Abstract The interaction of hydraulic fractures (HFs) and structural planes (SPs) fundamentally governs fracture geometry and stimulation effectiveness in naturally fractured reservoirs. Existing models typically treat HF-SP interaction as a single, isolated event and therefore miss the cumulative, history-dependent effects of repeated intersections. We address this gap with an LEFM-based analytical criterion that explicitly evaluates sequential HF-SP intersections at non-orthogonal angles, integrates the coupled effects of fluid-flow partitioning, stress-shadowing, poroelastic response, and fracture-tip plasticity, and is applicable across toughness and viscosity dominated regimes. The proposed criterion accurately predicts repeated HF–SP interactions under both toughness-dominated and viscosity-dominated regimes. The criterion has been validated against analytical solutions, laboratory experiments, and numerical simulations which confirms its predictive reliability. A systematic sensitivity analysis further identifies the dominant geological and fracturing controls. Results show that in toughness-dominated regimes, SP parameters (e.g., tensile strength, cohesion, and friction coefficient) primarily govern intersection behavior, whereas in viscosity-dominated regimes, injection rate and fluid viscosity play decisive roles. Increasing injection rate and fluid viscosity reduces the critical crossing angle by up to 21.62% and 16.89%, respectively. Within the proposed framework, the intersection angle, which is governed by the friction coefficient, is quantitatively identified as the key factor controlling slip tendency. This study establishes a novel analytical framework that extends the theoretical model of HF-SP interaction. It specifically elucidates the intersection behavior under the combined influence of multiple induced stresses across different propagation regimes. The framework provides a predictive tool for HF-multiple SP intersection and a reliable methodology for the rapid and accurate prediction of hydraulic fracture network geometry in complex reservoirs, such as coal seams and tight sandstones. This advancement offers critical theoretical support for optimizing hydraulic fracturing design and operations.
Tong et al. (2026) studied this question.