Effective stress, Terzaghi

According to the Terzaghi principle, the effect of pore fluid pressure (P) and total stress (5) on tensile failure can be described by the Terzaghi effective stress o (Hubbert and Rubey, 1959), given by... 

Zhao (1994) presented a model of coupled coal deformation and methane migration based on a consolidation theory of elastic medium with Darcy fluid flow and the Terzaghi effective stress law, and its numerical solution technique and applications to practical problems. Works using similar approaches were also reported in Liang et al. (1995,1996), Sun and Xian (1999), Ding et al. 

According to the Mohr-Coulomb Criterion and Terzaghi s effective stress principle, the maximum equilibrium pore pressure can be derived as... 

According to the revised Terzaghi s effective stress principle, the equilibrium equation of the reservoir matrix can be written... 

The equation (10) can be written in terms of transient hydraulic head, h. To do so, simply introducing Terzaghi s principle of effective stress o = ol + p (Terzaghi, 1925) and Hubbert s potential h = z+ply into (10) yields in terms of hydraulic head in the following form ... 

In this equation, the thickness h, pressure p and permeability K are in general coupled. To relate these, one must consider equilibrium of forces within the preform. At the foundation of such an analysis is Terzaghi s principle of effective stress, which states that the effective stress <7j carried by the solid skeleton is the difference between the total applied stress a and the pore fluid pressure p ... 

Any deformation of the solid skeleton is due to this effective stress. Being a principle, Terzaghi s Law does not rely on any proof, and indeed was formulated through experimentation and intuition .Nevertheless, because of its centrality to the theory, it is instructive to see how it relates to the underlying... 

Soil is a mixture of a solid phase, a liquid phase (i.e., water) and a gaseous phase. Saturated soil is a two-phase material which consists of a solid phase and a liquid phase. The formulation of a theory for a saturated soil commenced with the concept of the effective stress of Terzaghi at the beginning of the twentieth century, and Terzaghi s concept was extended by Biot to a three dimensional consolidation theory. 

Terzaghi expressed the total stress of particulate aggregate by the pressure in void P and the effective stress tr, as follows,... 

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