Indefinability of Effective Stress for Unsaturated Soils

For decades, researchers have searched for an unsaturated soil effective stress that performs analogously to effective stress for saturated soils and provides some simplifications over net stress and suction approaches. A recent debate is whether problems identified with unsaturated soil effective stress can be resolved via elastoplastic analyses. Effective stress equations are reviewed and categorized as being based on volume change, shear strength, yield, or degree of saturation. These equations are evaluated for consistency with saturated soil effective stress expectations using the Barcelona basic model (BBM), simplified into an integrated elastoplastic framework using the modified state surface approach (MSSA). Under isotropic conditions, saturated soil constant volume and yield curves are coincident, and the effective stress principle applies. In contrast, unsaturated soil constant volume and yield curves diverge, which is at root to the indefinability of an effective stress for unsaturated soils. Although effective stress for saturated soils has been defined on the basis of volume change, unsaturated soil effective stress is often defined on shear strength or degree of saturation, with attempted extrapolation to more general volume change and yield responses. Effective stress equations, when used for constitutive modeling of unsaturated soils, cannot recover the form of saturated soil effective stress models, nor provide the often-asserted simplifications or analytical economies. It is demonstrated that volume change and/or yield can occur under any constant unsaturated soil effective stress. It is shown that it is impossible to define an effective stress for unsaturated soils that functions analogously to that of saturated soils. An effective stress approach for unsaturated soils is demonstrated to be, at most, a mathematical transformation, which may provide simplifications for some limited usages.