On the propagation of an in-plane shear fault with super-S-wave velocity

The speedv, especially the problem whether super S-wave velocity in the classical model (linear elasticity fracture mechanics) exists, of spontaneous propagation of a shear fault is investigated theoretically. An in-plane shear crack propagating in the crack plane is taken as the model of the shear fault. The results obtained firstly by Kostrov (1975) is extended from sub-Rayleigh wave velocity to super S-wave velocity, and the analytical expression for the stress intensity factorK ₂ in the case ofα>v>β is derived. It is proved that for Poisson mediumK ₂ is positive and real in the velocity range (β, 1.70β). This demonstrates that (β, 1.70β) is the velocity range which fulfils the conditions for spontaneous crack propagation. The existence, convergence and positiveness or negativeness ofK ₂ forv in individual sections are examined, and it is found that for an in-plane shear crack: 1. There are three sections forv, i.e., 0.v _R], (β, 1.70β), andα, respectively, and 2. There are two physically reasonable sections forv, the first is v _R, β], and the second is 1.70β, α]. These two forbidden sections behave as barriers to fault propagation. The analytical expressions derived in this paper are not only suitable to classical model, but also to the other derivative models (e. g., the slip-weakening model and the renomalization model etc.). The model considered in this paper is more realistic than the static model employed by previous authors. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica, 15, 9–14, 1993.