EVALUATION OF EFFECTIVE PERIOD AND DAMPING OF STRUCTURES CONNECTED TO EMBEDDED STRIP FOOTING OVER INCOMPRESSIBLE SOIL

In this paper, effective period and damping of structures connected to an embedded strip footing are evaluated by consideration of soil structure interaction effect. Incompressible soil mass which may account for undrained behavior of saturated clay is modeled as a homogeneous and isotropic semi-infinite medium by using boundary element method. Boundary element method is suitable tool to model such media including infinite or semi-infinite boundaries. Incompressible soil medium has Poisson's ratio of 0.5. However, in this case the dilatational wave velocity approaches to infinity. Therefore, displacement and traction fundamental solutions in frequency domain which are utilized by boundary element method have to be expressed independent of dilatational wave velocity to prevent from numerical instability. These modifications have been performed using equalities relations. Having obtained the fundamental solutions of the incompressible soil medium, different problems considering soil structure interaction effect can be solved. Impedance functions of embedded strip footing rest on incompressible soil medium are obtained using boundary element method. In order to evaluate the components of impedance functions, three boundary value problems including unit displacement in horizontal, vertical and rotational directions of the footing have to be solved separately. The results are presented as a function of dimensionless frequency. There are good agreement between the obtained results and those of solution in the literature. The components of impedance functions are complex numbers. Real and imaginary parts represent respectively, stiffness and radiation damping of the semi-infinite soil medium. Impedance functions depend on excitation frequency, width of strip footing, shear wave velocity and Poisson's ratio. A single degree of freedom structure with flexible basement is replaced by an equivalent fixed base structure and its effective period and damping are then computed. Dimensionless parameters suitable for strip footing are introduced in this paper. The effective period and damping of structures with different heights are then obtained using an iterative procedure and compared to each other.