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Site response is afunction of soil profile and the probabledistribution of soil profile has a significanteffect on the site response. This study presents the effects of randomvariations of soil properties on the site response using the differentprobabilistic distributions. The important characteristics of local soil,including soil properties, the layering, and shear wave velocity ( ),whichare considered to implement the randomvariations. The stochastic processes are generated by using the differentdistribution models with the coefficient of variation. In this paper, a proposedprocedure is developed to perform thevariability of soil properties.

The coding of this new procedure is based onthe original SHAKE91 framework. However, instead of using the fixed the soilprofile, an uncertainty of layering and  is generatedas the input data. It is found that obtained statistical medians from allpossible input under the different stochastic processes give good agreements withbaseline data. Additionally, the results of these analyses indicate that thevariations of nonlinear soil property have a significant impact on the behavior of the soil, especially at highfrequencies.

On the other hand, the random of variation layering and  profile has small effects on the soil response.Keywords: site response analysis, probabilisticdistribution, random site properties, soil profile, shear modulus.1.      BackgroundSite response analysis is animportant method to simulate the seismic waves from the underlying bedrock motionto surface ground motion throughlocal soil conditions. The properties of the local soil conditions such as thelayering, the shear wave velocity ( )and the modulus reduction and damping (MRD) curves havesignificant influence to ground shaking.Characteristics of local soils havebeen carried out in many works. Byassuming constant values of both the shear modulus and the damping factor of asoil, Seed and Idriss (1969) provided anappropriate analysis to estimate the surface responseduring earthquakes.

Based on comparisonbetween the laboratory and experiment tests, Seed etal. (1986) proposed numerical models of relationshipbetween nonlinear shear modulus reduction and material damping increase curvesfor sandy and gravelly soils. Effects of nonlinear dynamic soil propertiesare investigated in studies of Hardin and Drnevich, (1972) – HD72; Anderson and Woods, (1975)– AW75; Darendeli, (2001) – Da2001. An analytical model of nonlinear soil behavior with shear strain, namely hyperbolic model was developed by HD72. Later amodified hyperbolic model has includedthe published results by Da2001 to model the relationship between materialdamping ratio and strain, using First-order, Second-moment Bayesian Method-FSBM (which can be found in Gilbert, 1999) toestimate the MRD curve.

Besides, AW75 defined acorrelation number for the Ramberg-Osgood curve, which describes the relationship of shear modulus with shear strain.A few formulas to predict theshear modulus and damping ratios of soil properties were proposed by reanalyzing the field data on dynamic soilproperties, which was developed by Ishibashi and Zhang(1993). Thereafter, Menq (2003) investigatedthe dynamic properties of sandy and gravelly soils using the multi-modeproposed device. Usually, in practical earthquakeengineering, there are no data available about the stochastic variable, such asthe layer thickness, ,density, shear modulus. Therefore, it is necessary to develop a simulationtechnique of uncertainty processes.

An essential part of the probabilisticmethods is the selection of probability distribution functions to represent theuncertainty of the random variables considered. A statistical model wasdeveloped by Toro (1995) – To1995 to randomizethe layering and ,that  variability was described a log-normaldistribution. Manyother authors also presented probabilistic approaches through several types ofresearch performed by (Koutsourelakis et al., 2002 –Ko02; Popescu et al., 2006; Rathje et al., 2010 – Ra10). A non-Gaussiandistribution for soil properties and a non-stationaryrandom process for ground motion have been examined by Ko02 for evaluating of soil-structure system due toliquefaction. The finite elementmodel for a soil profile under seismic excitation considering the influence of coefficientof variation (COV) was modelled byNour et al.

(2003) to analyze the behavior of site, thatthe  wasrandomized by non-Gaussian distribution. Effect of spatial random soil on theamplification between the groundshaking and the bedrock motion wasincluded the research presented by Bazzurro and Cornell (2004). Two earthquakes in Taiwan and California wasreanalyzed by Andrade and Borja (2006) to investigate the soil response by comparing theequivalent linear analysis (Idriss and Sun, 1993– IS1993) and time domain nonlinearanalysis (Borja et al, 2000). Kwok et al. (2008), who evaluated the soil behaviorof site-specific in Turkey Flat using the nonlinear and equivalent-linearground-response computer code DEEPSOIL (Hashashet al., 2012 – Ha2012) andcompared the prediction with measurement results together. In this study, the site responseanalyses are conducted using randomized soil deposit (soil profile andnonlinear soil properties) for specificsite due to the seismic excitation.

The property randomizations include (1) thevariation of dynamic soil properties based on the empirical model of Da2001, (2) the layering and  of soil deposit from the surface to bedrock with the differentstochastic process using the To1995 model orlog-normal distribution. The influence of COV of layering and  is also introduced to these procedures. Inaddition, the proposed solution, namely PSHAKEbased on the original SHAKE91 framework of site response analysis is developed.

The results of fifty randomized profiles are used to confirm the influence ofrandom fields for soil properties on the site response analyses. The results ofmaximum peak ground motion at each layer, the amplification and the spectralacceleration (Sa) of ground motion at surface under current approaches arecompared with the resulting equivalent linear ground response software SHAKE91.

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