�� . Powder Technology 109 2000 192���205 www.elsevier.comrlocaterpowtec Micro-deformation mechanism of shear banding process based on modified distinct element method Kazuyoshi Iwashita ), Masanobu Oda Department of Ci��il and En��ironmental Engineering, Saitama Uni��ersity, Urawa, Saitama 338-8570, Japan Accepted 21 September 1999 Abstract �� . Numerical simulation tests were carried out using the distinct element method DEM by paying much attention to the micro-deforma- tion mechanism leading to the development of shear bands. To do this, the conventional DEM was modified slightly such that the effect �� .. of rolling resistance at contact points could be taken into account called MDEM It is found that MDEM can be a powerful tool for simulating not only the generation of large voids inside a shear band but also the high gradient of particle rotation along the shear band boundaries, in a quite similar manner to those observed in natural granular soils. It is concluded, based on the numerical simulation tests, that the basic micro-deformation mechanism ending up with the formation of shear bands is in the generation of a column-like structure during the hardening process and its collapse in the softening process. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Numerical simulation Micromechanics Shear band development Dilatancy Granular material Column-like structure 1. Introduction In a plane strain test, a dense granular soil is first deformed homogeneously. Around a peak stress, however, the deformation suddenly localizes into narrow bands �� ., called the shear bands and the stress drops sharply down to a residual stress state. Understanding this behavior is of great importance to solve some engineering problems re- lated to soil stability. For example, slope stability is com- monly analyzed on the assumption that the failure occurs ��e.g., w x.. along a circular shear band Ref. 17 In order to clarify the mechanical meanings of the shear band, many research works have already been done for the past four ��e.g., w18, decades in the field of soil mechanics Refs. x.. 20,21,29 More importantly, the strain localization is still a hot topic in the theoretical, as well as experimental, ��e.g., study of mechanics of granular materials Refs. w x.. 10,12,19,32,33,37,39 It should be emphasized here that in spite of such extensive studies, the micro-deformation mechanism lead- ) Corresponding author. Fax: q81-48-858-7374 e-mail: iwashita@dice.dr5w.saitama-u.ac.jp ing to the development of shear bands is not yet well understood. This is partially because we did not have any skill to observe the micro-process taking place inside. Recently soil engineers are paying more attention to nu- merical simulation methods to overcome the present diffi- ��e.g., w x.. culty Refs. 3,6,4,8,9,13,16,35,34,36 To do this successfully, however, a question must be answered: does such a conventional numerical simulation method provide a sound basis for simulating the micro-process of the shear band development, as well as the overall stress���strain behavior? w x w x Oda 24 and Oda and Kazama 26 recently observed the microstructure of shear bands developed in several natural sands, by means of X-ray application and an optical method using a microscope and thin sections. The �� . two results are worth noting here: 1 very large voids are generated inside a shear band, while shear strain is being ��or concentrated, and as a result of this, the void ratio . porosity can exceed the corresponding maximum one �� . determined by a standard method and 2 particles rotate extensively in the shear band so that a high particle rotation gradient is generated along the boundaries. An important point is that nobody has succeeded in reproduc- ing such huge voids and a high rotation gradient by any conventional numerical method. In other words, there might 0032-5910r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. �� . PII: S 0 0 3 2 - 5 9 1 0 9 9 0 0 2 3 6 - 3

( ) K. Iwashita, M. Odar Powder Technology 109 2000 192���205 193 �� . �� . Fig. 1. Idealization of contact behavior in MDEM. a Conventional DEM b MDEM. be something to be done in order to improve such conven- tional methods. This is the motivation of starting the present study. Each particle can move against neighboring particles by sliding andror rolling at contact points. The dominant role of sliding was considered, in success, in classical theories of strength and dilatancy of granular soils. Some experi- mental results tell us that rolling, rather than sliding, is a dominant micro-deformation mechanism leading to exten- ��e.g., w x.. sive dilatancy of granular media Ref. 28 Even in conventional numerical simulation analyses, particles can move actively by rolling. The problem is that the mi- crostructure developed in such a simulation analysis is w x different from that observed in natural sands. Oda 24 and w x Oda and Kazama 26 have suggested that the difference may arise from the fact that rolling occurs without mobiliz- ing any resistance at contact points in such conventional analyses. Rolling occurs freely provided particles are in contact with their neighboring through points contacts �� �� ... Fig. 1 a However, real particles show rough surface texture, and are even covered with a thin film of weathered �� �� ... products Fig. 1 b If this is the case, the particles may be in contact with their neighboring ones through contact surfaces, not pure points, so that rolling resistance can play a role to some extent in the contact behavior. Bardet and w x Huang 5 showed analytically, as well as experimentally, that the rolling resistance exists even at contacts among cylindrical particles. w x Recently, Iwashita and Oda 14 proposed a modified �� ., version of the distinct element method called MDEM which is capable of dealing with the rolling resistance at contact points, and showed that MDEM provides a power- ful tool in the simulation of the micro-structure develop- ment as well as the overall stress strain relation. In the present study, we focus on the micro-deformation mecha- nism leading to the development of shear bands, based on analyses using MDEM, and examine with seeking the reason why the huge voids as well as the high gradient of particle rotation is generated in the shear bands. 2. MDEM �� . In the conventional distinct element method DEM by w x, Cundall 8 each contact point is replaced by a set of normal and shear springs, normal and shear dashpots, normal and shear no-tension joints and a shear slider, �� .. which respond to a contact force f acting on it Fig. 2 The contact force, which is resolved into normal fn and tangential ft forces, is in equilibrium with the resistance Fig. 2. Contact model in MDEM.