It is now generally recognized that mode I fracturing in saturated geomaterials is a stepwise process. This is true both for mechanical loading and for pressure induced fracturing. Evidence comes from geophysics, from unconventional hydrocarbon extraction, and from experiments. Despite the evidence only very few numerical models capture this behavior. From our numerical experiments, both with a model based on Standard Galerkin Finite Elements in conjunction with a cohesive fracture model, and with a truss lattice model in combination with Monte Carlo simulations, it appears that already in dry geomaterials under mechanical loading the fracturing process is time discontinuous. In a two-phase fracture context, in case of mechanical loading, the fluid not only follows the fate of the solid phase material and gives rise to pressure peaks at the fracturing event, but it also influences this event. In case of pressure induced fracture clearly pressure peaks appear too but are of opposite sign: we observe pressure drops at fracturing. In mode II fracturing, the behavior is brittle while in mixed mode there appears a combination of pressure rises and drops.