IMPEDANCE MATRICES FOR 2 AXIAL SYMMETRICAL FOUNDATIONS ON LAYERED MEDIUM

Abstract

An attempt is made to generate impedance matrices for two independent axial symmetric foundations on an elastic layered medium. The analytic solution of three dimensional wave equations for a layered medium with the prescribed traction due to vibration of one axial symmetric foundation can be found using the technique developed in Refs. [3,4,5]. Two analytic solutions for two prescribed tractions due to the vibrations of two axial symmetric foundations are found separately. The principle of superposition is then used to obtain the final solution. The interaction stresses at the interfaces between the foundations and layered soil medium are assumed to be piecewise linear in r-directions of both cylindrical coordinates for two axial symmetric foundations. Then, the variational principle and reciprocal theorem are employed to generate the impedance matrices for both foundations. Some numerical results of impedance matrices for the interaction of two closely spaced circular foundations are presented, in order to show the effectiveness and efficiency of the presented method and the effect of layered stratum on the vibrations of two independent foundations. Discussion and conclusions are made.