A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, F...A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.展开更多
A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of La...A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.展开更多
The problem of a rigid disk acting with normal force on saturated soil was studied using Biot consolidation theory and integral equation method and the Merchant model to describe the saturated soil rheology. Using int...The problem of a rigid disk acting with normal force on saturated soil was studied using Biot consolidation theory and integral equation method and the Merchant model to describe the saturated soil rheology. Using integral transform techniques, general solutions of Biot consolidation functions and the dual integral equations of a rigid disk on saturated soil were established based on the boundary conditions. These equations can be simplified using Laplace-Hankel and Abel transform methods. The numerical solutions of the integral equations, and the corresponding inversion transform were used to obtain the settlement and contact stresses of the rigid disk. Numerical examples showed that the soil settlement is small if only consolidation is considered, so the soil rheology must be taken into account to calculate the soil settlement. Numerical solution of Hankel inverse transform is also given in this paper.展开更多
基金the National Natural Science Foundation of China (50578121)
文摘A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.
基金supported by the National Natural Science Foundation of China (No. 50578121)
文摘A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.
文摘The problem of a rigid disk acting with normal force on saturated soil was studied using Biot consolidation theory and integral equation method and the Merchant model to describe the saturated soil rheology. Using integral transform techniques, general solutions of Biot consolidation functions and the dual integral equations of a rigid disk on saturated soil were established based on the boundary conditions. These equations can be simplified using Laplace-Hankel and Abel transform methods. The numerical solutions of the integral equations, and the corresponding inversion transform were used to obtain the settlement and contact stresses of the rigid disk. Numerical examples showed that the soil settlement is small if only consolidation is considered, so the soil rheology must be taken into account to calculate the soil settlement. Numerical solution of Hankel inverse transform is also given in this paper.
