# Deterministic Discrete Fracture Network Model and Its Application in Rock Mass Engineering
## 1 Introduction  
The three-dimensional structural model of rock mass is the basis for analyzing the mechanical properties of rock mass and evaluating engineering safety. It is of great significance and engineering value to quickly reverse calculate the complete three-dimensional structural surface distribution characteristics of rock mass based on the known structural surface parameters, and carry out rock mass quality assessment for tunnel information construction tools. In recent years, 3D virtual reality technology based on ground LiDAR, airborne LiDAR, UAV orthophotography, UAV oblique photogrammetry, and ground close-range photogrammetry has developed rapidly, achieving accurate extraction of structural surface parameters [1, 2, 3, 4, 5]. Based on the structural surface parameters, combined with statistical methods, research has been carried out on the distribution characteristics of internal rock mass structures [6, 7, 8]. The random distribution model constructed based on statistical methods can indeed reproduce the internal structure of rock mass, and thus carry out work such as rock mass quality assessment and surrounding rock grade classification. However, due to the uncertainty associated with statistical methods, the accuracy of the results of the random distribution model depends on the statistical results obtained after a large number ofsimulations. Therefore, there are problems such as high time cost and large memory occupation. In order to reduce the uncertainty of completely random modeling methods, many scholars strive to optimize the modeling methods, which can be divided into the following situations: (1) optimizing the probability distribution function used in the random distribution model, using multivariate joint distribution, variable sensitivity analysis, and other methods to improve the realism of the model [9; 10; 11], (2) combining deterministic structural surfaces with stochastic structural surfaces. Optimization of surface coupling, by incorporating deterministic structural surfaces to guide the mechanical behavior of rock masses; the degree of reconstruction is higher compared to completely stochastic modeling [12; 13; 14; 15]. (3) Based on stochastic modeling methods, optimization of structural surface characterization models has been developed [16; 17; 18]. The simplest disk model has been developed into elliptical disk models, polygonal models, and discrete element models with random shape and persistence. (4) Optimization of multi-scale modeling: Considering the large differences in structural surface persistence in fractured rock masses, especially in large-scale rock masses, in reality [19; 20], multiple-scale models are established to achieve effective representation and comprehensive analysis of fracture networks at different scales. The above method can provide a certain degree of reliability when facing typical large-scale regular rock masses. However, the mechanical behavior of small-scale rock masses is primarily controlled by deterministic structural surfaces. A large number of random structural surfaces can significantly reduce the reliability of the model. Therefore, this paper proposes a deterministic discrete fracture network modeling method for small-scale rock masses. By collecting parameters of exposed structural surfaces in the rock mass, including trace length, 3D coordinates of trace line centers, orientation, and spacing, the spatial distribution characteristics of structural surfaces are inferred based on the numerical relationships among these parameters, and a deterministic DFN model is subsequently constructed. During the modeling process, different types of structural planes, such as joints, layers, and faults, are represented using distinct geometric elements. Finally, the degree of blockiness within the model is calculated, and a rock mass quality assessment is conducted.