The Biot consolidation theory allows the formulation the effective stress law in the form of equation binding the components of the stress tensor with the value of pore pressure. This equation contains certain factors (the so-called Biot coefficients) which are mathematical functions of the rock porosity (n), rock bulk modulus (K and bulk modulus (KS) of rock solid phase (matrix). The article is devoted to the study of the impact of the pore fluid type on the values of Biot coefficients.
Some specimens cut from two rocks: sandstone and gaize were tested in the laboratory. At first the specimens were tested in pycnometer to determine their bulk and helium densities. Then, on the basis of the measured densities porosity of the studied rocks were calculated.
Compressibility tests were performed at four different pore fluids: two liquids (distilled water and kerosene), and the two gases (nitrogen and carbon dioxide). The K modulus was determined on the basis of experiments in which the pore fluid pressure was equal to atmospheric pressure, and KS modulus was based on experiments in which the pore fluid pressure was equal to the confining pressure. All compressibility tests were drained ones.
Experiments results have shown that the values of K and KS moduli (and thus the values of the Biot coefficients) depend on a relatively small extent on the type of fluid filling the pore space of the rock specimen. It seems that these values are determined by two main factors: the degree of filling the rock pore space with fluid and filtering capabilities of fluid in the rock pore space. The tests have indicated, that the Biot coefficients can be determined correctly only when the entire pore space is filled with fluid and porous fluid filtration is free within the sample.
The term "effective stress" was introduced into soil mechanics by the turn of the XIX century by Paul Fillunger (1913–1915) and Karl von Terzaghi (1923). It gave grounds to build a mathematical model of some phenomena taking place in soil with pore fluid under pore pressure pp. Maurice Biot (1941) developed Terzaghi's concept by using Hooke's lawequations and introducing proprietary sets of equations for elastic, homogeneous and isotropic porous medium given by (see Paterson & Wong (2005) – pp. 149–152, Fabre & Gustkiewicz (1998), Gustkiewicz (1989)):