A closed‐form equation for effective stress in unsaturated soil

TLDR

Suction stress is the interparticle tensile stress in unsaturated soils. The study proposes that the suction stress characteristic curve represents effective stress for shear strength in unsaturated soil. The authors hypothesize that the energy change of soil water is largely stored as suction stress, derive a closed‑form effective stress equation linked to the soil water characteristic curve via air entry pressure and pore size spectrum, and situate it within continuum mechanics. Validation with experimental data confirms the equation accurately represents effective stress across sands to clays, eliminating the need for new shear‑strength criteria, Bishop’s χ, and enabling classical limit‑equilibrium analyses under unsaturated conditions.

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 χ 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.