Two-dimensional plane strain consolidation of unsaturated soils considering the depth-dependent stress

In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.

Water content and modulus relationship of a compacted unsaturated soil

In order to assess the performance of the embankment soil under various climate conditions during the period of service, the modulus behaviour of an unsaturated compacted soil is evaluated using the constant water content triaxial test. Since the water content measurement method is simple and economical and it is used widely in engineering, the soil suction is replaced by the water content and the relationship between the water content and the modulus is developed. The compacted samples are prepared with different compacted water contents, and samples with a similar water content subjected to drying or wetting procedures prior to the triaxial test are also investigated. The effect of the water content and the confining pressure on the modulus is analyzed. The results show that the modulus decreases with the increase in the water content and a power function can be proposed to quantitatively describe the relationship between the modulus and the water content in the range of the measured water content. The modulus increases with the increase in the confining pressure of the compacted soil. However, the effect of the water content on the modulus is more pronounced than that of the confining pressure. This research can be referenced for the compacted embankment soil assessment in-service period.

Creep model for unsaturated soils in sliding zone of Qianjiangping landslide

The mechanical behavior of sliding zone soils plays a significant role in landslide. In general, the sliding zone soils are basically in unsaturated state due to rainfall infiltration and reservoir water level fluctuation. Meanwhile, a large number of examples show that the deformation processes of landslides always take a long period of time, indicating that landslides exhibit a time-dependent property. Therefore, the deforma- tion of unsaturated soils of landslide involves creep behaviors. In this paper, the Burgers creep model for unsaturated soils under triaxial stress state is considered based on the unsaturated soil mechanics. Then, by curve fitting using the least squares method, creep parameters in different matric suction states are obtained based on the creep test data of unsaturated soils in the sliding zones of Qianjiangping landslide. Results show that the predicted results are in good agreement with the experimental data, Finally, to fur- ther explore the creep characteristics of the unsaturated soils in sliding zones, the relationships between parameters of the model and matric suction are analyzed and a revised Burgers creep model is developed correspondingly. Simulations on another group of test data are performed by using the modified Burgers creep model and reasonable results are observed,

Isothermal diffusion of water vapor in unsaturated soils based on Fick’s second law

In arid regions, water vapor diffusion predominates the total water migration in unsaturated soil, which significantly influences agriculture and engineering applications. With the aim of revealing the diffusion mechanism of water vapor in unsaturated soil, a water vapor migration test device was developed to conduct the water vapor migration indoor test. The test results demonstrate that the characteristics of water vapor diffusion in unsaturated soil conformed to Fick’s second law. A mathematical model for water vapor diffusion under isothermal conditions in unsaturated soil was established based on Fick’s law. Factors including the initial moisture content gradient, initial moisture content distribution, soil type and temperature that affect the water vapor diffusion coefficient were analyzed. The results show that there was good agreement between the moisture content calculated by the mathematical model and obtained by the indoor experiment. The vapor diffusion coefficient increased with increasing initial moisture content gradient and temperature. When the initial moisture content gradient is constant, the vapor diffusion coefficient increases with the increase of matrix suction ratio in dry and wet soil section. The effect of soil type on the water vapor diffusion coefficient was complex, as both the moisture content and soil particle sizes affected the water vapor diffusion.

An Analytical Solution for One-Dimensional Water Infiltration and Redistribution in Unsaturated Soil

Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with semi-permeable drainage boundary

The semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations （PDFs）, which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pres- sures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are con- ducted on the pore-air and pore-water pressures at different ratios （the air permeability coefficient to the water permeability coefficient） and depths.

Analytical solution to one-dimensional consolidation in unsaturated soils

This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund＇s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained 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. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.

Critical embedment depth of a rigid retaining wall against overturning in unsaturated soils considering intermediate principal stress and strength nonlinearity

The overturning stability is vital for the retaining wall design of foundation pits, where the surrounding soils are usually unsaturated due to water draining. Moreover, the intermediate principal stress does affect the unsaturated soil strength; meanwhile, the relationship between the unsaturated soil strength and matric suction is nonlinear. This work is to present closed-form equations of critical embedment depth for a rigid retaining wall against overturning by means of moment equilibrium. Matric suction is considered to be distributed uniformly and linearly with depth. The unified shear strength formulation for unsaturated soils under the plane strain condition is adopted to characterize the intermediate principal stress effect, and strength nonlinearity is described by a hyperbolic model of suction angle. The result obtained is orderly series solutions rather than one specific answer; thus, it has wide theoretical significance and good applicability. The validity of this present work is demonstrated by comparing it with a lower bound solution. The traditional overturning designs for rigid retaining walls, in which the saturated soil mechanics neglecting matric suction or the unsaturated soil mechanics based on the Mohr-Coulomb criterion are employed, are special cases of the proposed result. Parametric studies about the intermediate principal stress, matric suction and its distributions along with two strength nonlinearity methods on a new defined critical buried coefficient are discussed.

Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior

A constitutive model of unsaturated soils with coupling capillary hystere- sis and skeleton deformation is developed and implemented in a fully coupled transient hydro-mechanical finite-element model （computer code U-DYSAC2）. The obtained re- sults are compared with experimental results, showing that the proposed constitutive model can simulate the main mechanical and hydraulic behavior of unsaturated soils in a unified framework. The non-lineaxity of the soil-water characteristic relation is treated in a similar way of elastoplasticity. Two constitutive relations axe integrated by an implicit return-mapping scheme similar to that developed for saturated soils. A consistent tan- gential modulus is derived to preserve the asymptotic rate of the quadratic convergence of Newton＇s iteration. Combined with the integration of the constitutive model, a complete finite-element formulation of coupling hydro-mechanical problems for unsaturated soils is presented. A number of practical problems with different given initial and boundary conditions are analyzed to illustrate the performance and capabilities of the finite-element model.

Coupled hydro-mechanical analysis of slope under rainfall using modified elasto-plastic model for unsaturated soils

Two modifications for the basic Barcelona model(BBM) are present. One is the replacement of the net stress by the average skeleton stress in unsaturated soil modeling, and the other is the adoption of an expression for the load-collapse(LC) yield surface that can match flexibly the normal compression lines at different suctions. The predictions of the modified BBM for the controlled-suction triaxial test on the unsaturated compacted clay are presented and compared with the experimental results. A good agreement between the predicted and experimental results demonstrates the reasonability of the modified BBM. On this basis, the coupled processes of groundwater flow and soil deformation in a homogeneous soil slope under a long heavy rainfall are simulated with the proposed elasto-plastic model. The numerical results reveal that the failure of a slope under rainfall infiltration is due to both the reduction of soil suction and the significant rise in groundwater table. The evolution of the displacements is greatly related to the change of suction. The maximum collapse deformation happens near the surface of slope where infiltrated rainwater can quickly reach. The results may provide a helpful reference for hazard assessment and control of rainfall-induced landslides.

General semi-analytical solutions to one-dimensional consolidation for unsaturated soils

This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

NONLINEAR AND ELASTO-PLASTICITY CONSOLIDATION MODELS OF UNSATURATED SOIL AND APPLICATIONS

The non-linear constitutive model suggested by the authors and the Alonso's elasto-plasticity model of unsaturated soil modified by the authors are introduced into the consolidation theory of unsaturated soil proposed by CHEN Zheng-han, and the non-linear and the elasto-plasticity consolidation models of unsaturated soil are obtained. Programs related to the two consolidation models are designed, and a 2-D consolidation problem of unsaturated sail is solved using the programs, the consolidation process and the development of plastic;one under multi-grade bad are studied. The above research develops the consolidation theory of unsaturated soil to a new level.

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain,water and gas.In this paper,the consolidation problem of unsaturated soil is investigated based on the theory of mixture.A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived.The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil.A mathematical model of consolidation of unsaturated soil is proposed,which consists of 25 partial differenfial equations with 25 unknowns.With the help of increament linearizing method,the model is reduced to 5 governing equations with 5 unknowns,i.e.,the three displacement components of solid phase,the pore water pressure and the pore gas pressure.7 material parameters are involved in the model and all of them can he measured using soil tests.It is convenient to use the model to engineering practice.The well known Biot's theory is a special case of the model.

Impacts of Soil Moisture Content and Vegetation on Shear Strength of Unsaturated Soil

It is analyzed that the impacts of vegetation type and soil moisture contenton shear strength of unsaturated soil through direct shearing tests for various vegetation types,different soil moisture contents and different-depth unsaturated soil. The results show that thecohesion of unsaturated soil changes greatly, and the friction angle changes a little with soilmoisture content. It is also shown that vegetation can improve shear strength of unsaturated soil,which therefore provides a basis thatvegetation can reinforce soil and protect slopes.

Energy analysis of geosynthetic-reinforced slope in unsaturated soils subjected to steady flow

Soils are actually unsaturated in nature. In the present study, a stability analysis of a geosynthetic-reinforced slope in unsaturated soils subjected to various steady flow conditions is conducted based on limit analysis. Work rate by apparent cohesion due to matric suction is calculated based on the effective stress-based equation. Analytical expression of the required cohesion/stability number of slope is derived from the energy balance equation. An optimization code is programmed to capture the optimized solution of the stability number. Comparison is made to verify the present work and a parametric analysis is conducted to investigate the effects of soil type, infilitration rate, reinforcement strength and soil suction on slope stability afterwards. A set of numerical solutions is presented at the end of the paper for preliminary design purposes.

Recent developments of generalized plasticity models for saturated and unsaturated soils

Soil undergoes both elastic and plastic deformations under different loading conditions. A relatively accurate constitutive model of soil behaviors should be capable of predicting the elastic and plastic deformations properly. Among a large number of elastoplastic constitutive models developed over the last several decades, constitutive models based on generalized plasticity have been successfully utilized in modeling the mechanical behavior of various soils. This paper attempts to present a review of the most recent developments of generalized plasticity models for geotechnical problems. After a brief review of generalized plasticity theories and constitutive models, limitations of the original Pastor-Zienkiewicz model in practical application are summarized. Afterwards, recent achievements in the generalized plasticity models for both saturated and unsaturated soils and their applicability are analyzed, and a general approach for modification of generalized plasticity models is highlighted.

3D Dynamic Response of Layered Unsaturated Soils to Harmonic Loads

Considering compression of solid grain and pore fluids,viscous-coupling interactions and inertial force of fluids,dynamic governing equations for unsaturated soils are established by adopting an exact constitutive formula of saturation.These equations are highly versatile and completely compatible with Biot's wave equations for the special case of fully saturated soils.The governing equations in Cartesian coordinates are firstly transformed into a group of state differential equations by introducing the state vector.Then the transfer matrix for layered media are derived by means of a double Fourier transform.Using the transfer matrix followed by boundary and continuity conditions between strata,solutions of steady-state dynamic response for multi-layered unsaturated soils are obtained.Numerical examples show that the echoes generated by boundary and stratum interfaces make the displacement amplitude of the ground surface fluctuate with distance;the relative position of soft and hard strata has a significant influence on displacement.

Semi-analytical solution to one-dimensional consolidation in unsaturated soils

In this paper, a series of semi-analytical solutions to one-dimensional consolidation in unsaturated soils are obtained. The air governing equation by Fredlund for unsaturated soils consolidation is simplified. By applying the Laplace transform and the Cayley-Hamilton theorem to the simplified governing equations of water and air, Darcy＇s law, and Fick＇s law, the transfer function between the state vectors at top and at any depth is then constructed. Finally, by the boundary conditions, the excess pore-water pressure, the excess pore-air pressure, and the soil settlement are obtained under several kinds of boundary conditions with the large-area uniform instantaneous loading. By the Crump method, the inverse Laplace transform is performed, and the semi-analytical solutions to the excess pore-water pressure, the excess pore-air pressure, and the soils settlement are obtained in the time domain. In the case of one surface which is permeable to air and water, comparisons between the semi-analytical solutions and the analytical solutions indicate that the semi-analytical solutions are correct. In the case of one surface which is permeable to air but impermeable to water, comparisons between the semi-analytical solutions and the results of the finite difference method are made, indicating that the semi-analytical solution is also correct.

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.

Stability Analysing of Unsaturated Soil Slope

The stability of unsaturated soil slope has been the hot point recently. Especially, the seeping rainfall makes losing stability of unsaturated soil slope, and causes enormous loss to the producation and safety of other people. The seeping rainfall makes volumetric water content of unsaturated soil slope changing, and the volumetric water content has directly relationship with matric suction. And matric suction also has directly relationship with the stability of unsaturated soil slope. So the change of matric suction influence the stability changing, that is, safety coefficient has decided relationship with volumetric water content. The profile of dangerous volumetric water content curves of unsaturated soil slope has been obtained. If a volumetric water content curve of some unsaturated soil slope belongs to one of these dongerous curves, the unsaturated soil slope could be in danger. So this is called DVWCCP(dangerous volumetric water content curves profile). By monitoring the volumetric water content curves can obtain the stability information of some soil slope to serve producing and safety.