A constitutive scaling law and a unified comprehension for frictional slip failure, shear fracture of intact rock, and earthquake rupture

[1] It is widely recognized that some of the physical quantities inherent in a rupture are scale- dependent, and the scale dependence is one of the most notable facts and features of rupture phenomena. The paper addresses how such scale- dependent shear rupture of a broad range from laboratory- scale frictional slip failure and shear fracture of intact rock to field- scale rupture as an earthquake source can be unified by a single constitutive law. Noting that the earthquake rupture is a mixed process between frictional slip failure and the shear fracture of intact rock, it is concluded that the constitutive law for the earthquake rupture be formulated as a unifying law that governs both frictional slip failure and shear fracture of intact rock. It is demonstrated that the slip- dependent constitutive law is such a unifying law, and a constitutive scaling law is derived from laboratory data on both frictional slip failure and shear fracture of intact rock. This constitutive scaling law enables one to provide a consistent and unified comprehension for scale- dependent physical quantities inherent in the rupture, over a broad range from small- scale frictional slip failure and shear fracture in the laboratory to large- scale earthquake rupture in the field.