Uniform Hazard Spectra on Soil Surface
3.2 Local Site Conditions
linear analysis is unable to appropriately describe the nonlinear characteristics of a soil site; (3) the annual probability of exceedance for PGA at the soil surface calculated by nonlinear seismic site response analysis cannot be facilitated by GMPEs method, due to the loss of detailed site information in GMPEs method; and (4) the result of annual probability of exceedance for PGA greatly depends on the standard deviation of the site amplification.
Cramer (Cramer, 2003) also proposed an equation to calculate the soil-hazard curve following the suggestions of McGuire. By applying the proposed equation to two sites, Cramer concluded that using the proposed method can make about a 10% difference or even larger in ground motion estimates over simply multiplying a bedrock probabilistic ground motion by a mean site amplification.
Bazzurro and Cornell (Bazzurro and Cornell, 2004a; Bazzurro and Cornell, 2004b) used Monte Carlo simulation to study the effects of soil parameter uncertainties and input motion uncertainties on site amplification at the soil surface. Based on two different example soil sites, they developed site amplification models for the two example sites, modified bedrock GMPEs and proposed equations to perform PSHA for soil sites. Using the proposed equations, soil UHS for the two example sites are constructed.
This chapter provides a probabilistic framework to construct soil UHS by PSHA for soil sites. Three issues should be considered in PSHA for soil sites: the variability of soil param- eters, the nonlinear property of soils, and the vector-valued site response analysis method (Li et al., 2012). In this study, the vector-valued seismic site response analysis considering the variability of soil parameters and the nonlinear property of soils is performed, and site amplification regression model for a specific soil site is obtained by regression analysis. Using the site amplification regression model, the bedrock GMPEs are first modified, and the modified GMPEs valid for the specific soil site are obtained. Using the modified GMPEs, PSHA for soil sites are performed, based on which soil UHS is constructed.
3.2 Local Site Conditions
During many earthquakes, the local geology and soil conditions profoundly influenced the important characteristics, i.e., amplitude, frequency content, and duration, of the strong
3.2 local site conditions
ground motions. The extent of their influences depends on the geometry and property of the subsurface materials, the topography of the sites, and the characteristic of the underlying ground motions. One-dimensional seismic site response analysis is usually used in practice based on three assumptions (Kramer, 1996):
❧ all boundaries are horizontal;
❧ the response of a soil deposit is predominantly caused by SH-waves propagating vertically from the underlying bedrock;
❧ the soil and bedrock surfaces extend infinitely in the horizontal direction.
3.2.1 Soil Parameters Affecting Seismic Site Response
It is widely accepted that shear-wave velocity, soil normalized shear modulus, and soil damping ratio greatly affect the seismic response of a soil site (Kramer, 1996; Hashash, Groholski, Phillips, et al., 2011; Villaverde, 2009; Hashash and Park, 2001).
Zhang and Andrus (Zhang et al., 2005) showed that there is a relation between soil normalized shear modulus G/Gmaxand damping ratio ξ :
ξ − ξmin =f(G/Gmax) =10.6(G/Gmax)2−31.6(G/Gmax) +21, (3.2.1)
ξmin = ξmin1 σ′ m Pa −k2 . (3.2.2)
The parameters ξmin1and k are determined by the soil types. Pais equal to 100 kPa; equation (3.2.2) converts ξmin1to ξminfor σm′ other than 100 kPa.
Based on these two equations, soil damping curves can be generated from the normalized shear modulus reduction curves.
3.2.2 Uncertainty of Soil Properties
Uncertainties pervade in many aspects of geotechnical earthquake engineering. The uncer- tainties in geotechnical properties of soils can be formally classified as aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty represents the natural randomness of soil properties. It results from inherent variability of soil properties, which is the consequence of natural geologic process that continually modify the properties of soils in situ. Epistemic
3.2 local site conditions
uncertainty represents the uncertainty due to the lack of knowledge and shortcomings in measurement or calculation. It results from equipment errors, procedural-operator errors, random testing effects, and transformation uncertainties.
Previous studies (Toro, 1993; Lumb, 1966) showed that the variability of soil parameters can be modeled by either normal distribution or lognormal distribution. The Electric Power Research Institute (Toro, 1993) tested soil samples from more than 200 different sites. The testing results showed that both shear-wave velocity and normalized shear modulus conform to lognormal distribution. Another laboratory testing results on natural soils indicated that most soil properties can be considered as random variables conforming to normal distribution (Lumb, 1966). Examples of randomized normalized shear modulus with average coefficients of variation 0.12 and randomized shear-wave velocity with average coefficients of variation 0.3 are shown in Figure 3.1.
The variabilities of normalized shear modulus, damping ratio, and shear-wave velocity vary with soil types, depths of soil samples, and values of the shear strain, which is another source of uncertainties in PSHA for soil sites. A completely probabilistic seismic hazard analysis is created by integrating the variabilities in both seismic sources and soil parameters into the whole analysis process.
In seismic site response analysis, soil parameters with variability are first randomized independently. These randomized soil parameters are then randomly paired with each other to obtain random profiles. For example, if 30 random profiles are to be created, the following steps will be required.
❧ Generate independently 30 sets of randomized normalized shear modulus, and 30 ran- domized shear-wave velocity profiles.
❧ Randomly pair the 30 sets of randomized normalized shear modulus with the 30 ran- domized shear-wave velocity profiles (one set of randomized normalized shear modulus with one randomized shear-wave velocity profile).
❧ 30 random profiles are generated that follow the distributions of the normalized shear modulus and the shear-wave velocity.
3.2 local site conditions