非饱和土层一维固结问题的解析解

对一有限厚度，处于一维受荷状态，表面为透水透气面，底面为不透水不透气面的非饱和土层，依据Fredlund的非饱和土一维固结理论，由液相及气相的控制方程、Darcy定律及Fick定律，经Laplace变换及Cayley-Hamilton数学方法构造了顶面状态向量与任意深度处状态向量间的传递关系；通过引入初始及边界条件，得到了Laplace变换域内的超孔隙水压力、超孔隙气压力以及土层沉降的解；实现Laplace逆变换，得到了时间域内的解析解；用一典型算例，与差分法结果进行对比，验证了其正确性．

Analytical Solution to One-Dimensional Consolidation in Unsaturated Soils

An analytical solution of Fredlund's one-dimensional consolidation equation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions was presented.The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air.The transfer relations between the state vectors at top surface and any depth was gained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air,Darcy's law and Fick's law.The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions;by performing the inverse Laplace transforms the analytical solutions were obtained in the time domain.Finally,comparisons between the analytical solutions and the results of the finite difference method indicate that the analytical solution was correct.