On Load Induced Anisotropy: Evolution Of Fabric Of Granular Materials

Marjan Oboudi

Dans les comptes rendus d’articles de la conférence: GeoVancouver 2016: 69th Canadian Geotechnical Conference

Session: FUNDAMENTALS - IX Physical & Numerical Modelling

ABSTRACT: The primary focusin this work is on developing an evolution law for the fabric of particulate materials as a function ofcontinuing deformation. The methodology involves performing a series of Discrete Element simulations for a granularassembly under evolving directionsof the principal strain and defining a correlation with the evolution of material axes. It isdemonstrated that granular materials with spherical particles may become anisotropic due to the initial compaction processand that the induced anisotropy is characterized by the coaxiality between the microstructure and the total strain tensors.R•SUM•L'objectif principal de ce travail est de d†velopper une loi d'†volution pour le tissu des mat†riaux particulaires en fonction dela d†formation permanente. La m†thodologie consiste ‡ effectuer une s†rie de simulations Discrete Element pour unensemble granulaire sous l'†volution des directions de la souche principale et d†finissant une corr†lation avec l' †volutiondes axes importants . Il est d†montr† que des mat†riaux granulaires avec des particules sph†riques peuvent …tre anisotropeen raison du processus de compactage initial et que l'anisotropie induite est caract†ris† par la coaxialit† entre lamicrostructure et le total des tenseurs dedeformation.1.INTRODUCTIONMany naturally occurring geomaterialsare anisotropicat the macroscale, which is strongly related to theirmicrostructure. Sedimentary rocks (like shales), forexample, display an inherent anisotropy, which resultsfrom the presence of bedding planes(Niandou et al.,1997).In certain geomaterials, in particular in granularmaterials, the inherent anisotropy isoftenweak andcan easily be altered in the course of deformationprocess. In this case the problem is more complex, asa specific fabric descriptor needstobe employed andan appropriate evolution law must be specified.Inthis study,a fabricdescriptor, whichisbased onstereological measurements,are reviewed.Aseriesof numerical simulations are carried out examining thecorrelation between the external load and theevolution of microstructure. It is demonstrated that ina typical granular medium, like sand at differentdegrees of initial compaction,anevolution lawformaterial microstructuremay be formulated byimposingcoaxialitybetween the microstructure andthe total strain tensors.2. DESCRIPTION OF STRUCTURAL ANISOTROPYOver the last few decades several different measuresof microstructure have been proposed. In this work,the focus is on descriptors that employ the basicprinciples of stereology. Stereological analyses havebeen broadly applied in the area of bone mechanics.An example here is the concept of —mean interceptlength– (MIL) introducedbyWhitehouse(1974)whichwas developed to describe the anisotropy oftrabecular bone architecture. In the areaofgeomechanics, the concepts of —directional porosity–(Pietruszczak and Krucinski, 1989)and/or the—arealpore size distribution– (Inglisand Pietruszczak, 2003)have been developed to quantify the spatialdistribution of void space within the REV.Consider the following basic measurement quantitiesderived from an array of parallel test lines. Let€()ilnbe the totallengthof test lines in the directionin.Furthermore, let€()iInðårepresent the sum of allintersections of these test lines with the void space,while()€iNncorresponds to the number ofintercepts.TheMILfabric measureemployed in thisworkasdefinedbelow(cf.Inglis and Pietruszczak,2003).Mean intercept length (MIL): For a grid of uniformlydistributed parallel lines aligned in the directionin, theMILdescriptor is defined as the total length ofintercepts with the void space divided by the numberof intercepts. Thus,ð(ð)ð(ð)ð(ð)€€iiiInMILnNnð=ðå(1)

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