Effective stress law for the permeability of a limestone

The effective stress law for the permeability of a limestone is studied experimentally by performing constant-head permeability tests in a triaxial cell with different conditions of confining pressure σ and pore pressure pf. Test results show that a pore pressure increase and a confining pressure decrease both result in an increase of the permeability, and that the effect of the pore pressure change on the variation of the permeability is more important than the effect of a change of the confining pressure. A power law is proposed for the variation of the permeability with the effective stress (σ′=σ–nkpf). The permeability-effective stress coefficient nk increases linearly with the differential pressure and is greater than unity as soon as the differential pressure exceeds few bars. The test results are well reproduced using the proposed permeability-effective stress law. A conceptual pore-shell model based on a detailed observation of the microstructure of the studied limestone is proposed. This model is able to explain the experimental observations on the effect of the total stress and of the pore pressure on the permeability of the limestone. Effective stress coefficients for the stress-dependent permeability which are greater than one are obtained. It is shown that the controlling factor is the ratio of the different bulk moduli of the various constituents of the rock. This ratio is studied experimentally by performing microhardness tests.