Mode I sub- and super-shear rupture and forerunning in porous media

Numerical simulations demonstrate the occurrence of both sub- and supershear ruptures in dry and saturated porous media during mode I fracture. Initially, the Finite Element Method is applied to investigate a case of sub -shear velocity in a dry beam on an elastic foundation subjected to sinusoidal loading. Subsequently, the Extended Finite Element Method is employed for fluid injection in both an infinite saturated porous medium and a plate. The results reveal a transition from smooth behavior to a stepwise pattern and eventually to forerunning as the injection rate increases. Notably, this progression has been observed for the first time. Finally, a hybrid Finite Element/Peridynamic model is utilized to explore both dry and fully saturated media under mechanical loading. In the case of saturated media, fluid injection is also considered. Both methods document velocities surpassing the shear wave. The noteworthy aspect is that these results, obtained through entirely different numerical methods and constitutive relations, justify confidence in the assertion that, in mode I fracture, speeds exceeding the shear wave and even the dilatation wave speeds can be achieved through forerunning. The loading condition investigated may be relevant in geophysics.