A constitutive model for granular materials is developed within the framework of strain hardening elasto-plasticity, aiming at describing some of the macroscopic effects of the degradation processes associated with grain crushing. The central assumption of the paper is that, upon loading, the frictional properties of the material are modified as a consequence of the changes in grain size distribution. One of the salient features of the proposed model is its capability of reproducing the stress dilatancy behaviour observed in Pozzolana Nera - a pyroclastic weak rock of the area of Rome (ltaly)- for which the minimum value of dilatancy follows the maximum stress ratio experienced by the material.
In recent years, considerable efforts have been devoted to the mathematical development of constitutive elasto-plastic models capable of reproducing those aspects of the observed behaviour of many natural geotechnical materials which are beyond the scope of classical Critical State elasto-plastic models for soils. These include: the occurrence of a peak in the stress-strain curve in a contractant as well as in a dilatant regime (Elliott & Brown 1985); the fact that the peak in the stress-strain curve does not correspond to the maximum rate of dilation (Aversa & Evangelista 1998; Elliott & Brown 1985; Maccarini 1987); the change of slope of the compressibility curve in one-dimensional and isotropic compression (Leroueil & Vaughan 1990). The experimental motivation for our work stems from the results of a laboratory investigation of the mechanical behaviour of a pyroclastic deposit from Central Italy (Pozzolana Nera). The material is a coarse-grained weak rock, whose physical properties and micro-structural features are described in detail in Cecconi & Viggiani (2001). For this material, bond deterioration and grain crushing upon loading occur at relatively low stress levels (of the order of 50 kPa) and are indistinguishable features of the mechanical behaviour. As typical for geotechnical materials, the mechanical behaviour of intact PozzolanaNera gradually changes from brittle and dilatant to ductile and contractant with increasing confining pressure. In the formulation of the model we assume that plastic straining induces a progressive reduction of the friction angle of the material; this is intuitively justified by the fact that grain crushing upon loading modifies the grading of the material and that finer granular materials exhibit lower friction angles (Herle & Gudehus, 1999; Miura et al. 1997). Each state is characterised by a one-to-one (say, linear) relationship between d and η while the d:η paths traced upon loading result from the material spanning with continuity different states.
In the following, attention will be restricted to quasi-static, isothermal processes and linear kinematics. The current state of the material is described in terms of the effective stress tensor σ and a set of internal (hardening) variables q. The evolution of the internal variables is associated to the macroscopically observable effects of the irreversible modifications in the microstructure, such as particle rearrangements or grain crushing, and is therefore linked to permanent deformations of the solid skeleton.