Transition from static to kinetic friction: Insights from a 2D model

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic slider/rigid substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory micro-slip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress build-up due to both elastic loading and micro-slip-related relaxations depend only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a non-trivial scaling parameter.Comment: 5 pages, 4 figures, accepted for publication in Physical Review Letter

Long-range effects in granular avalanching

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to $r^{-\rho}$, $r$ being the distance traveled by a grain in a single topling event. The exponent $\rho$ controls the average rolling distance. We have shown that the crossover from power law to stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for $1<\rho<2$ where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short range regime for $\rho>2$, where the average rolling distance is independent of the system size.Comment: 5 pages, 3 figure

Anomalous Transport in Conical Granular Piles

Experiments on 2+1-dimensional piles of elongated particles are performed. Comparison with previous experiments in 1+1 dimensions shows that the addition of one extra dimension to the dynamics changes completely the avalanche properties, appearing a characteristic avalanche size. Nevertheless, the time single grains need to cross the whole pile varies smoothly between several orders of magnitude, from a few seconds to more than 100 hours. This behavior is described by a power-law distribution, signaling the existence of scale invariance in the transport process.Comment: Accepted in PR

Universality classes for rice-pile models

We investigate sandpile models where the updating of unstable columns is done according to a stochastic rule. We examine the effect of introducing nonlocal relaxation mechanisms. We find that the models self-organize into critical states that belong to three different universality classes. The models with local relaxation rules belong to a known universality class that is characterized by an avalanche exponent $\tau \approx 1.55$, whereas the models with nonlocal relaxation rules belong to new universality classes characterized by exponents $\tau \approx 1.35$ and $\tau \approx 1.63$. We discuss the values of the exponents in terms of scaling relations and a mapping of the sandpile models to interface models.Comment: 4 pages, including 3 figure

Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice

We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are $\tau$ = 1.21(2) for the avalanche size distribution and $D$ = 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of $d_B$ = 1.58(2). Using a set of scaling relations, we can calculate the roughness exponent $\alpha = D - d_B$ = 0.41(3) and the dynamic exponent $z = D(2 - \tau)$ = 1.56(8). This result is compared with that obtained from a power spectrum analysis of the surface roughness, which yields $\alpha$ = 0.42(3) and $z$ = 1.5(1) in excellent agreement with those obtained from the scaling relations.Comment: 7 pages, 8 figures, accepted for publication in PR

Mechanisms of overburden deformation associated with the emplacement of the Tulipan sill, mid-Norwegian margin

The emplacement of igneous intrusions into sedimentary basins mechanically deforms the host rocks and causes hydrocarbon maturation. Existing models of host-rock deformation are investigated using high-quality 3D seismic and industry well data in the western Møre Basin offshore mid-Norway. The models include synemplacement (e.g., elastic bending-related active uplift and volume reduction of metamorphic aureoles) and postemplacement (e.g., differential compaction) mechanisms. We use the seismic interpretations of five horizons in the Cretaceous-Paleogene sequence (Springar, Tang, and Tare Formations) to analyze the host rock deformation induced by the emplacement of the underlying saucer-shaped Tulipan sill. The results show that the sill, emplaced between 55.8 and 54.9 Ma, is responsible for the overlying dome structure observed in the seismic data. Isochron maps of the deformed sediments, as well as deformation of the younger postemplacement sediments, document a good match between the spatial distribution of the dome and the periphery of the sill. The thickness t of the Tulipan is less than 100 m, whereas the amplitude f of the overlying dome ranges between 30 and 70 m. Spectral decomposition maps highlight the distribution of fractures in the upper part of the dome. These fractures are observed in between hydrothermal vent complexes in the outer parts of the dome structure. The 3D seismic horizon interpretation and volume rendering visualization of the Tulipan sill reveal fingers and an overall saucer-shaped geometry. We conclude that a combination of different mechanisms of overburden deformation, including (1) elastic bending, (2) shear failure, and (3) differential compaction, is responsible for the synemplacement formation and the postemplacement modification of the observed dome structure in the Tulipan area

1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments

We study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge-Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38, 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding (i) an internal viscosity, (ii) an interfacial stiffness and (iii) an initial tangential force distribution at the interface, we manage to (i) avoid the model's unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.Comment: 13 pages, 14 figures, accepted in Tribology Letter

The structure of reactive grain-boundaries under stress containing confined fluids

We present numerical experiments on structure development in grain-boundaries during dissolution–precipitation creep. Two solids that are represented by an elastic spring configuration are pressed together with a compressible fluid in the grain-boundary. The solid can dissolve or precipitate depending on elastic and surface energy as well as fluid pressure and concentration of dissolved material in the fluid. We perform a number of numerical experiments with different starting configurations that represent a large-scale island-channel interface with solid–solid contacts across the islands, a rough grain-boundary interface with a fluid along the whole interface and a smooth thin-film interface. The simulations suggest that the solid–solid islands become unstable by necking and anti-cracking so that the island-channel interface will develop into a grain-boundary interface. The rough interface of the grain-boundary will coarsen with time so that in the extreme case a smooth thin-film interface will emerge. However the thin-film interface is also not necessarily stable but may develop into a rough grain-boundary where the roughness is initiated by heterogeneous dissolution of the solid. Our numerical experiments suggest that interface structures during dissolution–precipitation creep are transient and that the dominance of one interface structure depends on material properties, the displacement rate, purity of the reacting solid and the scale of observation

Instabilities in stress corrosion and the transition to brittle failure

Studies on the dissolution of stressed crystals have shown that stress corrosion can lead to roughening of interfaces. The corrosion pattern develops due to gradients in elastic energy along a free crystal surface with an initial roughness. Dissolution will cause further increase in elastic energy, which in turn will speed up dissolution, the so-called Asaro-Tiller-Grinfeld instability. We present a numerical model in order to study the effect of stress corrosion that is observed in physical experiments of interface roughening of brittle salt crystals. In the simulations a salt crystal that is immersed in saturated brine is stressed and dissolution patterns develop. Stress corrosion can lead to an Asaro-Tiller-Grinfeld instability that develops into cusp instabilities and crack-like structures or anti-cracks. The system breaks its symmetry and produces a secondary instability where the number of growing anti-cracks is reduced. This coarsening of the surface roughness is due to stress-shielding effects of growing anti-cracks. Finally, one single anti-crack remains on each side of an initial hole as a "superstructure". The large anti-crack grows at an almost constant speed and eventually leads to brittle failure of the crystal. This mechanism may be important not only for dissolution-precipitation creep but also other phase-transitions and may lead to large scale brittle failure that can be associated with earthquakes