A new method for solving Biot's consolidation of a finite soil layer in the cylindrical coordinate system

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.

A new analytical solution to axisymmetric Biot's consolidation of a finite soil layer

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.

Solution of a rigid disk on saturated soil considering consolidation and rheology

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.

A New Mixed Finite Element Method for Biot Consolidation Equations

In this paper,we study a new finite element method for poroelasticity problem with homogeneous boundary conditions.The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity,i.e.,the stress tensor,displacement and pressure are unknown variables in the weak form.For the linear elasticity formula,we use a conforming finite element proposed in[11]for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow.We will show that the newly proposed finite element method maintains optimal convergence order.

Influences of soil hydraulic and mechanical parameters on land subsidence and ground fissures caused by groundwater exploitation

In order to study the influences of hydraulic and mechanical parameters on land subsidence and ground fissure caused by groundwater exploitation, based on the Biot＇s consolidation theory and combined with the nonlinear rheological theory of soil, the constitutive relation in Biot＇s consolidation theory is extended to include the viscoelastic plasticity, and the dynamic relationship among the porosity, the hydraulic conductivity, the parameters of soil deformation and effective stress is also considered, a three-dimensional full coupling mathematical model is established and applied to the study of land subsidence and ground fissures of Cangzhou in Hebei Province, through the analysis of parameter sensitivity, the influences of soil hydraulic and mechanical parame-ters on land subsidence and ground fissure are revealed. It is shown that the elastic modulus E , the Poisson ratio, the specific yield m and the soil cohesion c have a great influence on the land subsidence and the ground fissures. In addition, the vertical hydraulic conductivity zk and the horizontal hydraulic conductivity ks also have a great influence on the land subsidence and the ground fissures.

Numerical Analysis on Cnoidal Wave Induced Response of Porous Seabed with Definite Thickness

Severe water waves can induce seabed liquefaction and do harm to marine structures. Dynamic response of seabed with definite thickness induced by cnoidal water waves is investigated numerically. Biot＇s consolidation equations are employed to model the seabed response. Parametric studies are carried out to examine the influence of the air content in the pore water and the soil hydraulic conductivity. It is been shown that the air content and soil hydraulic conductivity can significantly affect the pore pressure in seabed. An increase of air content and/or a decrease of soil hydraulic conductivity can change the pore pressure gradient sharply.