Note on axisymmetric consolidation of multi-layered poroelastic soils with compressible constituents

In the conventional analysis of Biot's axisymmetric consolidation, the solid phase and the surrounding fluid were often assumed incompressible for simplicity. Such assumption in soil engineering ignored the effect of compressibility of constituents on the consolidation. In this article, the compressible fluid and solid in soil were taken into account for 3-D consolidation. The pore pressure, the displacements, and the stresses were expressed by two displacement functions, and the Laplace-Hankel transform was applied to set up the stiffness matrix between the generalized displacement and stress. The stiffness matrix consisted of negative exponential functions, ensuring that the computation is efficient and stable. Then the global stiffness matrix is extended by embracing the continuity of the interfaces and boundary conditions of soil base. The relationship between the generalized displacement and stress of the soil base reduces the number of unknowns of the global matrix. Such consideration reduced the number of unknowns of the global matrix and brought in more acceptable boundary conditions where the stiffness and the permeability of semi-infinite soil base can be taken into account. After the inversion of the Laplace-Hankel transform, the real solutions were obtained. The results show that the stiffness and permeability of the soil base can change the development consolidation and that the compressibility of solid particles has a great effect on the settlement in the beginning of consolidation.