Relationship Between Dilatancy, Stresses and Plastic Dissipation in a Granular Material with Rigid Grains
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RELATIONSHIP BETWEEN DILATANCY, STRESSES AND PLASTIC DISSIPATION IN A GRANULAR MATERIAL WITH RIGID GRAINS PIERRE EVESQUE* AND CHRISTIAN STEFANI** "*Laboratoire de Mdcanique: Sols-Structures-Mat(riaux, Ecole Centrale Paris, F-92295 CHATENAY-MALABRY Cedex, FRANCE ** Laboratoire Central des Ponts et Chauss6es, Antenne d'Orly, 58 boulevard Lefebvre, 75732 PARIS Cedex 15, FRANCE
ABSTRACT : By considering a drained cohesionless granular sample made up of rigid grains and submitted to a triaxial test, we derive an equation relating the dilatancy K, the deviatoric stress q and the confining pressure p to the energy losses Dpib& due to plastic yielding. We demonstrate that the system is contracting (K < 0) at q=0, when q is increasing and that spontaneous uncontrolled yielding begins occurring when dilatancy K is maximum. We also demonstrate the existence of the characteristic state introduced by Luong and Habib and the existence of the critical state of Schofield and Wroth. We give at last a method to determine the plastic losses during a triaxial cell test using the experimental data.
INTRODUCTION : Physics of "sandpile" has been attracting a great deal of works recently[ 1-91, especially on avalanches, I/f noise and self-organized criticality. Unfortunately, most of the experimental studies[4-5] on sandpile avalanches has proved the existence of a typical avalanche size, which is in contradiction with the theoretical l/f noise predictions; (it is only when the pile is small enough that one may observe avalanches obeying scaling laws and a 1/f noise [6]. A possible reason of the discrepancy between the BTW model and the experimental results has been described by one of us recently [7-9], and the sketch of a coherent view which predicts both a quasi-periodic regime of intermittences, with quasi-periodic avalanches, and finite size effects which exhibit self-organized criticality has been sketched[7-9]. The trick to obtain this unified scheme is to introduce in the BTW model of sandpile the effect of dilatancy; (dilatancy and its mechanical properties will be defined later in the text, see Eq. 2). It turns out that a classical procedure in soil mechanics to understand and quantify the effect of dilatancy is to study the soil behaviors through a triaxial test [7-9]. We will try to give a better understanding of the deformation and dissipation processes occurring in a pile; this will be done by deriving some relationships between different quantities measured with this set-up. So, we will get some theoretical explanation of the main features of the triaxial data; the main assumption is the form of the energy dissipation (Eq. (6)). We hope this will make soil behaviors more understandable. It is worth noting that most of these connections have been already observed experimentally and are basic experimental evidences in soil mechanics, although we have not found these equations derived in literature. We also derive new relationships that may be used as a test for the validity of our approach. Furthermore, if calculations base
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