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[en] The key objective of this work is to establish a fully coupled pore pressure and stress model in order not only to investigate multi-stage hydraulic fractures (HFs) according to several completion designs, but also to study the complex problem of intersection of an HF and a pre-existing natural fracture (NF). First, this work concentrates on a computational finite element model based on the cohesive phantom node method (CPNM) to simulate initiation and propagation of multiple curving fractures. The primary contribution of this part is to shed light on the stress shadowing effect on conventional completion designs, i.e. simultaneous HF (Sim-HF) and sequential HF (Seq-HF), and in particular newly introduce the Texas two-step method (TTSM). Furthermore, the rock medium in the entire simulation domain is considered using the elasto-plastic constitutive equations of the Mohr–Coulomb and Drucker–Prager models. The impact of formation plasticity on the fracturing process is investigated, and the results obtained are compared with those based on the poro-elastic model. Second, in order to simulate the intersection of an HF with an NF, a cohesive crack-based finite element model (CCFEM) is developed along with a novel technique for the HF/NF intersection. Implementation of this technique at the intersection of HF and NF is considerably more straightforward in comparison with those in the available literature. In addition, this part aims at highlighting the crucial role of horizontal stress contrast in determining the type of HF/NF intersection scheme.