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.     

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).     

Field Infiltration Characteristics of Natural Rainfall in Compacted Roadside Slopes

Wetting depth in a slope is an important indicator to properly evaluate the rainfall-induced slope instability. This rainfall infiltration has potential to induce shallow slope failures. It is necessary to characterize the field infiltration and movement of the wetting front due to a natural rainfall. To monitor important infiltration characteristics of a field slope, a compacted roadside slope in an express highway (South Korea) was instrumented to measure variations of matric suction and water content. The monitored variations of matric suction and water content in vegetated and nonvegetated areas are discussed. The pattern of field infiltration by severe rainfall storms is also compared with the estimation results obtained by widely used 1D infiltration models. The Chu model, by considering the ponding and run-off at each time interval, showed a good agreement with the field measurements.     

Hysteresis in Shallow Water Sloshing

Hysteresis in sloshing of shallow water in horizontally excited tanks is explored experimentally. In particular the wave response to relatively large shaking amplitude near the resonant frequency is investigated for two tank configurations: a tank with horizontal bottom and vertical walls, and a tank with horizontal bottom and sloping beaches. The hysteresis behavior is clearly observed within a narrow frequency range around the shifted resonant frequency. The wave response is either in the form of smooth nonbroken waves or in the form of violent breaking waves for exactly the same set of parameters depending only on how the target oscillation frequency is tuned: i.e., whether the forcing frequency of the prior state is higher or lower than the target frequency. The consequence is that it is not possible to define a unique value for the jump frequency as it depends on the direction of the frequency tuning.     

Evaluation of Surficial Stability for Homogeneous Slopes Considering Rainfall Characteristics

Shallow slope failures in residual soil during periods of prolonged infiltration are commonly occurring in the world. This study examines an infinite slope analysis to estimate the influence of infiltration on surficial stability of slopes by the limit equilibrium method. An approximate method that accommodates the boundary condition of a uniform rainfall has been proposed to evaluate the likelihood of shallow slope failure that is induced by a particular rainfall event. The method based on the Mein and Larson model, which provides an explicit solution for preponding infiltration, has been applied to various types of soil having measured unsaturated hydraulic properties. To compare results with those obtained from the approximate method, a series of numerical analyses were carried out. According to the results, with the use of properly estimated input parameters, the approximate method was found to give results that compare reasonably well with those of more rigorous finite element analyses.     

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.     

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.     

Shear Strength of Compacted Soil under Infiltration Condition

Landslides in residual soil slopes are commonly induced by rainfall infiltration. These residual soils are typically in an unsaturated state with negative pore-water pressures or matric suctions since the groundwater tables in steep slopes are often deep. The net normal and shear stresses of the soil remain essentially constant during rainwater infiltration into the slope. Failure of the slope during rainfall can be primarily associated with the decrease in the matric suction of the soil. The objective of the study was to investigate the strength and deformation characteristics of a residual soil of the Bukit Timah Granitic Formation during infiltration that leads to slope failure. There were two modified direct shear apparatuses used. One apparatus was used for the determination of shear strength under controlled suction conditions while the other apparatus was used for shearing-infiltration tests. The shearing-infiltration test results were compared with the shear strength values obtained from the shearing tests under constant suction. The shearing-infiltration test results indicate a close relationship between the decreasing matric suction and the increasing displacement rate of the soil specimen. At the initial part of the infiltration process, there is a rapid reduction in matric suction that is accompanied by little movement in the soil. When failure of the soil is imminent, the soil movement will accelerate.     

Hysteresis of Matric Suction and Capillary Stress in Monodisperse Disk-Shaped Particles

The dependences of matric suction and capillary stress on the degree of saturation in monodisperse disk-shaped particles are established for the full range of the degree of saturation. A thermodynamic free energy approach is employed to obtain both the soil–water characteristic curve (SWCC) and the capillary stress characteristic curve (CSCC) for both wetting and drying processes. It is shown that the thermodynamic energy stability concept can lead to the establishment of hysteresis in both the SWCC and CSCC without explicit involvement of the contact angle and ink-bottle hysteresis. The air-entry pressure value and capillary condensation pressure value are quantified and their functional dependencies on the average pore sizes are established. For particle sizes ranging between 0.001 and 1?mm, the air-entry and capillary condensation pressures decrease from several hundred kPa to several kPa and capillary forces are found to range between tens and hundreds of micronewtons.     

Airborne Acoustic Method to Determine the Volumetric Water Content of Unsaturated Sands

This paper presents an innovative experimental approach for simultaneous measurements of the suction head, volumetric water content, and the acoustic admittance of unsaturated sands. Samples of unsaturated sands are tested under controlled laboratory conditions. Several types of uniform sand with a wide range of particle sizes are investigated. The reported experiments are based on a standard Buchner funnel setup and a standard acoustic impedance tube. It is a novel, nondestructive, and noninvasive technique that relates the key geotechnical parameters of sands such as volumetric water content, density, and grain-size distribution to the acoustic admittance and attenuation. The results show a very sensitive dependence of the acoustic admittance on the volumetric water content controlled by the value of suction head applied. Analysis of the obtained data demonstrates that the relationship between the volumetric water content and the real part of the surface admittance in the frequency range of 400–1,200 Hz can be represented using a logarithmic equation. It is found that the coefficients in the proposed equation are directly related to the uniformity coefficient and the acoustic admittance of the dry sample, which can easily be measured or predicted for a broad range of sands. A validation exercise is conducted to examine the accuracy of the proposed equation using a sand sample with markedly different properties. The results of the validation exercise demonstrate that the proposed relations can be used to determine very accurately the volumetric water content within the porous specimen from the acoustical data. The error in the acoustically measured volumetric water content is found to be ±2.0% over the full range of volumetric water contents (0 ≤ θ ≤ n, where n is the sample porosity).     

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.     

Water Flow in Unsaturated Soils in Microgravity Environment

In this study, two types of soils with varying soil water potentials were used for evaluating the effect of gravity on water flow through unsaturated soils. Experiments were conducted in both 1- and 0-g environments. Water content distributions were evaluated as a function of distance from the source of water intake and time. The experimental results indicated that the capillary potential and the advective forces due to interfacial tension gradients are overshadowed by the gravitational potential in a 1-g environment. The fast water movement in the 0-g condition is attributed to the capillary potential as well as to the advective forces that developed. In addition, microstructural changes have contributed to water flow in the 0-g condition. Depending on soil type, the magnitude of such an effect (i.e., water movement) varies from three- to four-fold. To analyze the experimental results, a one-dimensional model, based on Darcy’s law and the conservation of mass equations, was developed and solved numerically by the finite difference method. A nondimensional Bond number was extracted from the resulting flow equation and used as a basis for incorporating the gravitational component of the flow process into the formulation. The numerical results compare quite well in some instances with the experimental results. In other cases, significant departures are noted. The departure was attributed to the significant changes in microstructure of soil samples under the 0-g condition. Consequently, the requisite water retention and hydraulic conductivity functions used in the model may not apply in outer space.     

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.     

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.     

Numerical Study of Finite Element Method Based Solutions for Propagation of Wetting Fronts in Unsaturated Soil

The accurate prediction of the propagation of a wetting front in an unsaturated soil subjected to surficial infiltration is of practical importance to many geotechnical and geoenvironmental problems. The finite element method is the most common solution technique as the hydraulic soil properties are highly nonlinear. Two important issues are often found to create difficulties in such analyses. First, numerical oscillations are usually observed in the calculated pore pressures at the wetting front. Second, when a reasonable mesh size and time step are used, the elevation of the wetting front may be seriously overpredicted. This paper is focused on the second issue. The under-relaxation (UR) technique used in the iterative process within each time step is found to have a serious impact on rate of convergence with refinement in mesh size and time step. Two different techniques are typically used; the first evaluates the hydraulic conductivity using an average of heads calculated from the preceding time node and the most recent iteration of the current time node (UR1), and the second evaluates the hydraulic conductivity using the average of heads calculated from the two most recent iterations of the current time nodes (UR2). The study shows that UR1, which is adopted in programs such as SEEP/W, ensures that the solution converges rapidly to a stable solution within a time step, but may converge to the wrong wetting front at a given elapsed time unless a sufficiently refined mesh is used. UR2 converges much more slowly within a time step, but the error in the wetting front is smaller than that generated by UR1.     

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.     

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.”     

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.     

Critical Review of the Methodologies Employed for Soil Suction Measurement

Modeling the behavior of unsaturated soils necessitates the measurement of soil suction and the establishment of its variation with the water content, which is commonly known as the soil-water characteristic curve (SWCC). Several methodologies have been developed for measuring either total suction ψ (sum of matric suction ψm and osmotic suction ψo) or ψm. While employing different methodologies for suction measurement, there is a possibility that various factors (viz., type of the soil, measurement methodology, range of the suction measurement, equilibration time, and presence of salts or contaminants in the soil) may influence the results and hence the SWCC. Therefore, it is essential to investigate the uniqueness of SWCC, determined by using some commonly adopted suction measurement methodologies. This study indicates that the SWCC established by adopting different methodologies may not be unique and is primarily influenced by the range of suction measurement. As such, it is essential to highlight the range of suction values involved for establishing the SWCC, to facilitate unambiguous modeling and to precisely understand the behavior of unsaturated soil.     

Normalizing Behavior of Unsaturated Granular Pavement Materials

One of the important components of a flexible pavement structure is granular material layers. Unsaturated granular pavement materials (UGPMs) in these layers influence stresses and strains throughout the pavement structure, and have a large effect on asphalt concrete fatigue and pavement rutting (two of the primary failure mechanisms for flexible pavements). The behavior of UGPMs is dependent on water content, but this effect has been traditionally difficult to quantify using either empirical or mechanistic methods. This paper presents a practical mechanistic framework for determining the behavior of UGPMs within the range of water contents, densities, and stress states likely to be encountered under field conditions. Both soil suction and generated pore pressures are determined and compared to confinement under typical field loading conditions. The framework utilizes a simple soil suction model that has three density-independent parameters, and can be determined using conventional triaxial equipment that is available in many pavement engineering laboratories.