基于扩展有限元法的岩体水力劈裂耦合模型

Hydraulic fracturing coupling model of rock mass based on extended finite element method

考虑裂隙水流与岩体开裂之间的相互作用,在含裂隙单元的附加节点上引入反映裂隙局部特性的附加函数,然后基于考虑裂隙面水压力作用的虚功原理,推导出了采用扩展有限元法分析水力劈裂问题的控制方程,给出了裂隙水流与岩体开裂相互作用的扩展有限元实现方法,并采用该方法对岩石试件与压力隧洞在裂隙水压作用下的开裂过程进行了数值模拟。数值计算结果表明:岩石试件裂纹内水压变化规律与试验结果相吻合;裂隙长度较小时,裂隙的存在对压力隧洞周围岩体应力、位移场的影响较小,随着裂隙的扩展,其影响范围将逐步扩大;水力劈裂对隧洞的径向位移影响较小,而对环向位移的影响较大,考虑水力劈裂耦合分析得到的环向位移要大于不考虑裂隙内水压分析得到的结果。

The extended finite element method(XFEM) is presented for hydro-mechanical modeling of impermeable discontinuities in rock. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. The governing equation of extended finite element method for hydraulic fracture modeling is derived by the virtual work principle of the fracture problem considering the water pressure on crack surface. Then the XFEM for hydraulic fracture modeling is implemented. The proposed method is applied to simulate the fracture propagation of pressure tunnel and rock specimen under the action of water pressure. The numerical analysis results show that the variation of water pressure in rock specimen is consistent with the experimental results. When the length of fissure is small, the existence of fissure affects little on the stress and displacement field of rock mass around the pressure tunnel. With the crack propagation, the scope of its influence will be gradually expanded. Hydraulic fracture influences little on the radial displacement, and affects greatly on the circumferential displacement. Considering the coupling analysis of hydraulic fracturing, the circumferential displacement is greater than that obtained without considering the water pressure inside the fissure.