Application of a modified Griffith criterion to the evolution of fractal damage during compressional rock failure

Abstract

A modified Griffith criterion for a fractal ensemble of cracks is applied to the interpretation of Acoustic Emission (AE) statistics during the compressional deformation of intact and artificially pre‐cut rock specimens in the laboratory. A mean energy release rate per unit crack surface area 〈;G〉 is recovered from the observed AE event rate N and the seismic b value, by calculating an inferred mean crack length and measuring the differential stress s̀ for a range of experimental conditions. Temporal variations in 〈;G〉 under compressive deformation show very similar trends to those predicted by a synoptic model determined by direct extrapolation from observations of subcritical crack growth under tension. (In the tensile case, deformation is centred on a dominant macrocrack and the stress intensity K, which scales as the square root of G, is the relevant measured variable.) The three independent variables measured during the tests (s̀, N, b) are reduced to points that map out a path through a 3‐D phase space (〈G〉, N, b), which depends on the material type and the experimental conditions. 2‐D slices through this phase space [(〈;G〉, b)] (〈;G〉, b)] are compared with results from the tensile tests [(K, N), (K, b)]. The event rate N is found to scale with √〈;G〉 according to a power law, with an exponent n’ which is smaller than that for tensile fracture, reflecting the greater stability of compressional rock fracture in its early stages. The effective subcritical crack growth index n’ is correlated with the material type and degree of apparent ’ductility’ on a macroscopic scale, with more brittle behaviour corresponding to higher n’. The value of n’ is similar on unloading of the stress after dynamic faulting as on the loading portion, though the curve is systematically offset, most probably due to the material weakening associated with faulting. The model does not apply near the period of dynamic failure, where strong local interactions are dominant. The seismic b value is also found to scale negatively with √〈;G〉, in a manner similar to experiments where K can be measured independently. The acceleration of the mean seismogenic crack length =f(t) has a similar power‐law form to that predicted from Charles’ law for a single tensile macrocrack, with an implied subcritical crack growth index n smaller than that for fracture in compression. The extra dimension introduced by the time dependence of allows an independent check on the validity of the theory used to calculate 〈;G〉. In particular n’ from the diagram (, t) is found to be similar in magnitude to the exponent obtained from the event rate dependence (〈;G〉, N), a phenomenon first discovered by empirical observation of tensile subcritical crack growth. Copyright © 1993, Wiley Blackwell. All rights reserved