UTILIZING NONLINEAR SEISMIC GROUND RESPONSE ANALYSIS PROCEDURES FOR TURKEY FLAT BLIND PREDICTIONS

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1 Third International Symposium on the Effects of Surface Geology on Seismic Motion Grenoble, France, 3 August - September 26 Paper Number: 5 UTILIZING NONLINEAR SEISMIC GROUND RESPONSE ANALYSIS PROCEDURES FOR TURKEY FLAT BLIND PREDICTIONS On-Lei Annie KWOK, Jonathan P. STEWART 2, Youssef M.A. HASHASH 3, Neven MATASOVIC 4, Robert PYKE 5, Zhiliang WANG 6, Zhaohui Yang 7 Graduate Student, Dept. of Civil and Envir. Engrg., Univ. of California, Los Angeles, USA 2 Associate Professor, Dept. of Civil and Envir. Engrg., Univ. of California, Los Angeles, USA 3 Associate Professor, Dept. of Civil and Envir. Engrg., Univ. of Illinois at Urbana-Champaign, USA 4 Associate, GeoSyntec Consultants, Huntington Beach, California, USA 5 Consulting Engineer, Lafayette, California, USA 6 Senior Engineer, Geomatrix Consultants, Oakland, California, USA 7 Engineer, URS Corporation, Oakland, California, USA ABSTRACT - Blind predictions of Turkey Flat ground motions are carried out using a series of nonlinear ground response analysis codes. The prediction exercise is structured in two phases so as to formally consider several sources of uncertainty. The first phase involves analysis of the site response considering various sources of material variability and model variability. Specifically, these analyses utilized five different nonlinear analysis codes, each exercised with a suite of small strain shear wave velocity profiles and modulus reduction/damping curves that encompass the range of reported material properties. The second phase of this prediction exercise involves comparisons of results obtained by independent analysis teams for a baseline set of material properties. This second phase of work is of interest to see how much variability in estimated ground motions arises from user-to-user differences in code usage and parameter selection when all users have the same basic information on site condition and the same code. We compare the contributions of all these sources of variability (shear wave velocity, nonlinear curves, code-to-code for the same user, and user-to-user for the same code) and identify the most critical sources for the Turkey Flat site.. Introduction A benchmarking project for nonlinear ground response analysis codes, organized through the Pacific Earthquake Engineering Research (PEER) center Lifelines program, is seeking to de-mystify nonlinear seismic ground response analysis routines by providing clear and well documented code usage protocols, verifying the codes at different strain conditions, and investigating the benefits of nonlinear analysis relative to equivalent-linear analysis. An important component of this project is the Turkey Flat blind predictions of ground motion, in which nonlinear seismic ground response analysis codes are exercised according to the code usage procedures previously developed in the project. Uncertainty in the predictions is examined by considering various sources of material variability and model variability. In addition, the results obtained by independent analysis teams are

2 compared to see how much variability in estimated ground motions arises from user-touser differences in code usage and parameter selection when all users have the same basic information on site condition and the same code. In Section 2 we present a suite of prediction results investigating parametric and model variabilities (by the first two authors). The best-estimate ( baseline ) geotechnical model and the associated uncertainties are described. The nonlinear ground response analysis codes and the usage procedures are also briefly described in Section 2. The results of the user-to-user variability study is given in Section Parametric and Model Variabilities (single user) Turkey Flat is a shallow stiff-soil alluvial valley near Parkfield, California. Figure shows a vertical schematic section of the valley and the array of surface and downhole accelerometers. We focus on the prediction of motions for the vertical array at mid-valley, in which the recorded motion at D3 is provided (by CSMIP) and motions D2 and V are to be predicted (those data were not provided). Pseudo acceleration response spectral ordinates for the recorded motion at D3 (both EW and NS directions) are plotted in Figure 2. In developing our predictions, we sought to evaluate the variability in the predictions due to uncertain geotechnical site properties (both stiffness profiles and nonlinear curves) and alternative models for predicting nonlinear ground response effects. The following sections describe the manner in which those sources of variability were considered. Protocols used in the calculations are also described.. R V V2 R2 D2 Soil D Rock D3 Figure. Schematic section of the Turkey Flat strong-motion array. D3 (Station # 3652, 24m) EW Recorded NS Recorded PSA (g)... Period (sec) Figure 2. Pseudo acceleration response spectral ordinates for motions recorded at D3. 2

3 2.. Geotechnical site properties and their uncertainty Three fundamental sets of soil properties need to be specified to perform nonlinear ground response analyses. The first is the shear wave velocity (V s ) profile. The available data for the V-D2-D3 array (mid-valley site) are summarized in Figure 3 along with the mean and ± one standard deviation profiles utilized for ground response analyses. The mean profile is obtained by averaging all the available velocity logging data. The two Oyo suspension logging data are given twice the weight for depth beyond 5 ft. The uncertainty in the shear wave velocity profiles are calculated by taking the standard deviation (in arithmetic units) among the velocity logging data across depth. Some smoothing is also applied on the calculated profiles. In all of the analyses performed herein, uncertainty in shear wave velocity profiles was considered using the ± one standard deviation curves shown in Figure 3. The second set of required soil properties are curves describing the nonlinear relationship between shear stress and shear strain and between hysteretic damping ratio and shear strain. The former are expressed in normalized form as modulus reduction curves (G/G max curves), the later as damping versus strain curves (β curves). Material specific testing of the soils from the mid-valley portion of Turkey Flat (obtained from Stepp et al., 25) are plotted on the left frame of Figure 4. Regression model-based predictions of G/G max and β curves from Darendeli (2) (which account for soil plasticity, OCR, and overburden pressure) are shown in right frame of Figure 4. The comparison between the material specific G/G max curves and Darendeli model predictions is generally favorable. There are differences in the damping, with the Daredeli damping predictions generally being lower than the measured values. It is possible that the laboratory data, which date from 986, have an overprediction bias (this is commonly the case with data from that time period). Accordingly, we use the Darendeli curves as the preferred model for modulus reduction and damping for the present analyses. The Darendeli model also includes estimates of standard deviation on the modulus reduction and damping curves. Those standard deviation estimates are based on the scatter of the laboratory data used to develop the regression model. We utilize those standard deviation estimates to evaluate the uncertainty on modulus reduction behavior. At G/G max =.5, the uncertainty on the modulus reduction curves corresponds to a coefficient of variation of approximately. Since in the nonlinear codes the shape of the backbone curve also affects the damping, uncertainty in damping curves was not considered separately (i.e., variability in damping was assumed to be perfectly correlated to variability in modulus reduction). The third set of required material properties needed for nonlinear analysis is density, ρ. The density values used in the analyses are shown in Table below. Variability in density within a layer was not considered. Table I. Values of density used for soil layers in ground response analyses Depth (ft) ρ (pcf) Halfspace 37 3

4 Depth (ft) LCA - Downhole(T5) D&M Crosshole (T5) D&M Crosshole (T4) Kajima Downhole (T4) Kajima Downhole (T6) QEST Downhole CDMG Downhole (T4) CDMG Downhole (T5) CDMG Downhole (T8) OYO Downhole (T5) OYO Downhole (T8) OYO Suspension (T5) OYO Suspension (T8) Mean Mean + Sigma Vs (ft/s) at Central Valley Figure 3. Shear wave velocity profile data at V-D2-D3 array (mid valley site) and assumed profiles (mean and mean±one standard deviation) for site response analysis. Data obtained from Stepp et al. (25). G/Gmax D&M (25',σ 3 =3ksf) D&M (25',σ 3 =6ksf) D&M (4',σ 3 =2.4ksf) D&M (4',σ 3 =4.8ksf) OYO (7') OYO (6') G/Gmax z = 3' z = 7' z = 3' z = 2' z = 25' z = 3' z = 4' z = 5' z = 6' z = 7' Damping (%) 2 5 Damping (%) Cyclic Shear Strain (%).... Cyclic Shear Strain (%) Figure 4. Modulus reduction and damping curves based on material-specific testing (left side) and Darendeli (2) model predictions (right side), mid-valley location. 4

5 2.2. Nonlinear seismic ground response analysis codes and usage protocols The ground response analyses utilized herein all assume -D propagation of shear waves. The codes differ in the way they simulate the nonlinear soil behavior and material damping. Six different ground response analysis codes were utilized SHAKE4 (Youngs, 2), which is a modified version of SHAKE9 (Idriss and Sun, 992); D-MOD_2 (Matasovic, 26); DEEPSOIL (Hashash and Park, 2, 22; Park and Hashash, 24); TESS (Pyke, 2); OPENSEES (Ragheb, 994; Parra, 996; Yang, 2; McKenna and Fenves, 2); and SUMDES (Li et al., 992). Code SHAKE4 utilizes the well-known equivalent-linear representation of nonlinear soil behavior. Equivalent viscous damping simulates the effects of hysteretic material damping. Required soil parameters are small strain shear wave velocity (V s ), modulus reduction curves (G/G max curves), hysteretic damping curves (β curves), and material density (ρ). In codes D-MOD_2 and DEEPSOIL, the stiffness and hysteretic damping of soil are represented with non-linear hysteretic springs connected to lumped masses. The dynamic equation of motion is solved in the time domain using the dynamic response scheme developed by Lee and Finn (978). Additional viscous damping is included through the use of viscous dashpots. The soil behavior is represented by a nonlinear backbone curve (which can be curve-fit to match G/G max curves) coupled with extended Masing rules that describe unload-reload behavior and establish the level of hysteretic damping. D-MOD_2 uses the MKZ constitutive model (Matasovic and Vucetic 993; 995) to define the initial backbone curve, whereas DEEPSOIL uses the extended MKZ model (pressuredependent reference strain and small strain damping). Both codes offer the use of simplified or full Rayleigh damping formulations (which match a target damping ratio at one or two frequencies, respectively). DEEPSOIL also offers an option for extended Rayleigh damping (four matching frequencies), which can be useful for deep profiles (Park and Hashash, 24). Both codes are utilized for the present application using total stress analyses (D-MOD_2 allows strength and modulus degradation in consideration of pore pressure generation, although those options are not utilized here). Code TESS is a one-dimensional nonlinear ground response analysis code that solves the equation of motion using an explicit finite difference method. As with D-MOD_2 and DEEPSOIL, the backbone curve is fit using coefficients, but instead of Masing rules, the Cundall Pyke hypothesis is used to model unloading and reloading behavior (Pyke, 979). Another difference is that TESS does not include viscous damping, however a small strain damping scheme is implemented for which a parameter VT is used to quantify the rate of loading effect on shear stress. This scheme produces small amounts of hysteretic damping even at very low strain levels. Codes OPENSEES and SUMDES utilize nonlinear finite element analyses that can solve the multi-directional ground response problem (shaking in two or three directions) with full coupling of wave propagation and pore water pressure generation and dissipation effects. Both have effective stress analysis capabilities, although total stress analyses are utilized here. OPENSEES utilizes a multi-surface plasticity model (Yang et al., 23) whereas SUMDES utilizes a bounding surface hypoplasticity model (Wang et al., 99). Both codes utilize Rayleigh damping, with OPENSEES utilizing full Rayleigh damping, and SUMDES utilizing simplified Rayleigh damping with the matching frequency set at Hz. Based in part on the preliminary parameter selection protocols developed by Kwok et al. (26), the nonlinear ground response analyses for the Turkey Flat vertical array were performed according to the following: 5

6 . The recorded (within) motions are taken as input without modification, and are used with a rigid base. 2. Viscous damping is specified using full Rayleigh damping when available, with the target frequencies set to the first mode site frequency (f s ) and 3 f s (3 f s is used because the match of linear frequency and time domain analyses is reasonably good; 5 f s, which is recommended in Kwok et al. (26), also provided a good fit.) The target damping is set to D min (small strain hysteretic damping ratio). In the case of TESS, strain rate parameters VT is set to 2 D min. In the case of SUMDES, the target damping ratio is modified so that the target D min is produced at the mean frequency of the input motion. 3. Curve fitting is performed to match the nonlinear backbone curve to the specified G/G max curves. This produces misfits between the β curves effectively utilized in the analysis and the β curves suggested by laboratory test data. This misfit is accepted for the present analyses in large part because its effects on the results are small Prediction results Ground response analyses are performed to estimate D2 and V using recording D3 as the input motion along with the soil properties indicated in Figures 3 and 4. Analyses are performed using the six different codes described above. For each code, a baseline set of site conditions is defined as the mean shear wave velocity profile and mean modulus reduction and damping curves. Each code is exercised for the baseline site condition. In addition, uncertainty in the predictions is evaluated by using () the baseline condition except velocities are varied to reflect ± one standard deviation profiles; (2) the baseline condition except modulus reduction and damping curves are varied to reflect ± one standard deviation values. The results of the six sets of baseline runs are used to evaluate variability arising from the different simulation codes. This variability is roughly log-normal, and the standard deviation associated with that variability is termed σ m (subscript m for model). The variability associated with velocity is assessed using the three runs/code (for the three different velocity profiles) for all six codes. For a non-baseline velocity profile (e.g., mean + one standard deviation velocities), a mean set of predicted ground motions is evaluated (the mean is evaluated across the results for the six codes). The mean ground motions for the other non-baseline velocity are similarly calculated (e.g., mean one standard deviation velocities). The standard deviation of the ground motions due the variability in velocity (denoted σ v ) is taken as the absolute value of half the difference between these means. The variability associated with variable modulus reduction and damping curves is similarly evaluated and termed σ G. Values of each of these standard deviation terms are summarized in Figure 5 for the case of pseudo velocity spectra at location V. The most significant source of dispersion at very low periods is model variability, whereas velocity variability dominates at low and middle periods. Variability due to modulus reduction and damping curves is the smallest among all sources of variability considered. The total standard deviation is taken as: σ = σ + σ + σ () m v G The above equation assumes these sources of variability are uncorrelated. 6

7 Figure 6 presents for location V the mean and mean ± one standard deviation estimates of pseudo-velocity response spectra and pseudo-acceleration response spectra for the EW direction..7 Ts Model Variability, σ m Standard Deviation in PSV (ln unit) Velocity Variability, σ v Material Curve Variability, σ G Overall Variability, σ User-to-User Variability, σ u. Period (s) Figure 5. Standard deviation terms associated with pseudo velocity response spectral ordinates for location V. T s denotes the site period. V (EW Direction).9 V (EW Direction).8 PSV (cm/s) PSA (g) Period (s). Period (s) Figure 6. Mean and mean ± one standard deviation estimates of pseudo-velocity response spectra and pseudo-acceleration response spectra for the EW direction at location V. 3. Comparison of prediction results from different analysis teams The geotechnical model and prediction results presented above were developed by the first two authors. Each of the other authors made independent predictions using geotechnical models based on their engineering judgment and a single nonlinear ground response analysis code with which the user has considerable expertise (i.e., the user is a developer of the code). Figure 7 compares the pseudo-acceleration response spectra predicted by the UCLA group (first two authors) and the independent users for a given 7

8 code. It is observed that there are large differences in the predictions by different users at small and mid-periods for a number of the codes (e.g., DEEPSOIL, OPENSEES). This is largely due to discrepancies between the geotechnical models used by different users. An overall measure of user-to-user variability at a given period is taken as the standard deviation of the predictions among users and is plotted in Figure 5 (denoted as σ u ). The σ u term is comparable in magnitude to the velocity variability at periods less than the site period, although its effect is negligible at longer periods. This exercise illustrates that engineering judgment plays an important role in the outcome of nonlinear ground response analysis at short periods. PSA (g) PSA (g) PSA (g) UCLA - Deepsoil Hashash - Deepsoil UCLA - SUMDES Wang - SUMDES UCLA - TESS Pyke - TESS.. Period (s) UCLA - OpenSees Yang - OpenSees UCLA - D-MOD_2 Matasovic - D-MOD_2.. Period (s) Figure 7. Comparison of predicted pseudo acceleration response spectral coordinates for location V from different users. 4. Conclusion Previously developed parameter and usage protocols for nonlinear ground response analysis codes are utilized for the Turkey Flat blind prediction. The recordings at locations D2 and V are not yet available as of this writing, which precludes an evaluation of prediction accuracy. However, the results presented in this paper illustrate that variability 8

9 in the simulation results is dominated by model-to-model variability at very short periods and velocity profile variability at low-to-moderate periods. Moreover, by comparing predictions from different users, it is found that engineering judgment on the material model can have a large effect (similar to that of velocity variability) on the variability of simulation results at periods less than the site period. 5. Acknowledgements Financial support for the benchmarking of nonlinear ground response analysis procedures was provided by PEER Lifelines project 2G2, which is sponsored by the Pacific Earthquake Engineering Research Center s Program of Applied Earthquake Engineering Research of Lifeline Systems. The PEER Lifelines program, in turn, is supposed by the State Energy Resources Conservation and Development Commission and the Pacific Gas and Electric Company. This work made use of Earthquake Engineering Research Centers Shared Facilities supported by the National Science Foundation under Award #EEC In addition, the support of the California Department of Transportation s PEARL program is acknowledged. This project has benefited from the helpful suggestions of an advisory panel consisting of Drs. Susan Chang, I.M. Idriss, Steven Kramer, Faiz Makdisi, Geoff Martin, Lelio Mejia, Walter Silva, and Joseph Sun. The Turkey Flat strong-motion blind test is supported by the California Department of Conservation, California Geological Survey, Strong Motion Instrumentation Program, Contract 5-8. DEEPSOIL development was supported in part by the Earthquake Engineering Research Centers Program of the National Science Foundation under Award Number EEC ; the Mid-America Earthquake Center. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. 6. References Darendeli, M. (2). Development of a new family of normalized modulus reduction and material damping curves, Ph.D. Dissertation, Univ. of Texas. Hashash, Y.M.A. and D. Park (2). Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment, Engrg. Geology, 62(-3), Hashash, Y.M.A. and D. Park (22). Viscous damping formulation and high frequency motion propagation in nonlinear site response analysis, Soil Dynamics and Earthquake Engrg., 22(7), Kwok, O.L.A., J.P. Stewart, Y.M.A. Hashash, N. Matasovic, R.M. Pyke, Z. Wang, and Z. Yang (26). Practical implementation of analysis routines for nonlinear seismic ground response analysis, Proc. 8 th U.S.National Conference on Earthquake Engineering, April 8-22, San Francisco, CA,, Paper 546. Lee, M.K.W. and W.D.L. Finn. (978). DESRA-2: Dynamic effective stress response analysis of soil deposits with energy transmitting boundary including assessment of liquefaction potential, Soil Mechanics Series No. 36, Dept. of Civil Engrg., Univ. of British Columbia, Vancouver, Canada, 6 p. Li, X.S., Z. Wang and C.K. Shen (992). SUMDES: A nonlinear procedure for response analysis of horizontally-layered sites subjected to multi-directional earthquake loading, Dept. of Civil Engrg.. Univ. of Calif., Davis Matasovic, N. (26). D-MOD_2 A Computer Program for Seismic Response Analysis of Horizontally Layered Soil Deposits, Earthfill Dams, and Solid Waste Landfills, User s Manual, GeoMotions, LLC, Lacey, Washington Matasovic, N. and M. Vucetic (993). Cyclic characterization of liquefiable sands, J. of Geotech. Engrg., ASCE, 9 (), Matasovic, N. and M. Vucetic (995). Generalized cyclic degradation-pore pressure generation model for clays, J. Geotech. Engrg., ASCE, 2 (),

10 McKenna, F. and G.L. Fenves (2). The OpenSees command language manual, version.2., Pacific Earthquake Engineering Research Center, Univ. of Calif., Berkeley. ( Park, D. and Y.M.A. Hashash (24). Soil damping formulation in nonlinear time domain site response analysis, J. of Earthquake Engineering, 8(2): Parra, E. (996). Numerical modeling of liquefaction and lateral ground deformation including cyclic mobility and dilation response in soil systems, PhD Dissertation, Dept. of Civil Engrg., Rensselaer Polytechnic Institute, Troy, NY. Pyke, R.M. (979). Nonlinear soil models for irregular cyclic loadings, J. of Geotech. Engrg. Div., ASCE, 5(GT6), Pyke, R.M. (2). TESS Users' Manual, TAGA Engineering Software Services, Lafayette, CA. Ragheb, A. M. (994).Numerical analysis of seismically induced deformations in saturated granular soil strata, PhD Dissertation, Dept. of Civil Engrg., Rensselaer Polytechnic Institute, Troy, NY. Stepp, J.C. and other authors. (25). Turkey Flat, USA site effects test area. Report 7, strong motion test: prediction criteria and data formats, CSMIP Report OSMS 5-, California Geological Survey, Department of Conservation. Yang, Z., A. Elgamal and E. Parra (23). Computational model for cyclic mobility and associated shear deformation, J. Geotechnical and Geoenvironmental Engineering, ASCE, 29(2), Youngs, R.R. (2). Software validation report for SHAKE4, Geomatrix Consultants Yang, Z. (2). Numerical modeling of earthquake site response including dilation and liquefaction, PhD Dissertation, Dept. of Civil Engrg. and Engrg. Mech., Columbia University, N.Y.