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8 al. 2006; RspMatch 2010 by Al Atik and Abrahamson 2010) site. The shear wave velocity profile and its variability across or as part of software suites (SHAKE2000/D-MOD2000, the site is another key parameter. Direct measurement of the Ordonez 2000; Matasovic and Ordonez 2007). shear wave velocity is now commonplace using techniques such as the seismic cone penetration test (sCPT), down- For sites near faults, the ground motion time history needs hole logging, suspension logging, Refraction Microtremor to include additional characteristics beyond spectral match- (ReMi), and spectral analysis of surface waves (SASW) ing. These include directivity, velocity pulses, and fling techniques. The details of field investigations to character- effects (e.g., Somerville 1998; Munfagh et al. 1999; Bray et al. ize the soil profile is beyond the scope of this report and can 2009). Significant specialized expertise is required to prop- be found in other sources (e.g., Kavazanjian et al. 1997a,b; erly represent these effects in ground motion time histories; Sabatini et al. 2002). discussion of these issues is beyond the scope of this report. Development of Soil Properties Typically, the input time histories for site response anal- ysis are specified as rock outcrop acceleration time histo- Site response analysis also requires index properties such ries that are then modified within the program to represent as density, Atterberg limits, and relative density of the vari- time histories in bedrock underlying the site. For nonlinear ous layers. Strength properties such as friction angle and analysis, an "outcropping" motion is used in a simulation by undrained shear strength are important input properties, introducing a layer representing an elastic half space (trans- especially for soft soils and areas with high levels of shak- mitting boundary) at the base of the soil column. Similarly, ing. In addition to these properties, dynamic soil properties an "in-hole" (i.e., "within") motion, commonly obtained of the soil layers need to be defined. Laboratory tests using from a downhole array, is used in a simulation by using a cyclic triaxial, cyclic direct simple shear (DSS), and reso- rigid half-space. Some site response analysis programs, nant column devices are by far the most common devices for such as PLAXIS, OpenSees, and ABAQUS, allow the input defining the dynamic behavior of soils at a given site. These motion to be entered as acceleration, velocity, or displace- tests hinge on the availability of high-quality undisturbed ment time history. On the other hand, FLAC allows the input samples, which might be available for cohesive soils, but are motion to be entered only as a velocity time history. difficult to obtain for cohesionless soils. In areas where "competent rock" is too deep (e.g., Mis- Cyclic laboratory tests are therefore not as commonly sissippi embayment where competent rock is at depths of 1 available, and engineers often rely on standardized dynamic km or more south of Memphis), significant debate remains soil response curves in the form of normalized modulus as to what depth could be used in site response analysis, what reduction and damping curves as a function of shear strain material/shear wave velocity needs should represent "com- that approximate the nonlinear hysteretic soil behavior. petent rock," and what type of design motion can be used at Figure 3 shows the hysteretic stress strain behavior of soils such depth (e.g., simulated motion, bedrock outcrop motion, under symmetrical cyclic loading by (1) an equivalent shear or deconvoluted motion). modulus (G ) that corresponds to the secant modulus through the endpoints of a hysteresis loop; and (2) equivalent viscous Recent research at the Pacific Earthquake Engineering damping ratio (), which is proportional to the energy loss Research Center (PEER) by Haselton (2009) and Baker et from a single cycle of shear deformation. Both G and are al. (2011) provides a detailed review on the topic of ground functions of shear strain amplitude (), as can be inferred motions selection and scaling with a focus on structural appli- from Figure 3a. Plots of shear modulus normalized by the cations. Baker et al. (2011) introduce a new ground motions maximum shear modulus and damping as a function of shear selection procedure whose response spectra match a target strain are then developed, as shown in Figure 3b. mean and variance. The procedure avoids the use of spec- tral matching approaches by taking advantage of availability Over the years, a number of standardized families of of the large PEER ground motion data base. The literature curves have been developed and used in the practice. These review and experience clearly indicate that ground motion include Seed and Idriss (1970), Vucetic and Dobry (1991), selection, scaling, and matching for site response analysis EPRI (1993), and more recently, Darendeli (2001) and Menq remain unsettled issues and more studies are needed in this (2003). These curves are used in both equivalent-linear and area to provide better guidance to practicing engineers. nonlinear site response analysis. Definition of Subsurface Stratigraphy EQUIVALENT-LINEAR SITE RESPONSE ANALYSIS A site response analysis requires detailed information on subsurface stratigraphy. A thorough field investigation is The equivalent-linear analysis approach was first introduced required to understand the geologic history of the soil depos- by Seed and Idriss (1970) and has remained substantially the its and define the soil and rock units and water level at a same since. The wave propagation through the soil deposit is

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9 (a) density of soil , and strain-dependent normalized modulus reduction and damping curves. As indicated in the survey responses, the equivalent-lin- ear site response analysis method is, by far, the most widely used method for evaluation of site-specific ground motions. Advantages of the equivalent-linear method include its requirement for few, well-understood, input parameters, broad experience with its application, a large publicly avail- able database of input parameters, and minimal computa- tional effort. The most commonly used equivalent-linear computer code is SHAKE (Schnabel et al. 1972). Modified versions of this program include SHAKE91 (Idriss and Sun 1992) and SHAKE2000 (Ordonez 2000). DEEPSOIL (Hashash and Park, 2001, 2002; Hashash et al. 2011), ProShake (EduPro Civil Systems 1999), CyberQuake (Modaressi and Foer- (b) ster 2000). These programs use the same computational procedure as that applied in SHAKE, but they were devel- oped independently. The equivalent-linear model has also been incorporated in 2-D site response programs such as QUAD-4 (Idriss et al. 1973), derivatives of QUAD-4 (e.g., QUAD4M, Hudson et al. 1994), and in advanced 2-D and 3-D site response models such as FLAC (Itasca 2005; latest iteration is Version 6.0). Modified frequency-domain methods have also been developed (e.g., Assimaki and Kausel 2002; Kausel and Assimaki 2002) in which soil properties in individual layers FIGURE 3 Approximation of soil nonlinear behavior (a) are adjusted on a frequency-to-frequency basis to account Hysteresis loop of soil element loaded by a single cycle of shear for the strong variation of shear strain amplitude with fre- strain; (b) Variation of normalized modulus (G/Gmax ) and with quency. This approach is used as a proxy for representation shear strain () (modulus reduction and damping curves). of nonlinear site response analysis in time domain. Another, although rarely used, improvement includes the introduction solved in the frequency domain, and any given soil layer is of a vertical component of ground shaking into the analysis assumed to have a constant modulus and damping through- (Idriss et al. 1973). Vertical site response analysis remains a out shaking. Equivalent-linear site response analysis uses an research topic. iterative procedure in which initial estimates of G and are provided for each soil layer. Using those linear, time-inde- Another, less used method for equivalent-linear site pendent properties, linear-elastic analyses are performed response analysis is the random vibration theory (RVT, e.g., and the response of the soil deposit is evaluated. Shear Rathje and Ozbey 2006), based on the equivalent-linear strain histories are obtained from the results, and peak shear method. The advantage of this approach is that the user does strains are evaluated for each layer. Effective shear strains not need to develop input ground motion time histories, and are calculated as a fraction of the peak shear strains. The the analysis will directly provide a surface spectrum. Recent effective shear strain is then used to evaluate an appropriate work (E.M. Rathje, personal communication, 2011) shows G and using shear straindependent normalized modulus that the use of RVT with a single set of soil profile properties reduction and damping curves described earlier. The pro- results in amplifications of the peaks of the transfer function cess is repeated until the strain-compatible properties are that is not observed in conventional equivalent-linear analy- consistent with the properties used to perform the dynamic sis approaches. These peaks can be reduced if the soil profile response analyses and the analysis converges. properties are randomized (e.g., Monte Carlo simulation of material properties). Equivalent-linear modeling of site response is based on a total-stress representation of soil behavior. The soil proper- The equivalent-linear analysis approach has been in use ties needed for equivalent-linear site response analysis are since the advent of SHAKE in 1972. Hence, it is supported shear wave velocity Vs, used to compute Gmax = Vs2, mass by a number of verification studies, including back-analy-