Charles S. Campbell

Large‐scale landslide simulations: Global deformation, velocities and basal friction

The cause of the apparent small friction exhibited by long runout landslides has long been speculated upon. In an attempt to provide some insight into the matter, this paper describes results obtained from a discrete particle computer simulation of landslides composed of up to 1,000,000 two-dimensional discs. While simplified, the results show many of the characteristics of field data (the volumetric effect on runout, preserved strata, etc.) and with allowances made for the two-dimensional nature of the simulation, the runouts compare well with those of actual landslides. The results challenge the current view that landslides travel as a nearly solid block riding atop a low friction basal layer. Instead, they show that the mass is completely shearing and indicate that the apparent friction coefficient is an increasing function of shear rate. The volumetric effect can then be understood. With all other conditions being equal, different size slides appear to travel with nearly the same average velocity; however, as the larger landslides are thicker, they experience smaller shear rates and correspondingly smaller fractional resistance.

Granular shear flows at the elastic limit

This paper describes computer simulation studies of granular materials under dense conditions where particles are in persistent contact with their neighbours and the elasticity of the material becomes an important rheological parameter. There are two regimes at this limit, one for which the stresses scale with both elastic and inertial properties (called the elastic–inertial regime), and a non-inertial quasi-static regime in which the stresses scale purely elastically (elastic–quasi-static). In these elastic regimes, the forces are generated by internal force chains. Reducing the concentration slightly causes a transition from an elastic to a purely inertial behaviour. This transition occurs so abruptly that a 2% concentration reduction can be accompanied by nearly three orders of magnitude of stress reduction. This indicates that granular flows near this limit are prone to instabilities such as those commonly observed in shear cells. Unexpectedly, there is no path between inertial (rapid) flow and quasi-static flow by varying the shear rate at a fixed concentration; only by reducing the concentration can one cause a transition from quasi-static to inertial flow. The solid concentrations at which this transition occurs as well as the magnitude of the stresses in the elastic regimes are strong functions of the particle surface friction, because the surface friction strongly affects the strength of the force chains. A parametric analysis of the elastic regime generated flowmaps showing the various regimes that might be realized in practice. Many common materials such as sand require such large shear rates to reach the elastic–inertial regime that it is unattainable for all practical purposes; such materials will demonstrate either an elastic–quasi-static behaviour or a pure inertial behaviour depending on the concentration – with many orders of magnitude of stress change between them. Finally, the effects of nonlinear contacts are investigated and an appropriate scaling is proposed that accounts for the nonlinear behaviour in the elastic–quasi-static regime.

The stress tensor for simple shear flows of a granular material

The complete stress tensor has been measured using a computer simulation of an assemblage of rough, inelastic spheres in an imposed simple shear flow. Only five components of the stress tensor were found to be significantly different from zero. These represent the disperssive normal stresses τ xx , τ yy and τ zz and the in-the-shear-plane shear stresses τ xy and τ yx ; furthermore, the two off-diagonal stresses, τ xy and τ yx , were found to be equal so that the resultant stress tensor is symmetric. Two modes of microscopic momentum transport produce the final macroscopic stress tensor: the streaming or kinetic mode by which particles carry the momentum of their motion as they move through the bulk material, and the collisional mode by which momentum is transported by interparticle collisions. The contribution of each to the final result is examined separately. The friction coefficient, the ratio of shear to normal force, is shown to decrease at dense packings for both the collisional and streaming modes. Also observed were normal stress differences, both in and out of the shear plane, reflecting anisotropies in the granular temperature.

Self-Lubrication for Long Runout Landslides

This paper, by simple model studies, demonstrates that the low friction observed for long runout landslides can be explained in terms of simple particle dynamics, without the intervention of extraneous devices such as air-layers. The proposed mechanism assumes that the bulk of material rides on a thin layer of highly agitated particles at low concentration. By employing the technique of two-dimensional particle dynamic computer simulation, I demonstrate that (1) this is the state to which a granular material tends when sliding down an inclined plane and (2) it is sufficient to explain the friction reduction. Finally, I present a simple mathematical model that yields order of magnitude predictions of runout distance. The argument suggests that there may be nothing particularly special about long runout landslides (except, perhaps, in the way they are initiated) and that they behave as would be expected given the current state of knowledge of particle flows.

The stress tensor in a two-dimensional granular shear flow

A computer simulation is used to make a detailed study of the stress tensor in a simple shear flow of two-dimensional disks. The stresses are shown to arise from two momentum-transfer mechanisms : the ‘streaming ’ or kinetic mode, by which momentum is carried by particles as they move through the bulk material; and the collisional mode, by which momentum is transferred from one point to another in the material by interparticle collisions. As might be expected, the results show that the streaming mode dominates at disperse packings and the collisional mode dominates at dense packings. The friction coefficient, the ratio of shear to normal forces, is shown to decrease at high particle packing for both the collisional and streaming modes of transport. Normal-stress differences are observed within the shear plane and are evident in both the streaming and collisional parts.

The interface between fluid-like and solid-like behaviour in two-dimensional granular flows

The effective phase change from fluid behaviour to solid behaviour, that too often occurs in granular flow and brings with it such unwelcome events as funnel flows in hoppers and clogging of other material handling devices, is studied using a discrete particle computer simulation of a Couette flow with gravity. This simulation exhibits the full range of granular flow behaviour, from a stagnant solid-like material, through a quasi-static transition zone, to a rapid granular flow. The most important result is that the first movement in the material just above the static bed occurs in a quasi-static mode at a fixed value of the stress ratio τ xy /τ yy . Thus, it appears that the primary transition from solid to fluid behaviour is a yield-like phenomenon and can be described by a Mohr-Coulomb-type failure criterion.

Self-diffusion in granular shear flows

The collisionally induced random particle velocities in a rapid granular shear flow drive the diffusion of particles in manner directly analogous to the thermal diffusion of molecules or the eddy-induced diffusion in a turbulent flow. This paper reports measurements, via computer simulation, of the anisotropic diffusion tensor for a granular shear flow. The components are determined both by particle tracking and through velocity correlations, which are found to agree with reasonable accuracy. As might be expected from symmetry arguments, there are four non-zero components generated in a simple shear flow: the three diagonal components and one off-diagonal component.

Liquid–solid flows using smoothed particle hydrodynamics and the discrete element method

Abstract This study presents a computational method combining smoothed particle hydrodynamics (SPH) and the discrete element method (DEM) to model flows containing a viscous fluid and macroscopic solid particles. The two-dimensional numerical simulations are validated by comparing the wake size, drag coefficient and local heat transfer for flow past a circular cylinder at Reynolds numbers near 100. The central focus of the work, however, is in computing flows of liquid–solid mixtures, such as the classic shear-cell experiments of Bagnold. Hence, the simulations were performed for neutrally buoyant particles contained between two plates for different solid fractions, fluid viscosities and shear rates. The tangential force resulting from the presence of particles shows an increasing dependence on the shear rate as observed in the Bagnold experiments. The normal force shows large variations with time, whose source is presently unclear but independent of the direct collisions between particles and the walls.

Self‐lubrication for Long Runout Landslides: Examination by computer simulation

This paper describes the use of a discrete particle computer simulation to test whether the apparent low friction exhibited by long runout landslides could be explained in terms of simple granular mechanics. The flow structure consists of an active basal shear zone supporting the majority of the landslide, which travels as a relatively solid plug. The observed runout appears to depend on the total energy dissipation which is a trade-off between (1) the inelasticity of the particles, which governs the energy dissipated in each event, and, (2), the size of the dissipating shear zone, which governs the number of particles that are actively dissipating energy. Very inelastic particles quickly dissipate the work performed at boundaries and result in thin dissipative zones. As a result, these two factors balance and the runout is nearly independent of particle inelasticity. Along the same lines, increasing the boundary roughness was found to increase the size of the dissipative shear zone and markedly decrease the runout. Also, a distribution of particle sizes destroyed ordered structures within the body which, once again, increases the dissipation and decreases the runout. Unfortunately, the simulations also indicate that the runout should be independent of the depth of the flow and thus cannot account for the observed volumetric effect on runout.

Computer simulation of impact-induced particle breakage

Abstract The breakage induced in single circular particles that impact on solid plates has been studied using a two-dimensional simulation of solid fracture. The simulation allows the computer ‘experimenter’ to vary independently material properties such as Youngs modulus, Poissons ratio and work of fracture, flexibility that is unavailable in direct experimentation. Where comparison is possible, the simulation appears to mimic experimental results accurately. This study shows that the size distributions are, as would be expected, most strongly dependent on the collisional energy. Of secondary importance is the ratio of the impact velocity to the sound speed within the solid material. Finally, the size distributions show little effect of Poissons ratio.