Observations often display an intact rock strength decrease as specimen size increases. Existing attempts for reproducing this scale effect mainly rely on the introduction of defects as discrete cracks or veins. We propose a continuous approach where the rock micro-scale strength properties are spatially correlated. The correlation law is a correlated multi-Gaussian random field (CRF). We develop and test Synthetic Rock Masses with PFC3D. In these conditions, we show that SRM specimens reproduce the scale effect and we define the relation between their properties and the CRF parameters. The relation can then be used to calibrate SRM specimens for practical applications.

1 Introduction

The well-known rock strength scale effect (Yoshinaka et al. 2008) has been observed up to some meters in length, in various conditions, from laboratory tests on various type of rocks (Hoek & Brown 1997), in the context of underground excavations (Bieniawski & Van Heerden 1975) or cave mining (Laubscher 1994). It is likely caused by small-scale heterogeneities within the rock, including embedded discontinuities and spatial variations of rock micro properties.

Reproducing the intact rock strength scale effect in numerical simulations is not a common practice. Existing attempts mainly rely on the introduction, within an intact rock model, of various discontinuities, either as small cracks (Zhang et al. 2011), veins (Pierce et al. 2009) or discrete fracture networks (Scholtès et al. 2011). In these cases, the scaling properties of the discontinuities population exert some control on the resulting rock strength. Observations show that this intact rock strength scale effect vanishes beyond the meter length scale.

At larger scales too, the rock mass (as an intact rock with embedded discrete fracture networks or DFN) effective elastic properties (Le Goc et al. 2014) or rock fragmentation characteristics (Brzovic & Villaescusa 2007) are strongly related to DFN properties. In numerical modeling, it is therefore difficult to consider explicitly simultaneously very small-scale defects and larger scale fractures (joints to faults). Using continuous modeling and spatial correlations of the micro-scale intact rock properties is an alternative for modeling the small-scale spatial heterogeneity of rock masses. This can be done with correlated multi-Gaussian random fields (noted CRF thereafter). A CRF is a statistical description of a random three-dimensional variable whose spatial distribution is defined by a correlation function. CRF are widely used in geostatistics (Chilès & Delfiner 2012) with numerous applications in hydrogeology to model the permeability structure of heterogeneous media (Le Goc et al. 2010). In rock mechanics, correlation patterns in rocks are acknowledged (Howarth & Rowlands 1987) but their use to model the rock heterogeneities is limited. Griffiths et al. (2002) show that rock strength variability in the form of a CRF can significantly reduce the compressive strength of an axially loaded rock pillar and Griffiths et al. (2009) show that modeling shear strength parameters with CRF significantly improve the predictions in the context of slope stability.

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