ABSTRACT
Geological faults are shear fractures in rock that may range in length from a cm to 1000 km, allowing for a the study of scaling over an unusually broad range. Their shear displacements are found to scale linearly with fault length, with a proportionality constant of the order of 102. Their displacement profiles are self-similar, with linear displacement tapers near the tips. These tip tapers are scale-independent. Faults propagate by forming a brittle process zone in the region surrounding their tips. These consist of intergranular tensile microcracks oriented parallel to the maximum compressive stress in the crack-tip stress field. Their maximum crack density is at the edge of the fault and is scale independent. Crack density falls away exponentially with distance from the fault and the width of the process zone increases linearly with fault length. All of these observations are consistent with an elastic-plastic (CTOA) crack model in which yielding occurs in a volume surrounding the crack tip. This implies that fracture energy increases linearly with fault length such that a classical Griffith type instability will not occur. Similar scaling laws apply to earthquakes and joints (macroscopic opening mode fractures in rock).
