Dynamic site response analysis in the face of uncertainty–an approach based on response surface method

Abstract

Although advanced modeling techniques such as the finite element method (FEM) have been used successfully in dynamic site response analysis, the high computational expense has hindered the incorporation of input parameter uncertainty in such analysis. Thus, when the variation of the peak ground acceleration (PGA) at the ground surface, which is the outcome of the site response analysis, has to be evaluated in the face of uncertainty, a surrogate model such as Response Surface Method (RSM) model is often used in lieu of the FEM model. In this paper, the RSM surrogate model was implemented in the context of seismic site response analysis to evaluate the variation (or uncertainty) of the PGA due to the propagation of input parameter uncertainty. The engineering implication of the variation of the surface PGA is significant as this knowledge is required for such tasks as reliability analysis of soil liquefaction and probabilistic seismic risk analysis. To derive the RSM model specifically for a site response analysis, a parametric study of the dynamic site responses using FEM code ABAQUS with the modified Davidenkov soil constitutive model implemented as a user‐defined material subroutine is first conducted. The input parameters, including the soil profile, soil properties, and input ground motion, in a typical dynamic site response analysis are then characterized and screened for their suitability to be included in the RSM model. For a given site response problem in the face of uncertainty, representative “samples” are taken for site response analysis using ABAQUS, and the analyses are carried out and finally the response surface is constructed using the outcomes of the ABAQUS numerical experimentations. The accuracy of the developed RSM model is then validated using the results of ABAQUS on cases not used in the development of the RSM model. Once the RSM model is deemed satisfactory, the reliability‐based formulation for evaluating the mean and standard deviation of the surface PGA is established. Example is provided to illustrate the RSM approach for dynamic site response analysis in the face of input parameter uncertainty.

Spatially correlated Vs30 estimation in the Beijing area

“…Moreover, the most fatal disadvantage of the deterministic method is that it can't take into account the uncertainty of parameters. It has been well-recognized that the soil profile and the associated parameters are usually not known with certainty (Liu et al, 2017a,b;Liu et al, 2021;Zhang et al, 2021;Stewart and Afshari, 2021;Ching et al, 2018;Phoon et al, 2022). These uncertainties will eventually be expressed and propagated in further applications such as the uncertainty of site response and the degree of earthquake disasters (Liu et al, 2021).…”

“…It has been well-recognized that the soil profile and the associated parameters are usually not known with certainty (Liu et al, 2017a,b;Liu et al, 2021;Zhang et al, 2021;Stewart and Afshari, 2021;Ching et al, 2018;Phoon et al, 2022). These uncertainties will eventually be expressed and propagated in further applications such as the uncertainty of site response and the degree of earthquake disasters (Liu et al, 2021). Therefore, other than the accuracy prediction of V s30 values for a certain region, the uncertainty distribution of V s30 needs to be evaluated.…”

Uncertainty propagation of soil property in dynamic site response under different site conditions

“…These uncertainties will eventually lead to the inaccuracy of site response analysis and earthquake disaster prediction. In general, the sources of uncertainty in dynamic site response can be divided into three categories, firstly, the uncertainties of basic soil parameters, for example, shear wave velocity, dynamic shear modulus, and damping ratio 5–14 . Secondly, uncertainties brought by numerical modeling, including numerical analysis software, calculation methods, and nonlinear constitutive models that describe the soil behavior 15–18 .…”

“…Li et al 10 investigated the effects of soil parameter uncertainty and concluded that the variability of ground motion is more sensitive to the discontinuities in the velocity profile especially the soil layer near the surface; Tran et al 21 tested the influences of soil properties such as material degradation, shear wave velocity, and density of soil, especially, they compared the variability in Vs from the Toro model and the log-normal distribution model in Sas and AF for different periods; Sun et al 14 used a real site in Italy to evaluate the possible impact of the uncertainty in shear wave velocity on the ground motion prediction, and proved that the uncertainty in predicted ground motion can be reduced by declining the variation of shear wave velocity. Liu et al 11 implemented a Response Surface Method surrogate model to evaluate the variation in dynamic site response due to the uncertainty of input parameters and found that both the shear wave velocity and input ground motion govern the uncertainty propagation.…”

“…Too little attention has been paid to site conditions, which have been shown to contribute significantly to dynamic site response prediction. 11 Hence, the major objective of this study is to investigate the uncertainty propagation in site response analysis under different site conditions.…”