The near-surface properties of the earth modify seismic waves as they propagate from depth to the surface where they are felt and effect society. This process is often called site response, and is an important factor that contributes to the seismic hazard at a specific location. As observed in past earthquakes, the slower materials near the free surface influence damage patterns over short distances. Site response is a function of both the physical properties of near surface materials and the spatial distribution of those properties. Unfortunately, blind prediction experiments both in the linear and nonlinear range for soil behavior have consistently shown that predicted amplifications rarely match the observed amplifications. We hypothesize that the poor performance of existing site response models is that the standard assumptions do not adequately represent the complexity of site response behavior in many cases. The majority of site response models rely on the assumption of vertically propagating S-waves through laterally homogeneous media (SH1D). In this research, we set out to evaluate site response at multiple sites where both weak and strong motions have been measured and three-dimensional (3D) soil information exists. The selected sites provide a sequence from simple to complex site response behavior. Site response models will include 3D wave propagation through a 3D spatially variable and nonlinear medium. This reserach will test whether or not a more complex site response model can explain the behavior that is observed at some of these sites. Further, we will outline a method to identify and model complex site response when needed.
This research will focus on four KiK-net sites. The sites fulfill two criteria: (1) the sites recorded large accelerations from the 2003 M8.3 Tokachi-Oki earthquake (with maximum accelerations from 0.40 to 0.51 g), and (2) the suite of sites include those that are characteristic of the best, intermediate, and worst fit to the SH1D response for weak ground motions (i.e., simple to complex site response behavior). With this dataset we will test the accuracy of both spatial and constitutive models for predicting complex site response behavior. The principle of parsimony demands that numerical models be only as complex as the data require. Thus, we will quantify the accuracy that can be achieved at various levels of complexity so that practitioners can make informed decisions about the extent of spatial data and complexity of the constitutive model needed for a particular project. We will consider a sequence of constitutive models from linear-elastic to hyperelastic-plastic.
The intellectual merit of the research is to challenge the standard assumptions of one-dimensional vertical propagation of S-waves through a laterally constant medium and lay the groundwork for more complex and more accurate site response models. The available computational power is continually increasing and is approaching the ability to model wave propagation from source to site; however, the most common approaches currently model nonlinear effects and 3D effects independently. This research is a first step toward combining these two important aspects of modeling. The broader impacts of this work include mentoring within and beyond the project team with specific focus on the undergraduate engineering population at Tufts, and the broad dissemination of in situ data for four site response sites of varying complexity with through the online Geohazards Database Consortium @ Tufts.
The purpose of this work was to improve our understanding of uncertainty (bias and variability) in site response models, using records from the KiK-net database of vertical seismic arrays. Using the Kiban-Kyoshin network (KiK-net) downhole array data in Japan, analyses were performed at 100 stations that have recorded at least one strong ground motion with PGA greater than 0.3g at the ground surface. Using the 3720 ground-motion records at these sites, linear and equivalent-linear site response analyses were performed, and critical parameters that most greatly contribute to uncertainty in site response analyses were identified, through both accuracy (bias) and variability (precision). The focus of this component of the work was on linear and equivalent-linear site response analyses because the purpose was to identify trends in model performance of widely used site response models using a large database. We found that the maximum shear strain in the soil profile, the observed peak ground acceleration at the ground surface, and the predominant spectral period of the surface ground motion are the best predictors of where the evaluated models become inaccurate and/or imprecise. The peak shear strains beyond which linear analyses become inaccurate inpredicting surface pseudo-spectral accelerations (PSA) are a function of vibration period, and are between 0.01% and 0.1% for periods less than 0.5 s. Equivalent linear analyses become inaccurate at peak strains of approximately 0.4% over thisrange of periods. We found that, for the sites and ground motions considered, site response residuals at spectral periods greater than 0.5 s do not display noticeable effects of nonlinear soil behavior. To test nonlinear models we developed an overlay model. Using parallel load-carrying elements with varying stiffness and yield stress, the behavior of any given backbone stress-strain relation can be replicated. To represent overlay elements in a finite element model, the user simply needs to define identical finite elements and assign each of the finite elements identical node numbers in the finite-element mesh. One of the reasons that equivalent-linear analyses are so widely used in engineering practice is that they can be implemented with a limited amount of site data. Similarly, the nonlinear site response modeling methodology described in our work does not require any additional input parameters beyond those for an equivalent-linear analysis. In the final phase of the work, we tested the nonlinear overlay model with several linear, equivalent-linear, and nonlinear site response models at a subset of the 100 sites studied in Chapter 2. In this study, comprehensive linear, equivalent-linear, and nonlinear site response analyses are performed for 191 ground motions recorded at six well-behaved sites in the KiK-net database. These sites, which span a broad range of geologic conditions, are selected because they strongly meet the assumptions of 1D wave propagation, and are therefore ideal for validating and calibrating 1D site response models. Because the focus is on sites that are well-modeled by 1D wave propagation, the observed misfit for strong motions can be attributed to the nonlinear soil behavior model (and not other factors, such as 3D effects). The equivalent-linear site response program SHAKE, the nonlinear site response program DEEPSOIL, and an overlay model within the general finite element program Abaqus/Explicit, which allows for a multilinear representation of any backbone stress-strain curve, are the programs employed in this study. Across all sites, ground motions, and spectralperiods, one of the most consistent findings is that the differences in accuracy arelargest between the linear model and the other models, and that there arerelatively small differences in accuracy between equivalent-linear and nonlinearsite response models. The critical level of maximum shear strain (γmax) at which the linear site response model breaks down is 0.01%–0.1% (with a midpoint ofapproximately 0.05%), confirming the results when we used 100 sites; similar trends were observed in linear frequency-domain and linear time-domain site response models. Beyond strains of approximately 0.05% (to maximum strains of 0.3% considered in this chapter), equivalent-linear and nonlinear site response models both offer significant improvements over linear site response models. When observed and predicted amplification spectra are compared over a range of spectral periods (instead of at a single period or a set of discrete periods), nonlinear site response models are shown to exhibit a slight improvement over equivalent-linear site response models for shear strains greater than 0.05%. In engineering practice, however, site response model selection will be determined by the ultimate goal of the site-specific ground motion study, and whether the limitations of frequency-domain modeling are adequate for the problem at hand. Finally, this project educated one graduate student and one undergraduate student in earthquake engineernig and prepared them for their future careers. The graduate student has since taken a faculty position and the undergraduate is now pursuing a graduate degree.
