Modeling of scale effects of damage in cemented granular rocks

We propose a probabilistic model of cemeted cemented granular material cons isting of elastic grains and of weak brittle cement which may be present in contacts between grains. The central assumption of the model is that the d amage of such a material under the effect of external mechanical loading is principally controlled by the two following factors: 1) heterogeneous dist ribution of cement in the sample; and 2) heterogeneous (typically exponenti al) distribution of inter-granular forces and the associated elastic energy produced by the macroscopic attain. These assumptions, which can be justif ied by direct observations in granular rock (Menendez et al., 1990) and by experimental and numerical studies of force distributions in granular media (Mueth et al., 1998; Makse et al., 2000), combined with a simple fracture criterion fur a single cemented contact, lead to a percolation-type damage behavior. An important feature of the proposed model is an explicit scale d ependence of certain macroscopic damage parameters for a material with fixe d microscopic properties and given distributions of heterogeneities. This s cale dependence may be important for interpretation of numerical simulation s of granular materials using a moderate number of grains, as well as in at tempts to extrapolate damage criteria in rock from laboratory to larger sca les. The predictions of the probabilistic damage model are qualitatively co nfirmed by 3D numerical simulations using a Discrete Element Model of cemen ted granular material. (C) 2001 Elsevier Science Ltd. All rights reserved.