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
