Finite-infinite element for dynamic analysis of axisymmetrically saturated composite foundations: Fid-Bau Portal

Finite-infinite element for dynamic analysis of axisymmetrically saturated composite foundations

Wang, Guocai / Chen, Longzhu / Song, Chunyu

In this paper, a coupled finite-infinite element method for the dynamic analysis of axisymmetrically vertical vibrations of unbounded saturated composite foundations is presented. Biot's theory of linear, isotropic poroelasticity is employed. This formulation assumes that the porous material is constructed so that the solid phase forms a structure that contains statistically distributed small pores filled with a Newtonian-viscous compressible fluid. The bulk material is assumed to be homogeneous on a macroscopic scale, and the pores are assumed to be interconnected. The solid skeleton is taken to be linear elastic and undergoing small deformations. The fluid flow is assumed to be of Poiseuille type so that the fluid inertia and friction are uniquely characterized by density, viscosity and pore dimensions. The element decay functions are derived using the analytical solutions of the equations governing the deformation of poroelastic materials in axially symmetric configurations. Using the proposed finite-infinite element method, the surface vertical displacements of air-saturated soil and of water-saturated soil with extremely low permeability subjected to a surface point excitation are calculated and the results agree very well with the existing theoretical solutions of single-phase elastic media, which indicate that the accuracy and precision of the proposed method and compiled program are satisfactory. As an application, the velocity admittances of a concrete block resting on cement mixing-pile or gravel-pile saturated composite foundations are calculated. The influence of soil permeability and pile rigidity on the dynamic response of the composite foundations is investigated. The parametric analysis demonstrates that with the increasing of soil permeability and pile rigidity, the amplitude-frequency of the block's velocity admittance will increase a great deal, but the phase-frequency curves do not change much generally. On account of keeping the basic merits of the finite element methods, the coupled finite-infinite element method proposed by this paper can not only be used to solve axisymmetrically dynamic problems of homogeneous and layered saturated foundation, but also be used to study vertical vibration characteristics of single-pile composite foundations, which can provide firmer theoretical basis for the dynamic testing methods of composite foundations (such as resonance methods, additional mass method, etc.).