## 6 Conclusions  
In this study, the jointed rock mass of the surrounding rock of the roadway was employed as the research object. The digital image of the RDFN model of various geometric forms was established in the MATLAB platform by considering the random distribution characteristics and roughness characteristics of the joint structural surface. By employing the principle of image recognition, numerical modelling of the real joint geometric distribution of rock mass on the two-dimensional particle flow code, PFC2D, was achieved. Finally, biaxial compression tests and excavation of different RDFN models were carried out to study the anisotropic mechanical characteristics of RDFN models. The main conclusions drawn are as follows:  
(1) A rough discrete joint network model representation method based on the Fourier transform principle was proposed and combined with digital image recognition technology to establish a particle flow discrete element numerical calculation model, which provides a new mathematical representation method and mechanical calculation model for the study of the mechanical properties of jointed rock masses. (2) The geometric shape of joints is an important factor affecting the final failure mode of rock mass, and the failure modes differ with different joint shapes. The compression failure mode of rough-jointed rock mass is more complex than that of intact rock mass, which may possess multiple shear slip surfaces. Therefore, the stress-strain curve will change and multiple peaks will appear. The strength and failure development modes of fractured rock mass in different directions also differ, and the discrete joint network model considering the geometric shape of complex joints can effectively analyse the mechanical properties of rock mass with complex natural structural planes. (3) The loading anisotropy of the complex RDFN model is significant. In different loading directions from 0\({}^{\circ}\) to 180\({}^{\circ}\), the peak compressive strengths are 17.77 MPa, 32.04 MPa, 24.51 MPa, 17.58 MPa, 13.94 MPa, 20.93 MPa, and 19.81 MPa, respectively. Further, the anisotropy is 2.30 and the maximum direction is 30\({}^{\circ}\). The peak compressive strength of joint models in different directions is significantly different, and the failure modes of the jointed rock masses in different loading directions is significantly affected by the geometric distribution of the structural planes. (4) The failure modes of the opening are highly affected by the orientation of the fracture sets. Meanwhile, certain joint sets will dominate the failure of the surrounding rock mass. The existence of the rough fracture sets could influence the failure area of different excavation situations. The influence of the distribution and geometry should be taken into account when assessing the failure modes and area of underground openings. The proposed RDFN model could provide a new reasonable model for estimating the failure modes of jointed rock mass. Figure 13: Comparison of fracture patterns observed around openings with structural planes. **(a)** The present numerical simulation. **(b)** The convergence area of a circular tunnel (after [PERSON] [41]). **(c)** The failure pattern of a circular tunnel in a bedded rock (after [PERSON] et al. [42]). **Author Contributions:** Methodology, P.W. ; software, C.L. and Z.Q. ; investigation, P.W. ; data curation, Z.L. ; writing--review and editing. P.W. ; supervision, M.C. ; project administration, P.W. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was financially supported by the National Natural Science Foundation of China (No. 52074020), the National Key R&D Program of China (Nos. 2021 YFC2900500, 2021 YFC3001302), and the Open Fund of State Key Laboratory of Water Resource Protection and Utilization in Coal Mining (No. WPUKFJ2019-06). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.