渗透各向异性多层地基的轴对称Biot固结 English Version
Axisymmetric Biot's consolidation of multi-layered soils with anisotropic permeability
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摘要: 从轴对称Biot固结基本方程出发，通过对时间t和坐标z进行Laplace变换，对坐标r进行Hankel变换，建立了单层地基中6个状态量在土层顶面和任意深度z间的传递矩阵关系。结合层间连续条件和边界条件，进一步求得了渗透各向异性多层地基在Laplace-Hankel变换域内的解。通过Laplace-Hankel逆变换可求得该问题物理域内的真实解。编制了相应的计算程序，并对数值计算结果进行了比较和分析。计算结果表明，土的渗透各向异性对固结过程中的地表位移有比较显著的影响。
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关键词:
- 渗透各向异性 /
- 轴对称Biot固结 /
- 传递矩阵 /
- Laplace-Hankel变换
Abstract: The axisymmetric Biot's consolidation of multi-layered saturated soils with anisotropic permeability is studied. Based on the governing equations of axisymmetric Biot's consolidation, the transfer matrix for 6 basic variables between the ground surface and an arbitrary depth of z is obtained by taking Laplace transform with respect to t and z and Hankel transform with respect to r. Considering the continuity conditions between layers and boundary conditions, the solutions for the axisymmetric Biot's consolidation of multi-layered soils with anisotropic permeability in the Laplace-Hankel transformed domain are obtained, and the actual solutions in the physical domain can be acquired by inverting the Laplace-Hankel transforms. Numerical analysis is carried out by using the corresponding program based on the present theory. The results show that the anisotropic permeability of soils has a remarkable effect on the surface displacement in the process of consolidation.
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