  We investigate numerically and theoretically the precursory intermittent
activity characterizing the preliminary phase of damage accumulation prior to
failure of quasi-brittle solids. We use a minimal but thermodynamically
consistent model of damage growth and localization developed by Berthier et al.
(2017). The approach accounts for both microstructural disorder and non-local
interactions and permits inferring a complete scaling description of the
spatio-temporal structure of failure precursors. By developing a theoretical
model of damage growth in disordered elasto-damageable specimen, we demonstrate
that these scaling relations emerge from the physics of elastic manifolds
driven in disordered media, while the divergence of these quantities close to
failure is reminiscent of the loss of stability of the specimen at the
localization threshold. Our study sorts out a long-standing debate on the
nature of the compressive failure point and the origin of the universal
statistics of the precursors preceding it. Our analysis rules out a
critical-point scenario in which the divergence of the precursor size close to
failure is signature of a second-order phase transition governed by the
microstructural disorder. Instead, we show that while the jerky evolution of
damage prior to failure results from the presence of material disorder, the
latter does not significantly change the nature of the localization process,
which is an instability well described by standard bifurcation theory of
homogeneous systems. Finally, we harness our detailed understanding of the
precursory statistics to design a methodology to estimate the residual lifetime
of a structure from the statistical analysis of precursors. This method
relevant for structural health monitoring is shown to perform rather accurately
on our data.
