Abstract-Both earthquake prediction and failure prediction of disordered brittle media are difficult and complicated problems and they might have something in common. In order to search for clues for earthquake prediction, the common features of failure in a simple nonlinear dynamical model resembling disordered brittle media are examined. It is found that the failure manifests evolutioninduced catastrophe (EIC), i.e., the abrupt transition from globally stable (GS) accumulation of damage to catastrophic failure. A distinct feature is the significant uncertainty of catastrophe, called sample-specificity. Consequently, it is impossible to make a deterministic prediction macroscopically. This is similar to the question of predictability of earthquakes. However, our model shows that strong stress fluctuations may be an immediate precursor of catastrophic failure statistically. This might provide clues for earthquake forecasting.

The concept “sample-specific” is suggested to describe the behavior of disordered media close to macroscopic failure. It is pointed out that the transition from universal scaling to sample-specific behavior may be a common phenomenon in failure models of disordered media. The dynamical evolution plays an important role in the transition.

-Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

Abstract-Based on the concepts of statistical mesoscopic damage mechanics, the rupture of a heterogeneous medium is investigated in terms of numerical simulations of a network model, subjected to simple shear loading. The heterogeneities are simulated by varying the sizes and fracture strains of the elements of the network. Progressive damage is governed by a damage field equation and a dynamic function of damage (DFD). From the damage field equation, a criterion for damage localization can be derived, and the DFD can be extracted from the simulations of the network. Importantly, the DFD intrinsically governs the damage localization. Both stress-free and periodic boundary conditions for the network are examined. It is found that damage localization may be the underlying mechanism of eventual rupture and thus could be used as a possible precursor of earthquake rupture.