Empirical Assessment of the Mean Block Volume of Rock Masses Intersected by Four Joint Sets

The estimation of a representative value for the rock block volume (V _b) is of huge interest in rock engineering in regards to rock mass characterization purposes. However, while mathematical relationships to precisely estimate this parameter from the spacing of joints can be found in literature for rock masses intersected by three dominant joint sets, corresponding relationships do not actually exist when more than three sets occur. In these cases, a consistent assessment of V _b can only be achieved by directly measuring the dimensions of several representative natural rock blocks in the field or by means of more sophisticated 3D numerical modeling approaches. However, Palmström’s empirical relationship based on the volumetric joint count J _v and on a block shape factor β is commonly used in the practice, although strictly valid only for rock masses intersected by three joint sets. Starting from these considerations, the present paper is primarily intended to investigate the reliability of a set of empirical relationships linking the block volume with the indexes most commonly used to characterize the degree of jointing in a rock mass (i.e. the J _v and the mean value of the joint set spacings) specifically applicable to rock masses intersected by four sets of persistent discontinuities. Based on the analysis of artificial 3D block assemblies generated using the software AutoCAD, the most accurate best-fit regression has been found between the mean block volume (\(V_{{{\text{b}}_{\text{m}} }}\)) of tested rock mass samples and the geometric mean value of the spacings of the joint sets delimiting blocks; thus, indicating this mean value as a promising parameter for the preliminary characterization of the block size. Tests on field outcrops have demonstrated that the proposed empirical methodology has the potential of predicting the mean block volume of multiple-set jointed rock masses with an acceptable accuracy for common uses in most practical rock engineering applications.