The fracture network structure of coal is very complex, and it has always been a hot issue to characterize the fracture network structure of coal by using a tree-like branching network. In this paper, a new rough fracture permeability model of water injection coal based on a damaged tree-like branching network is proposed. In this model, fractal theory and sine wave model are used to characterize the rough characteristics of fracture structure. In addition, the applicability of the model is verified by the self-developed experimental system, and the sensitivity analysis and weight analysis of the influencing factors in the model are carried out. The results show that the factors affecting the permeability of the established permeability mathematical model are mainly the amplitude factors of sinusoidal fluctuation, length ratio, maximum branch series, number of damaged fractures, opening ratio, opening fractal dimension and initial fracture length. Among them, the sinusoidal fluctuation amplitude factor has the greatest influence on the permeability and the other two are inversely proportional. Therefore, with pulsating water injection, the frequency of changes in the water pressure was altered to improve the water injection efficiency in coal fractures with sinusoidal distribution to increase permeability. The research results provide a theoretical basis for further improving the theoretical models for seepage in porous media and fluid flow analysis of damaged tree-like branching networks.

煤的裂隙网络结构非常复杂，利用树状分支网络表征煤的裂隙网络结构一直是研究热点。本文提出了一种基于受损树状分支网络的注水煤粗糙裂缝渗透率模型。该模型采用分形理论和正弦波模型来表征裂缝结构的粗略特征。此外，通过自主开发的实验系统验证了模型的适用性，并对模型中的影响因素进行了敏感性分析和权重分析。结果表明，所建立的渗透率数学模型影响渗透率的因素主要有正弦波动幅度因素、长度比、最大分支系列、破损裂缝数、开孔率、开孔分形维数和初始裂缝长度。其中，正弦波动幅度因子对渗透率影响最大，其余两者成反比。因此，脉动注水时，改变水压变化频率，提高正弦分布煤缝注水效率，提高渗透率。研究成果为进一步完善多孔介质渗流理论模型和受损树状分支网络流体流动分析提供了理论基础。