Abstract
The causes leading to slow earthquakes and multiple earthquakes are theoretically investigated. The unsteady propagation of longitudinal shear cracks are analysed as a mathematical model. The inhomogeneous distributions of initial stress, sliding frictional stress and specific fracture energy are introduced. The specific fracture energy is the amount of energy needed to creat a unit area of new crack surface. The energy rate balance is considered as the fracture criterion. The inhomogeneously distributed initial stress is regarded as an internal stress.
If the rate of decrease of initial stress minus sliding frictional stress, with respect to the distance from the rupture initiation point is low and if the nondimensional specific fracture energy that represents the material strength relative to the degree of stress concentration is high, then slow earthquakes will easily occur. In this case, even slight irregularities of initial stress and/or sliding frictional stress may contribute to rupture motions.
Multiple earthquakes will be caused by the discontinuous distributions of the specific fracture energy and/or the stress difference given by the initial stress minus the sliding frictional stress.
