ABSTRACT

One of the most significant parameters in hydromechanical analyses is Biot coefficient. This coefficient which was presented by Biot, is used when the Terzaghi's effective stress equation is considered for a porous medium. Since determination of this coefficient is complicated, its value, generally, is assumed equal 1 while this coefficient has a noticeable effect on hydro-geo mechanical analysis' results. According to the known relationship among elastic moduli, Biot coefficient was defined as a function of rock porosity and elastic modulus for porous rocks such as sandstone. Since elastic modulus (E) and porosity can be easily determined by conventional laboratory tests, calculation of Biot coefficient will be possible by the method proposed in this paper.

1.
Introduction

In stability analysis of tunnels, wells, etc., where underground space is excavated in or drilled into an immersed or semi-immersed porous medium, performing a coupled hydro-mechanical stability analysis is unavoidable. Such analyses are more popular for well stability, sand production, etc. where a high pressure fluid is flowing through a porous medium. In these cases, Terzaghi's effective stress theory should be used [1]. Therzagh's theory was reviewed by Biot and a coefficient was added to original equation [2]. Based on Biot formula, value of effective stresses is considerably affected by Biot coefficient; hence, its determination is necessary. Since calculation of this coefficient is not simple, a practical simple method was proposed in this paper in which Biot coefficient could be calculated as a function of elastic modulus (E) and porosity of rocks. At the end of the paper, the value of Biot coefficient was calculated for sandstone cores obtained from a reservoir in southwe.

2.
Definition of Biot Coefficient

Terzaghi presented the concept of effective stress between 1925 and 1936 as Eq. (1) [1]: ij ij ij σ ′ =σ − pδ (1) In this equation, σ´ij is components of effective stresses, σij is components of total stresses and p is pore pressure. On the basis of mathematical equations Biot modified the Eq. (1) for homogenous porous media and then presented Eq. (2): ij ij ij σ ′ =σ −αpδ (2) In Eq. (2), α is the Biot coefficient and varies from 0 through 1. If α=1, the Eq. (2) will be changed to Terzaghi's equation (Eq. (1)). Biot presented the α coefficient as follow: s K α = 1− K (3) In this equation, K is bulk modulus of porous medium and Ks is bulk modulus of solid parts of porous medium. Since Ks>>K, the K/Ks ratio tends to zero; therefore, α will become one. Because determination of K and Ks is not easy in laboratory, it is not possible to calculate the α coefficient using Eq. (3).

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