Shear cracks in thermoplastic and poroelastic media

Abstract

T o understand the mechanism of quasi-static plane strain fracture in poro- and thermoelastic materials for arbitrary stress fields, it is necessary to consider not only tensile fracture but also shear fracture. An impulsively sheared semi-infinite crack is considered for the mathematically analogous cases of coupled quasi-static thermo- and poroelastic materials. The exact solution is obtained in Laplace and Fourier transform domains using the Wiener—Hopf technique. The crack tip behaviour is then analysed. The stress intensity factors as a function of the Laplace transform variable are identified for cracks with either permeable (conducting) or impermeable (insulating) crack faces, and are inverted numerically for all times and asymptotically for small times. The case of a steadily propagating shear crack with either permeable or impermeable crack faces is also examined; the crack tip behaviour is examined in detail and compared with the result for a permeable fault. Analytical results are found in the neighbourhood of the crack tip. The pore pressure fields are found explicitly for all x and y.The case where the entire fault is assumed impermeable is reworked and an analytical solution is given for the pore pressure. The relevance of the results for stabilising shear faults and earthquake mechanics is briefly discussed. For the most part, the solutions in this paper and an earlier one refer to situations involving a complete coupling of the poroelastic equations and boundary conditions. This occurs when the material ahead of the crack is continuous and is relevant to the fracture of “virgin” rock. In the other papers cited in this article and elsewhere this has not usually been the case; the interface along which the crack propagates has usually been assumed to have a particular property as far as the pore pressure is concerned. It is worth stressing that the most complete situation is considered here; the pore pressure condition ahead of the crack is set only by the anti-symmetry (or symmetry) of the problem and the condition on the crack faces is set by the physical situation.