Theory of earthquakes

Summary

A scale independent failure theory governing the initiation and subsequent growth of the shear fault in rock is presented in this article. Four distinct phases of behavior in this theory are shown to precede fault growth in rock. 1)Dilatant Phase: Cracks form in the rock in response to the applied stresses. This phase begins at a maximum principal stress whose magnitude is usually well below the ultimate strength of the rock. 2)Inclusion Phase: Clusters of cracks develop in the rock at a point in time when the rock is within a few per cent of its ultimate strength. The clusters behave physically as low modulus elastic inclusions embedded within a host material of higher modulus. As a result of this ‘elastic’ contrast, there is a rotation of the principal stress axes and a decrease in the magnitude of the principal stress difference in the focal region of the inclusion; that is, the region into which the inclusion will grow at failure. 3)Closure Phase: In this phase, there is closure of cracks in the focal region in response to the decrease in the magnitude of the principal stress difference due to the formation of the inclusion. As a result of crack closure in the focal region, the stress concentration in the focal region increases and becomes a maximum once all cracks which opened during the dilatant phase are closed. At this time, the transverse tensile stress in the interior of the inclusion also reaches a maximum. Macrocrack growth within the inclusion begins. 4)Growth Phase: Fault growth commences during this phase. Reopening of previously closed cracks occurs due to the increase in the principal stress difference in the focal region resulting from macrocrack growth within the inclusion. New cracks form and rapid growth of the macrocrack (in its own plane) occurs once the length of the mecrocrack exceeds a critical value. The fault represents the portion of the macrocrack which has closed.