Along with source and path effects, site response analysis is a vital component of earthquake ground motion prediction. Semi-empirical ground motion prediction equations (GMPEs) include terms for modeling site response that are based on simple metrics of site condition, such as the time-average shear-wave velocity in the upper 30 m of the site (VS30). Because site terms in GMPEs are derived from global ground motion databases and are based on incomplete information on the site condition, their predictions represent average levels of site response observed at sites conditional on VS30. Such predictions are referred to as ergodic.
Actual site response at a given site is likely to be different from this global average. Viewed in this context, the actual site response for a particular site and intensity measure can be understood as being the sum of the ergodic estimate from a global model and a (generally unknown) site term (denoted ηS). If the level of site-specific error ( ηS) can be identified and used to adjust the ergodic model, the ground motion analysis becomes more accurate (i.e., bias is removed), and the dispersion of the predicted ground motions is reduced. Therefore, site-specific evaluations of site response are always useful. The question is how that evaluation should be undertaken.
In this report, we consider the use of one-dimensional (1D) ground response analysis (GRA) to estimate site-specific site response. We show that previous studies investigating the usefulness of GRA to estimate observed site response (as evaluated from recordings) have achieved mixed success. This occurs because actual site response involves a variety of physical processes, some of which are not captured by 1D analysis. Resolution of questions related to the effectiveness of GRA, given the mixed results from the literature, is beyond the scope of this project. Instead, we summarize the relevant literature and describe future work that may resolve these questions.
Most of the work presented in this report concerns recommendations for performing GRA and using the results of those analyses to develop hazard-consistent estimates of site- specific ground motions. We describe in some detail recommendations for performing the GRA, assuming the analyst has a good working knowledge of the fundamentals of site response. Some important aspects of these recommendations include the following:
- Shear-wave velocity profiles should be based on measurements, not estimates;
- Nonlinear modulus reduction and damping versus strain curves can be derived from material-specific tests or generic relationships derived from test databases, but these relationships are generally not reliable at strains beyond about 0.3-0.5%;
- The shear strength of soil should be considered in developing modulus reduction (MR) relationships at large strains;
- Equivalent-linear methods of GRA should be used for small- to moderate-strain problems, and diagnostics are presented for identifying when such methods become unreliable;
- Nonlinear methods of GRA should be used for large strain problems, and procedures are presented for identifying a priori when such analyses are likely to be required; and
- Input ground motion selection for GRA should follow, with some modification, accepted norms for structural engineering applications, and we provide detailed recommendations for developing target spectra, selecting motions, and scaling or modifying the selected motions for compatibility with the target spectra.
Once GRA have been completed, it is necessary to interpret the results in the form of ground motion amplification functions that are conditioned on the amplitude of the input shaking. We suggest a three-parameter function for this relationship and provide detailed recommendations for how to estimate the parameters given suites of GRA results.
The standard deviation of the site amplification (denoted ΦlnY) computed directly from GRA results is considered unreliable. It is generally too high below the fundamental site period and too low above. For this reason, we recommend the use of standard deviations inferred from ground motion data analysis. We find these values of ΦlnY to be consistent (between-periods and between-studies) at ΦlnY ≈ 0.3. This level of consistency is not found with the standard deviation term representing site-to-site variability (i.e., the variability that can, in principal, be removed with a site-specific analysis). That standard deviation, denoted ΦS2S,exhibits regional variations and variations across periods. We present expressions for computing site-specific within-event standard deviation terms based in part on ΦlnY and ΦS2S. A significant consideration in this regard is whether the site response computed from GRA is non-ergodic. This is currently unknown and falls within the realm of engineering judgment.
Armed with a mean amplification function and the applicable standard deviation terms, the most robust merging of GRA with PSHA requires replacement of the site term in a GMPE with the mean amplification function, and use of that modified GMPE in the hazard integral. We developed a local version (i.e., not housed on a public server) of the open-source seismic hazard software platform OpenSHA that performs these calculations. This implementation properly handles modified standard deviation terms, which produces the most accurate hazard analysis results (i.e., hazard curves, uniform hazard spectra). This implementation also accounts for site effects in the disaggregation.
When implementation of GRA within the hazard integral is not considered practical, then the reference site (usually rock) hazard curves are modified using the mean site amplification function and (in some cases) ΦlnY . We present various options for this modification, but the method having the least bias relative to the probabilistic approach is the modified hybrid approach. This method involves modifying the reference site ground motion for a point on the hazard curve using the mean site amplification derived from mean expected ground motion levels for the reference site. Spreadsheet solutions for this, and other approximate methods, are provided in an electronic supplement:
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