Seismic Response of Statistically Varied Soil Column Profiles for SSI Analyses

This paper presents a statistical approach to develop the soil column profiles and surface seismic response spectra for soil-structure interaction (SSI) analyses of structures founded on layered soil sites. The soil profile is developed using the statistical mean value of measured in-situ soil properties as determined from site boreholes and soil testing. The individual randomized soil profiles are input into a separate iterative soil column seismic analysis program to develop the seismic strain compatible soil profiles and surface acceleration response spectra consistent with the site design basis earthquake hazard. The median and median plus one standard deviation of the statistically developed surface response spectra developed using the results of thirty randomized soil columns are presented to demonstrate the influence of variation in soil properties and layer geometry. The development of median design response spectra based on the mean seismic hazard established for the site is recommended by the US Department of Energy [1, Section 2.3] for the design and evaluation of structures, systems and components. The statistically developed spectra are compared with spectra developed using soil profiles based on ASCE 4-98 soil modulus uncertainty factors [2, Section 3.3. 1.7]. The USNRC NUREG-0800 provides similar specific guidance regarding the variation in soil properties [3, 3.7. 2]. A layered site having three different soil types overlying bedrock is used as an example. Statistically derived soil profiles and response spectra (or acceleration time histories) in an SSI analysis utilize available soils information while avoiding designing for extreme site subsoil conditions which have a low probability of occurrence and provide a means to select an appropriate level of seismic risk. Additionally, the use of statistically derived soil profiles are appropriate to develop Uniform Hazard Spectra (UHS) at the surface given a UHS defined at bedrock. INTRODUCTION Seismic evaluations of important structures in moderate to high seismic zones founded on soil need to consider the uncertainties associated with the variability of soil materials and layering in order to adequately develop seismic strain compatible soil profiles and seismic responses. Soil test data can include, in part, characterizations of soil types, layer depths and thickness, depth to bedrock, and in-situ measurements of soil shear wave velocities. For each soil layer, the measured shear wave velocities (Vs) are used to calculate the site “low-strain” soil shear moduli (Gls) using the soil density (w): 2 Vs g w Gls × = (1) Soil properties, such as the shear modulus and damping, are strain dependent. This means that soil properties developed based on the relatively low strains involved with shear wave velocity testing will be changed when subjected to the relatively high strains that can be expected during a large earthquake. At higher strain levels, soil shear modulus is reduced while the soil material damping is increased. This strain dependency is usually presented in the form shear modulus (also damping) strain degradation curves determined for each soil type by additional testing or comparison with generically available curves when appropriate. In order to estimate the higher strain level “seismic strain compatible” properties, an analysis is conducted which passes the site design seismic motion through a one dimensional model of the soil column constructed using the low strain properties. The analysis uses an equivalent non-linear iterative time history procedure along with the soil strain degradation curves to develop the soil properties corresponding to strains that can be expected to occur during the earthquake. The resultant strain compatible properties become the basis of the soil model used in the SSI analyses. This analysis also calculates the corresponding strain compatible acceleration response spectra (and associated acceleration time histories) that define the SSI analysis seismic input motion. Thus, it is seen that variability and uncertainty associated with the measured low strain soil properties would also affect the results of SSI analyses using strain compatible properties. ASCE 4-98, Section 3.3. 1.7 and NUREG-0800, Section 3.7. 2, provide guidance to account for these uncertainties in the seismic analyses. Three sets of low strain soil properties are developed including the “best estimate” properties. “Upper bound” and “lower bound” properties are developed by multiplying and dividing the best estimate properties by the uncertainty factor 1 + Cv. The uncertainty factor is dependent upon the amount of soils data available. Cv can be directly calculated by statistically evaluating the soils test data. At a minimum, Cv should not be less than 0.5 [2]. If sufficient soil data is not available, Cv = 1.0 should be used [2], [3]. ASCE 4-98 recommends conducting analyses that range the low strain