Estimation of the in Situ Block Size in Jointed Rock Masses Using Three-Dimensional Block Simulations and Discontinuity Measurements

"The in situ block size is a key parameter in the geomechanical characterization of rock masses. It describes the fracturing of the rock mass and thus is a measure for the degradation of the rock mass strength. Several classification systems use the in situ block size. For instance, the Geological Strength Index (GSI) requires the “blockiness” and joint surface condition factor as key input parameters. The “blockiness” has recently been related to the in situ block volume (Cai et al., 2004). Due to the limited information about the internals of a rock mass, it is not possible to determine the in situ block size directly. Currently, the in situ block size is determined by calculations using oversimplified models, vague estimations or, due to the lack of relevant information, it is neglected. As remote measurement systems have become available for rock mass characterization, a more comprehensive record of discontinuities can take place. Measurements can be performed on exposed rock outcrops and in particular on tunnel faces and walls, delivering the location, orientation, spacing and persistence of discontinuities at an arbitrary number and locations. An estimation of the in situ block size at the same level of sophistication is still not available. This paper aims at examining the relationship between visible and measureable information at the rock surface, and the in situ block size. Three-dimensional block model simulations were performed using the block model engine of the distinct element code 3DEC. Initial investigations focussed on the minimally required observation area in order to obtain reliable block size distributions. Based on a representative volume element, a reference distribution of the block area at the observation area for a specific discontinuity system was determined. Subsequently, the size of the observation area was decreased stepwise and each new distribution was compared to the reference distribution. For all analyzed systems, it turned out that the mean block area must be smaller than 1% of the observation area to achieve a reliable block size distribution. Further simulations focussed on discontinuity systems with three non-persistent sets. The results were compared to the formula proposed by Cai et al. (2004). A transformation factor T was introduced which replaces the persistence terms in Cai et al.’s proposed formula. The factor describes the correlation between block volumes generated by persistent and corresponding non-persistent discontinuity sets. The simulations included the variation of the discontinuity set spacing, persistence, and orientation. The mean and additionally the 25%-, 50%- and 75%-quantiles of the block size distribution were analyzed. Examining all values for the transformation factor the distribution can be described by a power function with a negative exponent. The function depends on the persistence only. Finally, the results of random simulations were compared to the analytical formula using the transformation factor. The predicted mean and selected quantiles show a good agreement with the simulation results. It gives a comprehensive picture about the block size distribution in discontinuity systems with three non-persistent sets."