Abstract

The author of this paper has published in recent years a concept for defining and developing mathematical models for calculating the effective stress in cohesive rocks. The present paper describes two applications of this concept on cohesive, porous and non-fractured rocks. The first application shows the evaluation methodology for constants of the material and geometrical parameters, quantifying pores' size, shape, distribution and arrangement. The second application shows the effective stress distribution around a vertical drill hole. In both applications, the author's results are compared with those obtained by Terzaghi model – one of the models commonly used in similar situations.

1 Introduction
The first appeared (published in 1936) and one of the most known and used calculation models of effective stresses in discontinuous rocks is Terzaghi model (Terzaghi & Peck 2010):
$σ′=σ−p, τ′=τ$
(1),(2)

where σ and τ are apparent values of normal, respectively tangential stress, σ' and τ' are the real (effective) stress values, and p is the fluid pressure in pores. Usually, the apparent values are called apparent stresses, and real values – effective stresses.

Terzaghi developed the model based on experimental research studies conducted on soils, grounds and – mostly, on non-cohesive rocks. Later and so far, some experts used this model for any type of rock, including cohesive rocks. Besides Terzaghi model, in published literature there are other effective stress models, but – it seems that there is no general valid concept to define used notions and to regulate development of calculation mathematical models for any situation, as type of rock and mechanical loading.

Starting from known principles of Deformable Solid Mechanics – which are used to define and evaluate stress in continuous materials, the author of this paper proposes a concept of definition and evaluation of effective stresses in discontinuous cohesive rocks materialized by the following rules (Ciobanu 2011a):

• Within calculation of effective stresses to be included all mechanical loadings, both external forces – acting on the boundary that separates the gross volume of rock, and internal forces acting on the surface of existing discontinuities within rock.

• Internal forces must be calculated in compliance with the rules used in case of external and known forces in Mechanics.

• The parameters and measurement techniques of rock discontinuities shall be improved for a more accurate assessment of the effective area whereby transmitting internal tensions of material.

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