Earthquake using finite element method for the domain

Earthquake makes enormous damages when hits an area. Damages can be
in human lives and structures. When a
structure is connected to the earth, the connection has effects on structures
and increases structure’s flexibility thereby the natural period of the
structure also increases. Scattering, diffraction, reflation, and refraction
change when material properties are changed. The soil structure interaction is
a nonlinear phenomenon. Two essential issues
are involved in the phenomenon of soil structure interaction. The first issue
is kinematic interaction which deals with wave propagations. Wave propagation has effects on the structure
foundation considering the geometry and stiffness properties of the structural
foundation and soil. The seismic wave
propagation happens by deformation in the soil medium. The foundation cannot
deform by the same amount as the soil because of the foundation is considered to be very rigid in comparison to the soil deposits. So, this
vision faces a mathematical difficulty which is hard to account for the
mathematical models for practical vibration analysis. In this aspect, only the
wave propagation in an elastic medium is
involved. Therefore, the effects which starch from the wave propagation
considerations is known as kinematic interaction effects. The second issue of
the soil structure interaction analysis is inertial interaction. This issue
deals with the deformations and stresses in supporting soil which is encouraged from the base shears and moments
generated in vibrating structure. The direct and the
substructure approaches are adopted in this paper to investigate the problem of
soil- structure interaction. The main idea of the direct approach is
including the soil medium in the mathematical model which is developed for
dynamic analysis. Dynamic analysis is made by using finite element method for
the domain with appropriate absorbing / transmitting boundaries. Absorbing /
Transmitting boundaries prevent the seismic energy is reflected back into the problem domain. May some analysis’
results have errors if the site has deep deposits and the bottom boundary of the finite
element model is placed at shallow depth instead of rock level. Deformation and
stresses in the structural system are
essential components of the design. The
soil medium is taken as a massless medium
in order to overcome the problem of owing more flexible nature of soil by the
lower modes with the superstructure locating on the top of soil mass as a rigid
body. This consideration inforces the modes of
soil deformation to move to the higher end of the Eigen spectrum thus, providing structural modes at the lower end of
the Eigen spectrum.
The substructure approach is divided to
three – steps solution for SSI problem. The first
step is getting foundation input motion after solving the kinematic interaction
problem. The second step is soil springs
which are computing the frequency of
dependent impedance functions. This step
represents the stiffness and damping characteristics of the soil- foundation
interacting system. The third step is
determination the response of the real supported on frequency dependent soil springs and subjected at the base of these
springs to the foundation input motion computed. The formulas which
are used for soil-structure interaction
analysis is taken from Pais and Kasual and modified by Gazetas. The substructure approach may be identical with direct
approach if the structural foundations are completely rigid. From substructure, the approach can be concluded that the primary effect of inertial
interaction in the lengthening of the natural
period and increases in damping ratio of the dynamical system. Finally, this
paper shows two ways of designing and modeling
soil-structure interaction without determining
which one is better.

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