 = SPT blow count corrected to an effective overburden stress of 1 atm; (N1)60 = SPT blow count corrected to 60% hammer energy ratio and an effective overburden stress of 1 atm; (N1)60–CS = equivalent clean-sand corrected SPT blow count. Table 5-2. Information needed to model material response to cyclic loading. (a) (b) Figure 5-1. Example of element test on CM sub-model (LE-MC). Test results are for WLA site silty sand (see Figure 6-4 for test results).

40 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines conform to target values. Target values can be either published curves or, in relatively rare cases (e.g., this study), developed based on the results of project-specific advanced laboratory testing. Upon several iterations, fitting parameters that correspond to a satisfactory fit are input into the software. The presentation is in a semi-log space to facilitate the curve fitting over a broad range of strains. An upward shift due to the addition of Rayleigh damping at low strain is not shown in Figure 5-1a. In effective-stress constitutive modeling, a satisfactory fit of modulus reduction and damping may not be sufficient. Modulus reduction and damping curves are representative of the initial loading conditions (typically of the first or second cycle of cyclic loading) when excess PWP is, in most cases, very small. Therefore, additional evaluation (i.e., element testing) is required to account for excess PWP buildup [i.e., to fit the parameters of the PWP model(s)]. This is illus- trated for two main types of effective-stress constitutive models considered herein, as schemati- cally presented in Figures 5-2 and 5-3. Figure 5-2 shows two options for fitting of excess PWP data from CyDSS test by means of a semi-empirical constitutive model. The first option [Figure 5-2(a)] is in the normalized shear stress–cyclic shear strain space. The second option [Figure 5-2(b)] is in the normalized shear stress– number of cycles (N) space. An ability to independently fit the two types of recorded cyclic response (drained response used to develop modulus reduction and damping curves and undrained CyDSS testing used to fit excess PWP response) may be regarded as an advantage of semi-empirical models over their more advanced, theory of plasticity-based counterparts. As explained in Section 3.4.2.3, advanced CMs are fully coupled (i.e., stress–strain and excess PWP responses are calculated simultaneously). Therefore, stress–strain and excess PWP responses are fitted with these models accordingly in an element test. Figure 5-3 shows results of element testing of silty sand with an advanced CM. While Fig- ure 5-3(b) shows good fit of calculated excess PWP to its measured counterpart, Figure 5-3(a) does not show good agreement between measured and calculated stress–strain response. This is (a) (b) Figure 5-2. Example element test with semi-empirical CM and excess PWP from strain- controlled CyDSS test (MKZ CM; test data are from GRI, 2012).

Research Approach 41   a common result of element testing of silty sand. The goodness-of-fit fit may be reversed by the parameter selection. It is very difficult to obtain a simultaneous good fit on both stress–strain and excess PWP response. 5.3.3 Calibration of SRA Model The SRA model is first developed from the information listed in Table 5-1 (inferred stratifi- cation, depth to significant impedance contrast and to groundwater, shear wave velocity, mass density, etc.) and Table 5-2 (two options for modeling of material response). Adjustments to the information from the geotechnical report might be required to account for the minimum and maximum layer thickness, as outlined in Section 3.3. Further adjustments might be required to account for the most probable groundwater elevation (or even for the historic-high groundwater elevation, which is, although highly improbable,24 a requirement in some jurisdictions) or to account for other historic groundwater elevations such as the elevation that may have existed at the time of the earthquake (e.g., for evaluation of case histories). As shown in the previous sec- tion, even the best-estimate modulus reduction or damping curves might not fit well, other CM parameters might have to be assumed, and overall system (i.e., SRA model) damping might be under- or overestimated. Therefore, calibration of the analysis at the soil profile level is warranted. The calibration at the soil profile level is performed after the SRA model has been assembled. There are several options, but the reference analysis (i.e., reference model) method is the most common. The reference model is usually a model developed for use with well-known and veri- fied SRA software such as SHAKE (see discussion in Section 3.2) and a constitutive model such as the S-I model (i.e., modulus reduction and damping curves directly input into equivalent- linear analysis; see discussion in Section 3.2). After the reference model is assembled, calibra- tion of the nonlinear SRA model proceeds. The calculated response (i.e., acceleration response spectrum) using a nonlinear model is compared to a target response spectrum computed using a reference model. The calibration is performed at a low-intensity motion level [typically with bedrock peak hori- zontal ground acceleration (PHGA) of 0.05 g to 0.1 g; see Kwok et al., 2007]. A significant dis- crepancy between the target and calculated spectra can be minimized in several ways, including by making adjustments to the CM parameters. If 2D or 3D software is used in 1D mode, a choice of damping type, boundary conditions, or selected finite or grid element aspect ratios might be (a) (b) Figure 5-3. Example element test with advanced CM and CyDSS test results on silty sand (UCSDSAND3 CM; soil testing results are in Appendix C-2; element test is in Appendix D-2).

42 Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines required. Finally, in almost all solutions involving Rayleigh damping (see Section 3.3), an itera- tive25 process to evaluate the Rayleigh damping parameters might be beneficial. This process has been used herein and is explained in detail in Section 7.2.3. An example using the results from this study is presented in Figure 5-4. 5.4 Measure of Success It is difficult to measure success in nonlinear effective-stress SRA. All measures of success are subjective. Measures may depend on the type of analysis (back analysis of case history or a multi- motion forward analysis carried out in support of design), the extent of the site characterization effort (did the project budget allow for recovery of intact samples in every layer in the profile and advanced laboratory testing thereof?), whether the model was calibrated with multiple time histories (e.g., to minimize the mean square error), and how results will be processed/used (e.g., will response analysis performed using a suite of design ground motions with an average of cal- culated response be used for design?). The fits shown in Figures 5-1, 5-2(a), 5-2(b), 5-3(b), and 5-4 are considered successes by the authors of this study. To facilitate review of the information presented in this study and for practical applications, the research team developed the nonlinear effective-stress SRA measure of success matrix pre- sented in Table 5-3. The first two items in the table refer to the discussion provided in this section. Figure 5-4. Comparison of surface spectra (EL 5 equivalent- linear; NL-TS 5 nonlinear total-stress). Input motion was scaled down to 0.05 g. Parameter Measure 1. F-F surface response 2. Element test 3. Pore water pressure response 4. Soil liquefaction 5. Other 1. Match F-F surface response (surface spectrum) over the period range of interest (0.01 – Ts seconds). 2. Reasonably match recorded material response (see examples in Figures 5-1 through 5-3). See the degree to which dilation features are captured or not. 3. Match excess PWP response where PWP information within the profile is available (case histories only). 4. The model should signal liquefaction where information is available (recorded) or inferred (sand boils reported), or where liquefaction potential is assessed by means of the simplified method. 5. Where possible, match recorded shear strain profile or the magnitude of ground surface settlement. Notes: F-F = free-field (no structure on top of the profile and no structural inclusion within the profile); Ts = period of soil column. Table 5-3. Nonlinear effective-stress SRA – measure of success matrix.

Research Approach 43   The last three items (items 3 through 5) are included in the table for completeness. They refer to the evaluation of case histories and are therefore discussed in Chapter 7. While many engineers have a natural tendency to numerically match targets as closely as pos- sible, other elements of the analysis are often more important and should be considered as well. It is well known that, in practical applications, proper site characterization and simulation of material behavior are important, but ground motion characterization is essential. The results of site response analysis depend mostly on the characteristics and number of input ground motions and how the results of SRA are processed. The processing options for calculated surface response (acceleration response spectra) include calculation of averages and statistical bounds, establish- ing the upper bound(s) of calculated response, and use of one of the several options for smooth- ening the results of calculations. Last but not least, the success of nonlinear effective-stress SRA also depends on the capabilities of the software and CM(s) employed.

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One-dimensional (1D) equivalent-linear total-stress site response analysis (SRA) is the de facto standard for state department of transportation (DOT) highway facilities at locations where site-specific ground response analyses are conducted. However, many users and various DOTs have concerns about the applicability of equivalent-linear analyses for the cases where site-specific SRA is most relevant.

NCHRP Research Report 1092: Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines, from TRB's National Cooperative Highway Research Program, presents guidelines for the selection and use of methods for 1D nonlinear seismic SRA with excess pore water pressure generation and dissipation.

Supplemental to the report is NCHRP Web-Only Document 383: Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation.

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