Bifurcation and catastrophe of seepage flow system in broken rock

• Published in: Mining science and technology (China) 2009, Vol.19 (1), p.1-7
• Main Authors: MIAO, Xie-xing, LI, Shun-cai, CHEN, Zhan-qing
• Format: Article
• Language: English
• Subjects: broken rock; fold catastrophe; non-Darcy flow; saddle-node bifurcation; stability; 井下作业; 安全作业; 矿井安全
• ISSN: 1674-5264; 2212-6066
• DOI: 10.1016/S1674-5264(09)60001-6

The study of dynamical behavior of water or gas flows in broken rock is a basic research topic among a series of key projects about stability control of the surrounding rocks in mines and the prevention of some disasters such as water inrush or gas outburst and the protection of the groundwater resource. It is of great theoretical and engineering importance in respect of promotion of security in mine production and sustainable development of the coal industry. According to the non-Darcy property of seepage flow in broken rock dynamic equations of non-Darcy and non-steady flows in broken rock are established. By dimensionless transformation, the solution diagram of steady-states satisfying the given boundary conditions is obtained. By numerical analysis of low relaxation iteration, the dynamic responses corresponding to the different flow parameters have been obtained. The stability analysis of the steady-states indicate that a saddle-node bifurcaton exists in the seepage flow system of broken rock. Consequently, using catastrophe theory, the fold catastrophe model of seepage flow instability has been obtained. As a result, the bifurcation curves of the seepage flow systems with different control parameters are presented and the standard potential function is also given with respect to the generalized state variable for the fold catastrophe of a dynamic system of seepage flow in broken rock.