Measuring Terzaghi’s effective stress by decoding force transmission in fluid-saturated granular media

Abstract

Force transmission between solid and fluid phases in fluid-saturated granular systems is yet to be fully resolved. This is rooted in our inability to measure inter-particle forces in opaque systems in the presence of fluids. At the same time, the concept of effective stress was introduced by Karl Terzaghi a century ago, but this empirical approach is yet to be linked to grain-scale phenomena experimentally. To this end, we derive an expression for the effective stress based on inter-particle forces and use a hybrid optical–mechanical method to directly measure the evolution of inter-particle forces and effective stress, offering a new perspective on how forces are distributed between solid and fluid phases. While our derivation and measurement of effective stress focuses on the limiting case of the Terzaghi stress, the methodology presented herein could be extended to more general situations, such as unsaturated conditions, where the micro-mechanical origin of effective stress remains elusive.