1.1 Introduction: past developments and current trends in assessing seismic risks
Probabilistic seismic hazard analysis (PSHA) is concerned with the evaluation of the likelihood of strong ground motion intensities (Cornell, 1968; McGuire, 2004, 2008), which may cause destruction of buildings and infrastructure and disruption of economic and social activities. Popular measures for quantifying ground motion intensity include peak ground acceleration (PGA), peak ground velocity (PGV), and spectral accelerations (SAs) at different vibration periods. One of the most important features of PSHA is a comprehensive accounting of uncertainties related to earthquake occurrence, source rupture, wave propagation, and site effects by integrating hazard contributions over all scenarios. Over the past decades, the PSHA methodology has evolved significantly by incorporating more detailed and extended components, such as seismic hazard deaggregation (McGuire, 1995), nonlinear site response analysis (Bazzurro and Cornell, 2004), vector-value PSHA (Baker and Cornell, 2005), near-fault effects (Tothong et al., 2007), and aftershock hazard (Yeo and Cornell, 2009). The outputs from site-specific PSHA are seismic hazard curves (i.e. plot of expected ground motion levels as a function of probability) and uniform hazard spectra (i.e. ordinates of expected ground motion levels for a given probability as a function of vibration period). These are essential tools for developing national seismic hazard maps and modern seismic design provisions in national building codes. For instance, the current seismic design codes in the United States and Canada specify expected ground motion intensities at 2% probability of exceedance in 50 years (i.e. 2475 years return period level). The adopted probability level is related to regional seismicity and historical progress of seismic design requirements (including intended risk targets) and should be determined by balancing with other social requirements, such as health and welfare (Rosenblueth, 1986).
The conventional PSHA is composed of three major modules: (1) earthquake occurrence in time and space and earthquake source characteristics, (2) ground motion prediction (including path and site effects), and (3) integration of hazard contributions and treatment of uncertainties. An illustration of a typical PSHA procedure (and its extension to conduct more advanced analyses, as described below) is shown in Fig. 1.1. The spatiotem-poral earthquake occurrence is often characterised by fault/areal seismic sources. The delineated sources reflect past seismic activities in a region (historical and instrumental earthquake catalogue), and their activity rates can be determined based on a slip rate for a fault segment, and/or characterised by a magnitudeârecurrence relationship for an areal zone. As the first module of PSHA, a synthetic regional seismic catalogue can be generated using Monte Carlo simulation (Musson, 2000; Hong et al., 2006). The second module evaluates seismic intensity measures at a site of interest for all significant earthquake scenarios (generated by the first module), typically by using a ground motion prediction equation (GMPE). Internally consistent magnitude and distance measures should be considered in evaluating the ground motions expected at the site (Scherbaum et al., 2004; Bommer et al., 2005). Random scatter of motions about the median GMPE must be incorporated in the assessment. Alternatively, more extensive approaches based on stochastic simulation methods can be adopted (Wen and Wu, 2001). Although the implementation of modules 1 and 2 captures some uncertainties, a more comprehensive consideration of possible alternatives is needed. Such alternatives include: different source characterisations/zones (e.g. kernel smoothing and tessellation; Woo, 1996; Beauval et al., 2006; Hong et al., 2006), time-dependent seismic hazard (e.g. renewal model; Goda and Hong, 2006), uncertainties associated with magnitude-recurrence relationships (e.g. parametric uncertainties and bias due to completeness and magnitude-scale inhomogeneity; Weichert, 1980; Atkinson and McCartney, 2005), and choice of multiple regional GMPEs (e.g. selection of suitable equations and their weighting in a logic tree; Bommer et al., 2005). The above-mentioned issues have been already addressed and incorporated in modern PSHA studies through the use of a logic tree method (Petersen et al., 2008; Atkinson and Goda, 2011). Nevertheless, difficulties arise, because not all the models that analysts wish to apply are based on consistent data/assumptions and, more importantly, a full range of alternatives and uncertainties is not conceivable. This is an on-going issue in PSHA, and needs to be improved in the near future. Furthermore, it is important to carry out detailed and comprehensive sensitivity analyses as a part of PSHA. The final step of PSHA is the integration of hazard contributions due to all possible scenarios and models/assumptions. This is conventionally done using numerical integration, while Monte Carlo simulation can be used as an alternative (Musson, 2000; Hong et al., 2006). Because the latter is versatile in dealing with various probabilistic models and is easily extendable to advanced earthquake engineering analyses, this chapter is focused on the Monte Carlo approach.
1.1 General probabilistic seismic hazard analysis procedure and its extension to advanced earthquake engineering applications.
PSHA is an essential part of probabilistic seismic risk analysis (PSRA) in the performance-based earthquake engineering (PBEE) framework (Cornell et al., 2002; McGuire, 2004; Goulet et al., 2007; Ruiz-Garcia and Miranda, 2007). The objective of advanced engineering analyses is to quantify the extent of inelastic seismic demand (e.g. maximum inter-story drift) and consequence (e.g. building damage cost and indirect cost related to business down time) caused by extreme ground motions probabilistically. Such analyses are facilitated by the use of a so-called fragility curve, ...