系统地认知裂隙岩体结构对岩体力学和水力学行为的影响机制是我国推进防灾减灾、能源结构转型和可持续发展的必然要求。近几十年来，有关裂隙网络结构及其影响的定量研究大多还是围绕裂隙网络的几何特征展开，忽视了裂隙网络的拓扑特征及其影响。为此本文从复杂网络理论的角度出发，首先根据表示裂隙的几何实体与图中元素的对应关系，总结了两类表征方法（FE表征和FV表征），并以此为基础，开展了多方面研究。具体来说，本文的主要贡献有：1.发展了裂隙网络图表征体系，评价了裂隙尺寸分布形式和分形维数对裂隙网络拓扑特征的影响，给出了常见离散裂隙网络的拓扑类别。2.系统地探究和对比了四种岩性天然裂隙网络的复杂网络特征，分析了它们所属的复杂网络类型。结果表明在FE表征下，本文研究的大多天然裂隙网络属于异配、非无标度、高度模块化的小世界网络，同时提出了基于裂隙网络FE图的拓扑参数判断其所属岩体岩性的两种流程。3.提出了一种从图的角度搜索多锁固段岩质边坡潜在滑面的方法。该方法通过添加虚拟边的方式巧妙地表示了边坡内部具有潜在贯通破坏可能的岩桥，同时结合已有的试验结论，以给虚拟边赋权的方式考虑了不同岩桥的破坏难度，从而将岩质边坡滑面搜索问题转化为了在加权图的指定节点间搜索最短路径的问题。4.探讨了子网络拓扑度量对裂隙岩体等效渗透率的影响。在二维裂隙网络中，其无悬挂-逾渗子网络的有效逾渗密度和平均节点介数的比值与等效方向渗透率存在正向线性关系；在三维裂隙网络中，全局逾渗（骨干）子网络的平均节点介数以及平均节点接近中心性均与平均等效渗透率主值呈负指数幂关系，而随全局逾渗（骨干）子网络的平均节点加权度中心性的增大，平均等效渗透率主值呈指数增长。5.提出了一种基于图表征和节点流量守恒原则的快速预测冰湖下岩体隧道渗水风险和涌水量的方法。该方法充分考虑了围岩结构对渗流影响，克服了理论计算方法更适用于等效均质介质的缺点，与离散裂隙网络数值计算模型相比，基于图的求解方法在保证计算精度的同时节约了63%的计算时间。综上所述，本文从理论上发展了裂隙网络图表征方法体系，也从图的角度针对一些实际问题提出了新方法，提升了对裂隙网络拓扑特征及其影响的认知。
It is of great significance to systematically recognize the influence mechanism of their structures on rock mechanics and hydrodynamic behavior for disaster prevention and alleviation, energy structure transformation and sustainable development in China. In recent decades, most of the quantitative studies on the fracture network structure and its influence always foucus on the geometric characteristics of the fracture network, ignoring the topological characteristics of the fracture network and its effect. For this reason, from the perspective of complex network theory, this dissertation summarizes two types of characterization methods (Fracture-Edge characterization and Fracture-Vertex characterization) according to the correspondence between the geometric entities representing fractures and the elements in the graph. Based on this, various studies are conducted. Specifically, the main contributions of this dissertation are:1. A system of charactering fracture network by graph is developed. The effects of fractal size distribution form and fractal dimension on the topological characteristics of the fractal network are evaluated.2. The topological characteristics of fracture networks mapped from natural outcrops are systermatically explored and compared, and the complex network types to which they belong are analyzed. The results tell that under FE characterization, most of the natural fracture networks studied in this dissertation are disassortative, non-scale-free, highly modular small-world networks. Meanwhile, two methods for recognizing the lithology of the fracture network it belongs to based on the topological features are proposed.3. A method for searching potential slip surfaces of rocky slopes with multiple locking sections from the perspective of a graph is proposed. The method subtly represents the rock bridges with potential penetration damage inside the slope by adding virtual edges, and considers the damage difficulty of different rock bridges by assigning weights to virtual edges in combination with the existing experimental findings. Thus, the problem of searching slip surface of rocky slope with multiple locked segments is transformed into a problem of searching the shortest path between specified nodes of the weighted graph. The effectiveness of the above method is illustrated by numerical tests.4. The impact of subnetwork topology metrics on the equivalent permeability of fractured rock masses is discussed. In the two-dimensional fracture network, the ratio of effective fracture density to average nodal betweenness centrality of its unsuspended percolation subnetwork has a positive linear relationship with the equivalent directional permeability. In the three-dimensional fracture network, both the average nodal betweenness centrality and the average nodal closeness centrality of the full percolation (backbone) subnetwork have a negative exponential relationship with the mean of the three principal permeability of the equivalent permeability tensor, while the mean of the three principal permeability of the equivalent permeability tensor increases exponentially with the average nodal weighted degree centrality of the full percolation (backbone) subnetwork.5. A method based on graph representation and the principle of nodal flow conservation is proposed for the rapid prediction of seepage risk and influx of water in rock tunnels located below glacial lakes. The method fully considers the influence of the structure of surrounding rock mass on seepage flow, overcomes the drawback that the theoretical prediction method, which is more applicable to the equivalent homogeneous medium. Compared with the discrete fracture network numerical calculation model, the graph-based solution method can save the calculation time by 63% while ensuring the calculation accuracy.In summary, the dissertation theoretically refines the system of charactering fracture network by graphs, and also proposes new methods for some practical problems from the perspective of graphs. The findings can enhance the knowledge of the topological characteristics of fracture network and their effects.
