Equivalent Stress Equation for Unsaturated Soils. II: Solid-Porous Model

Based on the study of the equilibrium of the particles of a soil showing a bimodal structure and subject to certain suction, it was possible to establish an analytical expression for the value of Bishop’s parameter χ (see the companion paper). This parameter can be written as a function of the saturated fraction and the degree of saturation of the unsaturated fraction of the soil. However, the determination of these last two parameters cannot be made from current experimental procedures. Therefore, a solid-porous model simulating the structure of the soil is proposed herein and used to determine these parameters. The data required for the solid-porous model are obtained from the grain and pore size distributions, void ratios, and secondary soil–water retention curves of the soil. The plots of the deviator stress versus equivalent stress shows a unique failure line for a series of tests performed at different confining net stresses and suctions, confirming that the proposed equivalent stress equation is adequate to predict the shear strength of unsaturated soils. It also results in different strengths for wetting and drying, as the experimental evidence suggests.     

Effective Stress in Unsaturated Soils: Review with New Evidence

The application of the effective stress principle to unsaturated soils is critically reviewed, and the reasons underlying the difficulties in previous investigations of the effective stress in unsaturated soils are highlighted. The validity of the relationship proposed by Khalili and Khabbaz in 1998 for the determination of the effective stress parameter, χ, is examined using an extensive array of experimental data. It is shown that quantitative predictions of shear strength and volume change in unsaturated soils can be made using the effective stress concept. The uniqueness of the critical state line in the deviatoric stress–effective mean stress plane for saturated as well as unsaturated soils is investigated, and the incremental form of the effective stress parameter is derived.     

Profiles of Steady-State Suction Stress in Unsaturated Soils

Application of the effective stress principle in unsaturated geotechnical engineering problems often requires explicit knowledge of the stress acting on the soil skeleton due to suction pore water pressure. This stress is defined herein as the suction stress. A theoretical formulation of suction stress profiles, based on the soil water characteristics curve, the soil permeability characteristic curve, and previous shear strength experimental verification, is developed. The theory provides a general quantitative way to calculate vertical suction stress profiles in various unsaturated soils under steady flow rate in the form of infiltration or evaporation.     

Suction Stress Characteristic Curve for Unsaturated Soil

The concept of the suction stress characteristic curve (SSCC) for unsaturated soil is presented. Particle-scale equilibrium analyses are employed to distinguish three types of interparticle forces: (1) active forces transmitted through the soil grains; (2) active forces at or near interparticle contacts; and (3) passive, or counterbalancing, forces at or near interparticle contacts. It is proposed that the second type of force, which includes physicochemical forces, cementation forces, surface tension forces, and the force arising from negative pore-water pressure, may be conceptually combined into a macroscopic stress called suction stress. Suction stress characteristically depends on degree of saturation, water content, or matric suction through the SSCC, thus paralleling well-established concepts of the soil–water characteristic curve and hydraulic conductivity function for unsaturated soils. The existence and behavior of the SSCC are experimentally validated by considering unsaturated shear strength data for a variety of soil types in the literature. Its characteristic nature and a methodology for its determination are demonstrated. The experimental evidence shows that both Mohr–Coulomb failure and critical state failure can be well represented by the SSCC concept. The SSCC provides a potentially simple and practical way to describe the state of stress in unsaturated soil.     

Shear Strength Equations for Unsaturated Soil under Drying and Wetting

Shear strength of unsaturated soil is an important engineering property in various geotechnical designs. In response to varying climatic conditions, unsaturated soil behaves differently under the drying and wetting processes due to hysteresis. Many research works were conducted and numerous equations were proposed for unsaturated shear strength, however, most of them were limited to the soil under the drying process. In this study, shear strength equations were categorized according to the nature of equation, i.e., fitting and prediction type equations. The purpose of this study is to propose prediction type shear strength equations for unsaturated soil under drying and wetting. Twelve published shear strength equations were selected for evaluation. A series of unsaturated consolidated drained triaxial tests were conducted on statically compacted sand-kaolin specimens under drying and wetting to examine the validity of the proposed equations. The experimental results indicated that the specimens on the drying path had a higher shear strength and exhibited more ductility, less stiffness, and contraction during shearing while the specimens on the wetting path had a lower shear strength and exhibited more brittleness, more stiffness, and dilation during shearing. The proposed equations were shown to provide the best predictions on the drying and wetting shear strength results from this study as well as published data in the comparison study.     

Nonisothermal Multicomponent Reactive Transport Model for Unsaturated Soil

A multicomponent reactive transport model, coupled with an existing thermal, hydraulic, and mechanical model for porous media, is investigated. The model is based on conservation of mass/energy principles for the flow and stress-strain equilibrium for the mechanical behavior. The resultant model is coupled with a geochemical model to capture geochemical interactions. Numerically, the Galerkin FEM is employed for spatial discretization and an implicit Euler method for temporal discretization. The coupling of the transport and geochemical models is achieved through both noniterative and iterative approaches. A series of applications are considered to demonstrate the numerical performance and qualitative behavior, specifically in the context of multicomponent behavior. The model shows good convergence and computational efficiency.     

Centrifuge Permeameter for Unsaturated Soils. I: Theoretical Basis and Experimental Developments

A new centrifuge permeameter was developed with the specific objective of expediting the measurement of the hydraulic characteristics of unsaturated soils. The development, theoretical basis, and typical results associated with using the centrifuge permeameter for concurrent determination of the soil-water retention curve (SWRC) and hydraulic conductivity function (K function) of unsaturated soils are presented in this paper. Components developed for the centrifuge permeameter are described, including the centrifuge, permeameter, water flow control system, and instrumentation used to concurrently and nondestructively measure the infiltration rate (flow pump and outflow transducer), volumetric water content (time domain reflectometry), and matric suction (tensiometers) in flight during steady-state infiltration. A companion paper focuses on definition of the SWRC and K function for a clay soil using the procedures described in this paper. While conventional geotechnical centrifuges are used to reproduce the response of earth structure prototypes, the centrifuge developed in this study is used to accelerate flow processes. Accordingly, it required a comparatively small radius (0.7 m) but high angular velocity (up to 875 rpm or 600 g’s) to impart a wide range of hydraulic gradients to an unsaturated soil specimen. Analytical solutions to Richards’ equation in the centrifuge indicate that steady-state infiltration allows direct determination of the relationships between suction, volumetric water content, and hydraulic conductivity from the instrumentation results. Typical instrumentation results during a drying stage are presented to illustrate determination of data points on the SWRC and K function at steady state. These results were found to be consistent with analytical flow solutions.     

Analytical Analysis of Rainfall Infiltration Mechanism in Unsaturated Soils

To improve the understanding of the influence of hydraulic properties and rainfall conditions on rainfall infiltration mechanism and hence on the pore-water pressure distributions in single and two-layer unsaturated soil systems, an analytical parametric study has been carried out. Parameters considered in this study include saturated permeability (ks), desaturation coefficient (α), water storage capacity (θs?θr), and antecedent and subsequent rainfall infiltration rate (qA and qB). Moreover, the influence of soil profile heterogeneity is also investigated. The calculated results demonstrate that the infiltration process and pore-water pressure response are primarily controlled by both qα/ks and ks/α. Generally the larger the value of qα/ks?, the greater the reduction of negative pore-water pressure in shallow soil layer. The larger the ratio of ks/α, the faster is the advancement of wetting front. Among the three hydraulic parameters, the effects of α and ks on pore-water pressure response are much more significant than that of (θs?θr). However, the relative importance of ks and α depends on the initial negative pore-water pressure range in the ground. In addition, the influence of antecedent infiltration rate (qA) on pore-water pressure response appears to be much more significant than that of subsequent infiltration rate (qB).     

Limitations in the Constitutive Modeling of Unsaturated Soils and Solutions

Over the past six decades, significant attention has been paid to the elastoplastic behavior of unsaturated soils. In the past two decades alone, elastoplastic theory for unsaturated soils has been established and experimental techniques for measuring the elastoplastic behavior of unsaturated soils have become more sophisticated. However, less effort has been directed at developing the best strategy for constitutive modeling of unsaturated soils. At present, there is no standard method for developing constitutive models for unsaturated soils from experimental data, and owing to the extreme complexity of unsaturated soil behavior, there are limitations in the existing modeling methods. If these limitations are not recognized, misleading results in the constitutive modeling of unsaturated soil behavior may occur. This paper discusses the origins of and possible solutions to these limitations. Experimental data from the recent literature are used to demonstrate the use of existing methods for the constitutive modeling of unsaturated soils and potential associated problems. A modified state-surface approach (MSSA), recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic conditions, was applied to overcome the limitations and develop a constitutive model that can best represent the behavior of unsaturated soil. A comparison of the proposed method and existing methods is discussed, and from this discussion, the capability and effectiveness of the proposed method are evaluated.     

Shear Strength and Shear-Induced Volume Change Behavior of Unsaturated Soils from a Triaxial Test Program

A series of unsaturated soil triaxial tests were performed on four soils including sand, silt, and a low plasticity clay. Attempts were made to correlate unsaturated soil properties from these tests and data from the literature with soil-water characteristics curve (SWCC), soil gradation, and saturated soil properties. The feasibility of estimating unsaturated soil property functions from saturated soil properties, SWCCs and gradation data, is demonstrated. A hyperbolic model for estimation of the unsaturated soil parameter, ?b, versus matric suction is presented. Shear induced volume change behavior was also studied, and results are included in this paper. Although not correlated with soil index properties, these shear-induced volume change data are important to complete stress-deformation analyses, and represent a significant addition to the existing data base of unsaturated soil properties.     

Centrifuge Permeameter for Unsaturated Soils. II: Measurement of the Hydraulic Characteristics of an Unsaturated Clay

This paper presents the hydraulic characteristics of an unsaturated, compacted clay, including its soil-water retention curve (SWRC) and hydraulic conductivity function (K function), determined using a new centrifuge permeameter developed at the University of Texas at Austin. A companion paper describes the apparatus, its instrumentation layout, and data reduction procedures. Three approaches are evaluated in this study to define the SWRC and K function of the compacted clay under both drying and wetting paths, by varying the inflow rate, the g level, or both. For imposed inflow rates ranging from 20 to 0.1 mL/h and g levels ranging from 10 to 100 g, the measured matric suction ranged from 5 to 70 kPa, the average volumetric water content ranged from 23 to 33%, and the hydraulic conductivity ranged from 2×10?7 to 8×10?11?m/s. The SWRCs and K functions obtained using the three different testing approaches were very consistent, and yielded suitable information for direct determination of the hydraulic characteristics. The approaches differed in the time required to complete a testing stage and in the range of measured hydraulic conductivity values. The g level had a negligible effect on the measured hydraulic characteristics of the compacted clay. The SWRCs and K functions defined using the centrifuge permeameter are consistent with those obtained using pressure chamber and column infiltration tests. The K functions defined using the centrifuge permeameter follow the same shape as those obtained from predictive relationships, although the measured and predicted K functions differ by two orders of magnitude at the lower end of the volumetric water content range.     

Equivalent Effective Stress and Compressibility of Unsaturated Kaolinite Clay Subjected to Drying

Three-dimensional compressibility tests performed on unsaturated kaolinite clay subjected to drying showed that the volume change is a function of the equivalent effective stress (EES). The EES in the clay at different water contents was measured by performing direct tensile tests. When the clay has high water content (saturated funicular state), its volume decreases notably as the water content is reduced, i.e., the equivalent effective stress is increased. If the clay has a water content in an intermediate interval (complete pendular state), the volume is almost constant because the equivalent effective stress is almost constant. For the interval of low water contents (partial pendular state), the volume of the clay increases as the water content is reduced. This occurs because the equivalent effective stress is reduced when the moisture content in the clay is reduced, and contrasts with the saturated funicular state. The minimum volume in the clay was reached when the maximum equivalent effective stress was developed. A conceptual framework explains the influence of the different states of water distribution to the EES.     

Determining the Shapes of Yield Curves for Unsaturated Soils by Modified State Surface Approach

Attention is increasingly paid to the elastoplastic behavior of unsaturated soils. In the development of an elastoplastic framework for unsaturated soils, it is necessary to determine the initial shape of the yield curve and its evolution with yielding. Accordingly, correct determination of shapes of yield curves is of significant importance. Existing methods rely on use of a series of specimens with “identical” stress history to determine the initial shape of yield curve. Preparation of such specimens requires thoughtful preparation, careful instrumentation, and lengthy equilibrium time, which makes identical specimens very difficult to obtain. As a result, the yield curve obtained through the existing methods could be misleading. Hence, this paper presents a simple method to correctly and rapidly determine the shapes of the yield curves and their evolution during yielding even if the soil specimens do no have identical stress histories. In this new method, a modified state surface approach, recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic conditions, was applied. It overcomes the limitations in the existing methods, and allows correct and rapid determination of the elastic and plastic hardening surfaces, and then shapes of yield curves without additional laboratory work. An example was used to demonstrate the application of the proposed method. The comparison between the proposed method and other methods was discussed from which the capability and effectiveness of the proposed method were evaluated.     

Analysis of Deep Moisture Barriers in Expansive Soils. I: Constitutive Model Formulation

Expansive soils cause important economical losses in many arid or semiarid countries in the world. Considering the large economic impact, relatively few efforts have been devoted to develop analytical methods that may help practitioner engineers to adequately design civil infrastructure on this type of soil. A rational design method should be able to quantify the heave or subsidence of the soil associated with the suction changes during water diffusion, as well as the contact pressures on soil-structure interfaces. Accordingly, in this and in a companion paper, the problem of volume changes due to nonpermanent water flow in expansive soils is studied and applied to the case of vertical moisture barriers. In this paper, a constitutive model for expansive soils is proposed. This model is an extension of that developed by Alonso et al. in 1990, in the sense that it can take into account the behavior of expansive soils. The advanced model is evaluated by comparing the numerical results with experimental data.     

Implicit Algorithm for Modeling Unsaturated Soil Response in Three-Invariant Stress Space

An implicit integration algorithm has been refined to predict the stress–strain–strength response of unsaturated soil under suction-controlled, multiaxial stress paths that are not achievable in a conventional cylindrical cell. The algorithm supports numerical analyses in a deviatoric plane by using a mixed control constitutive driver, in conjunction with a generalized Cam-Clay model that also incorporates the influence of a third stress invariant, or Lode-angle θ, within a constant-suction scheme. True triaxial data from a previously accomplished series of suction-controlled triaxial compression, triaxial extension, and simple shear tests on 10-cm cubical specimens of silty sand, were used for the tuning and validation of the refined algorithm. The elliptical Willam–Warnke surface was adopted for simulation of unsaturated soil response in three-invariant stress space. Reasonably satisfactory agreement was observed between experimental and predicted deviatoric stress versus principal strain response for different suction states, as well as between experimental and predicted strength loci in a deviatoric plane.     

Effect of Fine Particle Migration on the Small-Strain Stiffness of Unsaturated Soils

The paper presents the results of an experimental investigation of fine particle migration from pore body to the pore throat and toward the contact between particles and its effect on skeleton stiffness of granular materials. We hypothesize that the suspended colloids in the pore fluid migrate and deposit on the contact surface between the skeleton-forming particles and change the magnitude of the soil stiffness. Three specimens were prepared using uniform spherical glass particles that were saturated with deionized water and kaolinite or silt-base slurries. The specimens were drained by evaporation which retained the fines in the soil while increasing the matric suction. Changes in soil dynamic stiffness were evaluated using piezoelectric transducers while the migration of fines and the changes of the properties of the pore fluid were monitored using synchrotron X-ray microcomputed tomography (SMCT) on identical specimens. The wave propagation experiments show that the stiffness of the tested specimens increased at different rates during the drying processes. These measurements were complemented with SMCT scanning analysis that shows an increase in mass density of the remaining slurry as the pore fluid concentrated near the particle contacts. The results indicate that the soil stiffness increase due to the alteration of the pore fluid at the particles’ contact and changes caused at the contact behavior itself. These results provide an insight about parameters that influence soil stiffness which may help in better predictions of stiffness changes in compacted soils during moisture changes.     

Improved Approach to Construct Constitutive Surfaces for Stable-Structured Soils Covering Both Saturated and Unsaturated Conditions

Constitutive surfaces are indispensable for investigation of the behavior of soils. Saturated and unsaturated soils coexist in most engineering problems and it is meaningful to develop constitutive surfaces covering both saturated and unsaturated conditions which help to investigate the behavior for both saturated and unsaturated soils in a unified way. At present, the methodologies used for saturated and unsaturated soils are different and few researchers consider the constitutive surfaces for saturated soils. For unsaturated soils, the suction-controlled triaxial tests are usually laborious, time consuming, costly, and may not justify routine engineering projects. This paper discusses the role of constitutive surfaces in soil mechanics and presents an improved approach over existing interpolation methods to construct the constitutive surfaces for saturated and unsaturated conditions for a stable-structured soil using simple laboratory tests.     

Modulus-Suction-Moisture Relationship for Compacted Soils in Postcompaction State

Despite clear evidence, changes in mechanical properties (i.e., stiffness or modulus) of compacted subgrades in response to subgrade moisture regime changes after construction have rarely been investigated in the geotechnical profession. In particular, when in-service assessment of pavement subgrade is made, the modulus-moisture variation should be addressed on the basis of unsaturated soil mechanics. This study presents the unsaturated small-strain modulus behavior of five predominately fine-grained compacted subgrade soils. The small-strain shear modulus (Go) of saturated compacted specimens subjected to a desorption soil-water characteristic curve (SWCC) was evaluated using bender elements. A test apparatus was designed to apply two stress state variables, the net confining pressure and matric suction, during the Go measurements. The relationship between Go and the SWCC under a constant mean net stress was developed. Additionally, the effect of compaction moisture content, compaction energy, and soil type on the Go-SWCC relationship was investigated. Finally, a relationship describing the small-strain modulus behavior of unsaturated compacted soils is proposed.     

Not Making the Grade: Expansive Soils and Higher Education in Texas

Expansive soils are a serious geologic hazard in Texas; accordingly, one would expect Texas engineering colleges to offer a strong educational program on expansive soils at both the undergraduate and graduate levels. However, data from the geotechnical programs within the civil engineering departments of Texas engineering colleges suggest that while Texas educational programs cover the topic of expansive soils in varying degrees, the educational effort is highly skewed toward traditional geotechnical and foundation issues. In most cases, treatment of the expansive soil problem is limited and is not adequate when measured against the scope and extent of expansive soil problems in Texas.     

Fractal Approach to Unsaturated Shear Strength

Great efforts have been made to determine the shear strength of unsaturated soils using both elaborate laboratory tests and empirical methods. However, elaborate laboratory tests are difficult and time consuming to perform, and the physical meaning of empirical parameters is not obvious in empirical methods. A simple method to determine the unsaturated shear strength is proposed based on a fractal model for the pore surface. The unsaturated shear strength can be easily estimated using the surface fractal dimension and air-entry value, which can be calculated from the soil–water characteristic curves. The unsaturated shear strength obtained from the proposed method is in satisfactory agreement with the experimental data found in the literature. The proposed method is critically examined and its advantages and limitations are also discussed.