Fracturing speed, fracture toughness, and boundary conditions in fast hydraulic fracturing

Recent studies have revisited near-sonic and supersonic crack growth, particularly in mode I fractures, challenging the traditional belief that cracks cannot exceed the Rayleigh wave speed ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">R</mml:mi> </mml:mrow> </mml:msub> </mml:math> ). While classical fracture mechanics suggest that mode I fractures are limited to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">R</mml:mi> </mml:mrow> </mml:msub> </mml:math> , recent work shows that cracks can surpass both shear wave velocity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) and dilatation wave speed ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">P</mml:mi> </mml:mrow> </mml:msub> </mml:math> ) under certain conditions. This paper investigates pressure-induced fracturing in porous media, where high fluid injection rates can lead to crack propagation speeds exceeding wave velocities. Using a hybrid peridynamic/finite-element model, where failure and cracks are characterized by a damage model, we simulate the dynamic hydraulic fracture propagation in a rectangular porous domain and explore the influence of fracture energy (related to fracture toughness), permeability, and boundary conditions on crack behavior. Results reveal that forerunning (mother–daughter) fracture events, and mixed lifting-separation and crack-like propagation mechanisms, significantly accelerate crack growth, particularly under low-permeability conditions. We also include a validation of the model through comparison with results from extended finite-element method. These findings have important implications for earthquake rupture dynamics, volcanic activity, and hydraulic fracturing in geophysical applications.