The simulation of the behavior of soil-structure interaction (SSI) systems subjected
to seismic waves can be conveniently carried out in the frequency domain, to account for the
frequency-dependent properties of the infinite soil. However, the soil exhibits nonlinear behavior
even at small values of the strain level, so that its shear modulus and damping ratio vary
as a functions of the strain. It is important to consider the strain- and frequency-dependent
properties of the soil in a seismic SSI simulation. Since frequency domain (FD) analyses are
not suitable for nonlinear systems, time domain (TD) integration algorithms are commonly
adopted. An accurate way of including the frequency-dependent soil into a transient analysis is
to use convolution integrals, which requires linearity of the system and leads to a high computational
cost. Hybrid frequency–time domain (HFTD) methods represent an efficient alternative.
Most of the existing HFTD methods idealize the soil behavior according to the one-dimensional
(1D) wave propagation theory, which is a major simplification of the complex three dimensional
(3D) theory.
In this contributions we present a HFTD method, where the soil is described as a 3D continuum
governed by Lam´e’s equation of elastodynamics and the problem is solved with the integral
transform method (ITM). The shear modulus and the damping of the soil are nonlinear functions
of the strain level. The seismic waves (the loading) can be represented by spatial waves
with an arbitrary distribution in time and space. The response of the soil to the seismic waves is
first solved in the FD assuming a linearized elastic soil subjected to input waves, the response
is transformed into the TD and the maximum strain is evaluated at different depths. According
to the maximum strain, the shear modulus and the damping at different depths is updated and
the process is iterated until convergence. The proposed method is compared to the reference
1D nonlinear method and it is applied for a multi-dimensional analysis of a nonlinear soil. The
limitations of the method are also described.
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The simulation of the behavior of soil-structure interaction (SSI) systems subjected
to seismic waves can be conveniently carried out in the frequency domain, to account for the
frequency-dependent properties of the infinite soil. However, the soil exhibits nonlinear behavior
even at small values of the strain level, so that its shear modulus and damping ratio vary
as a functions of the strain. It is important to consider the strain- and frequency-dependent
properties of the soil in a seism...
»
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