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The mean stress, as a fundamental statistical property of a group of stress data, is essential for stress variability characterisation. However, currently in rock mechanics, the mean stress is customarily and erroneously calculated by separately averaging the principal stress magnitudes and orientations. In order to draw the attention of our community to the appropriate approach for stress variability characterisation, here we compare the customary scalar/vector mean with that obtained by the mathematically rigorous tensorial approach—the Euclidean mean. Calculation of mean stress using both a small group of actual in situ stress measurement results and a large group of simulated stress data (obtained using the combined finite-discrete element method, FEMDEM) demonstrates that the two approaches yield different results. Further investigation of these results shows that the scalar/vector approach may yield non-unique and non-orthogonal mean principal stresses, and these may deviate significantly from those of the Euclidean mean. Our calculations and comparisons reveal that the scalar/vector approach is deficient because it processes the principal stress magnitudes and orientations separately as independent quantities and ignores the connection between them. Conversely, the tensorial approach appropriately averages the tensors that simultaneously carry not only the information of stress magnitudes and orientations, but also the inherent relations between them. Therefore, arbitrarily using scalar/vector mean stress of in situ stress measurements as input in further rock engineering analyses may yield significantly erroneous results. We advise that stress data should be statistically processed in a tensorial manner using tensors referred to a common Cartesian coordinate system. [ABSTRACT FROM AUTHOR]

A study about the influence of polyaxial (true-triaxial) stresses on the permeability of a three-dimensional (3D) fractured rock layer is presented. The 3D fracture system is constructed by extruding a two-dimensional (2D) outcrop pattern of a limestone bed that exhibits a ladder structure consisting of a 'through-going' joint set abutted by later-stage short fractures. Geomechanical behaviour of the 3D fractured rock in response to in-situ stresses is modelled by the finite-discrete element method, which can capture the deformation of matrix blocks, variation of stress fields, reactivation of pre-existing rough fractures and propagation of new cracks. A series of numerical simulations is designed to load the fractured rock using various polyaxial in-situ stresses and the stress-dependent flow properties are further calculated. The fractured layer tends to exhibit stronger flow localisation and higher equivalent permeability as the far-field stress ratio is increased and the stress field is rotated such that fractures are preferentially oriented for shearing. The shear dilation of pre-existing fractures has dominant effects on flow localisation in the system, while the propagation of new fractures has minor impacts. The role of the overburden stress suggests that the conventional 2D analysis that neglects the effect of the out-of-plane stress (perpendicular to the bedding interface) may provide indicative approximations but not fully capture the polyaxial stress-dependent fracture network behaviour. The results of this study have important implications for understanding the heterogeneous flow of geological fluids (e.g. groundwater, petroleum) in subsurface and upscaling permeability for large-scale assessments. [ABSTRACT FROM AUTHOR]