Predicting fracture swarms — the influence of subcritical crack growth and the crack-tip process zone on joint spacing in rock

Abstract

Swarms or clusters represent an exception to the widely accepted idea that fracture spacing in sedimentary rock should be proportional to mechanical layer thickness. Experimental studies and static stress analysis do not provide adequate explanation for fracture swarm occurrence. The problem is re-examined numerically, accounting for the dynamics of pattern development for large populations of layer-confined fractures. Two crucial aspects of this model are: (1) the inclusion of three-dimensional effects in calculating mechanical interaction between simultaneously propagting fractures; and (2) the use of a subcritical crack-propagation rule, where propagation velocity during stable growth scales with the crack-tip stress intensity factor. Three regimes of fracture spacing are identified according to the magnitude of the subcritical index of the fracturing material. For low subcritical index material ( n = 5) numerous fractures propagate simultaneously throughout a body resulting in irregular spacing that is, on average, much less than layer thickness. For intermediate subcritical index ( n = 20) one fracture propagates at a time, fully developing its stress shadow and resulting in a pattern with regular spacing proportional to layer thickness. For high subcritical index cases ( n = 80) fractures propagate in a fashion analogous to a process zone, leaving a fracture pattern consisting of widely spaced fracture clusters.