A numerical study of stress variability in heterogeneous fractured rocks
We conduct numerical simulations to investigate the variability of local stresses in heterogeneous fractured rocks subjected to different far-field stress conditions. A realistic fracture network is constructed based on a real outcrop mapped at the Hornelen Basin in Norway. The heterogeneity of the rock material is modelled using a Weibull distribution of Young’s modulus characterised by a homogeneity index m. As m decreases, the rock material becomes less homogeneous. The distribution of local stresses in the fractured rock under far-field stress loading is derived from a hybrid finite-discrete element model, and the stress variability is further analysed using a tensor-based formalism that faithfully honours the tensorial nature of stress data. The local stress perturbation is quantified using the Euclidean distance of each local stress tensor to the mean stress tensor, and the overall stress dispersion is measured using the effective variance of the entire stress tensor field. We show that the local stress field is significantly perturbed when the far-field stresses are associated with a high stress ratio and imposed at a critical direction in favour of intense sliding along preferentially-oriented fractures. The strong correlation between fracture sliding and local stress variability are further revealed from a scanline sampling analysis through the domain. Furthermore, larger perturbation of local stresses can be induced as the inhomogeneity of the rock materials increases (i.e. m decreases). Whether the stress field is dominated by fractures or matrix depends on the far-field stress state, material inhomogeneity, and fracture properties. If the rock material is highly heterogeneous, stress variability is controlled by the matrix when the far-field stress ratio is low; however, the stress distribution becomes more affected by fractures as the stress ratio increases. If the rock material is more homogeneous, the system tends to be more dominated by fractures even under a relatively low stress ratio.
Keywords: Stress variability, Fractured rock, Far-field stress, Material inhomogeneity, Effective variance, Finite-discrete element method,