Avalanches in dry and saturated disordered media at fracture

Abstract

This paper analyzes fracturing in inhomogeneous media under dry and fully saturated conditions. We adopt a central force model with continuous damage to study avalanche behavior in a two-dimensional truss lattice undergoing dilation. Multiple fractures can develop at once and a power-law distribution of the avalanche size is observed. The values for the power-law exponent are compared with the ones found in the literature and scale-free behavior is suggested. The fracture evolves intermittently in time because only some avalanches correspond to fracture advancement. A fully saturated model with continuous damage based on the extended Biot's theory is developed and avalanche behavior is studied in the presence of fluid, varying the fluid boundary conditions. We show that power-law behavior is destroyed when the fluid flux governs the problem. Fluid pressure behavior during intermittent crack tip advancement is studied for the continuous-damage fully saturated model. It is found that when mechanical loading prevails, the pressure rises when the crack advances, while when fluid loading prevails, the pressure drops when the crack advances.

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

“…When studying fracturing of heterogeneous media with and without fluid with methods of statistical physics in quasi-static situations, the following two requirements have to be satisfied, apart from heterogeneity [1,3,27] 1. External drive has a much slower timescale than fracture propagation; 2. increments of the external load (drive) are applied only when the internal rearrangement of fracture is over.…”

“…The central force model previously developed for quasi-static situations [27] will be briefly recalled in the next sub-section and extended to consider inertia forces. In the same section, we will also explain how the concept of the self-organization of rupture is built inside this model.…”

“…The model is the continuous-damage fully saturated model (CDFSM) of [27] based on the generalized Biot's theory [41,42] under the following assumptions:…”

“…In Figure 9, continuous line, both pressure rises and drops can be observed. This corresponds to the full scenario of [27], i.e. the second partial scenario of section 2 has to be completed by a first partial scenario which reads "if a load, pressure, or displacement boundary condition is applied suddenly (all these conditions acting on the equilibrium of the solid-liquid mixture), then the fluid bears initially almost all the induced load because its immediate response is undrained (rigid and non-flowing).…”

Fatigue behavior of HPC and FRC under cyclic tensile loading: Experiments and modeling

“…One approach to account for the mechanics of disorder is to introduce a certain strength distribution into a homogeneous solid. Analytical approaches include the fiber‐bundle model, while computational approaches include the random fuse network model, lattice models, or voxel models . In Section 4.3 of this paper the matrix‐fiber‐bundle approach is used for the sake of simplicity to capture the most relevant qualitative characteristics that govern failure of FRC under fatigue loads.…”