Rupture by damage accumulation in rocks

The deformation of rocks is associated with microcracks nucleation and propagation, i.e. damage. The accumulation of damage and its spatial localization lead to the creation of a macroscale discontinuity, so-called “fault” in geological terms, and to the failure of the material, i.e. a dramatic decrease of the mechanical properties as strength and modulus. The damage process can be studied both statically by direct observation of thin sections and dynamically by recording acoustic waves emitted by crack propagation (acoustic emission). Here we first review such observations concerning geological objects over scales ranging from the laboratory sample scale (dm) to seismically active faults (km), including cliffs and rock masses (Dm, hm). These observations reveal complex patterns in both space (fractal properties of damage structures as roughness and gouge), time (clustering, particular trends when the failure approaches) and energy domains (power-law distributions of energy release bursts). We use a numerical model based on progressive damage within an elastic interaction framework which allows us to simulate these observations. This study shows that the failure in rocks can be the result of damage accumulation.

💡 Research Summary

The paper presents a comprehensive investigation of rock failure through the lens of progressive damage accumulation. Damage is defined as the nucleation, growth, and coalescence of microcracks that progressively degrade the elastic stiffness of the material. The authors combine static observations—microscopic examination of thin sections that reveal fractal‑like crack networks and gouge textures—with dynamic monitoring of acoustic emission (AE) events generated by propagating cracks. Across scales ranging from laboratory specimens (decimetre) to natural faults (kilometre), the data exhibit three consistent signatures: (1) spatial fractality of damage structures (roughness and gouge particle size distributions follow power‑law scaling), (2) temporal clustering of AE bursts that intensifies as failure approaches, and (3) power‑law distributions of released energy, analogous to the Gutenberg‑Richter relation for earthquakes.

To rationalize these observations, the authors develop a numerical framework based on progressive damage within an elastic interaction field. The model discretizes the rock into a lattice where each node possesses a damage threshold. When the local stress exceeds this threshold, the node’s elastic modulus is reduced, and the resulting stress redistribution is propagated to neighboring nodes via an elastic Green’s function. Damage events are stochastic, so early‑stage micro‑damage appears randomly, but as the external load increases, damaged zones begin to percolate, leading to a rapid, system‑wide failure. Simulations reproduce the experimentally observed fractal dimension of damage patterns, the power‑law statistics of synthetic AE events (including a b‑value comparable to seismic catalogs), the acceleration and clustering of events prior to macroscopic rupture, and the abrupt drop in global strength and modulus at failure.

The study demonstrates that rock failure is not a simple threshold phenomenon but the emergent outcome of a self‑organized critical process driven by damage accumulation and elastic interaction. This insight bridges laboratory rock mechanics, field seismology, and theoretical concepts of self‑organized criticality. Practically, the framework offers a unified basis for interpreting precursory AE signals in engineering applications (e.g., tunnel excavation, mining, hydraulic fracturing) and for improving earthquake forecasting models that rely on the statistical properties of micro‑seismicity. By integrating observation and modeling, the paper convincingly argues that the progressive build‑up of damage is the fundamental mechanism behind the formation of macroscopic faults and the catastrophic loss of mechanical integrity in rocks.