PSI - Issue 66

Amani J. Majeed et al. / Procedia Structural Integrity 66 (2024) 212–220 Author name / Structural Integrity Procedia 00 (2025) 000–000

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post-modification, the model displays a unique zigzag pattern, reflecting the evolution of the fracture in terms of length and width over time. Naturally, hydraulic fracture surfaces are non-linear. Both the length and width of the fractures change during propagation, resulting in the formation of irregular, zigzag edges.

Fig. 4. Modified PKN model fracture factors.

The comparison between the current modified models for both KGD and PKN, and those used in Arash's study (Nasiri, 2015), is shown in Figs. 5 and 6, respectively. The current models account for fracture angle and direction, providing a more realistic representation of the crack path under the influence of hydraulic pressure. Consequently, non-linear behavior can be simulated. In contrast, the earlier model from Arash's study did not incorporate these factors. Despite this, good agreement between the models has been achieved, enhancing the reliability of the current models for simulating fracture behavior.