Earthquake using finite element method for the domain

Earthquake makes enormous damages when hits an area. Damages can bein human lives and structures. When astructure is connected to the earth, the connection has effects on structuresand increases structure’s flexibility thereby the natural period of thestructure also increases. Scattering, diffraction, reflation, and refractionchange when material properties are changed. The soil structure interaction isa nonlinear phenomenon. Two essential issuesare involved in the phenomenon of soil structure interaction.

The first issueis kinematic interaction which deals with wave propagations. Wave propagation has effects on the structurefoundation considering the geometry and stiffness properties of the structuralfoundation and soil. The seismic wavepropagation happens by deformation in the soil medium. The foundation cannotdeform by the same amount as the soil because of the foundation is considered to be very rigid in comparison to the soil deposits.

So, thisvision faces a mathematical difficulty which is hard to account for themathematical models for practical vibration analysis. In this aspect, only thewave propagation in an elastic medium isinvolved. Therefore, the effects which starch from the wave propagationconsiderations is known as kinematic interaction effects. The second issue ofthe soil structure interaction analysis is inertial interaction.

This issuedeals with the deformations and stresses in supporting soil which is encouraged from the base shears and momentsgenerated in vibrating structure. The direct and thesubstructure approaches are adopted in this paper to investigate the problem ofsoil- structure interaction. The main idea of the direct approach isincluding the soil medium in the mathematical model which is developed fordynamic analysis. Dynamic analysis is made by using finite element method forthe 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 finiteelement model is placed at shallow depth instead of rock level. Deformation andstresses in the structural system areessential components of the design.

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Thesoil medium is taken as a massless mediumin order to overcome the problem of owing more flexible nature of soil by thelower modes with the superstructure locating on the top of soil mass as a rigidbody. This consideration inforces the modes ofsoil deformation to move to the higher end of the Eigen spectrum thus, providing structural modes at the lower end ofthe Eigen spectrum.The substructure approach is divided tothree – steps solution for SSI problem. The firststep is getting foundation input motion after solving the kinematic interactionproblem. The second step is soil springswhich are computing the frequency ofdependent impedance functions. This steprepresents the stiffness and damping characteristics of the soil- foundationinteracting system. The third step isdetermination the response of the real supported on frequency dependent soil springs and subjected at the base of thesesprings to the foundation input motion computed.

The formulas whichare used for soil-structure interactionanalysis is taken from Pais and Kasual and modified by Gazetas. The substructure approach may be identical with directapproach if the structural foundations are completely rigid. From substructure, the approach can be concluded that the primary effect of inertialinteraction in the lengthening of the naturalperiod and increases in damping ratio of the dynamical system. Finally, thispaper shows two ways of designing and modelingsoil-structure interaction without determiningwhich one is better.