Effective Stress Principle for Partially Saturated Rock Fractures

Abstract

Soils and rocks are commonly characterized as a porous or fractured medium, with liquid and gaseous fluids occupying and moving in the void space. The presence of water in the void space remarkably influences the deformation behaviors, mechanical properties and stress states of soils and rocks. It has been well recognized that the induced volume change, deformation and shear strength decrease of soils and rocks do not depend on the total stress applied, but on the effective stress defined at the saturated state due to the difference between the total stress and the fluid pressure in the pore space. The deformation of soils and rocks further alters the pore or fracture network and induces a nonnegligible variation in hydraulic properties (Kirby 1991; Chen et al. 2007; Li et al. 2014a). Therefore, the concept of effective stress plays a dominant role in understanding the coupled hydromechanical behaviors of soils and fractured rocks. Von Terzaghi (1923) pioneered the principle of effective stress for saturated soils, in which the effective stress was defined as the difference between the total stress and the pore water pressure: r0 1⁄4 r uw ð1Þ where r denotes the total stress, uw the pore water pressure, and r0 the effective stress. The pores and voids of an unsaturated soil, however, are only partially occupied by water, with the rest being occupied by air, which leads to a different stress state in the soils. A modification of Terzaghi’s effective stress principle is therefore required for unsaturated soils. Bishop (1959) proposed the principle of effective stress for unsaturated soils by introducing an effective stress parameter into Eq. (1): r0 1⁄4 r ua ð Þ v uw ua ð Þ ð2Þ