Abstract - Several outcrop studies of Mode I joints and veins interpret fractures with straight, regular fracture paths and an absence of forking to be diagnostic of the slow, stable fracture growth associated with subcritical or quasi-static crack-tip propagation. This mode of fracturing may be the norm under conditions of long-term loading, which are likely to be widespread throughout the crust.
The crack-tip velocity of an isolated fracture growing by subcritical fracture propagation can be expressed as follows:
where, v is the velocity, A is a constant of proportionality, KI is the opening mode stress intensity and n is the subcritical crack-tip velocity exponent. Published values of n determined from experimental rock tests range between ca 15 and 130 for carbonate rocks.
Calcite veins in lower Carboniferous limestones of The Burren, Co. Clare, Ireland provide a superbly-exposed natural example of a Mode I fracture pattern interpreted to have developed subcritically. Karstified veins, clearly resolvable on low-level aerial photographs, have been mapped on the tiered summit of Cappanawalla, providing a detailed fracture map with an areal extent of 114,400 m2. Quantitative analysis of the various geometric parameters of these fracture patterns has been carried out on sub-samples that range in area from 2500m2 to 40,000 m2.
Numerical simulations of fracture patterns have been performed in software to ascertain the values of n, subcritical crack-tip velocity exponent, required to create fracture patterns that are quantitatively similar to The Burren dataset. The numerical code used is a boundary element method based on Linear Elastic Fracture Mechanics (LEFM) theory. Simulations were constrained by realistic fracture frequencies obtained from The Burren dataset (0.03m-2), and were run with the aim of reaching a dimensionless spatial density of 1, equivalent to the mean spatial density of The Burren veins.
Numerical simulations with higher values of n never attain spatial densities equivalent to The Burren dataset, due to the propensity for a single fracture to dominate. Only values of n = 2 can achieve the spatial densities, length and spatial distributions of the veins of the natural example. These low values of n are one to two orders of magnitude less than experimentally determined values. Although many factors must exert a control on fracture propagation rates (e.g. crack-tip displacement mode, temperature, pressure, effective pressure, solubility of solid in environmental agents, microstructural variables, residual strain) the availability of fluid to the fracture is of key importance in the fluid saturated crust. We provide a simple mathematical rationale to explain why fluid flow into the fractures limits the crack-tip exponent to low n values.
Abstract of talk given to:
Tectonic Studies Group Annual Meeting, Tectonic Studies Group, University of Leicester, January 2002