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Site response is a
function of soil profile and the probable
distribution of soil profile has a significant
effect on the site response. This study presents the effects of random
variations of soil properties on the site response using the different
probabilistic distributions. The important characteristics of local soil,
including soil properties, the layering, and shear wave velocity (

),
which
are considered to implement the random
variations. The stochastic processes are generated by using the different
distribution models with the coefficient of variation. In this paper, a proposed
procedure is developed to perform the
variability of soil properties. The coding of this new procedure is based on
the original SHAKE91 framework. However, instead of using the fixed the soil
profile, an uncertainty of layering and

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 is generated
as the input data. It is found that obtained statistical medians from all
possible input under the different stochastic processes give good agreements with
baseline data. Additionally, the results of these analyses indicate that the
variations of nonlinear soil property have a significant impact on the behavior of the soil, especially at high
frequencies. On the other hand, the random of variation layering and

 profile has small effects on the soil response.

Keywords: site response analysis, probabilistic
distribution, random site properties, soil profile, shear modulus.

1.      
Background

Site response analysis is an
important method to simulate the seismic waves from the underlying bedrock motion
to surface ground motion through
local soil conditions. The properties of the local soil conditions such as the
layering, the shear wave velocity (

)
and the modulus reduction and damping (MRD) curves have
significant influence to ground shaking.

Characteristics of local soils have
been carried out in many works. By
assuming constant values of both the shear modulus and the damping factor of a
soil, Seed and Idriss (1969) provided an
appropriate analysis to estimate the surface response
during earthquakes. Based on comparison
between the laboratory and experiment tests, Seed et
al. (1986) proposed numerical models of relationship
between nonlinear shear modulus reduction and material damping increase curves
for sandy and gravelly soils. Effects of nonlinear dynamic soil properties
are 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 a
modified hyperbolic model has included
the published results by Da2001 to model the relationship between material
damping ratio and strain, using First-order, Second-moment Bayesian Method
-FSBM (which can be found in Gilbert, 1999) to
estimate the MRD curve. Besides, AW75 defined a
correlation number for the Ramberg-Osgood curve, which describes the relationship of shear modulus with shear strain.
A few formulas to predict the
shear modulus and damping ratios of soil properties were proposed by reanalyzing the field data on dynamic soil
properties, which was developed by Ishibashi and Zhang
(1993). Thereafter, Menq (2003) investigated
the dynamic properties of sandy and gravelly soils using the multi-mode
proposed device.

Usually, in practical earthquake
engineering, there are no data available about the stochastic variable, such as
the layer thickness,

,
density, shear modulus. Therefore, it is necessary to develop a simulation
technique of uncertainty processes. An essential part of the probabilistic
methods is the selection of probability distribution functions to represent the
uncertainty of the random variables considered. A statistical model was
developed by Toro (1995) – To1995 to randomize
the layering and

,
that

 variability was described a log-normal
distribution. Many
other authors also presented probabilistic approaches through several types of
research performed by (Koutsourelakis et al., 2002 –
Ko02; Popescu et al., 2006; Rathje et al., 2010 – Ra10). A non-Gaussian
distribution for soil properties and a non-stationary
random process for ground motion have been examined by Ko02 for evaluating of soil-structure system due to
liquefaction. The finite element
model for a soil profile under seismic excitation considering the influence of coefficient
of variation (COV) was modelled by
Nour et al. (2003) to analyze the behavior of site, that
the

 was
randomized by non-Gaussian distribution. Effect of spatial random soil on the
amplification between the ground
shaking and the bedrock motion was
included the research presented by Bazzurro and Cornell (2004). Two earthquakes in Taiwan and California was
reanalyzed by Andrade and Borja (2006) to investigate the soil response by comparing the
equivalent linear analysis (Idriss and Sun, 1993
– IS1993) and time domain nonlinear
analysis (Borja et al, 2000). Kwok et al. (2008), who evaluated the soil behavior
of site-specific in Turkey Flat using the nonlinear and equivalent-linear
ground-response computer code DEEPSOIL (Hashash
et al., 2012 – Ha2012) and
compared the prediction with measurement results together.

In this study, the site response
analyses are conducted using randomized soil deposit (soil profile and
nonlinear soil properties) for specific
site due to the seismic excitation. The property randomizations include (1) the
variation 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 different
stochastic process using the To1995 model or
log-normal distribution. The influence of COV of layering and

 is also introduced to these procedures. In
addition, the proposed solution, namely PSHAKE
based on the original SHAKE91 framework of site response analysis is developed.
The results of fifty randomized profiles are used to confirm the influence of
random fields for soil properties on the site response analyses. The results of
maximum peak ground motion at each layer, the amplification and the spectral
acceleration (Sa) of ground motion at surface under current approaches are
compared with the resulting equivalent linear ground response software SHAKE91.

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