Study On Consolidation Behavior Of Unsaturated Soils Under One-dimensional And Two-dimensional Conditions

The consolidation theory of soil is one of hot issues in soil mechanics.A considerable amount of research focusing on Terzaghi's consolidation theory for saturated soils has been conducted,and great progress achieved.However,there are a few of the research achievements on the consolidation theory of unsaturated soils proposed by Fredlund,and these results are much fragmentary and unsystematic.Therefore,in this paper,a set of semi-analytical solutions of pore pressures and settlement was obtained by the Laplace transform on the basis of one-dimensional consolidation theory and two-dimensional consolidation theory for unsaturated soils,respectively.These semi-analytical solutions can be used to investigate the consolidation behavior of unsaturated soil layer with the initial values changing linearly along the depth under time-dependent loadings and the Dirichlet boundary,the Neumann boundary and the third conditions.Then Crump's method was adopted to perform the inverse of Laplace transform to obtain the analytical solutions in time domain.At last,several numerical examples are provided to investigate the behavior of one-dimensional and two-dimensional plane strain consolidations for a single-layer unsaturated soil.Main eontents can be drawn as follows:(1)A general semi-analytical solution to Fredlund and Hasan's one-dimensional consolidation equations for unsaturated soils is presented.Two variables ?1 and ?2 are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations,which are easily solved by the Laplace transform method.Then,four sets of semi-analytical solutions of the pore-water pressure,pore-air pressure,and soil settlement are obtained in the Laplace domain according to the initial condition linearly along the depth,homogeneous or mixed boundary conditions and time-dependent loadings.At last,one-dimensional consolidation behavior for unsaturated soils is investigated under homogeneous and mixed boundary conditions with instantaneous,construction,exponential and sinusoidal loadings,respectively.(2)The semi-permeable drainage boundary(the third boundary)is introduced for the first time to investigate one-dimensional consolidation behavior,and semi-analytical solutions to Fredlund and Hasan's one-dimensional consolidation equations for unsaturated soils under single-sided semi-permeable and symmetric semi-permeable drainage boundary conditions are obtained.Several numerical examples are provided to investigate the one-dimensional consolidation behavior under the semi-permeable drainage boundary condition with time-dependent loadings.(3)Finite difference expressions of semi-permeable drainage boundary are derived firstly,and then combining the finite difference equations of Fredlund and Hasan's one-dimensional consolidation euqations,the numerical solutions to one-dimensional consolidation equations are obtained under the semi-permeable drainage boundary condition.By comparing results of the semi-analytical solutions and the numerical solutions,it indicates that the semi-analytical solutions under semi-permeable drainage boundary condition are reliable.(4)A general semi-analytical solution to Dakshanamurthy and Fredlund's two-dimensional plane strain consolidation equations for unsaturated soils is presented firstly.By using the Laplace transform method,the two coupled governing equations of pore-water and pore-air pressures was transformed into an equivalent set of ordinary differential equations,which are easily solved by the substitution method.Then,four sets of semi-analytical solutions of the pore-water pressure,pore-air pressure,and soil settlement are obtained in the Laplace domain according to the initial values changing linearly along the depth,homogeneous or mixed boundary conditions and time-dependent loadings.At last,the two-dimensional plane strain consolidation behavior for unsaturated soils was investigated under homogeneous and mixed boundary conditions with instantaneous,construction,exponential and sinusoidal loadings,respectively.(5)The semi-permeable drainage boundary(the third boundary)is introduced firstly to investigate the two-dimensional plane strain consolidation behavior under considering smear effect of the sand drains,and semi-analytical solutions to Dakshanamurthy and Fredlund's two-dimensional plane strain consolidation equations for unsaturated soils under laterally semi-permeable drainage boundary condition are obtained.Several numerical examples are provided to investigate the two-dimensional plane strain consolidation behavior under laterally semi-permeable drainage boundary condition with time-dependent loadings.In this paper,some linear assumptions associated with the flow laws of air and water phases and constitutive equations are made to obtain a set of semi-analytical solutions to one-dimensional and two-dimensional plane strain consolidation equations for unsaturated soils.Although there are some unreasonable assumptions in the introduction and derivation of one-dimensional and two-dimensional plane strain consolidation equations for unsaturated soils,it is of great academic significance and engineering value to investigate one-dimensional and two-dimensional plane strain consolidation behavior and to solve some practical problems on the basis of the proposed semi-analytical solutions.