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This paper presents a method to estimate a representative element volume (REV) of a fractured rock mass based on the volumetric fracture intensity P32 and statistical tests. A 150 m × 80 m × 50 m 3D fracture network model was generated based on field data collected at the Maji dam site by using the rectangular window sampling method. The volumetric fracture intensity P32 of each cube was calculated by varying the cube location in the generated 3D fracture network model and varying the cube side length from 1 to 20 m, and the distribution of the P32 values was described. The size effect and spatial effect of the fractured rock mass were studied; the P32 values from the same cube sizes and different locations were significantly different, and the fluctuation in P32 values clearly decreases as the cube side length increases. In this paper, a new method that comprehensively considers the anisotropy of rock masses, simplicity of calculation and differences between different methods was proposed to estimate the geometrical REV size. The geometrical REV size of the fractured rock mass was determined based on the volumetric fracture intensity P32 and two statistical test methods, namely, the likelihood ratio test and the Wald–Wolfowitz runs test. The results of the two statistical tests were substantially different; critical cube sizes of 13 m and 12 m were estimated by the Wald–Wolfowitz runs test and the likelihood ratio test, respectively. Because the different test methods emphasize different considerations and impact factors, considering a result that these two tests accept, the larger cube size, 13 m, was selected as the geometrical REV size of the fractured rock mass at the Maji dam site in China. [ABSTRACT FROM AUTHOR]

The clustering and classification of fracture orientation data are crucial tasks in geotechnical engineering and rock engineering design. The explicit simulation of fracture orientations is always applied to compensate for the lack of direct measurements over the entire rock mass. In this study, a single step approach based on the theory of finite mixture models, where the component distributions are Fisher distributions, is proposed for automatic clustering and simulation of fracture orientation data. In the proposed workflow, the spherical K-means algorithm is applied to select the initial cluster centers, and the component-wise expectation-maximization algorithm using the minimum message length criterion is used to automatically determine the optimal number of fracture sets. An additional advantage of the proposed method is the representation of orientation data using a full sphere, instead of the conventional hemispherical characterization. The use of a full spherical representation effectively solves the issue of clustering for fractures with high dip angles. In addition, the calculation process of the mean direction is also simplified. The effectiveness of the model-based clustering method is tested with a complicated artificial data set and two real world data sets. Cluster validity is introduced to evaluate the clustering results. In addition, two other clustering algorithms are also presented for comparison. The results demonstrate that the proposed method can successfully detect the optimal number of clusters, and the parameters of the distributions are well estimated. In addition, the proposed method also exhibits good computational performance. [ABSTRACT FROM AUTHOR]

Fracture intensity, the degree of fracturing in rock masses, is one of the fundamental parameters used in characterizing rock mass as a fracture network. Among fracture intensity measures, volumetric fracture intensity (P 32 ) is the most useful, since it directly reflects the degree of rock mass fracturing, independent of fracture orientation and size distribution. P 32 represents the total area of fractures per cubic meter, and it can simultaneously reflect the spacing and size component of fractures. Because P 32 cannot be directly measured in the field, previous works have developed various inference methods based on available 1D and 2D measures collected from field surveys. At present, discrete fracture network (DFN) models are deemed to be a suitable method for the characterization of fractured rock mass. Hence, calculating P 32 from a DFN model is also a widely accepted approach. However, the geometry-based method cannot effectively address the irregular simulation space, and the methods employed are ill-suited if polygonal fractures appear in the DFN model. To solve these deficiencies, a computational framework based on the Delaunay triangulation of 3D uniformly distributed random points is introduced, and a detailed description is presented. The proposed computational framework is suitable for various types of DFN models, such as Baecher disk models, elliptical disk models and Dershowitz polygon models. A simulated example was generated to verify the proposed computational framework. Finally, a DFN model is built based on fracture data acquired from the Songta hydropower station, and the proposed computational framework was used to calculate P 32 for the DFN model. [ABSTRACT FROM AUTHOR]

A stepwise algorithm for determining the intersections between fractures is presented. The stepwise approach is based on the bounding volume technology and separating axis theorem. The length and orientation distribution of the fracture intersections can be obtained by the stepwise approach. The stepwise approach is used to study the connectivity of the rock mass at Songta hydropower station. According to the traces data acquired from a tunnel namely PD231, a DFN model was generated for intersection analysis and connectivity analysis. The results of intersection analysis show that the stepwise approach is effective. Connectivity parameters such as the average number of fracture intersections per fracture, and the length of intersection lines per unit volume, can be calculated. The mean length of intersections is 1.184 m and the variance is 0.622 m. The self-intersection behavior and direction vector of the intersections are studied. The simulations show that the sub-vertical joint set 3 and the shallow joint set 1 constitute the main flow pathways in the fractured rock at dam site. Besides, the results suggest that the sub-vertical joint sets (joint set 2 and 3) are more connected than the shallow joint set (joint set 1). [ABSTRACT FROM AUTHOR]