Analytical Theory for 3D Consolidation of Layered Viscoelastic Soils Based on Displacement Function Method

Abstract

The analysis of long-term rheological consolidation behaviors of soft soils is the research focus in geotechnical and geological engineering. This paper develops an analytical theory to explore such behavior within layered viscoelastic sediments in a three-dimensional (3D) Cartesian coordinate system. Starting from the governing equations of 3D consolidation problems and introducing the displacement functions, the state vectors between the surface and an arbitrary depth of a finite soil layer are established in the transform domain. With the aid of this relationship and continuity conditions between adjacent layers and the boundary conditions of the layered system, an analytical solution for viscoelastic soils is then obtained. Detailed comparisons are given to confirm the applicability of the theory, followed by typical examples examining the effect of types of viscoelastic model, fractional order, and soil layered properties on the coupled rheological and consolidation responses. In the present theory, the state space equation containing eight coupling state vectors is uncoupled into two sets of equations of six and two state vectors based on three displacement functions and a decoupling transformation, which has the advantage of cutting the computation amount and proves to be remarkably efficient and practicable in solving the 3D rheological consolidation problems.