Yuhao Hu

The pores in rocks are multi-scale and highly complex. Based on complex network theory, the topological properties of a sandstone flow network are studied. The results show that the sandstone pore scale network is a small-world network with an average shortest path of 5.720, and 80% of the network node degree is less than 3. This network structure can improve the security of the network and ensure the permeability of the pores under the action of external forces. In addition, nodes with appropriate degree distribution have a significant influence on permeability. Nodes with a larger degree will significantly reduce the average shortest path of the network, while nodes with a smaller degree will expand the coverage of the seepage network.

As one of the most basic materials of engineering coatings, rock has complex structural characteristics in its medium space. However, it is still difficult to quantitatively characterize the microstructure of rock coatings, such as connectivity and aggregation degree. For this paper, based on a CT-scan model of rock coating, we extracted the network topology of a rock coating sample and verified that its microstructure parameter distribution accords with Barabasi and Albert (BA) scale-free theory. Based on this result, relying on the BA scale-free theory, a dual-porosity network model of rock coating was constructed. We extracted the network structure of the model to verify it, and analyzed the distribution of the microstructure parameters of the model, such as degree distribution, average path length and throat length distribution. At the same time, we analyzed the evolution trend of the permeability of the coating model with the microscopic parameters. Then we discuss the influence of the change of structural parameters on the microstructure of the coating model, and compared with the mainstream rock models at the present stage, the rationality and accuracy of the models are analyzed. This provides a new method for studying the mechanical and permeability properties of engineering coating materials.

The pore structure is an important factor of tunnel coating failure, cracking and water leakage. Some investigations on the statistical law of pores and pore networks have been conducted, but little quantitative analysis is observed on topology structure of the pore network, and even the pore structure of sandstone is complex and cross-scale distributed. Therefore, it is of theoretical and engineering significance to quantitatively characterize the connectivity of the pore network in sandstone. This study proposes a new complex network theory to analyze the three-dimensional nature of pore network structure in sandstone. The topological network structure, such as clustering degree, average path length and the module, which cannot be analyzed by traditional coordination number and fractal dimension methods, is analyzed. Numerical simulation results show that a scale-free network model is more suitable for describing the sandstone pore network than random models. The pore network of sandstone has good uniformity. The connectivity of sandstone pore networks has great potential for permeability enhancement. Therefore, this new method provides a way to deeply understand the pore connectivity characteristics of sandstone and to explore the distribution of crack grids in the arch of tunnel coatings.