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| A SEMI -ANALYTICAL SOLUTION FOR ONE-DIMENSIONAL TRANSIENT RESPONSE OF SINGLE LAYERED SATURATED POROUS MEDIA |
| LING Daosheng，FANG Zhihui，SHAN Zhendong |
| (MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering，Zhejiang University，Hangzhou，Zhejiang 310058，China) |
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Abstract Based on Biot theory，a semi-analytical approach is proposed to analyze the transient response of one-dimensional porous media；and the first typical boundary condition is adopted as an example. The dimensionless displacement governing equations with its initial and boundary conditions in matrix form are derived. A proper transform is applied to homogenizing the boundary condition；and the corresponding characteristic problem for the governing equations with viscous coupling omitted is solved to get a series of eigenvalues and characteristic functions，which are proved to be orthogonal. Using the orthogonality of characteristic functions，a series of ordinary differential equations and their initial conditions are derived. The ordinary differential equation system is only coupled in damping matrix and is solved by precise time-integration method when it is truncated as a finite ordinary differential equation system. Some examples are presented to demonstrate the influence of the dynamic permeability coefficient on propagation of waves. The method is valid for arbitrary non-homogeneous boundary conditions and suitable for problems considering inertia，viscous and mechanical couplings；and no limitation of compressibility of fluid and solid particles is required.
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Received: 23 December 2010
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2011, Vol. 30 
