Model For Unsaturated Soils Research Articles

An Improved Mechanistic-Empirical Creep Model for Unsaturated Soft and Stabilized Soils.

Soft soils are usually treated to mitigate their engineering problems, such as excessive deformation, and stabilization is one of most popular treatments. Although there are many creep models to characterize the deformation behaviors of soil, there still exist demands for a balance between model accuracy and practical application. Therefore, this paper aims at developing a Mechanistic-Empirical creep model (MEC) for unsaturated soft and stabilized soils. The model considers the stress dependence and incorporates moisture sensitivity using matric suction and shear strength parameters. This formulation is intended to predict the soil creep deformation under arbitrary water content and arbitrary stress conditions. The results show that the MEC model is in good agreement with the experimental data with very high R-squared values. In addition, the model is compared with the other classical creep models for unsaturated soils. While the classical creep models require a different set of parameters when the water content is changed, the MEC model only needs one set of parameters for different stress levels and moisture conditions, which provides significant facilitation for implementation. Finally, a finite element simulation analysis of subgrade soil foundation is performed for different loading levels and moisture conditions. The MEC model is utilized to predict the creep behavior of subgrade soils. Under the same load and moisture level, the deformation of soft soil is largest, followed by lime soil and RHA–lime-stabilized soil, respectively.

A bounding surface plasticity model for unsaturated structured soils

A bounding surface plasticity model based on the effective stress concept is presented to describe the behaviour of unsaturated structured soils subjected to hydro-mechanical loadings. The structural degradation effects on the compressive and tensile strength are considered through controlling the size of the bounding surface, allowing for a smooth transition of the response from structured to unstructured states. The structural degradation is modelled using a work hardening approach, considering both the effects of stress magnitude and accumulated plastic strain on the degradation process. A void ratio-dependent water retention model is adopted, taking the effect of hydraulic hysteresis into account. Attention is also given to the stiffening effect of a decrease in the degree of saturation on the mechanical response of unsaturated structured soils and the wetting-induced collapse. A radial mapping rule with a mobile centre of homology is adopted to capture the response of the soil under unloading–reloading conditions. The predictive capability of the model is demonstrated through the comparison of the model simulations with experimental data for different conventional laboratory tests including constant-suction oedometer and triaxial shearing and wetting tests.

Numerical Implementation of a Hydro-Mechanical Coupling Constitutive Model for Unsaturated Soil Considering the Effect of Micro-Pore Structure

An unsaturated soil constitutive model considering the influence of microscopic pore structure can more accurately describe the hydraulic–mechanical behavior of unsaturated soil, but its numerical implementation is more complicated. Based on the fully implicit Euler backward integration algorithm, the ABAQUS software is used to develop the established hydro-mechanical coupling constitutive model for unsaturated soil, considering the influence of micro-pore structure, and a new User-defined Material Mechanical Behavior (UMAT) subroutine is established to realize the numerical application of the proposed model. The developed numerical program is used to simulate the drying/wetting cycle process of the standard triaxial specimen. The simulation results are basically consistent with those calculated by the Fortran program, which verifies the rationality of the developed numerical program.

Determination of soil water hydraulic parameters from infiltration data

PurposeTraditional laboratory measurements of soil water diffusivity (D) and soil water retention curve (SWRC) are always time-consuming and labor-intensive. Therefore, this paper aims to present a simple and robust test method for determining D and SWRC without reducing accuracy.Design/methodology/approachIn this study, a D model of unsaturated soil was established based on Gardner–Russo model and then a combination of Gardner–Russo model with one-dimensional horizontal absorption method to obtain n and a parameters of Gardner–Russo model. One-dimensional horizontal absorption experiments on loam, silt loam and sandy clay loam were conducted to obtain the relationships between measured infiltration rate and cumulative infiltration with wetting front distance. Based on the obtained relationships, the measured infiltration data from the one-dimensional horizontal absorption tests were used to calculate n and a parameters and further constructing D and SWRC.FindingsBoth the calculated D and SWRC inversed from the infiltration data were in good agreement with the measured ones that obtained from the traditional horizontal absorption method and the centrifuge method, respectively. Error analysis indicated that only the infiltration data are enough to reliably synchronously determine D and SWRC.Originality/valueA simple and robust method is proposed for synchronous determination of soil water diffusivity and water retention curve.

Dilatancy Characteristics and Constitutive Modelling of the Unsaturated Soil Based on Changes in the Mass Water Content

Most soil mechanics theories are limited to strain hardening and shrinkage under high compressive stresses, and there are some shortcomings in the selection of suction or degree of saturation as the water content state varies in the constitutive models of unsaturated soil. Based on the triaxial shear tests of unsaturated compacted soil (a silt of high plasticity) with different water content and confining pressure (low-confining), a shear dilatancy model of unsaturated soil based on the mass water content is proposed in this paper. The influence of the water content on the shear deformation characteristics of the unsaturated soil is analysed. The stress–dilatancy relationship and the prediction equation of the minimum dilatancy rate of the unsaturated soil under different water content and different confining pressure are provided. Selecting the mass water content as the state variable, a constitutive model suitable for the dilatancy of unsaturated soil is established. The method of determining model parameters based on the mass water content is analysed. The applicability of the model is verified by comparisons between the predicted and experimental results.

A unified small-strain shear stiffness model for saturated and unsaturated soils

This paper presents a model for calculating the small-strain shear stiffness of saturated and unsaturated fine-grained soils as the product of a dimensionless stiffness index and four individual functions of the mean average skeleton stress, the over-consolidation ratio, the reference saturated void ratio and the degree of saturation. The main element of novelty of the model resides in the introduction of a reference saturated state, which results in a dependency of the small-strain stiffness on the degree of saturation. The reference saturated state is calculated according to a recently published constitutive law that relates the quotient between the unsaturated void ratio and the reference saturated void ratio to the degree of saturation. The model requires only two extra parameters for unsaturated states, i.e. one parameter for the volumetric behaviour and one for the stiffness behaviour. These two parameters may also be correlated to the saturated parameters, which simplifies the calibration of the model. The proposed framework is validated against laboratory experiments on three different materials resulting in generally accurate predictions compared to other published models. The good predictive capabilities and the simplicity of the formulation justify the implementation of the model into numerical codes for the analysis of geotechnical problems.

Seismic stability analysis of slopes with cracks in unsaturated soils using pseudo-dynamic approach

In practice, soil slopes are commonly unsaturated and may suffer from the adverse effects of earthquakes. Stability assessment of slopes subjected to earthquakes tends to consider whether the soils are dry or saturated while neglecting the time and spatial effects of seismic waves; in such assessments, the actual features cannot be reflected sufficiently. In the present study, a framework considering unsaturated soils was developed to investigate the seismic stability of slopes accounting for tension cracks using the pseudo-dynamic approach. Several expressions for apparent cohesion were applied to analyze the influence of matric suction, and seepage under different phreatic levels was also included. The pseudo-dynamic approach was applied to characterize the time and spatial effects of earthquakes. Two types of cracks, open cracks (cracks existing prior to slope failure) and formation cracks (cracks forming as part of a slope failure mechanism), were considered. A closed-form solution for the critical height of the slopes was derived from the energy balance equation of the Limit Analysis upper bound method, and the safety factor was obtained. The validity of this approach was verified by comparison with published solutions. Through the parametric analysis, it was found that higher amplification factors and seismic coefficients led to a smaller discrepancy in the safety factor between the slopes with open cracks and formation cracks, yet a reverse trend was observed at a higher value of matric suction. The effect of matric suction on slope stability was more apparent with a lower water level. Different shear strength models of unsaturated soils led to different safety factors.

Laboratory Assessment of the Mechanical Properties of an Unsaturated Mid-Atlantic Silty Sand

Natural soil formation processes involve variable particle size distributions that vary spatially within a deposit, giving rise to an array of soils that transition from one general soil type to another within essentially similar deposits. Characterization of such transition soils in the active zone is something past research has largely overlooked. An evaluation of the unsaturated strength behavior of a transition soil was carried out on a native mid-Atlantic silty sand. A suite of unsaturated consolidated drained axisymmetric triaxial shear tests was performed, and the stress–strain and volume change characteristics of the transition silty sand under different values of matric suction, confining pressure, strain rate, and fines content were investigated. It is found that the triaxial shear strength increases with increasing matric suction, confining pressure, strain rate, and fines content. The volumetric strain increases with increase in matric suction and confining pressure, and it decreases as fines content and strain rate are increased. The experimental results are used to further validate a state-dependent constitutive model for unsaturated soils that was recently proposed based on the theory of bounding surface plasticity and the framework of hyperelasticity. It is shown that the model simulations are in good agreement with the experimental data.

Small-strain behaviour of unsaturated silty clay: experiments and model interpretation

The experimental data dealing with the so-called small strain stiffness of soils are indispensable in developing and calibrating advanced numerical models. A literature review revealed a lack of such data for unsaturated soils. In this study, the laboratory measurements of very small and small strain stiffness are carried out in a double-walled triaxial cell using bender elements and LVDT transducers. The tested soil is a reconstituted silty clay, representing a typical soil encountered in engineering practice. A so-called effective stress for unsaturated soil is used in interpreting and numerically simulating the effects of suction magnitude, net stress magnitude and suction history on the initial elastic shear modulus, and on its decrease with increasing strain. The increase of both net stress and suction leads to increase in stiffness. This is observed by both elastic shear modulus and shear modulus reduction curve measurements. The “overconsolidation” by suction leads to the increase of stiffness, too. The experimental data are used for calibrating constitutive parameters and for assessing the capabilities of an advanced hypoplastic model for unsaturated soils. The model predictions are consistent with the laboratory measurements and the model can capture the increase of stiffness with respect to the increase of suction and net stress reasonably well. Moreover, the model is able to predict the increase of stiffness due to suction “overconsolidation”.

Field test and semi-analytical simulation of unsaturated road subgrade in various water content subjected to a heavy duty truck

Field test is the most direct and essential way to evaluate subgrade dynamic responses, which is of great importance in designing and ensuring long-term subgrade performance. Many researchers have performed field tests considering the dynamic responses of subgrade. However, in the previous tests, the water content of the soil, which decides the mechanical properties of unsaturated soil, is rarely considered. In this paper, the dynamic responses of subgrade in different saturations are investigated by both field tests and analytical simulations. The vertical stress and acceleration tested in the field under different water contents, depths, truck speeds, and axle weights are presented. The result shows that as the water content in the subgrade rises, vertical stress variation is insignificant, while the amplitude of acceleration increases. According to the distribution of water content of the subgrade, a double-layer unsaturated soil model was proposed using the stiffness matrix method. The comparison between field test and simulation results shows that the agreement is good.

Undrained Spherical Cavity Expansion in Unsaturated Soils: Semianalytical Solution Coupling Hydraulic and Mechanical Behaviors

A coupled hydromechanical solution to undrained spherical cavity expansion problem in unsaturated soil is proposed with an elastoplastic model for unsaturated soil. The mechanical response and hydraulic behavior of soil during expansion are coupled together through a soil–water characteristic curve (SWCC) that evolves with the void ratio. A system of four first-order differential governing equations is derived based on the equilibrium equation, large stain theory and coupled hydromechanical constitutive relationship of soil. The present solution can reduce to unified hardening parameter model based solution under saturated condition, which validates the proposed solution. The effects of overconsolidation ratio and initial suction on expansion responses are explored based on extensive parametric studies. Special attention is paid to investigate the distributions of the principal stresses, suction, and saturated degree of soil around the expanded cavity; the stress trajectory of a representative element at the cavity surface; and cavity pressure–displacement curves. The proposed analytical solution can serve as a theoretical framework for modelling of some fundamental geotechnical problems in unsaturated soils using critical state soil models.

Strength Model of Unsaturated Clays with Adsorptive Effects

The interactions between liquid phase and solid matrix in unsaturated clays can be divided into capillary effects and physicochemical effects according to their formation mechanism. The physicochemical effects (that is, the adsorption effects) become significant at low saturation degrees. However, current strength models for unsaturated soils almost are established on the basis of capillary mechanism, and the contribution of adsorption effects to soil strength is neglected. A binary-medium shear strength model is firstly proposed, involving the capillary and adsorption effects. The unsaturated clay is assumed to consist of two ideal parts, i.e., the ideal capillarity part and the ideal adsorption part, and then the corresponding ideal strength formulas are established. Furthermore, a participation function is used to reflect the degrees of capillary effects and adsorption effects. Finally, predictions are performed on the shear strength of unsaturated clays. After comparing predicted results and exiting test results, it is shown that the proposed model can well describe the strength of unsaturated clays.

A bounding surface model for unsaturated soils considering the microscopic pore structure and interparticle bonding effect due to water menisci

The interparticle bonding effect due to water menisci plays an important role in the hydromechanical coupling properties of unsaturated soils. This paper presents an unsaturated hydromechanical coupling model that considers the influence of matric suction, degree of saturation, and microscopic pore structure on the interparticle bonding effect. The enhanced effective stress and bonding variable are selected as constitutive variables. The bonding variable is correlated with the ratio between unsaturated void ratio and saturated void ratio. The deformation characteristics of unsaturated soils are described based on the bounding surface plasticity theory. A soil–water characteristic model that considers deformation and hydraulic hysteresis is integrated into the constitutive model to achieve hydromechanical coupling. The proposed model can effectively describe the hydromechanical coupling characteristics and the meniscus bonding force of unsaturated bimodal structure soils; the model parameters can be easily obtained through routine experiments. The experimental results of unsaturated isotropic compression, the wetting/drying cycle, and unsaturated triaxial shear tests are used to validate the capability of the proposed model.

Examining the predictive capabilities of a bounding surface plasticity-based hyperelastic constitutive model for unsaturated granular soils

The performance of a recently developed state-dependent constitutive model for unsaturated granular soils is evaluated. The model employs the Bounding Surface plasticity framework and evaluates elastic strains assuming hyperelastic behavior. To realistically simulate the deformation of unsaturated granular soils, the mechanical behavior was modeled without a purely elastic component. The inherent hydro-mechanical coupling was realized by introducing a Bishop-type effective stress, an appropriate work-conjugate variable, and a soil-water characteristic curve function. Relevant details about the model development, parameter estimation, and the assessment of the model’s predictive capabilities are presented. The model performance is evaluated with experimental data obtained for drained and constant-water stress paths. With a given a set of parameter values, the model realistically simulates the main features that characterize the shear and volumetric behavior of unsaturated granular soils over a wide range of matric suction, density, and net confining pressure. This is found to be true for both drained and constant-water stress paths.

A semi-analytical solution to spherical cavity expansion in unsaturated soils

This paper presents a rigorous solution for spherical cavity expansion in unsaturated soils under constant suction condition. The hydraulic behavior that describes the saturation-suction relationship is modeled by a void ratio-dependent soil-water characteristic curve, which allows the hydraulic behavior to fully couple with the mechanical behavior that is described by an extended critical state soil model for unsaturated soil through the specific volume. Considering the boundary condition and introducing an auxiliary coordinate, the problem is formulated to a system of first-order differential equations with three principal stress components and suction as basic unknowns, which is solved as an initial value problem. Parameter analyses are conducted to investigate the effects of suction and the overconsolidation ratio on the overall expansion responses, including the pressure-expansion response, the distribution of the stress components around the cavity, and the stress path of the soil during cavity expansion. The results reveal that the expansion pressures and the distribution of the stress components in unsaturated soils are generally higher than those in saturated soils due to the existence of suction.

Triple-Shear Elastoplastic Constitutive Models for Normally Consolidated Unsaturated Soils Based on the Coordinate Translation Method

The unified triple-shear strength criterion for unsaturated soils was established with the single-stress variable method and the double-stress variable method, and the corresponding triple-shear failure stress ratios were derived with the coordinate translation method. Then the triple-shear failure stress ratios were combined with the modified Cambridge model for unsaturated soils, the triple-shear elastoplastic constitutive models for normally consolidated unsaturated soils under the single-stress variable and double-stress variable were built, and the secondary development of ABAQUS was carried out. With the Nanchang unsaturated remolded clay as the research object, the consolidation and drainage (CD) test verification and true triaxial CD test simulation of unsaturated soils were done, and the effects of intermediate principal stress influence coefficient b and matrix suction s on the calculation model for the gravity retaining wall were studied. The results show that, the proposed 2 constitutive models can well describe the deformation characteristics of normally consolidated unsaturated soils in CD tests, and the simulation results of the coordinate translation method under double-stress variables are more close to the real test data. In the simulation of true triaxial CD tests, the shear stress and the volume strain obtained with the double-stress variable method are more close to the results of the single-stress variable method. With the increase of intermediate principal stress influence coefficient b, the shear stress and the volume strain of the 2 constitutive models will also increase. The gravity retaining wall calculation model with the double-stress variable method is more stable. With the increase of intermediate principal stress influence coefficient b or matrix suction s, the soil displacement of the retaining wall model will decrease, while the strength and stability of the soils behind the wall will increase.

Numerical modeling of unsaturated soil behavior considering different constitutive models

Recent advances, not only in fluid flow but also in soil mechanics, have allowed the understanding and forecasting of common engineering problems such as slope stability, soil shrinkage and soil collapse. However, owing to limited access to data or more sophisticated numerical tools, the modeling of soil behavior is usually carried out considering simpler constitutive models which cannot predict some important features of unsaturated soils. This study is focused on the numerical modeling of unsaturated soils, adopting four constitutive models based on theories of elasticity and plasticity. For each model, a numerical simulation of a circular footing resting over a soil that is subject to drying and wetting processes is analyzed. Through the comparison of results, it is possible to highlight the use of more sophisticated constitutive models for unsaturated soil behavior, particularly forecasting the phenomenon of pore collapse during wetting processes.

Expansion responses of a cylindrical cavity in overconsolidated unsaturated soils: A semi-analytical elastoplastic solution

This paper presents a semi-analytical elastoplastic solution for cylindrical cavity expansion in overconsolidated (OC) unsaturated soils under constant water content condition, in which both the OC features and the coupled hydro-mechanical behaviour of soils are properly addressed. The unified hardening model for OC unsaturated soil is further coupled with a void ratio-dependent soil-water characteristic curve to model the coupled hydro-mechanical soil responses during expansion. With the aid of an auxiliary variable, the coupled hydro-mechanical constitutive matrix for the investigated problem is finally formulated as a set of first-order ordinary differential equations in terms of Lagrangian description, with the three net stress components, the suction, and the void ratio as the basic unknowns. The governing differential equations are solved as an initial value problem with the code developed based on the Runge-Kutta algorithm. Parametric studies show that both the overconsolidation ratio and the suction have remarkable impacts on the expansion responses, including the distribution of stress components, the change of degree of saturation as well as the expansion pressures. The proposed solution could provide a reasonable tool for interpretation of the pressuremeter tests and prediction of pile installation effects in overconsolidated unsaturated soils.

Comparison of the hydraulic conductivity between saturated frozen and unsaturated unfrozen soils

Knowledge of the hydraulic conductivity of warm frozen soil is crucial for accurately calculating the deformation of buildings built in permafrost, and the objective of this study is to provide an experimental and theoretical method for obtaining the hydraulic conductivity of warm saturated frozen soil. The permeability experiments were carried out on warm frozen soil in the low temperature rock triaxial testing system, which provides a precise measurement of the water flow rate through the warm frozen soil. Repeated experiments were conducted to verify the validity of the experimental results. Subsequently, based on the experimental results and given the shortcomings of the ice impedance model, the equivalent model was proposed to predict the hydraulic conductivity of saturated frozen soil. The model suggested that saturated frozen soil and unsaturated unfrozen soil with the same liquid water content have the same hydraulic conductivity. To illustrate the validity of the model, the predictions of seven hydraulic conductivity models for unsaturated unfrozen soil were compared with the measured hydraulic conductivity of saturated frozen soil. The results show that the predictions are close to the measured data, which shows the validity of the model. Thus, the hydraulic conductivity of saturated frozen soil can be directly predicted by the hydraulic conductivity model for unsaturated unfrozen soil. The results provide a new method for obtaining the hydraulic conductivity of saturated frozen soil, which can provide a reference for the design and construction of buildings built in permafrost.

Coupled hydraulic-mechanical-air simulation of unsaturated railway embankment under rainfall and dynamic train load

Performance evaluation of the embankment subject to climate change and dynamic train loads is important to the safety of high speed railway (HSR). In this study, based on an elasto-plastic unsaturated soil model, a coupled hydraulic-mechanical-air finite element analysis method is proposed, which integrates the analysis under rainfall condition and the analysis under dynamic load in one numerical simulation. A finite element analysis program called DBLEAVES-X is improved from its previous version (DBLEAVES) to consider the hydraulic-mechanical-air coupled behavior in unsaturated soils under dynamic condition. In order to verify the feasibility of the proposed method, a reduced-scale model test was first simulated. The calculating results showed that the measured displacement and acceleration can be well reproduced by the proposed method. Analyses on the effect of rainfall conditions, train loads and embankment materials were then conducted for a full scale prototype model of typical HSR embankment. The results of the analyses show that higher intensity of rainfall infiltration increases the risk of local failure. A higher train speed and heavier train axle load result in larger displacements. The frequency of the acceleration response is only influenced by the train speed. The embankment performance worsens with the degradation of the embankment material. Preceding rainfall condition results in a larger displacement of the track slab after the dynamic load is applied.