A Micromechanical Model For Coupled Damage And Permeability In Quasi-Brittle Rock Based On The Deformation And Growth Of Elliptic Microcracks

Microcracks and microvoids are the main microdefects in quasi-brittle rocks. Damage develops with the nucleation and growth of microcracks during deformation processes. The permeability of materials may change with the development of damage. When water (fluid) infiltrates into a microcrack, an additional opening stress is applied to the surface of microcracks, which may accelerate the growth of microcracks and the evolution of the damage of materials. In many rock engineering applications, damage and its evolution play a significant role in the constitutive behavior and permeability of materials subjected to coupled stress and seepage. Much effort has been made in constitutive modeling of coupled damage and permeability in quasi-brittle rocks, which is based on the deformation and growth of microdefects and could realistically describe the development of damage and permeability. In order to describe the properties of a microcracks system more exactly, the microcracks in materials should generally be assumed to be elliptic. In this dissertation, based on a micro-mechanics damage model and a statistical method, the influence of the deformation, growth, frictional sliding, and kinked growth of microcracks on the compliance and permeability of quasi-brittle rock materials is studied. These microcracks are assumed to be embedded in infinite isotropic elastic matrix subjected to different states of stress. A unified constitutive model for the damage and permeability of quasi-brittle rock materials is obtained with the Taylor's scheme, taking into account the hydraulic pressure on the surfaces of microcracks. The compliance and its changes of a representative volume element (RVE) containing an embedded elliptic crack is analyzed, taking into account different patterns of deformation and growth of the crack under different states of stress, for example, the deformation and growth under tensile stress, and the frictional sliding and kinked growth under compressive stress. The steady growth of the mirocrack and the influence of confined pressure on the kinked growth of the microcrack are considered. The additional compliance tensor induced by a randomly oriented embedded elliptic microcrack is then derived.The deformation and growth of the elliptic microcrack under general states of stress are considered. The additional compliance induced by a single closed elliptic microcrack is derived. A simplified method to analyze the kinked deformation of the closed elliptic microcrack is suggested. The permeability of quasi-brittle rocks may consist of two parts: the permeability of the matrix, and the additional permeability induced by microcracks. Microcracks may open under some states of stress and hydraulic pressure, and form numerous additional seepage channels, which significantly increase the permeability of the rocks. The variation of permeability is closely related to the growth of microcracks. Based on these concepts and making use of the Darcy's law and the modified cubic law of laminar flow, the additional permeability of a single crack is deduced. The seepage channels and crack connectivity coefficient during the deformation and growth of microcracks are discussed, and the effect of a randomly oriented microcracks system on the permeability of a rock material is then derived.A three dimensional unified micro-mechanical constitutive model for coupled damage and permeability is constructed by combining the model obtained under triaxially tensile stress with that under triaxially compressive stress. A user subroutine UMAT for the materials with randomly oriented elliptic microcracks is developed and embedded in commercially available finite element code ABAQUS. Taking the underground gas reservoir Yunying Salt Mine as an example, the deformation at different internal pressures is studied, and its influence on the permeability is predicted.A micromechanical damage model is built for laminated salt rocks with a mixture theory. The triaxial compressive testing result of Yunying laminated salt rock is analyzed. The influence of confined pressure on the equivalent additional stress is discussed. The numerical results agree well with experimental results, demonstrating the validity of the developed approach.