Effective Stress from Force Balance on Submerged Granular Particles

Abstract

A new equation for effective stress is derived from a physically based approach of force balance on submerged granular particles. The Euler cut principle and the Euler’s first law of mechanics are used to analyze the interparticle contact stress in a fluid saturated porous media. The analysis starts from basic principles and provides a detailed derivation of the formulas. Tensor algebra together with Coulomb’s friction law, the mean value theorem and area weighted averaging techniques are used to simplify the mathematical formulation leading to effective stress. A new mathematical constraint, requiring spatially averaged interparticle contact stress to be orders of magnitude larger than spatially averaged pore pressure, is presented for the widely used Terzaghi’s effective stress equation.