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

作者：Ian G Main, Peter R. Sammonds, Philip George Meredith · 发表于：Geophysical Journal International · 年份：1993 · DOI：10.1111/j.1365-246x.1993.tb01192.x · 被引用次数：104 · 研究领域：Rock Mechanics and Modeling、Geophysical Methods and Applications、Earthquake Detection and Analysis

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 〈c〉 and measuring the differential stress σ 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 (σ, 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...