Accurate prediction of softening and failure behavior of rocks are essential to hydraulic fracturing simulation using strain-softening type models. Failure to preserve the fracture energy causes these continuums based numerical models to suffer from mesh-size dependency. The virtual Multi-dimensional Internal Bond Model (VMIB) is derived from a particle-based constitutive law at the micro scale. It has been implemented in a 3D Finite Element Method in which material softening and energy dissipation occur over the “representative elementary volume”. However, in realistic materials, energy dissipation is due to fracture surfaces creation instead of material softening in the element. In this work we present an improved VMIB model to bridge the energy dissipation over the representative elementary volume and the fracture surfaces using a virtual bond potential that incorporates the material fracture energy to eliminate the mesh-size sensitivity. The virtual bond potential considers both the critical fracture energy and element size. The 3D model is calibrated and verified by carrying out simulations of a group of three-point-bend tests using different mesh sizes. Then, by incorporating a three-dimensional element partition method, the model is applied to a series of laboratory scale hydraulic fracturing experiments. Furthermore, multiple hydraulic fracturing from closely-staged clusters is simulated. It is found that the model can accurately capture the fractures growth pattern that is influenced by the stress boundary conditions and the stress shadow interaction among the fractures. The results also show the predicted breakdown pressure reasonably agree with the experiment data.

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