Computer simulation of three dimensional shearing of granular materials: Formation of shear bands

Department of Physics, University Duisburg-Essen, GermanyABSTRACT: We used computer simulations to study spontaneous strain localization in granular materi-als, as a result of symmetry breaking non-homogeneous deformations. Axisymmetric triaxial shear testswere simulated by means of standard three-dimensional Distinct Element Method (DEM) with spheri-cal grains. Carefully prepared dense specimens were compressed between two platens and, in order tomimic the experimental conditions, stress controlled, (initially) axisymmetric boundary conditions wereconstructed. Strain localization gave rise to visible shear bands, previously found experimentally undersimilar conditions by several groups, and different morphologies could be reproduced. We examinedthe stress-strain relation during the process and found good agreement with experiments. Formationmechanism of shear bands is discussed.1 INTRODUCTIONSpontaneous symmetry breaking in granular mate-rials occurs in many different forms. Here we focuson strain localization and subsequent developmentof shear bands. Shear bands appear nearly alwaysif dry granular material is subjected to shear. Itsfirst study dates back to the nineteenth centuryand since then it was investigated in many differ-ent geometries and specially designed laboratorytests (e.g. plane strain, biaxial, and triaxial tests).Here we present numerical studies of axisymmetrictriaxial tests, the most common laboratory tests inGeomechanics.In a simplified picture, a triaxial test typicallyconsists of a cylindrical specimen enclosed betweentwo end platens and surrounded by a rubber mem-brane. An external pressure is applied on the mem-brane, either by placing the system into a pressur-ized fluid, or creating a relative vacuum inside thesystem. The end platens are pressed against eachother in a controlled way, either with constant ve-locity (strain control) or with constant force (stresscontrol). The force resulting on the platens, or thedisplacement rate of the platens is recorded, as wellas the volume change of the specimen.The triaxial test is an elementary test, per-formed to obtain mechanical properties of soils.Antifriction devices (lubricated end platens) weredesigned in order to suppress strong heteroge-neous responses, such as barreling and local-ization of deformation along failure planes. Inthe past 20 years the study of localization pat-terns gained more attention and strain localiza-tion became an important research field, as ex-perimental tools as Computed Tomography (CT)became available to study the internal struc-ture of strained specimens (Desrues et al. 1996;Batiste et al. 2004). Such studies revealed complexlocalization patterns and shear band morphologiesdepending on the test conditions.2 SIMULATION METHODWe used standard three-dimensional DistinctElement Method (Cundall & Strack 1979) (alsoknown as Molecular Dynamics) to perform sim-ulations of strain controlled triaxial shear tests.As an advantage, contrary to the Finite Ele-ment Method (FEM) commonly used in sim-