关键词: 三维固结, 可压缩性, 层状岩基, Laplace-Fourier变换, 传递矩阵

Abstract: This paper uses state vector method to solve the three-dimensional consolidation problems of a poroelastic layered rock by taking into account the compressibility of pore fluid. Starting from the governing equations of a saturated poroelastic rock with compressible constituents in the Cartesian coordinate system, the state space equations of the three-dimensional Biot’s consolidation problems are obtained by introducing the Laplace-Fourier transform. The transfer matrix of displacements, stresses, excess pore water pressure and flux between the ground surface and an arbitrary depth z is obtained by using the Cayley-Hamilton theorem. Then the transfer matrix method is utilized to derive the solutions for three-dimensional consolidation of a layered rock in the transformed domain by combining the continuity conditions between the adjacent layers and the boundary conditions. The actual solutions in the physical domain are acquired by inverting the Laplace-Fourier transform. Numerical analysis is carried out for a layered rock, which illustrates the influences of the compressibility of pore fluid on the consolidation behavior of the rock.