A precise integration approach for dynamic impedance of rigid strip footing on arbitrary anisotropic layered half-space

The precise integration method (PIM) is proposed for the dynamic response analysis of rigid strip footing resting on arbitrary anisotropic multi-layered half-space. In the frequency domain, the governing equation of wave motion is converted into dual vector form of first-order ordinary differential equations which is solved by PIM. Each layer is divided into a large number (say, 2N) of mini-layers of equal thickness, within which characteristic matrices are assumed to vary following the Taylor series expansion to the fourth order. As a result, any desired accuracy of the displacements and stresses can be achieved by PIM. In addition, dual vector form equation makes it quite easily to combine two adjacent mini-layers into a new one. Each pass of combination reduces the total number of mini-layers by a half. The computational effort for the evaluation of the dynamic impedance of rigid strip footing can be reduced to a great extent. Numerical examples are provided to validate the efficiency and accuracy of the proposed approach.

► A new approach for the dynamic response analysis of soil-footing interaction. ► The soil can be any anisotropic multi-layered half-space. ► PIM can solve problem with less calculated effort and high accuracy. ► PIM can avoid the index overflow problems of transfer matrices method. ► No limitation is imposed on the thickness of the layer for the new approach.