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.

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,

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.

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.

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.

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.

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.

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.

Cylindrical cavity expansion responses in anisotropic unsaturated soils under plane stress condition

In this paper,an anisotropic critical state model for saturated soils was extended to unsaturated conditions by introducing suction into its yield function.Combining this model with soil-water characteristic curves related to porosity ratio was employed to characterize the coupled hydromechanical behavior of unsaturated anisotropic soil.Based on the plane stress condition,the problem of the cylindrical cavity expansion in unsaturated anisotropic soils was transformed into first-order differential equations using the Lagrangian description.The equations were solved as an initial value problem using the Runge-Kutta algorithm,which can reflect the soil-water retention behavior during cavity expansion.Parametric analyses were conducted to investigate the influences of overconsolidation ratio(OCR),suction,and degree of saturation on the expansion responses of a cylindrical cavity in unsaturated anisotropic soil under plane stress condition.The results show that the above factors have obvious influences on the cavity responses,and the plane strain solution tends to overestimate expansion pressure and degree of saturation but underestimates suction around the cavity compared to the proposed plane stress solution.The theoretical model proposed in this paper provides a reasonable and effective method for simulating pile installation and soil pressure gauge tests near the ground surface of the unsaturated soils.

On the thermo-mechanical properties of unsaturated soils

The establishment of energy balance equation is necessary to study the thermo-mechanical properties of unsaturated soils.To solve this equation,the determination of two fundamental parameters as volumetric specific parameter and thermal conductivity coefficient is essential.In this paper,the effective thermal conductivity coefficient of dry soil grain is analyzed for soils with different compositions,and the thermo-mechanical properties of porous media with water and gas are studied by considering the soil water retention curve（SWRC）.Different methods,i.e.volumetric average method,self-consistent method,Hashin-Strikman method,are employed to calculate thermal conductivity coefficients,and a new method is proposed to determine the thermo-mechanical parameters.Comparison of the results obtained by different methods shows that the proposed method is in a good agreement with the experimental results and is suitable for describing the main properties of the thermo-mechanical behaviors of soils.The relationship between the SWRC and the seepage curve is further studied by the natural proportional rule.The characteristics of the SWRC,its differential coefficient and the seepage curve,are investigated by considering the physico-mechanical mechanism;the limit scopes of the indices of the SWRC and the seepage curve are also given.

Determining osmotic suction through electrical conductivity for unsaturated low-plasticity soils

Determining osmotic suction from the electrical conductivity(EC)of soil pore water was widely reported in the literature.However,while dealing with unsaturated soils,they do not have enough soil pore water to be extracted for a reliable measurement of EC.In this paper,the chilled-mirror dew-point hygrometer and contact filter paper method were used to determine the total and matric suctions for low-plasticity soils with different salinities(0.05‰,2.1‰,and 6.76‰).A new piecewise function was proposed to calculate the osmotic suction,with the piecewise point corresponding to the first occurrence of precipitated salt in mixed salt solutions(synthetic seawater).EC,ion and salt concentrations used for osmotic suction calculation were transformed from the established relationships of mixed salt solution instead of experimental measurement.The calculated osmotic suction by the proposed equation and the equations in the literature was compared with the indirectly measured one(the difference between the measured total and matric suctions).Results showed that the calculated osmotic suction,especially the one calculated using the proposed function,was in fair agreement with the indirectly measured data(especially for specimens with higher salinity of 6.76‰),suggesting that the transformation of EC and concentrations from the established relationship is a good alternative to direct measurement for lowplasticity soil.In particular,the proposed method could be applied to unsaturated low-plasticity soils which do not have enough soil pore water for a proper EC measurement.

Determination of effective stress parameter of unsaturated soils:A Gaussian process regression approach

This article examines the capability of Gaussian process regression(GPR)for prediction of effective stress parameter(χ)of unsaturated soil.GPR method proceeds by parameterising a covariance function,and then infers the parameters given the data set.Input variables of GPR are net confining pressure(σ_(3)),saturated volumetric water content(θ_(s)),residual water content(θ_(r)),bubbling pressure(h_(b)),suction(s)and fitting parameter(l).A comparative study has been carried out between the developed GPR and Artificial Neural Network(ANN)models.A sensitivity analysis has been done to determine the effect of each input parameter onχ.The developed GPR gives the variance of predictedχ.The results show that the developed GPR is reliable model for prediction ofχof unsaturated soil.

Thermal-water-salt coupling process of unsaturated saline soil under unidirectional freezing

Salinization and desertification are closely related to water-salt migration caused by a temperature gradient.Based on the Darcy Law of unsaturated soils,the law of energy conservation and the law of mass conservation,the thermal-water-salt coupling mathematical model of unsaturated frozen saline soil was established.The model considered the latent heat of phase change,crystallization impedance,crystallization consumption and complete precipitation of solute crystallization in ice.In order to verify the rationality of the model,the unidirectional freezing test of unsaturated saline soil was carried out in an open system with no-pressure water supplement to obtain the spatial distribution of temperature,moisture and salt in the saline soil.Finally,numerical simulations are implemented with the assistance of COMSOL Multiphysics.Validation of the model is illustrated by comparisons between the simulation and experimental data.The results demonstrated that the temperature within saline soil changes with time and can be divided into three stages,namely quick freezing stage,transitional stage and stable stage.The water and salt contents in the freezing zone are layered,with peak values at the freezing front.The coupled model could reveal the heat-mass migration mechanism of unsaturated frozen saline soil and dynamically describe the freezing depth and the movement law of the freezing front,ice and salt crystal formation mechanism,and the change law of thermal conductivity and permeability coefficient.

Stability analysis of layered slopes in unsaturated soils

This study presents stability analyses of layered soil slopes in unsaturated conditions and uses a limit equilibrium method to determine the factor of safety involving suction stress of unsaturated soil.One-dimensional steady infiltration and evaporation conditions are considered in the stability analyses.An example of a two-layered slope in clay and silt is selected to verify the used method by comparing with the results of other methods.Parametric analyses are conducted to explore the influences of the matric suction on the stability of layered soil slopes.The obtained results show that larger suction stress provided in unsaturated clay dominates the stability of the layered slopes.Therefore,the location and thickness of the clay layer have significant influences on slope stability.As the water level decreases,the factor of safety reduces and then increases gradually in most cases.Infiltration/evaporation can obviously affect the stability of unsaturated layered slopes,but their influences depend on the soil property and thickness of the lower soil layer.

Structural bonding-breakage constitutive model for natural unsaturated clayey soils

The natural clayey soils are usually structural and unsaturated,which makes their mechanical properties quite different from the remolded saturated soils.A structural constitutive model is proposed to simulate the bonding-breakage micro-mechanism.In this model,the unsaturated soil element is divided into a cementation element and a friction element according to the binary medium theory,and the stress-strain coordination for these two elements is obtained. The cementation element is regarded as elastic,whereas the friction element is regarded as elastoplastic which can be described with the Gallipoli＇s model.The theoretical formulation is verified with the comparative experiments of isotropic compressions on the saturated and unsaturated structural soils.Parametric analyses of the effects of damage variables on the model predictions are further carried out,which show that breakage deformation of natural clayey soils increases with the rising amount of initial defects.

Thermal-hydro-mechanical coupled analysis of unsaturated frostsusceptible soils

Damage caused by frost heave leads to costly maintenance in cold regions, like Hokkaido, Japan. Therefore, thestudy of the frost mechanism with experimental and numerical methods has been of great interest. Numerousmodels have been developed to describe the freezing process of saturated soil, which differs from the partiallysaturated conditions in the field. In fact, most subsurface soils are unsaturated. The freezing process of partiallysaturated soils is more complex than saturated soils, as the governing equations show strongly nonlinear characteristics. This study proposes a thermo-hydro-mechanical coupled model considering the heat transfer, waterinfiltration, and deformation of partially saturated soil to reproduce the freezing process of partially saturatedfrost susceptible soils distributed in Hokkaido. This model better considers the water-ice phase change and soilfreezing characteristic curve (SFCC) during freezing under field conditions. The results from the multiphysicssimulations agree well with the frost heave and water migration data from frost heave tests of Touryo soil andFujinomori soil. In addition, this study discussed the influence of the various factors on frost heave amount,including temperature gradients, overburden pressures, water supply conditions, cooling rates, and initial saturation. The simulation results indicate that the frost heave ratio is proportional to the initial degree of saturationand is inversely proportional to the cooling rate and overburden pressure.Moreover, simulation under the open system generates much more frost heave than under the closed system.Finally, the main features of the proposed model are revealed by simulating a closed-system frost heave test. Thesimulation results indicate that the proposed model adequately captures the coupling characteristics of water andice redistribution, temperature development, hydraulic conductivity, and suction in the freezing process. Togetherwith the decreased hydraulic conductivity, the increased suction controls the water flow in the freezing zone. Theinflow water driven by cryogenic suction gradient feeds the ice formation, leads to a rapid increase in total watercontent, expanding the voids that exceed the initial porosity and contributing to the frost heave.

Fractional derivative statistical damage model of unsaturated expansive soil based on unified hydraulic effect

Unsaturated expansive soil is widely distributed in China and has complex engineering properties.This paper proposes the unified hydraulic effect shear strength theory of unsaturated expansive soil based on the effective stress principle,swelling force principle,and soil–water characteristics.Considering the viscoelasticity and structural damage of unsaturated expansive soil during loading,a fractional hardening–damage model of unsaturated expansive soil was established.The model parameters were established on the basis of the proposed calculation method of shear strength and the triaxial shear experiment on unsaturated expansive soil.The proposed model was verified by the experimental data and a traditional damage model.The proposed model can satisfactorily describe the entire process of the strain-hardening law of unsaturated expansive soil.Finally,by investigating the damage variables of the proposed model,it was found that:(a)when the values of confining pressure and matric suction are close,the coupling of confining pressure and matric suction contributes more to the shear strength;(b)there is a damage threshold for unsaturated expansive soil,and is mainly reflected by strength criterion of infinitesimal body;(c)the strain hardening law of unsaturated expansive soil is mainly reflected by fractional derivative operator.

Surficial Stability Analysis of Unsaturated Loess Slopes Subjected to Rainfall Infiltration Effects

According to theory of unsaturated soil strength and Green-Ampt model, an analysis method based on limit equilibrium theory is introduced to consider rainfall infiltration effects in loess slope stability analysis. The relationships between wetting band depth and surficial stability of slopes are analyzed. It is found that the infiltration adds to the weight of the soil and at the same time reduces the shear strength provided by matric suction of the soil. The wetting band depth plays a key role in the stability of slopes. The minimum rainfall intensity and the minimum rainfall duration needed to infiltrate to the wetting front depth are calculated based on the Green-Ampt model. The method in this paper will contribute to the predication of slope stability considering rainfall characteristics.