A closed‐form equation for effective stress in unsaturated soil

Abstract

[1] We propose that the recently conceptualized suction stress characteristic curve represents the effective stress for the shear strength behavior of unsaturated soil. Mechanically, suction stress is the interparticle stress called tensile stress. The working hypothesis is that the change in the energy of soil water from its free water state is mostly consumed in suction stress. We demonstrate that the suction stress lies well within the framework of continuum mechanics where free energy is the basis for any thermodynamic formulation. Available experimental data on soil water characteristic curves and suction stress characteristic curves are used to test the hypothesis, thus validating a closed-form equation for effective stress in unsaturated soil. The proposed closed-form equation is intrinsically related to the soil water characteristic curve by two pore parameters: the air entry pressure and pore size spectrum number. Both semiquantitative and quantitative validations show that the proposed closed-form equation well represents effective stress for a variety of earth materials ranging from sands to clays. Of important practical implications are (1) the elimination of the need for any new shear strength criterion for unsaturated soil, (2) the elimination of the need for determining the Bishop's effective stress parameter c because the new form of effective stress is solely a function of soil suction, and (3) the ready extension of all classical soil mechanics work on limit equilibrium analysis to unsaturated soil conditions.

Neutron Radiographic Study of the Effect of Heat-Driven Water Transport on the Tensile Strength of Bentonite-Bonded Moulding Sand

“…The increase in tensile strength is in accordance with the theoretical model of Lu et al (2009) for sands. The decrease at higher water contents indeed indicates a clay-like behaviour (Lu et al 2010).…”

“…The observed initial increase of green tensile strength with water content is in accordance with the numerical model derived by Lu et al (2009) for the tensile strength of moist sands. For clay, the numerical model of Lu et al (2010) yields a negative correlation of tensile strength with increasing moisture. The observed decrease of the green tensile strength at water contents higher than 3 wt.% (which corresponds to a saturation of less than 10 vol.%), therefore, may indicate that the mechanical behaviour of the moulding sand is increasingly dominated by the clay minerals.…”

Effect of Pore-Water Surface Tension on Tensile Strength of Unsaturated Sand

“…Another drawback of this approach is that it cannot be reconciled with classical soil mechanics, wherein, effective stress (single stress variable) can be used for both shear strength and deformation or volume change analyses (Lu et al 2010). Suction stress is a function of soil matric suction and, thus, it depends on degree of saturation as well.…”

Bridging Effective Stress and Soil Water Retention Equations in Deforming Unsaturated Porous Media: A Thermodynamic Approach

“…(4) and (5) indicates that the effective stress parameter and the effective degree of saturation are related. In fact, in the literature we find various equations for the effective stress parameter as a function of (or simply being equal to) effective degree of saturation (Lu et al 2010). Vanapalli et al (1996), for instance, expressed the contribution of the suction to shear strength of unsaturated soils τ us = χ p c tan φ , as follows:…”

“…The effect of net stress (stress level) on the soil water retention properties and consequently on the effective stress parameter has been mostly studied experimentally (Oh and Lu 2014) rather than through rigorous theoretical frameworks such as mixture theory. While some researchers such as Lu et al (2010) and Nikooee et al (2013) have resorted to an energetic and thermodynamic approach to formulate the effective stress in unsaturated soils, they have not looked into the stress-level dependency of hydraulic parameters directly and possible higher-order couplings it may bring about. A theoretical study is therefore essential to identify the scope of applicability of current formulations and to arrive at a most comprehensive formulation for the stress measures accounting for the all aspects of hydromechanical coupling.…”