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See discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/269777536 Comparison of 1D linear, equivalent-linear, and nonlinear site response models at six KiK-net validation sites ARTICLE in SOIL DYNAMICS AND EARTHQUAKE ENGINEERING · FEBRUARY 2015 Impact Factor: 1.22 · DOI: 10.1016/j.soildyn.2014.10.016 CITATIONS 4 READS 99 4 AUTHORS, INCLUDING: Laurie G. Baise Tufts University 67 PUBLICATIONS 466 CITATIONS SEE PROFILE Luis A Dorfmann Tufts University 100 PUBLICATIONS 1,816 CITATIONS SEE PROFILE All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. Available from: Luis A Dorfmann Retrieved on: 14 December 2015 Comparison of 1D linear, equivalent-linear, and nonlinear site response models at six KiK-net validation sites James Kaklamanos n, Laurie G. Baise, Eric M. Thompson 1, Luis Dorfmann Department of Civil and Environmental Engineering, Tufts University, 113 Anderson Hall, Medford, MA 02155, USA a r t i c l e i n f o Article history: Received 30 September 2013 Received in revised form 22 September 2014 Accepted 19 October 2014 Keywords: Earthquake ground motion Seismic analysis Seismic effects Nonlinear soil behavior Numerical modeling a b s t r a c t Vertical seismometer arrays represent a unique interaction between observed and predicted ground motions, and they are especially helpful for validating and comparing site response models. In this study, we perform comprehensive linear, equivalent-linear, and nonlinear site response analyses of 191 ground motions recorded at six validation sites in the Kiban–Kyoshin network (KiK-net) of vertical seismometer arrays in Japan. These sites, which span a range of geologic conditions, are selected because they meet the basic assumptions of one-dimensional (1D) wave propagation, and are therefore ideal for validating and calibrating 1D nonlinear soil models. We employ the equivalent-linear site response program SHAKE, the nonlinear site response program DEEPSOIL, and a nonlinear site response overlay model within the general ﬁnite element program Abaqus/Explicit. Using the results from this broad range of ground motions, we quantify the uncertainties of the alternative site response models, measure the strain levels at which the models break down, and provide general recommendations for performing site response analyses. Speciﬁcally, we ﬁnd that at peak shear strains from 0.01% to 0.1%, linear site response models fail to accurately predict short-period ground motions; equivalent-linear and nonlinear models offer a signiﬁcant improvement at strains beyond this level, with nonlinear models exhibiting a slight improvement over equivalent-linear models at strains greater than approximately 0.05%. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction A fundamental step in any seismic hazard analysis is the quantiﬁcation of the expected levels of ground motions for potential earthquakes. Analytical site response analyses are per- formed by propagating an input motion through the soil proﬁle in order to predict the ground motion at the surface of a site. Site response analyses can also be performed empirically by using seismic site coefﬁcients such as those in the National Earthquake Hazard Reduction Program (NEHRP) seismic provisions [1]. For analytical site response analyses (the focus of this paper), the state of the practice in earthquake engineering is to approximate non- linear soil behavior using equivalent-linear (EQL) site response models, such as SHAKE [2–4] or STRATA [5]. However, once the shear strains in the soil exceed some critical level, the equivalent- linear approximation becomes inadequate, and fully nonlinear site response analyses are needed to accurately predict surface ground motions [5–13]. Fully nonlinear site response analyses are per- formed in the time-domain by integrating the equation of motion in small time steps. Numerous nonlinear site response programs have been developed, although compared to equivalent-linear models, their usage in standard engineering practice is relatively limited. Examples include D-MOD2000 [14], DEEPSOIL [15], TESS [16], SUMDES [17], OpenSees [18], and NOAHW [7]. Given a range of model complexities (linear, equivalent-linear, and nonlinear) and speciﬁc site response codes, engineers would beneﬁt from increased insight to (a) the ranges of ground motions over which each type of model is accurate, and (b) which site response codes offer the strongest goodness-of-ﬁt between pre- dicted and observed ground motions. Vertical seismometer arrays, which have both surface and downhole recordings are an excellent opportunity for validating site response models. This study uses the Kiban–Kyoshin (KiK-net) strong-motion network of vertical seismic arrays in Japan [19,20]. This data-rich network provides numerous surface–downhole station pairs that have recorded many earthquakes with varying levels of ground motion. A number of studies have used downhole arrays such as KiK-net to quantify nonlinear soil behavior and site response model uncer- tainty. Assimaki et al. [9] developed a framework for quantifying the susceptibility of nonlinear behavior using data from three Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/soildyn Soil Dynamics and Earthquake Engineering http://dx.doi.org/10.1016/j.soildyn.2014.10.016 0267-7261/& 2014 Elsevier Ltd. All rights reserved. n Correspondence to: Department of Civil and Mechanical Engineering, Merri- mack College, 315 Turnpike Street, North Andover, MA 01845, USA. Tel.: þ1 978 837 3401; fax: þ1 978 837 5029. E-mail addresses: KaklamanosJ@merrrimack.edu (J. Kaklamanos), Laurie.Baise@tufts.edu (L.G. Baise), ethompson@mail.sdsu.edu (E.M. Thompson), Luis.Dorfmann@tufts.edu (L. Dorfmann). 1 Present afﬁliation: Department of Geological Sciences, San Diego State University, 5500 Campanile Dr, 237 Geology Mathematics and Computer Science Building, San Diego, CA 92182. Soil Dynamics and Earthquake Engineering 69 (2015) 207–219 downhole array sites in southern California, and concluded that fully nonlinear analyses are necessary when the rock-outcrop (input) peak ground acceleration (PGA) exceeds 0.2 g for soft (NEHRP class E) sites. Kwok et al. [10] performed a blind site response prediction test at the Turkey Flat downhole array using data from the 2004 Mw 6.0 Parkﬁeld, California, earthquake. They tested ﬁve nonlinear site response models, and found that the models underestimated the site response ampliﬁcations at high frequencies, and overestimated the site response ampliﬁcations at frequencies near the fundamental mode of the site [10]. Kim and Hashash [12] assessed KiK-net downhole array data from the 2011 Mw 9.0 Tohoku earthquake, and also found that equivalent-linear and nonlinear site response models underpredicted the site response ampliﬁcations at high frequencies, especially at soft sites. They found that the accuracies of equivalent-linear and nonlinear models were generally similar, but the predictions deviate when maximum shear strains exceed 0.3%. Yee et al. [13] studied surface–downhole ground motions from the 2007 Mw 6.6 Niigata-ken Chuetsu-oki earthquake, and found that equivalent-linear and nonlinear models offered similar predictions for maximum shear strains up to 0.2%, but that predictions deviated at greater strains. In prior work [11], we used the KiK-net database to analyze the accuracy (bias) and variability (precision) resulting from common site response modeling assumptions, and we identiﬁed critical parameters that signiﬁcantly contribute to the uncertainty in site response analyses. We performed linear and equivalent-linear site response analyses at 100 KiK-net sites using 3720 ground motions ranging from weak to strong in amplitude, in particular, with 204 records having PGA40.3 g at the ground surface. The present work builds upon the study of Kaklamanos et al. [11] by adding nonlinear analyses and additional equivalent-linear analyses at a subset of 6 of the 100 KiK- net sites originally studied. The six sites were selected using the methodology of Thompson et al. [21], which developed a classiﬁcation scheme for downhole arrays that identiﬁes stations where the one- dimensional (1D) wave propagation assumption is valid. A station's classiﬁcation is a function of (a) its inter-event variability and (b) the similarity between the empirical and 1D theoretical transfer functions (ampliﬁcation spectra). Of the 100 KiK-net sites used by Thompson et al. [21] and Kaklamanos et al. [11], 16 sites fall into the LG category, having Low inter-event variability and Good ﬁt between the empirical and theoretical transfer functions, and therefore are ideal for calibra- tion and validation of 1D site response models. By selecting appro- priate validation sites, confounding errors can be avoided, such as calibrating a 1D site response model at locations signiﬁcantly affected by three-dimensional (3D) effects [21]. In the present study, we perform linear, equivalent-linear, and nonlinear site response analyses of 191 ground motions recorded at six selected LG sites. This study focuses on 1D total stress site response models, which are the most commonly used site response models in engineering practice. We employ the equivalent-linear site response program SHAKE, the nonlinear site response program DEEPSOIL, and a nonlinear site response overlay model within the general ﬁnite element program Abaqus/Explicit, introduced by Kak- lamanos et al. [22]. Using the results from this broad range of ground motions, we quantify the prediction accuracies of the alternative site response models, and provide recommendations for modeling site response in engineering practice. 2. Data This study focuses on the six KiK-net sites detailed in Table 1. The raw site data available from the KiK-net website [23] are the seismic velocity proﬁles and geologic proﬁles with soil/rock descriptions. Table 1 includes basic information on the stations: the time-averaged shear-wave velocity over the top 30 m of the subsurface VS30, NEHRP site class [1], depth to ﬁrst rock layer Zrock, installed depth of the downhole seismometer Zmax, frequency of the fundamental peak of the 1D theoretical surface–downhole transfer function fo, damping ratio uploads/Management/ kaklamanos-et-al-sdee2015 3 .pdf