7 research outputs found
Existence of solutions for a higher order non-local equation appearing in crack dynamics
In this paper, we prove the existence of non-negative solutions for a
non-local higher order degenerate parabolic equation arising in the modeling of
hydraulic fractures. The equation is similar to the well-known thin film
equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann
operator, corresponding to the square root of the Laplace operator on a bounded
domain with Neumann boundary conditions (which can also be defined using the
periodic Hilbert transform). In our study, we have to deal with the usual
difficulty associated to higher order equations (e.g. lack of maximum
principle). However, there are important differences with, for instance, the
thin film equation: First, our equation is nonlocal; Also the natural energy
estimate is not as good as in the case of the thin film equation, and does not
yields, for instance, boundedness and continuity of the solutions (our case is
critical in dimension in that respect)
Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method
Verification of Coupled Hydraulic Fracturing Simulators Using Laboratory-Scale Experiments
Fracturing in Dry and Saturated Porous Media
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