Input seismic energy in object during soil-foundation-object interaction

We study the response of two-dimensional system soil-flexible foundationstructure during seismic excitation in form of half-sine pulse. The research was conducted using a computer simulation of the seismic wave propagation in the numerical model. The equation of the wave is determined using a numerical method of finite differences. The solution consists of replacing the partial derivatives in space and time with their approximations using finite differences. We use the definition of the wave equation through particle velocity, the relative deformations and stresses. By integrating the velocity we get displacements in the points. Velocities, displacements, stresses and the relative deformation of particles in the medium are updated at each time step. To verify the method, we first solve the one dimensional (1-D) linear model and study the phenomena depending upon boundary conditions of Dirichlet, Neumann and conditions of moving boundaries. For the 1-D linear model, using the continuity of displacements and stresses, the solution can be analytically determined, which gives us the opportunity to validate our numerical model. The ultimate goal of the research in this dissertation is to determine how various parameters: - angle of propagation of the wave, - rigidity of the foundation, - stiffness of the soil, - degree of nonlinearity of the soil, - the duration of the pulse, affect the amount of seismic energy that enters the building when we consider two dimensional (2-D) soil-foundation-structure system . Keywords: wave, seismic energy, displacement, velocity of propagation, pulse, stress, boundary conditions, soil – flexible foundation – structure interaction, deformation, numerical model, finite difference method