Theoretical Analysis Of Coupled Hydromechanical Modeling In Unsaturated Soils

In recent, many geotechnical engineering problems, such as rainfall-induced landslides, exploiting hydrate gas and embankment settlement,etc, are related to the coupled hydro-mechanical (HM) phenomena. The analytical solution to the coupled deformation and seepage problems for unsaturated soils with complex initial and boundary conditions plays an important role in better understanding of the geotechnical engineering problems. However, due to the presence of permeability coefficient and the coupling effect in the unsaturated hydraulic coupling process, coupled hydromechanical equations are nonlinear. Different initial and boundary conditions can also make coupled seepage and deformation difficult to be analytically solved. The key to solve the problem of hydraulic coupling is thus how to determine soil deformation, and distribution of pore water pressure in the analysis of the coupling process with different boundary conditions.In this paper, a mathematical model for the coupling skeleton deformation and water flow and gas transport was strictly obtained for unsaturated soils, which based on the continuum mechanics and the porous medium theory. On the basis of few constitutive assumptions, a nonlinear coupling model with different initial and boundary conditions was analytical solved by modern mathematical methods. In addition, hydraulic properties of soils were treated as random space functions. The theoretical model of non-stationary random unsaturated seepage to analyze random features of hydraulic factors for unsaturated seepage-deformation was derived after combination of deformation. The results are present as follows:(1) The nonlinear model of deformation and seepage problems was proposed for unsaturated soil under different initial and boundary conditions.In the present study, the unsaturated soils are three phase porous media, which is consisting of solid particles and a pore space filled with water and air. Each phase is endowed with its own kinematics, mass and momentum, occupying the entire volume of the unsaturated porous medium. The coupled field equations were derived from the Reynolds transport laws in continuum mechanics, integrated with fluid motions in porous media. The deformation of soil skeleton and the change in pore size distribution were the function of water retention behavior in unsaturated soils. However, water retention behavior of unsaturated soils is also dependent on soil deformation and the change in pore size distribution. Therefore, the coupled field equations are present to strong nonlinear characteristics. A general hydraulic coupling mathematical model in unsaturated soils was obtained for different initial conditions and boundary conditions and flow governed by different types law. Moreover, a general condition of the coupled system stability criterion was proposed based on the first-order constitutive relation and exponential perturbation model by a Talyor perturbation expansion. It can be found that the initial saturation, changes of the porosity, the ratio of the intake and the outlet values, and converting velocity from unsaturated to saturation can induce instability of the coupled system.(2) The analytical solutions of the simplified coupled model were obtained by a integral transform(IT) and a Green function method(GFM).This study presented solutions to the coupled seepage and deformation of unsaturated soils with arbitrary nonhomogeneous boundary conditions. Analytical solutions were derived for a finite thickness and confined lateral directions in unsaturated soils. Furthermore, the coupled seepage and deformation equation in one dimension was derived from the mass conservation principle integrated with Dakshanamurthy’s constitutive relationships, in which the water and air flows follow Darcy’s law in unsaturated soils. To simplify a governing equation, a general transform and several dimensionless variables were selected. Solutions were then obtained by applying a Laplace integral transform to a dimensionless linear equation under arbitrary initial and boundary conditions. After performing inverse Laplace transforms and using the residue theorem, analytical solutions were obtained in the time domain. Finally, three typical examples of nonhomogeneous boundary conditions were considered as case studies. It can be noted that the analytical solutions were consistent with the numerical results by a finite difference method. The result indicates that the boundary conditions and the hydromechanical coupling had a significant influence on the seepage in unsaturated soils.The analytical solutions were obtained by a Green function method to two-dimensional hydraulic coupling model under different boundary conditions. The typical example of nonhomogeneous boundary conditions was selected as case studies. The result indicates that the boundary conditions had a significant influence on the coupled seepage and deformation in unsaturated soils.(3) The analytical solutions of the nonlinear coupled model were obtained by a homotopy analysis method (HAM).Considering the strong nonlinear characteristics of the nonlinear flow situations, the HAM was introduced in the present study. As an analytic solution to nonlinear problems, homolopy analysis method (HAM) was efficient in the selection of series basis functions and auxiliary linear operators, and easily makes the solution convergence. Firstly, a governing equation in a dimensionless form was derived. The method was then used for a mapping technique to transfer the original nonlinear differential equations to a number of linear differential equations. These differential equations were not dependent on any small parameters, which was convenient to control the convergence region. After this transferring, a series solution to the equations was then obtained by the HAM after selection of auxiliary linear operator parameters.During the solution of consolidation equation, the pore air pressure was assumed as the atmospheric pressure. The equations with two unknown variables were then reduced to dimensionless pore water pressure as only one basic unknown variable subjected to the constant pore air pressure. Finally, comparisons were carried out between the analytical solutions and the finite difference method in case of compacted kaolin. It can be found that the series solutions indicate that the pore water pressure increased firstly, and then decreased with the depth after the consolidation of the compacted kaolin. The results also indicate that the analytical solution in the present study was reasonable.(4) Nonstationary stochastic analysis of the coupled seepage and deformation of unsaturated soils with arbitrary nonhomogeneous boundary conditions.In order to analyze random features of hydraulic factors of unsaturated seepage- deformation, hydraulic properties of soils were treated as random space functions. On basis of the constitutive relationship Genuchten-Mualem model, the theoretical model of non-stationary random unsaturated steady seepage was derived. The pressure head was expressed as Taylor series and using the perturbation method to establish a series of partial differential equations. The equation was solved by a finite differrnce method, and the mean and variance of pressure head were determined from its random expression. The numerical results were good agreement with existing models without considering the coupling effect, and it also shows that head was sensitive to the variability of soil deformation, especially in case of relatively dry soils. Drier soils could make greater variability in the water head.(5) Combining with the previous analytical solution and experimental data of unsaturated soils, a case study was carried out in process of rainfall triggered solpe failure on the Guang-Fo-Zhao highway.The hydraulic and strength characteristics of the silty clay were studied by laboratory experiment. According to the experimental data, the infiltration functions of undisturbed samples and compacted samples were obtained by non-linear curve fitting and the Mualem model. Triaxial experimental results show that the strength characteristics of the silty clay were greatly influenced by the dry density and confining pressure.After a typical slope was selected as a case study on the Guang-Fo-Zhao highway, the hydraulic coupling model of the slope was derived. The analytical solution of the coupled equations for different boundary conditions were then obtained by the GFM, which was combined with HAM. The displacement at the top of the slope and the suction distribution were then studied by the solution, which provides a basis for slope design and its construction.