Effective Stress for Saturated and Unsaturated Porous Media– A Differential Approach

Abstract

Here we theoretically derive the Terzaghi stress principle for saturated and partially saturated isotropic, porous media with compressible phases. We use previously derived thermodynamic deinitions of the drained and unjacketed compressibilities and total differentials to theoretically determine how the total pressure relates to isotropic strain and changes in luid pressures. We show that under simplifying assumptions we recover the varying forms of the Biot coeficient for saturated porous media and the Bishop parameter for partially saturated porous media. We compare this approach with four modern constructions: the mixture theoretic approaches of Coussy and Borja, Wang's differential approach, and the thermodynamically constrained averaging theory approach of Gray and Schreler. In doing so we theoretically clarify the often confused deinitions of the solid compressibility coeficient, the unjacketed and drained compressibilities, and the generalized Terzaghi stress principle in differential form.

Principle of Effective Stress in Variably Saturated Porous Media

“…In “Effective Stress for Saturated and Unsaturated Porous Media—A Differential Approach,” Schreyer‐Bennethum (2014) revisited Terzaghi's effective stress for saturated and unsaturated isotropic porous media filled with compressible fluids. She presents a theoretical framework based on previously derived thermodynamic definitions of the drained and unjacketed compressibility and total differentials (Bennethum, 2006), which determines how the total pressure relates to strain and changes in fluid pressures.…”

Deformation behaviour of geotechnical materials with gas bubbles and time dependent compressible organic matter

“…where ∆Vsks and ∆Vgs are the volumetric compression of the skeleton and grains due to the change of total confining pressure respectively; ∆Vsku and ∆Vgu are the volumetric compressions of the skeleton and grains due to the change in pore water pressure respectively; and ∆Vw and ∆Va are the volumetric compressions of water and air bubbles, respectively. Much research has been conducted thereafter to study the effect of particle and fluid compressibility on the behaviour of geotechnical materials (Borja, 2006;Vlahinic et al, 2011;Schreyer-Bennethum, 2014;Molenkamp, 2014).…”