Reliable prediction of fracture process in shale-gas rocks remains one of the most significant challenges for establishing sustained economic oil and gas production. This paper presents a modeling framework for simulation of crack propagation in heterogeneous shale rocks. The framework is on the basis of a variational approach, consistent with Griffith's theory. The modeling framework is used to reproduce the fracture propagation process in shale rock samples under standard Brazilian disk test conditions. Data collected from the experiments are employed to determine the testing specimens' tensile strength and fracture toughness. To incorporate the effects of shale formation heterogeneity in the simulation of crack paths, fracture properties of the specimens are defined as spatially random fields. A computational strategy on the basis of stochastic finite element theory is developed that allows to incorporate the effects of heterogeneity of shale rocks on the fracture evolution. A parametric study has been carried out to better understand how anisotropy and heterogeneity of the mechanical properties affect both direction of cracks and rock strength.

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Fractures tend to propagate along the least resistance paths, and homogeneous‐based models may not be able to reliably predict the true crack paths, as they are not capable of capturing nonlinearities and local damage induced by local inhomogeneity. This paper presents a stochastic numerical modelling framework for simulating fracturing in natural heterogeneous materials. Fracture propagation is modelled using Francfort and Marigo's variational theory, and randomness in the material properties is introduced by random field principle. A computational strategy on the basis of nonlinear dimensionality reduction framework is developed that maps domain of spatially variable properties of the materials to a low‐dimensional space. This strategy allows us to predict the most probable fracture patterns leading to failure by an optimisation algorithm. The reliability and performance of the developed methodology are examined through simulation of experimental case studies and comparison of predictions with measured data.