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Bottlenecks occur in a wide range of situations from pedestrians, ants, cattle, and traffic flow to the transport of granular materials. We examine granular flow across a bottleneck using simulations of monodisperse disks. Contrary to expectations but consistent with previous work, we find that the flow rate across a bottleneck actually increases if an obstacle is optimally placed before it. Using the hourglass theory and a velocity-density relation, we show that the peak flow rate corresponds to a transition from free flow to congested flow, similar to the phase transition in traffic flow.

[1] Dynamic simulations of homogeneous, heterogeneous and bimaterial fault rupture using modified slip-weakening frictional laws with static restrengthening are presented giving rise to both crack-like and pulse-like rupture. We demonstrate that pulse-like rupture is possible by making a modification of classical slip-weakening friction to include static restrengthening. We employ various slip-weakening frictional laws to examine their effect on the resulting earthquake rupture speed, size and mode. More complex rupture characteristics were produced with more strongly slip-weakening frictional laws, and the degree of slip-weakening had to be finely tuned to reproduce realistic earthquake rupture characteristics. Rupture propagation on a fault is controlled by the constitutive properties of the fault. We provide benchmark tests of our method against other reported solutions in the literature. We demonstrate the applicability of our elastoplastic fault model for modeling dynamic rupture and wave propagation in fault systems, and the rich array of dynamic properties produced by our elastoplastic finite element fault model. These are governed by a number of model parameters including: the spatial heterogeneity and material contrast across the fault, the fault strength, and not least of all the frictional law employed. Asymmetric bilateral fault rupture was produced for the bimaterial case, where the degree of material contrast influenced the rupture speed in the different propagation directions.

SUMMARY Numerical modelling of dynamic rupture is conducted along faults separating similar and dissimilar materials. Supershear transition is enhanced in the direction of slip of the stiffer material (the negative direction) due to the bimaterial effect whereby a decrease in normal stress in front of the crack tip supports yielding ahead of the rupture. In the direction of slip of the more compliant material (the positive direction), an increase in normal stress ahead of the rupture tip delays or prevents the supershear transition, whereas the impact of the bimaterial effect on subshear ruptures is to promote rupture in the positive direction due to the tensile stress perturbation behind the rupture tip in this direction. We demonstrate that the material contrast and the parameter S control whether the transition from sub‐ to supershear velocity (supershear transition) is smooth or follows the Burridge–Andrews mechanism. Supershear transition along interfaces separating dissimilar materials is possible for higher values of the parameter S than supershear transition along material interfaces separating similar materials. The difference between pulse‐like and crack‐like rupture is small with regard to the supershear transition type.

SUMMARYDynamic simulations of homogeneous and bi-material fault rupture are modeled using different loading approaches. We demonstrate that a numerical method of quasi-static loading is capable of immediately loading bi-material interfaces to rupture without the iteration over multiple time steps. We show that our method is a computationally inexpensive approach to tectonic loading and is capable of loading a fault to failure. We observe earthquake rupture speed, slip distances and slip rates for homogeneous and bi-material faults for various applied stresses, friction properties and material contrasts across the bi-material interface. We comment on causes for unilateral rupture growth. The results are consistent with experimental results and highlight the importance of material heterogeneity in determining the rupture characteristics of earthquake faults.

Summary Preexisting flaws and rock heterogeneity have important ramifications on the process of rock fracturing and on rock stability in many applications. Therefore, there is great interest in numerical modelling of rock fracture and the underlying mechanisms. We simulated damage evolution and fracture propagation in sandstone specimens containing a preexisting 3‐D surface flaw under uniaxial compression. We applied the linear elastic damage model based on the unified strength theory following the rock failure process analysis code. However, in contrast to the rock failure process analysis code, we used the finite element method with tetrahedron elements on unstructured meshes. It provided higher geometrical flexibility and allowed for a more accurate representation of the disk‐shaped flaw with various flaw depths, angles, and lengths through locally adapted meshes. The rock heterogeneity was modelled by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values were then interpolated to the computational finite element method mesh. This method introduced an additional length scale for the rock heterogeneity represented by the cell size in the sampling grid. The generation of three typical surface cracking patterns, called wing cracks, anti‐wing cracks, and far‐field cracks, were identified in the simulation results. These depend on the geometry of the preexisting surface flaw. The simulated fracture propagation, coalescence types, and failure modes for the specimens with preexisting surface flaw show good agreement with recent experimental studies.

One of the most challenging problems which arises in continuum damage mechanics is the selection of variables to describe the internal damage. Many theories have been proposed and various types of damage variables ranging from scalar to vector to tensor quantities have been used. In this paper we consider anisotropic damage and the most general form for damage by using a fourth order tensor for the damage variables. We demonstrate how experimentally measured quantities can be related to the internal tensorial damage variables. We apply this analysis to experiments of an initially isotropic solid becoming transverse isotropic under triaxial or uniaxial stress loading.

We investigate significant heterogeneous stresses along bimaterial interfaces in laboratory and numerical experiments. These stresses, partially induced by model or experimental configuration, affect the supershear transition length and rupture speed, mode and directivity in uniaxial compression tests and dynamic rupture experiments with bimaterial interfaces. Using numerical simulations we show that normal and tangential stresses at the fault are distorted by the different stress-strain relationships of the materials. This distortion leads to altered supershear transition lengths, higher rupture potencies and amplifies the preference for rupture in the direction of slip of the slower and more compliant material. We demonstrate how this stress-distortion can be decreased in laboratory experiments by using larger specimen samples and in numerical models by using periodic boundary conditions.