State space solution to three-dimensional consolidation of multi-layered soils |
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Authors: | ZY Ai ZY Cheng |
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Affiliation: | a Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, PR China b Department of Civil, Environmental, and Architectural Engineering, The University of Kansas, Lawrence, Kansas, USA |
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Abstract: | From the governing equations of a saturated poro-elastic soil in the Cartesian coordinate system, the state space equations of Biot’s three-dimensional consolidation problems are obtained by the Laplace transform and the double Fourier transform. Transfer matrix describing the transfer relation between the state vectors for a finite layer is derived explicitly in the transform space. Based on the continuity conditions between adjacent layers and the boundary conditions, the solution for three-dimensional consolidation of multi-layered soils is derived in a transformed domain. This solution is then transferred to that in a physical domain by the inversion of the double Fourier transform and the Laplace transform. Numerical analysis is carried out for three-dimensional consolidation of single, two, and multi-layered soils. The results for single and two-layered soils are compared well with those by the finite layer method in the literature. Numerical results for three-dimensional consolidation of five-layered soils are presented in this paper as an example to illustrate the use of the solution in this paper for three-dimensional consolidation of more than two-layered soils. |
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Keywords: | Multi-layered saturated poro-elastic soil Three-dimensional consolidation State space method Laplace transform Double Fourier transform |
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