Effective Stress and Shear Strength of Moist Uniform Spheres

In continuum soil mechanics, the mechanical behavior of an element of soil is related to the effective stress, which is a measure of the average stress transmitted through the solid matrix in the form of contact stresses. In unsaturated soils, the coexistence of water and air within the soil pore space complicates this concept because the microscopic distribution of each fluid phase in soil pores cannot be known. Because it is thus not possible to physically measure effective stress in unsaturated soils, it is often estimated through the experimentally measurable shear strength. A conceptual model based on contact shear forces was built on the contact normal force based models from the literature to link effective stress and shear strength of the continuum to total stress and microscopic pore fluid forces for the simplified case of uniform spherical particles at low water contents. The validity of both models was examined by comparing model predictions of shear strength with the results of drained triaxial compression tests performed on specimens of uniform glass spheres. Although the shear strength calculated by the new model was consistently larger than that calculated via the contact normal force models, values measured in the experiments were even larger. Nevertheless, the test results fit what the new model analytically showed: the friction angle of a soil does not change with desaturation, and introducing moisture in the form of liquid bridges at contacts is fundamentally different from applying an equivalent isotropic stress to the soil externally.