Dynamical stress in force chains of granular media traveling on a bumpy terrain and the fragmentation of rock avalanches

The dynamics of grain fragmentation is usually ignored in the study of rapid granular flows. This is realistic for experiments on small-scale chutes or in many industrial processes where the specific granular energy is too small for particles to break but is unrealistic for natural rock avalanches, where the extremely comminuted state is perhaps the most evident aspect of the deposit. Based on observations of natural landslide deposits, it has been suggested that the stress may increase along a sequence of force chains formed by the granular material. However, simple calculations show that rock avalanche deposits exhibit a much more advanced degree of fragmentation than explainable with the static chain model. It is thus deduced that fragmentation along force chains must be combined with the effect of a bumpy topography. A simple model of a force chain moving on a rugged incline is then introduced, which exhibits increased fragmentation rate in the presence of a bumpy topography. It is shown that both the wave number and amplitude of the topographic undulations are significant in the efficiency of fragmentation.     

Anticrack model for skier triggering of slab avalanches

Skiers caught in a slab avalanche often trigger the avalanche themselves. Preventing those accidents necessitates a better understanding of the factors contributing to the failure of the snowpack under the action of a skier. In the present work, a mathematical model based on the principles of mixed-mode anticracking is proposed for skier triggering. The respective influences of the slope-normal and slope-parallel components of the load exerted by a skier on the prospective fracture plane are taken into account. A criterion for fracture propagation under typical skier loads is derived. It manifests a small number of factors that, combined, multiply the risk of triggering an avalanche. The criterion indicates, contrary to a common perception, that fracture is not more difficult to trigger in gentle slopes than in steep slopes. This major result of the model is confirmed by data obtained from field experiments.     

场地条件对滑坡-碎屑流运动冲击特征的影响研究

滑坡碎屑流的运动场地条件差异性大,导致相同规模滑坡的运动参数以及冲击作用存在显著差异.为了量化场地条件的作用机制,运用三维离散元模拟方法,以场地条件为变量,开展滑坡碎屑流的冲击研究,以斜坡坡度、堆积区坡度和场地几何特征为变量因素进行数值模拟分析.研究结果表明:不同斜坡坡度下,颗粒的平均速度时程曲线都可以分为加速和减速两...     

冲击荷载作用下岩石破碎分形特征

为探究冲击荷载作用下岩石破碎分形特征,选取花岗岩和砂岩开展分离式霍普金森压杆(SHPB)岩石动力学试验,得到了不同应变率下岩石的应力-应变曲线、破碎特性、强度参数和能量参数;利用标准筛对破碎后的岩块进行筛分,获取了岩石破碎块度分布曲线,并基于碎块粒径分布的质量分形模型计算出分形维数D;最后分析了分形维数与加载参数、破碎特性和耗能特性之间的关系。结果表明,岩石在冲击荷载作用下的破碎块度分布符合分形规律;动态抗压强度随应变率增大而增大,两者满足乘幂函数关系;加载过程中岩石应变率越大,岩石破碎程度越深,分形维数越大;分形维数与岩石破碎耗能密度之间满足乘幂函数关系。采用分形维数可实现对岩石在冲击荷载作用下的破碎特性、力学特性和破碎耗能特性的定量研究。     

Rheology of a wet, fragmenting granular flow and the riddle of the anomalous friction of large rock avalanches

The effective friction coefficient of rock avalanches diminishes gradually as a function of the avalanche volume. Large rock avalanches can reach run-out distances as long as ten times the fall height, despite the fact that the physics of friction would indicate a run-out only a little greater than the fall height. Numerous suggestions have been put forward to explain this remarkable departure from the predictions of both small-scale experiments and basic theory. It is shown here that accounting for rock fragmentation within the avalanche in combination with the presence of water, leads to results in line with the data.     

Simple model for the parametric analysis of grid amplifiers

A simple method for parametric analysis of grid amplifier performances is presented here. The proposed approach is based on the development of an equivalent transmission line model where each element of the grid is represented by an S-matrix derived from a full-wave simulation in an infinite array environment. The proposed technique makes it possible to investigate the dependency of grid amplifier performance on its major parameters taking into account the actual geometry of each part of the circuit while preserving the simulation efficiency.     

Onset mechanism of granular avalanches in inclining layers using a continuum model

What is the onset mechanism of macro scale avalanches? How do macro scale avalanches happen in the granular layers in an inclining box? The answers to these questions are the main part of our article aims. Using 3-dimensional simulation method we show the stresses, the stress ratios and the packing fractions in the processes where the onset of macro scale avalanches takes place. Based on our results the critical conditions of the onset of avalanches are presented. The onset mechanism of granular avalanches is elucidated. The onset of macro scale avalanches occurs in the small area, about 2% of the whole area, in the inclining granular layers. These are the conditions for the onset of macro scale avalanches that the shear and normal stresses and the packing fraction reach the maximum values at the same inclining angle. Then the stress ratio should be larger than the static frictional coefficient of materials. Aggregates of stick-slip like event are formed in the longitudinal direction. The number of aggregates decreases and the physical quantities in the aggregates rapidly increase with increasing inclining angle in the small area in which the onset of macro scale avalanche occurs.     

Anisotropic dynamic damage and fragmentation of rock materials under explosive loading

This paper describes the development of a constitutive model for predicting dynamic anisotropic damage and fragmentation of rock materials under blast loading. In order to take account of the anisotropy of damage, a second rank symmetric damage tensor is introduced in the present model. Based on the mechanics of microcrack nucleation, growth and coalescence, the evolution of damage is formulated. The model provides a quantitative method to estimate the fragment distribution and fragment size generated by crack coalescence in the dynamic fragmentation process. It takes account of the experimental facts that a brittle rock material does not fail if the applied stress is lower than its static strength and certain time duration is needed for fracture to take place when it is subjected to a stress higher than its static strength. Numerical results are compared with those from independent field tests.     

A physical model for plastic deformation

A general theoretical model for plastic deformation is presented, which is based on considerations of the variation of internal stored energy during deformation. It is proposed that the deformation rate will always be such that the rate of energy dissipation in the deforming material is minimal. The physical justification of this principle is discussed. The model is applied to dislocation deformation in metals and the result is then compared with experimental observations in aluminium.     

A model for deformation and fragmentation in crushable brittle solids

A unified framework of continuum elasticity, inelasticity, damage mechanics, and fragmentation in crushable solid materials is presented. A free energy function accounts for thermodynamics of elastic deformation and damage, and thermodynamically admissible kinetic relations are given for inelastic rates (i.e., irreversible strain and damage evolution). The model is further specialized to study concrete subjected to ballistic loading. Numerical implementation proceeds within a finite element context in which standard continuum elements represent the intact solid and particle methods capture eroded material. The impact of a metallic, spherical projectile upon a planar concrete target and the subsequent motion of the resulting cloud of concrete debris are simulated. Favorable quantitative comparisons are made between the results of simulations and experiments regarding residual velocity of the penetrator, mass of destroyed material, and crater and hole sizes in the target. The model qualitatively predicts aspects of the fragment cloud observed in high-speed photographs of the impact experiment, including features of the size and velocity distributions of the fragments. Additionally, two distinct methods are evaluated for quantitatively characterizing the mass and velocity distributions of the debris field, with one method based upon a local energy balance and the second based upon global entropy maximization. Finally, the model is used to predict distributions of fragment masses produced during impact crushing of a concrete sphere, with modest quantitative agreement observed between results of simulation and experiment.     

截断式脉冲水射流冲蚀煤岩特性数值模拟

基于光滑粒子动力学和有限元法(smoothed particle hydrodynamics-finite element method,SPH-FEM)耦合算法,建立了截断式脉冲水射流冲蚀煤岩的数值计算模型.通过对比数值模拟结果与相同工况下的实验结果,验证了该模型的有效性.在此基础上,探究了在截断式脉冲水射流冲击作用...     

A cellular automaton for segregation during granular avalanches

Segregation is a complex and poorly understood phenomenon that is prevalent in many industrial and natural granular flows. When grains flow down a slope [1–5], are spun in a rotating drum [6–8] or shaken in a box [9], we observe those grains organising into intriguing patterns. Kinetic sieving is the dominant mode of segregation in granular avalanches, where separation of particles occurs according to size. Using a cellular automaton we have modelled kinetic sieving as the swapping of particles in a one-dimensional system. From the cellular automaton we have deduced a continuum model to describe the segregation.     

A more general model for the analysis of the rock slope stability

The slope stability analysis has many applications in the engineering projects such as the dams, the roads and open pits structures. The method of analysis is usually based on the equilibrium conditions of the potential plane and wedge failures. The zone of the potential failure is stable whenever the stability forces dominate instability characteristics of the slope. In most of the classic methods of slope stability analysis, the joint surfaces are assumed to be continuous along the potential failure zone. These can cause an underestimated solution to the analysis. In this research the joint trace length is considered to be discontinuous across the potential surface of failure as it happens in nature. Therefore, there exists a rock bridge between the local joint traces. Because of the numerous problems related to the rock slope stability the above assumption is satisfied and the shear strength characteristics of intact rock have taken part in the analysis. The analysis presented here gives a better concept, view, and idea of understanding the physical nature of rock slopes and includes more parameters governing the stability of the potential failure zone.     

A finite element model of the fragmentation test for the case of a coated fiber

The fiber/matrix interface in composite materials is generally studied by means of the fragmentation test by using a single filament embedded in a polymeric matrix. The average shear strength, , of the interface is computed from the well-known shear-lag theory. For the case of a fiber coated with a thin layer of an interphase having a low modulus, a finite element analysis model has been developed to describe the profiles of the tensile and shear stresses along a fiber fragment. The introduction of a soft interlayer decreases the stresses at the ends of the fragment, and as the interlayer thickness increases this effect becomes more important. This model shows the limits of the shear-lag theory and could explain experimental results obtained for the case of an elastomer-coated glass fiber in an epoxy matrix.     

Multi-planar detection optimization algorithm for the interval charging structure of large-diameter longhole blasting design based on rock fragmentation aspects

The charge structure is an important factor in the adjustment of the energy distribution of explosives and the control of the blasting effect, especially in an underground large-diameter longhole, for interval charge millisecond blasting design. To achieve a reasonable charge structure, a multi-planar detection optimization (MDO) algorithm for charge structures is proposed based on the Harries mathematical model and the superposition method. The vector size of a fragment is transformed into a scalar ruler, and the definition of the spatial non-uniformity evaluation factor is used in the MDO algorithm. A detailed methodology is implemented using a Visual LISP program and validated for a case study of the Fankou lead–zinc mine in China. The results reveal that the MDO algorithm can improve the rock fragmentation and increase the energy utilization rate of explosives in large-diameter longhole blasting operations. This algorithm could be extremely helpful in the process of underground mine blast optimization.     

On the dynamic fragmentation of glass: a meso-damage model

This paper presents an anisotropic damage model to deal with the fragmentation induced by impact loadings on glass samples. As small-scale (i.e. sub-element) damage is described as well as cracks extending above the element scale, an approach referred to as “meso-damage” is developed. The latter, which is based on the knowledge of random distributions of initiation sites, predicts different regimes such as single or multiple fragmentation. The experimental opening crack pattern obtained in edge-on-impact test is reproduced numerically.     

An engineering fragmentation model for the impact of spherical projectiles on thin metallic plates

In this paper, an engineering fragmentation model is presented for the case of hypervelocity impact of a spherical projectile on a thin bumper plate at normal incidence. The range of impact velocities covered is the solid fragmentation regime up to the limits of complete melting of projectile and target material. The model was developed for an axisymmetric fragment cloud by consideration of the conservation laws for mass, momentum, and energy, as well as making a few assumptions on the morphology of the cloud. The fragment cloud is modeled discretely, i.e. each particle of the fragment cloud is considered separately in the analytical calculation. The model consists of mainly analytical relationships and a few empirical fit functions, where no analytical formulation was available. The model distinguishes between fragments originating from the projectile and fragments originating from the bumper plate. The projectile fragments are split into the central fragment and spall fragments. An exponential distribution function is assumed for the mass distribution of the projectile's spall fragments. The fragments from the bumper are assumed to have a uniform mass. All fragments are assumed to be of spherical shape. The fragmentation model was applied and calibrated during experiments, in which Al spheres impact on thin Al plates. The calibration experiments, performed using a two-stage light gas gun, were in the range of impact velocities between 4.8 and 6.7 km/s. In this velocity range, the model was calibrated against residual velocities measured and fragment mass distribution, which was indirectly determined by measuring the crater depth distributions in rear walls.