Alvarez-Tostado Sanchez, Juan Manuel; (1998) Micromechanical model for dilatant crack growth in brittle materials, with applications to rock physical properties. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Brittle behaviour is an important characteristic of crustal rocks, it accounts for the seismic behaviour of the crust, helps to elucidate the flow of fluids and melts, the transport of dissolved minerals and the transmission of heat in the crust. This thesis is centred on the formulation of a theoretical model of microcrack growth to simulate the effect of cracks on deformation and the consequences on some physical properties of brittle materials subjected to external loads. The model, which is two-dimensional (using the plane theory of elasticity), is based on the formation of new dilatant cracks (NDCs) from pre-existing (Griffith type) cracks (PECs). The driving force that opens the NDCs is the intensified tensile stresses occurring near the PEC crack tips. NDCs relax the relative displacement between the crack surfaces of the PECs. The trajectories and lengths of the NDCs are calculated. They are a function of the PEC orientation. Their growth is stable over a range of applied compressive stresses, but at higher loads NDCs can become unstable. The introduction of confining pressure widens the range of stability and changes the direction of growth of the NDCs. The formation of NDCs depends on the PEC orientation relative to the applied stress field, so that as the stress increases, PECs with a wider range of orientations create NDCs. Although the orientation of PECs is isotropic, the resulting NDC population is highly anisotropic. Three consequences of the formation of NDCs are considered. The first of these is the cumulative acoustic emission (AE) which results from NDC formation, which is compared with experimental data. The second is the peak strength and fracture of a brittle body, and here again comparison is made with experimental data. Thirdly the effect of NDCs on elastic properties of a body is worked out. Because the theory is two-dimensional exact quantitative comparison can not be made with experimental data, which is inherently three-dimensional. However, qualitative comparison is possible. In addition, by using the concept of crack density tensor, information about the crack orientation distribution in an actual deformed body is obtained from measurements of elastic waves velocities. The variation of crack density ϵ and anisotropy coefficients (α11, α22, α33) with applied load is determined.

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