Multi-dimensional size effects and representative elements for non-persistent fractured rock masses: A perspective of geometric parameter distribution

This study takes a fractured rock mass in the Datengxia Hydropower Station, China as an example to analyze the size effects and determine the representative elementary sizes. A novel method considering geometric parameter distributions is proposed in this work. The proposed method can quickly and simply determine the size effects and representative elementary sizes. Specifically, geometric parameter distributions, including fracture frequency, size and orientation, are generated on the basis of the Bernoulli trial and Monte Carlo simulation. The distributions are assessed using the coefficient of variation (CV), and the acceptable variations for CV (5%, 10% and 20%) are used to determine representative elementary sizes. Generally, the representative element of rock masses is the representative elementary volume (REV). The present study extends the representative element to other dimensions, i.e. representative elementary length (REL) and representative elementary area (REA) for one and two dimensions, respectively. REL and REA are useful in studying the size effects of one- (1D) and two-dimensional (2D) characteristics of rock masses. The relationships among multi-dimensional representative elementary sizes are established. The representative elementary sizes reduce with the increase in the dimensions, and REA and REV can be deduced by REL. Therefore, the proposed method can quickly and simply determine REL and further estimate REA and REV, which considerably improves the efficiency of rock mass analysis.