We developed a new numerical model that is based on a combination of the 2D boundary element method and a complementarity algorithm to simulate the mechanical interaction behavior between a hydraulic fracture (HF) and a horizontal frictional interface (FI). The new model enforces the appropriate contact boundary conditions of the FI using the complementarity algorithm, where the contact modes of the FI are efficiently determined without iterative trial calculation. Heterogeneous FIs were considered and solved by the model, which we validated using the analytical solution of a uniaxial frictional fracture and previously published results related to an HF approaching a natural fracture. Simulation results show that weak horizontal FIs with large slipping zones and shear displacements induced by HFs can confine fracture height. Peak normal stress appears on the two sides of the contact position, and fracture offset occurs in most cases. Fracture offset can be suppressed by an FI with high frictional strength. Heterogeneous FI with variable friction and strength is a key mechanism for fracture offset. Increasing fluid pressure, such as increasing injection rate or fluid viscosity, is conducive to fracture cross.

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