Compressive Failure as a Critical Transition: Experimental Evidence and Mapping onto the Universality Class of Depinning

Abstract

Acoustic emission (AE) measurements performed during the compressive loading of concrete samples with three different microstructures (aggregate sizes and porosity) and four sample sizes revealed that failure is preceded by an acceleration of the rate of fracturing events, power law distributions of AE energies and durations near failure, and a divergence of the fracturing correlation length and time towards failure. This argues for an interpretation of compressive failure of disordered materials as a critical transition between an intact and a failed state. The associated critical exponents were found to be independent of sample size and microstructural disorder and close to mean-field depinning values. Although compressive failure differs from classical depinning in several respects, including the nature of the elastic redistribution kernel, an analogy between the two processes allows deriving (finite)-sizing effects on strength that match our extensive dataset. This critical interpretation of failure may have also important consequences in terms of natural hazards forecasting, such as volcanic eruptions, landslides, or cliff collapses. PACS: 62.20. 64.60.av, 89.75.Da, 83.80.Ab Classical fracture and failure theoretical frameworks or criteria, such as Griffith theory or the Coulomb failure criterion, do not consider material disorder. Consequently, they predict an abrupt global failure, without any precursory phenomenon. In that sense, failure can be interpreted as a firstorder transition from an intact to a failed state, as Griffith theory was inspired by the classical theory of nucleation [1,2]. Materials heterogeneity has been however considered for a long time, especially to account for failure strength variability and associated size effects [3]. Nevertheless, this weakestlink approach is based on strong assumptions such as the absence of mechanical interactions between defects and between rupture events, or a global failure dictated by the activation of the largest flaw (the weakest-link). These assumptions might appear reasonable for weakly disordered materials under tension, especially in the case of a pre-existing large crack or notch. However, in case of large enough disorder, the quasi-static propagation of such a crack can be interpreted as a dynamical critical transition [4,5]. The limitations of these classical frameworks appear even clearer for highly disordered systems without macro-scale heterogeneities [6] and/or loading conditions stabilizing crack propagation, such as compression (through the presence of friction). In those cases, it is known for a long time that failure is a process, involving the nucleation, interaction, propagation and coalescence of many microcracks [7,8], hence characterized by precursory phenomena. The presence/absence of

Dynamics of Microscale Precursors During Brittle Compressive Failure in Carrara Marble

“…Concerning the scaling of the incremental damage, d D φ / ∆ D (Figure a), it is worth stressing that the above‐mentioned models do not predict an increasing damage event rate d N / d∆ D when approaching the critical point. Therefore, our observations strongly differ from these models on this specific point but are in agreement with the acoustic emission monitoring of the compressive failure of nonporous heterogeneous materials (Vu et al, ). In our case, the incremental damage evolution results from both the evolution of the distribution of damage avalanche sizes and the evolution of the damage event rate.…”

“…These studies considered that during the initiation phase, the faults progressively unpin from the rock matrix before generalized frictional sliding takes place at the depinning transition. Brittle compressive failure of heterogeneous materials was also recently mapped to the depinning transition (Vu et al, ; Weiss et al, ), and associated predictions for system size effects on failure strength were proposed (Vu et al, ). The scaling predictions of the depinning framework are qualitatively consistent with our observations, in terms of incremental damage evolution, largest damage increment, or distribution of damage increments (see Table ).…”

“…As this volume scales as with d f ≈ 2.2 (Figure ), the so‐defined “size” actually measures essentially the rupture area. In the interpretation of fault slip initiation (Fisher et al, ) or of compressive failure as a depinning transition (Vu et al, ), the damage avalanche size is defined instead as the integral of slip or displacement u over this rupture area A , that is, scales as a seismic potency, P 0 = ∫ A d u . Therefore, in order to link our measure of the size s of the damage increment with the avalanche size (or potency), a hypothesis has to be done about the average slip 〈 u 〉 over the rupture area.…”

“…Our detailed tracking of microfracturing during compressive failure revealed that several observables such as the incremental damage, dD φ /dΔ D , the largest microfracture, S max , or the distribution of fracture increment sizes evolve toward failure following specific scaling laws, up to at least Δ D ≈ 10 −2 . These scaling laws argue for an interpretation of compressive failure as a critical phase transition from an intact to a failed state (Alava et al, 2006;Girard et al, 2010;Vu et al, 2019). Different theoretical models can be proposed to interpret such critical transition, yielding specific scaling laws and critical exponents (Renard, Weiss, et al, 2018).…”

“… σ 1 : axial stress, σ 3 = σ 2 : confining pressure, σ D = ( σ 1 − σ 3 ): differential stress, : differential stress at failure, ∆ D : stress control parameter. If failure is considered as a critical phenomenon (Girard et al, ; Vu et al, ), several power law scaling relationships should emerge among stress control parameter, ∆ D ; the cumulative microfracture (black line) volume fraction quantified by the damage parameter, D φ ; the volume fraction of the largest microfracture cluster, S max (red line); the volume fraction of damage increments (blue dotted and solid lines); the volume fraction of the largest damage increment, s max (red dotted line), dD φ / d∆ D ; the size (volume), s , and length, L , of a given microfracture increment; and the probability distribution of damage increments, P ( s ). γ f , γ i , d f , β , and α are the power law scaling exponents.…”