Fragmentation energy in rock avalanches

La fragmentation est un des mécanismes opérant lors d'avalanche rocheuses. La quantification de l'énergie associée à ce mécanisme permettrait d'apprécier l'influence de celui-ci sur la phase post-rupture d'une avalanche rocheuse. Dans cet article, les distributions des tailles des blocs du massif rocheux et des débris sont présentées et comparées pour neuf cas d'avalanches rocheuses : cinq dans les montagnes Rocheuses canadiennes et quatre dans les Alpes européennes. Des degrés de fragmentation ont pu être estimés. Pour évaluer l'énergie de fragmentation, deux méthodes on été examinées : l'une est basée sur l'énergie de concassage et l'autre est basée sur l'énergie de sautage utilisée dans le domaine minier. Les résultats obtenus portent à croire qu'il y aurait une relation entre l'indice de réduction de taille (Rr = D50/d50) et l'énergie potentielle par unité de volume, normalisée par la résistance au double poinçonnement (?HG/?c). Les énergies de fragmentation calculées pour les neuf cas étudiés donne en moyenne 20 % de l'énergie potentielle. Une relation empirique entre Rr et ?HG/?c est proposée, et est par la suite utilisée pour définir un indice de désintégration (ID). Cet indice reflète la physique du processus de désintégration puisqu'il considère que l'indice de réduction de taille est fonction de l'énergie dissipée et de la résistance de la roche. Ces facteurs connus depuis longtemps n'avaient jamais été présentés d'une façon cohérente pour des cas d'avalanches rocheuses.Mots clés : avalanches rocheuses, désintégration, énergie de fragmentation, Rocheuses canadiennes, Alpes européennes.

Experiments on substratum roughness, grainsize and volume influence on the motion and spreading of rock avalanches

The main objective of the research is to link granular physics with the modelling of rock avalanches. Laboratory experiments consist to find a convenient granular material, i.e. grainsize and physical behaviour, and testing it on simple slope geometry. When the appropriate sliding material is selected, we attempted to model the debris avalanche and the spreading on a slope with different substratum to understand the relationship between the volume and the reach angle, i.e. angle of the line joining the top of the scar and the end of the deposit. For a better understanding of the mass spreading, the deposits are scanned with a laser scanner. Datasets are compared to see how the grain size and volume influence a debris avalanche. The relationship between the roughness and grainsize of the substratum shows that the spreading of the sliding mass is increased when the roughness of the substratum starts to be equivalent or greater than the grainsize of the flowing mass. The runout distance displays a more complex relationship, because a long runout distance implies that grains are less spread. This means that if the substratum is too rough the distance diminishes, as well if it is too smooth because the effect on the apparent friction decreases. Up to now our findings do not permit to validate any previous model (Melosh, 1987; Bagnold 1956).

Avalanches in a fluctuationless first-order phase transition in a random-bond Ising model

We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

Statistics of avalanches in martensitic transformations, II. Modelling

Using a scaling assumption, we propose a phenomenological model aimed to describe the joint probability distribution of two magnitudes A and T characterizing the spatial and temporal scales of a set of avalanches. The model also describes the correlation function of a sequence of such avalanches. As an example we study the joint distribution of amplitudes and durations of the acoustic emission signals observed in martensitic transformations [Vives et al., preceding paper, Phys. Rev. B 52, 12 644 (1995)].

Hysteresis and avalanches in the random anisotropy Ising model

ches. The critical point is characterized by a set of critical exponents, which are consistent with the universal values proposed from the study of other simpler models.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Random-field Potts model with dipolarlike interactions: Hysteresis avalanches and microstructure

A model for the study of hysteresis and avalanches in a first-order phase transition from a single variant phase to a multivariant phase is presented. The model is based on a modification of the random-field Potts model with metastable dynamics by adding a dipolar interaction term truncated at nearest neighbors. We focus our study on hysteresis loop properties, on the three-dimensional microstructure formation, and on avalanche statistics.

Distributions of avalanches in martensitic transformations

An experimental study of the acoustic emission generated during a martensitic transformation is presented. A statistical analysis of the amplitude and lifetime of a large number of signals has revealed power-law behavior for both magnitudes. The exponents of these distributions have been evaluated and, through independent measurements of the statistical lifetime to amplitude dependence, we have checked the scaling relation between the exponents. Our results are discussed in terms of current ideas on avalanche dynamics.

Studying Avalanches in the ground-state of the two-dimensional random field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising model as a function of both the external applied field B and the standard deviation ¿ of the Gaussian random-field distribution. The equilibrium evolution of the magnetization consists in a sequence of discrete jumps. These are very similar to the avalanche behavior found in the out-of-equilibrium version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jumps and find that both exhibit power-law behavior for the same value of ¿. The corresponding exponents are compared.

Sequential partitioning: an alternative to understanding size distributions of avalanches in first-order phase transitions

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.