Delwyn G. Fredlund

TL;DR: The implementation of unsaturated soil mechanics into geotechnical engineering practice requires that there be a paradigm shift from classical soil mechanics methodology as discussed by the authors, and the primary drawback to this paradigm shift is that it requires a large amount of manual work.

Abstract: Several procedures have been proposed in the recent years to predict the shear strength of an unsaturated soil. The soil-water characteristic curve has been used as a tool either directly or indirectly in the prediction of the shear strength along with the saturated shear strength parameters in these procedures. This paper provides comparisons between the measured and predicted values of unsaturated shear strength using these procedures for three soils both for limited and large suction ranges. The three soils used in the study for comparisons have different gradation properties, percentages of clay and plasticity index, Ip values. The advantages and limitations associated with predicting the shear strength of unsaturated soils using the procedures is discussed in the paper. INTRODUCTION A theoretical framework for unsaturated soil mechanics that parallels saturated soil mechanics is available in terms of stress state variables, namely; net normal stress, (σn ua), and matric suction, (ua uw) where σn is the normal stress, ua is the pore-air pressure an uw is the pore-water pressure. (Fredlund and Rahardjo, 1993). The framework is based on experimental studies that are costly and time consuming. Several advancements have been made in the prediction of the engineering behavior of unsaturated soils in recent years. The soil-water characteristic curve has been found to be a useful tool in the estimation of engineering properties for unsaturated soils. Examples are the coefficient of permeability and the shear strength functions. Shear strength forms an important engineering property in the design of numerous geotechnical and geo-environmental structures such as earth dams, retaining walls, pavements, liners, covers, etc. Several procedures have been proposed in the literature during the past five years to predict the shear strength of an unsaturated soil. __________________________________________________________________________ Department of Civil Engineering, University of Saskatchewan, SK, Canada, S7N 5A9 These procedures use the soil-water characteristic curve as a tool either directly or indirectly along with the saturated shear strength parameters, c’ and φ’, to predict the shear strength function for an unsaturated soil (Vanapalli et al. 1996, Fredlund et al. 1996, Oberg and Sallfors 1997, Khallili and Khabbaz 1998 and Bao et al. 1998). The philosophy used in each of the prediction procedures proposed by these investigators is different. Comparisons have been provided between predicted and measured values of shear strength for a limited suction range for various soils (i.e., between 0 to 500 kPa). Escario and Juca (1989) measured the soil-water characteristic curves and the shear strength of three soils prior to the time when any proposals had been made for the shear strength functions. The three soils have different gradation properties, percentages of clay and plasticity indices, Ip. These results are used in this paper to provide comparisons between the predicted and measured shear strength values both for a limited suction range and a large suction range. The study presented in the paper highlights the advantages and limitations associated with the various procedures for predicting the shear strength of unsaturated soils. The simple procedures discussed in this paper are of value in bringing the shear strength theories for unsaturated soils into engineering practice. EQUATIONS FOR INTERPRETING THE SHEAR STRENGTH OF UNSATURATED SOILS Bishop (1959) proposed shear strength equation for unsaturated soils by extending Terzaghi’s principle of effective stress for saturated soils. Bishop’s original equation can be arranged as shown below. ( ) ( ) ( )( ) [ ] ' tan ' tan ' φ χ φ σ τ w a a n u u u c − + − + = [1] where: τ = shear strength of unsaturated soil, c’ = effective cohesion, φ’ = angle of frictional resistance, (σn ua ) = net normal stress, (ua uw ) = matric suction, and χ = a parameter dependent on the degree of saturation The value of χ was assumed to vary from 1 to 0, which represents the variation from a fully saturated condition to a total dry condition. Several investigators found limitations with respect to the quantification of the parameter χ both theoretically and experimentally. Fredlund et al. (1978) have proposed a relationship to explain the shear strength of unsaturated soils in terms two independent stress state variables as shown below: ( ) ( ) b w a a n u u u c φ φ σ τ tan ' tan ' − + − + = [2] The shear strength contribution due to matric suction, φ , was initially assumed to be linear based on the analysis of limited results published in the literature. Later experimental studies performed over a large range of suction values have shown that the variation of shear strength with respect to soil suction is nonlinear (Gan et al. 1988 and Escario and Juca 1989). Equation [1] can be applied for both the linear and non-linear variation of shear strength with respect to suction. Figure 1. Typical soil-water characteristic curve showing zones of desaturation. The Relationship between the Soil-Water Characteristic Curve and the Shear Strength of Unsaturated soils The soil-water characteristic curve defines the relationship between the soil suction and either the degree of saturation, S, or gravimetric water content, w, or the volumetric water content, θ (Figure 1). The soil-water characteristic curve provides a conceptual and interpretative tool by which the behavior of unsaturated soils can be understood. As the soil moves from a saturated state to drier conditions, the distribution of the soil, water, and air phases change as the stress state changes. A typical soil-water characteristic curve with various zones of desaturation are shown in Figure 1. The wetted area of contact between the soil particles decreases with an increase in the soil suction. There is a relationship between the rate at which shear strength changes in unsaturated conditions to the wetted area of water contact between the soil particles or aggregates. In other words, a relations hip exists between the soil-water characteristic curve and the shear strength of unsaturated soils. Different Procedures for Predicting the Shear Strength of an Unsaturated Soil Vanapalli et al. (1996) and Fredlund et al. (1996) have proposed a more general, nonlinear function for predicting the shear strength of an unsaturated soil using the entire soilwater characteristic curve (i.e., 0 to 1,000,000 kPa) and the saturated shear strength parameters as shown below: ( ) [ ] ( ) ( )( ) { } [ ] ' tan ' tan ' φ φ σ τ κ Θ − + − + = w a a n u u u c [3] where: κ = fitting parameter used for obtaining a bestfit between the measured and predicted values, and Θ = normalized water content, θw/θs. The shear strength contribution due to suction constitutes the second part of [Eq. 3], which is: ( ) ( )( ) { } [ ] ' tan φ τ κ Θ − = w a us u u [4] Equation [3] can also be written in terms of degree of saturation, S, or gravimetric water content, w, to predict the shear strength yielding similar results. The entire soil-water characteristic curve data (i.e., 0 to 1,000,000 kPa) is required along with the saturated shear strength parameters in the use of Equation [3]. A bestfit soilwater characteristic curve can be obtained in terms of a, n, and m parameters using the equation proposed by Fredlund and Xing (1994) which is shown below:

TL;DR: In this paper, the authors present an overview of constitutive modelling of unsaturated soils and numerical algorithms for solving the associated boundary value problems, and show how hysteresis in soil water characteristics can be incorporated into the elasto-plastic framework, leading to coupled hydro-mechanical models.

TL;DR: The analysis of flow through saturated/unsaturated soils has become routine in geotechnical and geo-environmental engineering as mentioned in this paper, and the analysis requires that the coefficient of permeability for an unsaturated soil be defined.