Subsonic and intersonic shear rupture of weak planes with a velocity weakening cohesive zone

Abstract

A substantial effort has been devoted in the past toward modeling earthquake source mechanisms as dynamically extending shear cracks. Most of the attention was focused on the subsonic crack speed regime. Recently, a number of reports have appeared in the seismological literature citing evidence of intersonic rupture speeds during shallow crustal earthquakes. In the first part of this paper, we discuss direct experimental observations of intersonic in-plane shear crack growth along a weak plane joining two homogeneous, isotropic, linear elastic plates. Associated with the primary intersonic crack and at locations behind the propagating shear crack tip, a series of secondary tensile cracks, at a steep angle to the shear crack plane, were also observed. Motivated by these observations, subsonic and intersonic mode II crack propagation with a velocity weakening cohesive zone is analyzed in the main body of the paper. A cohesive law is assumed wherein the cohesive shear traction is either a constant or decreases linearly with the local slip rate, the rate of decrease governed by a slip rate weakening parameter. The cohesive shear traction is assumed to vanish when the crack tip sliding displacement reaches a characteristic breakdown slip. It is shown that a positive energy flux into the rupture front is possible in the entire intersonic regime. The influence of shear strength and of the weakening parameter on the crack propagation behavior is investigated. Crack tip stability issues are also addressed, and favorable speed regimes are identified. Estimates of the slip rate weakening parameter are obtained by using the theoretical model to predict the angle of the secondary cracks. The rest of the parameters are subsequently estimated by comparing the isochromatic fringe patterns (contours of maximum in-plane shear stress) predicted by the solution with those recorded experimentally.

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