Coupling between anisotropic damage and permeability variation in brittle rocks

Abstract

SUMMARYIn this paper, a coupled constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks under deviatoric compressive stresses. The formulation of the model is based on experimental evidences and main physical mechanisms involved in the scale of microcracks are taken into account. The proposed model is expressed in the macroscopic framework and can be easily implemented for engineering application. The macroscopic free enthalpy of cracked solid is first determined by approximating crack distribution by a second-order damage tensor. The effective elastic properties of damaged material are then derived from the free enthalpy function. The damage evolution is related to the crack growth in multiple orientations. A pragmatic approach inspired from fracture mechanics is used for the formulation of the crack propagation criterion. Compressive stress induced crack opening is taken into account and leads to macroscopic volumetric dilatancy and permeability variation. The overall permeability tensor of cracked material is determined using a micro-macro averaging procedure. Darcy's law is used for fluid flow at the macroscopic scale whereas laminar flow is assumed at the microcrack scale. Hydraulic connectivity of cracks increases with crack growth. The proposed model is applied to the Lac du Bonnet granite. Generally, good agreement is observed between numerical simulations and experimental data.

Cyclic and Fatigue Behaviour of Rock Materials: Review, Interpretation and Research Perspectives

“…However, damage is inherently anisotropic since it depends on the orientation of cracks. Shao et al (2005) develop an anisotropic damage constitutive law for that purpose. However, in this case, a scalar damage variable is insufficient.…”

Influence of strain energy released from a test machine on rock failure process

“…Obviously, it is difficult to calibrate the post-peak deformation behavior of rock in the numerical experiment by referring to the laboratory test results because the mechanical behavior of rock is essentially heterogeneous (Feng and Hudson 2010;Martin and Chandler 1994;Tang et al 2000). In the post-peak deformation stage, localized failure normally takes place (Bobet and Einstein 1998;Hudson and Harrison 2001;Rudnicki and Rice 1975;Shao et al 2005). In addition, direct measurement of the stress state and the development of plastic strain in specimens in laboratory tests is difficult.…”

Computational modelling of crack-induced permeability evolution in granite with dilatant cracks

“…The tetrahedral elements are considered to have a fixed permeability, whereas the local permeability evolution in the interfaces is taken into account in the fluid transport simulations by means of relationships (26) and (28), with a factor f = 0.8. The resulting axial permeability evolution for the confining pressure of σ 3 = 10 MPa is given in Figure 5a, where experimental results reported in [11] are included, and where comparisons with modelling results from [64,87] are also depicted. As can be seen, the trend of perme-ability increase by several orders of magnitude is correctly reproduced, even though the sharp transition at a deviatoric stress of approximately 200 MPa is not present in the simulations.…”