Three-dimensional brittle failure: beyond Mohr-Coulomb

Coulombs rock deformation experiments and mathematical theory have been a cornerstone in our understanding of brittle failure since they were first presented in 1773; his principle findings formed the basis for Cauchys generalised formulation of stress, for which graphical representations were devised by Culmann (1866) and Mohr (1882). At that time, all deformation experiments followed Coulomb in using conditions of uniaxial compression (?1 > ?2 = ?3 = 0), and produced results consistent with Coulombs empirical and theoretical predictions. Further development of rock deformation apparatus allowed confined samples to be tested under axial compression (?1 > ?2 = ?3 > 0), and showed that at elevated temperatures and pressures there is often a slight departure from the linear failure criteria predicted by Coulomb (giving rise to the typical convex-upwards Mohr failure envelope). A key point is that although all experimental data available to Mohr were derived from uniaxial and axial testing (which is inherently incapable of determining the influence of the intermediate principal stress), Mohrs hypothesis assumed implicitly that failure would occur independently of ?2, and he depicted this in terms of a failure envelope on the Mohr diagram for 3D stress. This, together with Naviers consideration of Coulomb, was used by Anderson (1905, 1942) in his seminal work that still forms the basis for the dynamics of faulting presented in most structural textbooks today.

There is now ample evidence to show that Mohrs assumption was incorrect. Areas of outcrop containing arrays of polymodal brittle faults are generally best explained in terms of non-plane strain, in which 3D strain is inferred to depend upon the magnitude of the intermediate principal stress. These field observations are supported by rock deformation experiments carried out with polyaxial testing equipment (under triaxial stress conditions, ?1 > ?2 > ?3). In addition, there is a strong theoretical basis for understanding polyaxial fracture arrays in terms of non-Andersonian faulting. This is further supported by recent developments in the 3D numerical modelling of stress interactions between tensile microcracks (see Healy et al., this conference).

We aim to provide further constraints on the nature of faulting under non-plane strain conditions, by combining: (i) numerical modelling of stresses related to microcrack development, interaction and coalescence; (ii) results of deformation experiments using servo-controlled multi-axial testing apparatus; (iii) quantitative field observations from areas of complex brittle deformation. The latter includes very detailed analysis using laser-scanning equipment to constrain the precise 3D geometry and interconnectivity of outcrop-scale fracture arrays, as well as quantitative analysis of the contemporaneity of the constituent fracture sets.

Improved understanding of 3D brittle failure has important implications for seismic hazard prediction, rock stability studies, fluid flow (including hydrocarbon migration and reservoir performance), and palaeostress analysis.