A Uni ed Comprehension for Fracture of Intact Rock , Frictional Slip Failure , and Earthquake Rupture , and Scaling of Scale - Dependent Physical

There are increasing amounts of evidence that earthquake rupture is a mixed process between what is called frictional slip failure and fracture of intact rock mass. In fact, there is a strong possibility that what is called a 'barrier' or 'asperity' on earthquake faults is a local patch of high rupture growth resistance whose strength equals the strength of intact rock. In addition, the lithostatic pressure and temperature are high enough at crustal depths corresponding to the brittle-plastic transition regime, so that the shear frictional strength conforms to the shear fracture strength of intact rock at these depths. Shear fracture of intact rock is the upper end member of frictional slip failure on a preexisting fault. If, therefore, there is a constitutive law that governs the earthquake rupture, the constitutive law should be formulated as a unifying constitutive law that governs both frictional slip failure and shear fracture of intact rock mass. There are two types of physical quantities inherent in shear rupture: scale-dependent quantities, and scale-independent quantities. The scale-dependent quantities include the shear fracture energy G c , the breakdown zone size X c and its duration T c , the nucleation zone size L c and its duration t c , the slip acceleration D, and the cutoo frequency f s max of the power spectral density of the slip acceleration versus time record observed at a position on the fault. Speciically, for instance, G c = 10 6 ?10 8 J=m 2 has been evaluated for major earthquakes, while G c = 10 4 ? 10 5 J=m 2 for shear fracture of intact rock sample under lithospheric conditions, and G c = 0:1 ? 1J=m 2 for stick-slip dynamic failure on preexisting faults. Both L c and t c for large-scale earthquake rupture also diier greatly from those for shear rupture of small scale in the laboratory, as corroborated by existing data. How can these scale-dependent physical quantities be treated unifyingly in quantitative terms ? To answer this question, the introduction of the constitutive law is indispensable; however, the constitutive law is needed to be formulated appropriately so as to scale the above scale-dependent physical quantities consistently, and thereby a uniied comprehension should be provided for the shear rupture of any size scale-small scale in the laboratory to large scale in the Earth as an earthquake source. The shear rupture include a phase of stable, quasi-static …