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.

Multiple failures in or around a stiff inclusion embedded in a soft matrix under a compressive loading

“…Here A is a scaling coefficient, and p is the sub-critical index. The value of p varies considerably depending on the kind of rock and environment, from 20 for sandstone immersed into water to over 250 in dry for carbonates (Olson 2004). Nevertheless, following Bessinger et al, the values of p necessary to propagate multiple fractures should be lower by several orders of magnitude than those obtained experimentally, and these values have never been found in rocks.…”

“…v A K K = following a fatigue-like power law (Olson 2004). Here A is a scaling coefficient, and p is the sub-critical index.…”

A numerical study of fracture spacing and through-going fracture formation in layered rocks

“…Opening-mode tensile fractures are common in sedimentary rock, and their spacing is often proportional to the thickness of the fractured layer (Ladeira and Price, 1981;Tang et al, 2008;Wu and Pollard, 1995). Clearly, it would be advantageous for flow prediction if fracture spacing could be inferred from bed thicknesses deduced from drilling (Olson, 2004). The growth of fractures in layered sequences has been described in terms of 'Sequential Infilling', where the term 'Fracture Saturation' is given to the strata when no more fractures can infill even with increasing strain .…”

Numerical Analysis on the Optimization of Hydraulic Fracture Networks

“…Using the parameters given by Wu and Olson [37], the correction coefficient K proposed by Olson [38] can be written as:…”