Some numerical models treat masses of rock as assemblages of isolated blocks, whereas others treat them as continuous material. It needs to be determined at what level a rock is cut into assemblages of discrete blocks by fractures. This paper used a parameter $B$ to measure the degree to which rocks form an assemblage of blocks; $B$ is a dimensionless number in the range $0.0<B<1.0$ and is defined as the ratio of the aggregated volume of individual blocks in the investigated domain to the total volume of the rock mass in the investigated domain. The quantitative description scheme for fracture spacing and persistence suggested by the International Society for Rock Mechanics (ISRM) was used to construct different types of fractured rocks to conduct investigations into blockiness. Seventy-seven different types of fracture networks were studied. The fractures investigated covered all the fracture spacing and persistence ratings suggested by the ISRM. Based on the blockiness of the 77 samples, an analytical function was established to describe the relationship between the blockiness and the fracture spacing ($S$ ) and fracture disc diameter ($D$ ). The resulting function is an S-shaped curve.

The fractures of different sizes in rock masses are important for describing rock fragmentation. The distribution dispersion of fracture size influences the blockiness level of the rock masses. Based on a normal statistical distribution, the volume ratio of blocks to rock (B) was obtained to describe the blockiness level. For exploring the effect of the dispersion of fracture size on blockiness level and the representative elementary volume (REV) of rock masses, the laboratory model and numerical simulation were established, and the theory of statistics and the method of analytical solution were applied. In addition, 4,525 practical rock models were established to qualitatively reproduce the behavior of B with changing domain size. The results show that by comparing the degree of convergence, the REV of a rock mass is determined by the fracture size rather than the degree of fracture dispersion. The value of B increases with the distribution dispersion of fracture size, indicating a higher blockiness level. From the experimental analysis of coin tossing, when the number of trials exceeds 69, the random results are nearly stable. In this study, 100 calculations were performed. A formula to calculate the blockiness by considering the dispersion degrees of fracture size was obtained. Moreover, a positive linear correlation between B and the coefficient of variation of fracture size was obtained. The rate of increase in B has a parabolic relationship with the ratio of fracture size to fracture spacing (L).

Groundwater science and technology is among the most rapidly developing branches of earth science globally. Interdisciplinarity poses both a challenge and a historical mission for graduate education in groundwater science and technology. This paper first analyzes the characteristics of domestic and international graduate education in groundwater science and technology. In addition, taking the China University of Geosciences (Beijing) as an example, it shows the history and development of the field in China. The results indicate that: (1) the graduate courses in groundwater science and technology in China are based on the characteristics of geoscientific research and closely integrate the advantages in environmental studies, ecology, and computer science to promote cross-fertilization across disciplines, departments, and universities; (2) after a few twists and turns in conferring master’s and PhD degrees and in the construction of the discipline, groundwater science and technology has witnessed an increase in faculty members, expansion of the field of study, and the addition of modern educational and research facilities; (3) an increasing number of graduate students conduct research into the quality and safety of water supplies, rehabilitation technology of polluted water bodies, environment protection of river basin ecosystems, and so on.