Dynamics of fracturing saturated porous media and self-organization of rupture

Abstract

Analytical solutions and a vast majority of numerical ones for fracture propagation in saturated porous media yield smooth behavior while experiments, field observations and a few numerical solutions reveal stepwise crack advancement and pressure oscillations. To explain this fact, we invoke selforganization of rupture observed in fracturing solids, both dry and fully saturated, when two requirements are satisfied: i) the external drive has a much slower timescale than fracture propagation; and ii) the increment of the external load (drive) is applied only when the internal rearrangement of fracture is over. These requirements are needed to obtain clean Self Organised Criticality (SOC) in quasi-static situations. They imply that there should be no restriction on the fracture velocity i.e. algorithmically the fracture advancement rule should always be independent of the crack velocity. Generally, this is not the case when smooth answers are obtained which are often unphysical. Under the above conditions hints of Self Organized Criticality are evident in heterogeneous porous media in quasi-static conditions using a lattice model, showing stepwise advancement of the fracture and pressure oscillations. We extend this model to incorporate inertia forces and show that this behavior still holds. By incorporating the above requirements in numerical fracture advancement algorithms for cohesive fracture in saturated porous continua we also reproduce stepwise advancements and pressure oscillations both in quasi-static and dynamic situations. Since dynamic tests of dry specimens show that the fracture advancement velocity is not constant we replicate such an effect with a model of a debonding beam on elastic foundation. This is the first step before introducing the interaction with a fluid.

A refined two-scale model for Newtonian and non-Newtonian fluids in fractured poroelastic media

“…The inclusion of these terms can cause a stick-slip like behaviour for shear fractures, whereas the fracture propagation is continuous without these terms. Similar "physics-induced" stepwise propagation has also been claimed to occur for pressurised fractures [2,3,4,5]. However, the origin of the latter stepwise propagation and the accompanying pressure oscillations are unclear [6], and few finite element simulations have replicated this behaviour [7].…”

Periodic toughness distribution -- Can an average toughness concept be feasible? Case study: KGD fracture in an impermeable rock

“…In this paper we attempt to use a more rigorous approach to define the most appropriate -efficient and accurate -approximations. As this topic is of great interest to both scientific and industrial communities in recent years; including investigation of the effect on fracture propagation at the pore scale [1,24,27,28], as well as the recent work on an effective macroscale homogenisation of the toughness in [2]. Our work and objectives are quite similar to the latter, yet, we feel, complementary to theirs.…”

“…Also of interest, stress barriers effect the process in a similar manner to the toughness heterogeneity. Another area where non-uniform crack propagation has been observed is hydraulic fracture in poro-elastic media with saturation [1,27].…”

“…Finally, fracture propagation, in the context of the observed step-wise nature of the crack advancement (see e.g. [1,18,27]), is crucial for understanding the nature of this important technological and natural process (material destruction). Various scenarios are possible here, not only a monotonic (but non uniform in time) crack propagation but also branching, clustering and forerunning like behaviours have been already observed and analysed [18-20, 22, 23, 31].…”

Quasistatic cohesive fracture with an alternating direction method of multipliers

“…We consider a class of models composed of a bulk linear-elastic material in which cohesive surfaces with non-zero opening form at a sufficient level of stress. This property of the cohesive cracks, i.e., an initially-rigid behaviour, is responsible for the singularity of the potential function and for the fact that implicit quasistatic solutions are less commonly encountered in the literature [28][29][30][31]. The system considered is a connected shape Ω in two dimensions (the logic generalizes to three dimensions) with a predefined set of interfaces Γ d , taken to be finite element boundaries (see next section), interlacing the shape.…”