基于扩展有限元法的岩体水力劈裂耦合模型
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摘要
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.
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.
引文
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[15]王德法,高小云,师俊平.三维固体问题中M积分与总势能变化关系的研究[J].水利与建筑工程学报,2009,3(7):36-38.WANG De-fa,GAO Xiao-yun,SHI Jun-ping.Study on relation between M-integral and change of total potential energy in three-dimensional solids[J].Journal of Water Resources and Architectural Engineering,2009,3(7):36-38.
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[19]BRüHWILER E,SAOUMA V E.Water fracture interaction in concrete-part I:Fracture properties[J].ACIMaterials Journal,1995,92(3):296-303.
[2]仵彦卿,张倬元.岩体水力学导论[M].成都:西南交通大学出版社,1995.XU Yan-qing,ZHAN Dao-yuan.An introduction to rock mass hydraulics[M].Chengdu:Southwest Jiaotong University Press,1995.
[3]严成增,郑宏,孙冠华,等.模拟水压致裂的二维FDEM-flow方法[J].岩石力学与工程学报,2015,34(1):67-75.YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.A 2D FDEM-flow method for simulating hydraulic fracturing[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(1):67-75.
[4]严成增.模拟水压致裂的另一种二维FDEM-flow方法[J].岩土力学,2017,38(6):1789-1796.YAN Cheng-zeng.A new two-dimensional FDEM-flow method for simulating hydraulic fracturing[J].Rock and Soil Mechanics,2017,38(6):1789-1796.
[5]YAN Cheng-zeng,ZHENG Hong,SUN Guan-hua,et al.Combined finite-discrete element method for simulation of hydraulic fracturing[J].Rock Mechanics and Rock Engineering,2016,49(4):1389-1410.
[6]潘鹏志,冯夏庭,吴红晓,等.水压致裂过程的弹塑性细胞自动机模拟[J].上海交通大学学报,2011,45(5):722-727.PAN Peng-zhi,FENG Xia-ting,WU Hong-xiao,et al.Modeling hydraulic failure process using elasto-plastic cellular automation[J].Journal of Shanghai Jiao Tong University,2011,45(5):722-727.
[7]李根,唐春安,梁正召,等.水压致裂过程的三维数值模拟研究[J].岩土工程学报,2010,32(12):1875-1881.LI Gen,TANG Chun-an,LIANG Zheng-zhao,et al.Numerical simulation of 3D hydraulic fracturing process[J].Chinese Journal of Geotechnical Engineering,2010,32(12):1875-1881.
[8]陈胜宏,汪伟民,徐明毅,等.小湾高拱坝坝踵开裂的有限单元法分析[J].水利学报,2003,(1):66-71.CHEN Sheng-hong,WANG Wei-min,XU Ming-yi,et al.Finite element analysis of the crack propagation in high arch dam heel of Xiaowan project[J].Journal of Hydraulic Engineering,2003,(1):66-71.
[9]李全明,张丙印,于玉贞,等.土石坝水力劈裂发生过程的有限元数值模拟[J].岩土工程学报,2007,29(2):212-217.LI Quan-ming,ZHANG Bing-yin,YU Yu-zhen,et al.Numerical simulation of the process of hydraulic fracturing in earth and rockfill dams[J].Chinese Journal of Geotechnical Engineering,2007,29(2):212―217.
[10]方修君,金峰.裂隙水流与混凝土开裂相互作用的耦合模型[J].水利学报,2007,38(12):1466―1474.FANG Xiu-jun,JIN Feng.Coupling model for interaction between fissure water and cracking in concrete[J].Journal of Hydraulic Engineering,2007,38(12):1466-1474.
[11]董玉文,任青文.重力坝水力劈裂分析的扩展有限元法[J].水利学报,2011,42(11):1361-1367.DONG Yu-wen,REN Qing-wen.An extended finite element method for modeling hydraulic fracturing in gravity dam[J].Journal of Hydraulic Engineering,2011,42(11):1361-1367.
[12]盛茂,李根生.水力压裂过程的扩展有限元数值模拟方法[J].工程力学,2014,31(10):123-128.SHENG Mao,LI Gen-sheng.Extended finite element modeling of hydraulic fracture propagation[J].Engineering Mechanics,2014,31(10):123-128.
[13]石路杨,李建,许晓瑞,等.水力劈裂对岩体中自然裂隙的影响研究[J].岩土力学,2016,37(10):3003-3010.SHI Lu-yang,LI Jian,XU Xiao-rui,et al.Influence of hydraulic fracturing on natural fracture in rock mass[J].Rock and Soil Mechanics,2016,37(10):3003-3010.
[14]龚迪光,曲占庆,李建雄,等.基于ABAQUS平台的水力裂缝扩展有限元模拟研究[J].岩土力学,2016,37(5):1512-1520.GONG Di-guang,QU Zhan-qing,LI Jian-xiong,et al.Extended finite element simulation of hydraulic fracture based on ABAQUS platform[J].Rock and Soil Mechanics,2016,37(5):1512-1520.
[15]王德法,高小云,师俊平.三维固体问题中M积分与总势能变化关系的研究[J].水利与建筑工程学报,2009,3(7):36-38.WANG De-fa,GAO Xiao-yun,SHI Jun-ping.Study on relation between M-integral and change of total potential energy in three-dimensional solids[J].Journal of Water Resources and Architectural Engineering,2009,3(7):36-38.
[16]FLEMING M,CHU Y A,MORAN B,et al.Enriched element free Galerkin methods for crack tip fields[J].International Journal for Numerical Methods in Engineering,1997,40(8):1483-1504.
[17]WALTERS M C,PAULINO G H,DODDS R H.Interaction integral procedures for 3-D curved cracks including surface tractions[J].Engineering Fracture Mechanics,2005,72(11):1635-1663.
[18]李世愚,和泰名,尹祥础.岩石断裂力学导论[M].合肥:中国科学技术大学出版社,2010.LI Shi-yu,HE Tai-ming,YIN Xiang-chu,et al.Introduction of rock fracture mechanics[M].Heifei:University of Science&Technology China Press,2010.
[19]BRüHWILER E,SAOUMA V E.Water fracture interaction in concrete-part I:Fracture properties[J].ACIMaterials Journal,1995,92(3):296-303.