Unsaturated Soil Mechanics in Engineering Practice

Unsaturated soil mechanics has rapidly become a part of geotechnical engineering practice as a result of solutions that have emerged to a number of key problems (or challenges). The solutions have emerged from numerous research studies focusing on issues that have a hindrance to the usage of unsaturated soil mechanics. The primary challenges to the implementation of unsaturated soil mechanics can be stated as follows: (1) The need to understand the fundamental, theoretical behavior of an unsaturated soil; (2) the formulation of suitable constitutive equations and the testing for uniqueness of proposed constitutive relationships; (3) the ability to formulate and solve one or more nonlinear partial differential equations using numerical methods; (4) the determination of indirect techniques for the estimation of unsaturated soil property functions, and (5) in situ and laboratory devices for the measurement of a wide range of soil suctions. This paper explains the nature of each of the previous challenges and describes the solutions that have emerged from research studies. Computer technology has played a major role in achieving practical geotechnical engineering solutions. Computer technology has played an important role with regard to the estimation of unsaturated soil property functions and the solution of nonlinear partial differential equations. Breakthroughs in the in situ and laboratory measurement of soil suction are allowing unsaturated soil theories and formulations to be verified through use of the “observational method.”     

Frequency-Dependent Amplification of Unsaturated Surface Soil Layer

This paper presents a study of the amplification of SV waves obliquely incident on a surface soil layer overlying rock formation. Special attention is placed on the influence of the saturation states of the soil layer and the bedrock on the amplification in both horizontal and vertical directions as well as on the amplitude ratios between the two directions at the surface, where the vertical and horizontal amplification and the amplitude ratios are expressed as functions of the frequency of incident waves. The analysis indicates that while the influence of the saturation state of the bedrock is insignificant, a change of the saturation state of the soil layer may have a marked impact on the vertical amplification. For typical seismic frequencies, an unsaturated soil layer can generate greater vertical amplification than a saturated layer; it can also cause larger amplitude ratios between vertical and horizontal components at the surface. The analysis further confirms the potential importance of the saturation condition of near-surface soils in site response analysis.     

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.     

Hysteresis of Capillary Stress in Unsaturated Granular Soil

Constitutive relationships among water content, matric suction, and capillary stress in unsaturated granular soils are modeled using a theoretical approach based on the changing geometry of interparticle pore water menisci. A series of equations is developed to describe the net force among particles attributable to the combined effects of negative pore water pressure and surface tension for spherical grains arranged in simple-cubic or tetrahedral packing order. The contact angle at the liquid–solid interface is considered as a variable to evaluate hysteretic behavior in the soil–water characteristic curve, the effective stress parameter χ, and capillary stress. Varying the contact angle from 0 to 40° to simulate drying and wetting processes, respectively, is shown to have an appreciable impact on hysteresis in the constitutive behavior of the modeled soils. A boundary between regimes of positive and negative pore water pressure is identified as a function of water content and contact angle. Results from the analysis are of practical importance in understanding the behavior of unsaturated soils undergoing natural wetting and drying processes, such as infiltration, drainage, and evaporation.     

Behavior of a Loosely Compacted Unsaturated Volcanic Soil

In this paper, the stress-strain relationship and volumetric behavior of a loosely compacted unsaturated decomposed volcanic soil (fill) were studied by conducting three series of triaxial stress path tests: (1) consolidated undrained on the saturated fill; (2) constant water content; and (3) a reducing suction under constant deviator stress on the unsaturated fill. The last two series of tests were designed to simulate the effects of undrained response and rainfall infiltration in initially unsaturated slopes, respectively. It was found that the saturated loose volcanic soil behaves like clay under isotropic compression but it resembles sand behavior when it was subjected to undrained shear. For isotropically consolidated unsaturated specimens sheared under a constant water content, a hardening stress-strain and a nonlinear shear strength-suction relationship are observed. At relatively high suctions, both angle of friction and apparent cohesion appear to be independent of suction. Volumetric contraction during shear is observed in this series of tests. On the other hand, anisotropically consolidated loose unsaturated specimens subjected to a reducing suction change from contractive to dilative behavior as the net mean stress increases. This observed volumetric behavior, unlike the shear strength, is stress path-dependent and cannot be explained by using the existing elastoplastic critical state theoretical framework extended for unsaturated soils.     

Solute Transport through Unsaturated Soil due to Evaporation

A new method for predicting upward solute movement in unsaturated sand soil due to evaporation is developed and tested. Laboratory experiments were conducted in an unsaturated uniformly packed sand column with a cross section of 1.20 × 0.50 m2 and a constant shallow ground-water table. Evaporation was measured by a new ventilated chamber system. Solute movement from the ground water upward was monitored. Water and solute movement could be accurately reproduced by numerically solving Richards' equation and the convection-dispersion equation in one-dimension. The experimentally measured dispersivity for the unsaturated homogeneous sand agreed closely with the values which are available in the literature. This paper offers a new approach for investigating dispersion phenomena in unsaturated porous media exposed to evaporation.     

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.     

Estimation of Unsaturated Hydraulic Parameters from Infiltration and Internal Drainage Experiments

Inverse problem of determining unsaturated soil hydraulic properties from transient infiltration and internal drainage events are analyzed. Hydraulic properties are assumed to be described by van Genuchten’s relationships. The inverse problem is solved using Levenberg-Marquardt method while the forward problem is solved using a mass conservative finite difference numerical scheme. The bias induced by different objective functions on the parameter estimates with error free and noisy data are analyzed. Field experiments are conducted at two sites to compare the parameter estimates obtained from the infiltration and internal drainage tests. The results indicate that some objective functions induce undue bias in the estimated parameters in the presence of noise in the data and as such selecting a suitable objective function should be given due importance in the parameter estimation. The comparison of the parameter estimates from infiltration and internal drainage experiments at two sites indicates that the parameter estimates are close to each other. It is concluded that infiltration experiment, which is simpler and of short duration can be an alternative to internal drainage experiment for estimating the unsaturated soil parameters.     

Contaminant Transport Model for Unsaturated Soil Using Fuzzy Approach

Contaminant transport in the unsaturated zone is important for managing water resources and assessing the damage due to contamination in the field of irrigation, water management, wastewater management, and urban and agricultural drainage systems. Deterministic modeling which is widely used for contaminant transport is not adequate because it considers model input parameters as well-defined crisp values and hence does not account for uncertainties and imprecision. This paper presents a contaminant transport model based on fuzzy set theory to simulate water flow and contaminant transport in the unsaturated soil zone under surface ponding condition. Among all soil hydraulic parameters that have uncertainty associated with them, saturated hydraulic conductivity was found to be the most sensitive to model outputs. Trapezoidal fuzzy numbers were used to express the uncertainties associated with saturated hydraulic conductivity. The incorporation of uncertainties into contaminant transport model is useful in decision making, as it yields scientifically and practically based estimates of contaminant concentration.     

Laboratory Study of Loose Saturated and Unsaturated Decomposed Granitic Soil

Weathered soils are used extensively as fill materials in slope construction in tropical and subtropical cities such as Hong Kong. The mechanical behavior of loose decomposed fill materials, particularly in the unsaturated state, has not often been investigated and is not yet fully understood. The objective of this study was to understand the mechanical behavior of loose unsaturated decomposed granitic soil and to study the effects of the stress state, the stress path and the soil suction on the stress–strain relationship, shear strength, volume change, and dilatancy via three series of stress path triaxial tests on both saturated and unsaturated specimens. It was found that loose and saturated decomposed granitic soil behaves like clean sands during undrained shearing. Strain-softening behavior is observed in loose saturated specimens. In unsaturated specimens sheared at a constant water content, a hardening stress–strain relationship and volumetric contractions are observed in the considered range of net mean stresses. The suction of the soil contributed little to the apparent cohesion. The angle of friction appeared to be independent of the suction. In unsaturated specimens subjected to continuous wetting (suction reduction) at a constant deviator stress, the volumetric behavior changed from dilative to contractive with increasing net mean stress and the specimen failed at a degree of saturation far below full saturation. It was revealed that the dilatancy of the unsaturated soil depends on the suction, the state, and the stress path.     

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.     

Unsaturated Soil Seepage Analysis Using a Rational Transformation Method with Under-Relaxation

The finite-element method provides a convenient and effective means for solving problems of seepage in unsaturated soils. However, convergence difficulties exist in numerical simulations of unsaturated flow analyses because of the high nonlinearity of the soil hydraulic properties. This technical note presents a combination approach consisting of a rational function transformation method and a common under-relaxation technique to solve the h-based form of Richards equation. Numerical studies show that this combined method can use a larger time step and corresponding oscillation-free mesh size to produce acceptable results and also converge to a stable solution quickly in each time step.     

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.     

Impacts of Unsaturated Zone Soil Moisture and Groundwater Table on Slope Instability

The combined effect of soil moisture in unsaturated soil layers and pore-water pressure in saturated soil layers is critical to predict landslides. An improved infinite slope stability model, that directly includes unsaturated zone soil moisture and groundwater, is derived and used to analyze the factor of safety’s sensitivity to unsaturated zone soil moisture. This sensitivity, the change in the factor of safety with respect to variable unsaturated zone soil moisture, was studied at local and regional scales using an active landslide region as a case study. Factors of safety have the greatest sensitivity to unsaturated zone soil moisture dynamics for shallow soil layers (<2?m) and comparatively deep groundwater tables (1 m). For an identical groundwater table, the factor of safety for a 1 m thick soil mantle was four times more sensitive to soil moisture changes than a 3-m thick soil. At a regional scale, the number of unstable areas increases nonlinearly with increasing unsaturated zone soil moisture and with moderately wet slopes exhibiting the greatest sensitivity.     

Influence of Exogenous Lanthanum on Fertility Parameters of Red Soil and Paddy Soil

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An A Priori Hot-Tearing Indicator Applied to Die-Cast Magnesium-Rare Earth Alloys

Hot-tearing susceptibility is an important consideration for alloy design. Based on a review of previous research, an a priori indicator for the prediction of an alloy’s hot-tearing susceptibility is proposed in this article and is applied to a range of magnesium-rare earth (RE)-based alloys. The indicator involves taking the integral over the solid fraction/temperature curve between the temperature when feeding becomes restricted (coherency) and that when a three-dimension network of solid is formed (coalescence). The hot-tearing propensity of Mg-RE alloys is found to vary greatly depending on which RE is primarily used, due to the difference in the solidification range. Mg-Nd alloys are the most susceptible to hot tearing, followed by Mg-Ce-based alloys, while Mg-La alloys show almost no hot tearing. The proposed indicator can be well applied to hot-tearing propensity of the Mg-RE alloys. It is expected that the indicator could be used as an estimation of the relative hot-tearing propensity in other alloy systems as well.     

Identifiability and indistinguishability of nonlinear pharmacokinetic models

Three nonlinear model structures of interest in pharmacokinetics are analyzed to determine whether the unknown, independent, model parameters can be deduced if perfect input-output data were available. This is the problem of identifiability. The method used is based on the local state isomorphism theorem. In certain circumstances, the modeler may be undecided between several model structures and it is then of interest to determine whether different model structures can be distinguished from perfect input-output data. This is the problem of model indistinguishability. The technique used, again based on the local state isomorphism theorem, parallels the similarity transformation approach for linear systems described previously in this journal. The analysis is performed on three two-compartment examples having one linear and one nonlinear (Michaelis-Menten) elimination pathway. In each model there is, on physiological and other grounds, some uncertainty over the precise location (central compartment or peripheral compartment) of one of the elimination pathways.     

Calibration of Soil Constitutive Models with Spatially Varying Parameters

Soil constitutive models are frequently calibrated from laboratory tests that utilize global boundary measurements, which necessarily relegate soil response to that of a homogenized equivalent medium. This paper demonstrates the applicability of advanced experimental technologies to enhance the state of model-based predictions in soil mechanics by taking into account the possibility of material heterogeneity during model calibration. By utilizing the full-field displacement measurement technique of three-dimensional digital image correlation, displacements of the surfaces of deforming triaxial sand specimens are measured throughout deformation. These displacements are assimilated into finite-element (FE) models of the test specimen through solution of an inverse problem. During optimization, in which the difference between measured and predicted displacements across the specimen surface form the basis for the objective function, model parameters are allowed to vary spatially throughout the specimen volume. FE models allowing three different levels of spatial variability are tested. Results indicate that accommodating consideration of material heterogeneity during calibration leads to more accurate predictions of global stress-strain behavior that are more faithful to observed full-field response.