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6 when material (model) parameters are established through INFORMATION REQUIRED FOR SITE RESPONSE a reasonable site characterization effort (e.g., Kwok et al. ANALYSIS 2006, 2008). A number of numerical techniques are available for site A site response analysis is commonly performed under response analysis, including 1-, 2-, and 3-D equivalent-linear many conditions: (1) when soil conditions cannot be rea- (frequency domain) and nonlinear (time domain) analysis sonably categorized into one of the standard site conditions; approaches. All these techniques require a common set of (2) when empirical site factors for the site are not avail- information and input. able (e.g., such as site class F); (3) when special ground conditions govern the design (e.g., soil liquefaction, seis- The input to site response analysis requires (1) input mic settlement, lateral spreading, and slope stability); (4) ground motion time histories; (2) identification of subsur- for any case where the objective is to obtain ground motions face conditions, including geometry, stratification, and considered to be more representative of the local geologic depth to bedrock and groundwater; and (3) specification and seismic site conditions than motions obtained from the of basic and advanced material properties for each layer first two approaches; or (5) where (nonlinear) SFSI analysis of subsurface soil and of bedrock, such as unit weight and is undertaken. shear wave velocity (or low-strain shear modulus) and shear modulus and damping as a function of shear strain. More The attenuation relationship approach outlined above is advanced analyses require additional soil properties (e.g., addressed in greater detail elsewhere (e.g., Kramer 1996; saturated hydraulic conductivity and wet and saturated unit Kramer and Stewart 2004; Abrahamson et al. 2008). The weight), model (i.e., curve-fitting) parameters, and hysteretic code-factor approach is also addressed in these references and viscous damping model parameters (Rayleigh damping and in relevant codes (e.g., AASHTO 2010a; IBC 2006). parameters for frequency dependent formulations). The third approach for evaluation of soil effects on ground motions, commonly referred to as site response analysis, is Not all of the above-listed input information has the same discussed in detail in this study. influence on the results of the site response analysis. In most cases, input ground motions have the most influence on the The report presumes that the reader has basic familiarity results of site response analysis. The near-surface shear with earthquake engineering, geotechnical earthquake engi- wave velocity profile and material nonlinearity (e.g., the neering, and soil behavior. The reader is referred to a book modulus reduction and damping ratio curves) are, as noted such as Geotechnical Earthquake Engineering by Kramer by Roblee et al. (1996), the parameters that predominantly (1996) and Dynamics of Structures by Chopra (2006) for this control ground motion response expressed by the accelera- background information. tion response spectrum. Detailed information on the "uncer- tainty" related to soil property evaluation and assessment of spatial variability of ground motions can be found in Jones SITE RESPONSE ANALYSIS METHODS et al. (2002) and in Kwok et al. (2007). Site response analysis methods can be classified by the Input Ground Motion Time Histories domain in which calculations are performed (frequency domain or time domain), the sophistication of the constitu- It is generally recognized that the selection of input ground tive model employed (linear, equivalent-linear, and/or non- motion is one of the primary contributors, if not the primary linear), whether effects of pore water pressure generation are contributor, to uncertainty in site response analysis. Various neglected or not (total-stress and effective-stress analyses, codes and design guidance documents outline procedures respectively), and the dimensionality of the space in which for selection of design ground motions. For example, ASCE analysis is performed (1-D, quasi 2-D, 2-D, and 3-D). Other (2006) (ASCE 7-05, Chapter 21, Section 21.1.1) requires that considerations in classifying site response analysis methods "at least five recorded or simulated rock outcrop horizontal include modeling of cyclic reduction and degradation in a ground motion acceleration time histories be selected from total-stress mode. events having magnitudes and fault distances that are con- sistent with those that control the MCE [Maximum Con- The following section describes the input required for site sidered Earthquake]." To further minimize the uncertainty response analysis, followed by a discussion of the various related to selection of design ground motions, ASCE 7-05 methods available for site response analysis with increasing also requires that the time histories be scaled such that the complexity: (1) frequency domain equivalent-linear analy- average acceleration response spectrum of each time history sis; (2) nonlinear time domain total stress analysis; and (3) is approximately at the level of the MCE rock acceleration nonlinear time domain effective-stress analysis. response spectrum over the period range of significance to

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7 structural response. The AASHTO Guide Specification for period of interest. Bommer and Acevedo (2004) present a Seismic Isolation Design, 3rd Edition (AASHTO 2010b) series of recommendations applicable to the selection of real requires the use of three sets of time histories (a single set records for engineering analysis. Kottke and Rathje (2007) consists of two horizontal components and a vertical com- developed a semi-automatic procedure that facilitates the ponent). If three time-history analyses are performed, then selection of a suite of motions from a user-provided library of the maximum response is used for design. If seven or more records, and the scaling of the selected motions so that their time-history analyses are performed, then the average of the average fits a target response spectrum. Baker et al. (2011) response parameter of interest may be used for design, per (http://stanford.edu/~bakerjw/gmselection.html) developed the same code. a similar procedure, with time histories scaled up or down to match the target spectrum at a predominant period of the In general, regardless of the source cited, the approach facility of concern. for the development of site-specific design ground motions (acceleration time histories and/or acceleration response For the spectrum matching approach, a carefully spectra) considers two steps: initial selection of time histo- selected time history (seed motion) is adjusted either in the ries, and modification of time histories. frequency domain by varying the amplitudes of the Fou- rier amplitude spectrum, or in the time domain by adding The initial selection of time histories includes records wavelets in iterations until a satisfactory match to the target that closely match the site tectonic environment, controlling spectrum is obtained. Spectral matching is considered to be earthquake magnitudes and distances, local site conditions, an "art" (Abrahamson 2008) as it requires certain skills to response spectral characteristics, and, for geotechnical eval- produce a single time history that typically replaces three to uations, duration of strong ground shaking. Both recorded four natural records. At a minimum, magnitude, distance, time histories from past earthquakes and carefully gener- spectral content, and rupture directivity need to be con- ated synthetic time histories may be used. Multiple time sidered when selecting a seed motion. An example of time histories are considered; the number of records depends on history successfully matched to design (target) spectrum is the type of analysis and the modification method used (dis- shown in Figure 2. cussed below). The most popular sources of this information on the Internet are the PEER Strong Motion Database (www. peer.berkeley.edu), COSMOS Virtual Data Center (http:// db.cosmos-eq.org), and the KiK-net Digital Strong-Motion Seismograph Network (www.kik.bosai.go.jp). PEER pro- vides records mostly for crustal seismic events and offers a search tool that facilitates the selection of records based on a number of site and seismogenic parameters. For subduc- tion events, the COSMOS website provides records from a number of subduction zones around the world. Records for Japan are available from the KiK-net network. For areas in the Central and Eastern United States that lack an adequate number of recorded events, synthetic accelerograms are generated from the hazard deaggregation at the site, per- FIGURE 2 Spectrum matching approach for selection of formed through the U.S. Geological Survey national seis- design time histories. mic hazard mapping project website (http://eqint.cr.usgs. gov/deaggint/2002/index.php). The spectrum matching approach is gaining acceptance as the structural design is steadily moving away from a code- Modification of time histories is required because the based response spectrum approach to a response spectrum initially selected time histories often differ from the design developed as a part of site response analysis. This approach motions in terms of shaking peak amplitude and response is especially convenient for engineers because it calls for spectral ordinates; they would need to be modified for use analysis based on matching of suites of ground motions to a in analysis. Two modification methods are commonly used single spectrum, hence no "enveloping" of shear forces and in practice: simple scaling approach and spectrum matching moments generated by multiple time histories is required. It approach. is also adopted for geotechnical applications (e.g., Greater Vancouver Liquefaction Task Force 2007). "User friendly" In the simple scaling approach, the entire time history software for modifying the seed record in the time domain is is scaled up or down so that its spectrum approximately available, either in stand-alone form (e.g., the original Rsp- matches that selected for design (target spectrum) over the Match by Abrahamson 1992; RspMatch 2005 by Hancock et