[1] The acoustic emission (AE) and the mechanical behavior of granite samples during triaxial compression tests have been analyzed. The size of AE events displays power law distributions, conforming to the Gutenberg-Richter law observed for earthquakes, which is characterized by the b value. As the confining pressure increases, the macroscopic behavior becomes more ductile. For all different stages of the rock mechanical behavior (linear, nonlinear prepeak, nonlinear postpeak, shearing), there is a systematic decrease of the b value with increasing confining pressure. A numerical model based on progressive elastic damage and the finite element method allows simulations of the main experimental observations on AE and of a wide range of macroscopic behaviors from brittleness to ductility. The model reproduces a decrease in the b value that appears to be related to the type of macroscopic behavior (brittle-ductile) rather than to the confining pressure. Both experimental and numerical results suggest a relationship between the b value and the brittle-ductile transition. Moreover, these results are consistent with recent earthquake observations and give new insight into the behavior of the Earth's crust.
[1] We analyse the statistical pattern of seismicity before a 1-2 10 3 m 3 chalk cliff collapse on the Normandie ocean shore, Western France. We show that a power law acceleration of seismicity rate and energy in both 40 Hz-1.5 kHz and 2 Hz-10kHz frequency range, is defined on 3 orders of magnitude, within 2 hours from the collapse time. Simultaneously, the average size of the seismic events increases toward the time to failure. These in situ results are derived from the only station located within one rupture length distance from the rock fall rupture plane. They mimic the ''critical point'' like behavior recovered from physical and numerical experiments before brittle failures and tertiary creep failures. Our analysis of this first seismic monitoring data of a cliff collapse suggests that the thermodynamic phase transition models for failure may apply for cliff collapse.
We present a new modeling framework for sea-ice mechanics based on elasto-brittle (EB) behavior. the EB framework considers sea ice as a continuous elastic plate encountering progressive damage, simulating the opening of cracks and leads. As a result of long-range elastic interactions, the stress relaxation following a damage event can induce an avalanche of damage. Damage propagates in narrow linear features, resulting in a very heterogeneous strain field. Idealized simulations of the Arctic sea-ice cover are analyzed in terms of ice strain rates and contrasted to observations and simulations performed with the classical viscous–plastic (VP) rheology. the statistical and scaling properties of ice strain rates are used as the evaluation metric. We show that EB simulations give a good representation of the shear faulting mechanism that accommodates most sea-ice deformation. the distributions of strain rates and the scaling laws of ice deformation are well captured by the EB framework, which is not the case for VP simulations. These results suggest that the properties of ice deformation emerge from elasto-brittle ice-mechanical behavior and motivate the implementation of the EB framework in a global sea-ice model.
Abstract. Local damage processes that have been reported for ductile and brittle macroscopic behaviours are shown here to provide a possible link between these two contrasting behaviours. Using a local progressive damage law within a linear tensoffal elastic interaction model, we reproduce experimentally observed macroscopic non-linear behaviours that continuously range from ductility with diffuse damage to brittlepoint of view, AE is used as a relevant tool to monitor the crack nucleation and growth, i.e. damage increase, in space,
[1] We propose a numerical model based on static fatigue laws in order to model the time-dependent damage and deformation of rocks under creep. An empirical relation between time to failure and applied stress is used to simulate the behavior of each element of our finite element model. We review available data on creep experiments in order to study how the material properties and the loading conditions control the failure time. The main parameter that controls the failure time is the applied stress. Two commonly used models, an exponential t f Àexp (Àbs/s 0 ) and a power law function t f Às b0 fit the data as well. These time-to-failure laws are used at the scale of each element to simulate its damage as a function of its stress history. An element is damaged by decreasing its Young's modulus to simulate the effect of increasing crack density at smaller scales. Elastic interactions between elements and heterogeneity of the mechanical properties lead to the emergence of a complex macroscopic behavior, which is richer than the elementary one. In particular, we observe primary and tertiary creep regimes associated respectively with a power law decay and increase of the rate of strain, damage event and energy release. Our model produces a power law distribution of damage event sizes, with an average size that increases with time as a power law until macroscopic failure. Damage localization emerges at the transition between primary and tertiary creep, when damage rate starts accelerating. The final state of the simulation shows highly damaged bands, similar to shear bands observed in laboratory experiments. The thickness and the orientation of these bands depend on the applied stress. This model thus reproduces many properties of rock creep, which were previously not modeled simultaneously.Citation: Amitrano, D., and A. Helmstetter (2006), Brittle creep, damage, and time to failure in rocks,
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