We conduct combined numerical and mathematical analysis to investigate the variability of local stresses in heterogeneous fractured rocks subjected to different far-field stress loading conditions. A realistic fracture network is constructed based on a sandstone outcrop mapped at the Hornelen Basin in Norway. The inhomogeneous nature of rock 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 local stress field in the fractured rock under far-field stress loading is derived from a hybrid finite-discrete element model, and the stress variability is analysed using a novel tensor-based formalism that faithfully honours the tensorial nature of stress data. The local stress perturbation is quantified using the Euclidean distance of the local stress tensor to the mean stress tensor, while the overall stress dispersion is measured using the effective variance of the entire stress tensor field. We show that local stress field is significantly perturbed when the far-field stresses are imposed with a high stress ratio and at a critical direction in favour of sliding along pre-existing fractures.

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