Gravity-driven instabilities: interplay between state-and-velocity dependent frictional sliding and stress corrosion damage cracking

TL;DR

This paper models gravity-driven instabilities by examining the interaction between frictional sliding and stress corrosion cracking, revealing three regimes of failure based on internal damage and sliding time scales.

Contribution

It introduces a novel model combining state- and rate-dependent friction with stress corrosion damage to classify instability regimes in heterogeneous masses.

Findings

Internal stick-slip events lead to global runaway in slow damage regimes.

Fragmentation occurs with rapid damage, creating heterogeneous sliding blocks.

A critical regime features crack nucleation and propagation along curvature changes.

Abstract

We model the progressive maturation of a heterogeneous mass towards a gravity-driven instability, characterized by the competition between frictional sliding and tension cracking, using array of slider blocks on an inclined basal surface, which interact via elastic-brittle springs. A realistic state- and rate-dependent friction law describes the block-surface interaction. The inner material damage occurs via stress corrosion. Three regimes, controlling the mass instability and its precursory behavior, are classified as a function of the ratio $T_c/T_f$ of two characteristic time scales associated with internal damage/creep and with frictional sliding. For $T_c/T_f \gg 1$, the whole mass undergoes a series of internal stick and slip events, associated with an initial slow average downward motion of the whole mass, and progressively accelerates until a global coherent runaway is observed. For $T_c/T_f \ll 1$, creep/damage occurs sufficiently fast compared with nucleation of sliding, causing bonds to break, and the bottom part of the mass undergoes a fragmentation process with the creation of a heterogeneous population of sliding blocks. For the intermediate regime $T_c/T_f \sim 1$, a macroscopic crack nucleates and propagates along the location of the largest curvature associated with the change of slope from the stable frictional state in the upper part to the unstable frictional sliding state in the lower part. The other important parameter is the Young modulus $Y$ which controls the correlation length of displacements in the system.