Closure to “Two-Dimensional Discrete Element Theory for Rough Particles” by Mingjing Jiang, Serge Leroueil, Hehua Zhu, Hai-Sui Yu, and Jean-Marie Konrad

Abstract

The discusser was pleased and interested to see the application by Jiang et al. of discrete element method (DEM) technology to rough particles. In particular, the discusser was interested to see the claim by Jiang et al. that in the DEM, with a usual point-contact model, the couple/moment is neither available at the contact nor able to be transferred from one particle to the other. It would be for others more expert in DEM applications to judge the correctness of that claim; the discusser is happy to accept the claim at face value in relationship to the DEM methodology. However, it may be of interest to Jiang et al., and possibly the readership in general, to learn that a numerical model incorporating the couple/moment with the associated rotational mode of deformation was developed and published a very long time ago (Burman 1972). This development occurred as part of a doctoral research program by Burman at James Cook University of North Queensland in Australia under the guidance of well-known discontinuum instigator and long-term proponent, Professor Hugh Trollope. It so happened that at the time when Dr. Cundall was completing his initial work that lead ultimately to the DEM theory (Cundall 1971), Burman was engaged in a similarly directed effort to investigate the mechanics of blocky media, albeit by a different approach and for somewhat different ends. Dr. Cundall, working in the Royal School of Mines at Imperial College, was principally interested in miningrelated activities including dynamic phenomena, such as blasting and mass movements of blocky materials. Meanwhile, with a civil engineering bias, Burman was principally interested in the maintenance of structural integrity within blocky materials, including slopes and tunnels in jointed rock masses. This difference in emphasis was expressed in the greater attention by Burman to modeling rough contacts, whereas Dr. Cundall’s attention was directed to capturing the more spectacular and large block movements. Burman has always felt that the basic point-contact model used by Dr. Cundall was remarkably successful, in spite of its formational simplicity. In Burman’s view, this success demonstrated the power fundamentally involved in having specifically recognized the discrete nature of particles in a discontinuum regardless of the sophistication or otherwise of the micromodel used. The Burman model was developed for a system of rigid blocks interacting through a series of Goodman joint type finite elements (Goodman et al. 1968). The assumption of rigid blocks was necessitated at the time because of the severely restricted capacity of computers to deal with large sets of simultaneous equations. That restriction is no longer relevant, but it is still convenient to assume rigidity, as the writers have done, and to adopt the linearizing assumption of small incremental rotations. The Burman model, which is finite element based, employed the condition of static equilibrium together with the transformation of joint nodal displacements and nodal forces to associated block centroids yielding the basic matrix equation for equilibrium of an individual block (b) as