STEADY PROPAGATION OF PLANE STRAIN SHEAR CRACKS ON AN IMPERMEABLE PLANE IN AN ELASTIC DIFFUSIVE SOLID J. W. RUDNICKI and D. A. KOUTSIBELAS Department of Civil Engineering. Northwestern University. Evanston. IL 60101(. U.S.A. (Rwcired 7 Scprcmher 1989 : in rerisedfurm IO Junuur~ 1990) Abstract-Quasi-static shear crack propagation in a linear elastic fluid-saturated porous solid c;Iuses a change of pore pressure on the crack plane if it is impermeable but not if it is permeable. Assuming that the pore pressure induced on the crack plane reduces the efTcclive compressive stress (total stress minus pore fluid pressure) and. as a result. the frictional resistance. we find that the energy required to drive the crack is decreased by up to about 60% of the value required in a purely elastic solid. The required energy decreases with velocity at low and high velocities. but increases with velocity for C’//c in the range of IO” ‘-IO’. where c’is the speed of propagation, I is the loodcd length of the semi-infinite crack and c is the diffusivity. When the erect of the pore prcssurc induced on the crack plane is neglected. the results are quahtatively similar lo those of Rice and Simons (1976. 1. Gcvplr,u. Rcs. RI. 53 2?-SNJ) for the permeable crack: coupling bctwcwn dcformarion and _ dilrusion stabilizes propapalion in the sense that the energy that must bc supplied to drive rhc crack incrcascs with velocity within a tinitc range of the ratio 27/c. This range of I’/ c is about an order of magnitude lower than Ihat for the permcahlc crack. hut includes fhc range cited above and is wlthin the range of ohscrvcd creep events on the San Andrcas faull. INTRODIJCTION This paper annlyzcs the stress and pore prcssurc fields induced by ;I plane strain shear (Mode II) crack propagating steadily and quasi-statically in a linear elastic. fluid-infiltrated solid. The response of such a solid, unlike that of an ordinary elastic solid, dcpcnds on the time scale of the appiicd loads. More specifically. the response is stifi’cr for loads that arc appliccl rapidly by comparison with the time scale ofdifl’usion (undrained conditions) than for loads that arc applied slowly enough to allow time for port prcssurc equilibration by fluid mass difi’usion (drained conditions). Conscqucntly, the stress intensity factor of a crack propagating quasi-statically through a diffusive solid depends on the velocity of propagation. Furthermore, this dspendcnce is difT’crcnt dcpcnding on whether the crack plant: is pcrmcablc or impermeable to the diffusing spccics. Consideration of this problem is motivated by applications to the propagation of slip on faults in the Earth’s crust. For reasons that will bc explained in the body of the papsr, previous work on propagating shear cracks in fluid-saturated elastic solids (Rice and Simons, 1976; Simons, 1977 ; Cleary, 1978) is appropriate when the crack plant is pcrmcable to the difTusing pore fluid. [Hereafter, we will, for brevity. denote the rcfcrcncc Rice and Simons (1976) by RS]. However, faults in the Earth’s crust are often thought to be imper- meable (Wu rl al., 1975; Wang and Lin. 1978) because they contain clay or other fine- graincd material. Although slip is not always localized on a discrete plant. intense shear deformation is typically confined to :I narrow zone. Hcncc, for mathcmntical simplicity, WC‘ idcalizc this zone as an impcrmcable plant across which the slip displacement can be discontinuous. The purpose of this paper is to invcstigatc the effects of impcrmcability of the crack plane on the solution. Recent related work (Rudnicki. 1986. 1987; Rudnicki and Hsu. 1988; Rudnicki and Rocloll3;. 1990) has shown that the specification of an impermeable plane can have a significant effect on the stress and pore pressure fields induced by instan- tancous and steadily moving shear dislocations. Previous work on propagating cracks in fluid-infiltrated porous solids (RS; Simons. 1977; Ruina. 1978: Clcary. 1978) has demonstrated that the stifier rcsponsc of the fluid- saturated material to rapid deformations can contribute to stabilizing the crack against rapid propagation. RS (also, Rice and Cleary. 1976) have discussed this stabilizing effect 205
STEADY PROPAGATION OF PLANE STRAIN SHEAR CRACKS ON AN IMPERMEABLE PLANE IN AN ELASTIC DIFFUSIVE SOLID
May 21, 2023
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