重力坝水力劈裂分析的扩展有限元法
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摘要
水力劈裂是高坝在高水压作用下发生破坏的主要诱因之一。针对常规有限元法分析水力劈裂问题存在的缺点,研究了采用新兴的扩展有限元法(XFEM)进行重力坝水力劈裂数值模拟的方法。通过建立考虑裂纹面水压力作用问题的虚功原理,推导出了采用扩展有限元法分析水力劈裂问题的有限元列式;给出了反映裂纹面不连续性的不连续函数数值积分方法、开裂判断准则、应力强度因子的积分方法以及裂纹面扩展过程模拟方法,从而给出了模拟裂纹面有分布水压力载荷作用的水力劈裂问题扩展有限元实现方法。最后通过向家坝重力坝坝踵水力劈裂数值分析,展示了该方法的可行性和优越性。算例表明应用扩展有限元法进行水力劈裂分析可克服常规有限元法的缺点,不需要裂纹面与有限元网格一致,不需要在裂缝周围布置高密度网格,模拟裂纹扩展过程时不需要不断地重新划分网格,极大地简化了前处理工作。
Hydraulic fracture is a main inducement leading to high dam failure under the loading of large water pressure. Aiming at the drawback of FEM in modeling hydraulic fracture,an extended finite element method(XFEM) for modeling hydraulic fracturing process in gravity dam is studied. The governing equation of XFEM for hydraulic fracture modeling is derived by building the virtual work principle of the fracture problem considering water pressure loading on the crack surface. Then the implement method of XFEM for hydraulic fracture modeling is deduced,such as numerical integration of discontinuous functions reflecting discontinuity of the crack surface,crack growth criteria,integral method of stress intensity factors,and the modeling method of crack propagation. Finally,the feasibility and superiority of this method are exhibited through numerical analysis of the Xiangjiaba gravity dam with XFEM. Comparing with classical FEM,the crack growth in the gravity dam can be modeled by XFEM without making the crack surface associated to the mesh,without setting dense mesh near the crack tip and without remeshing after crack growth. Thus the disadvantages of hydraulic fracturing analysis with FEM are avoided and the pre-processing work is simplified.
Hydraulic fracture is a main inducement leading to high dam failure under the loading of large water pressure. Aiming at the drawback of FEM in modeling hydraulic fracture,an extended finite element method(XFEM) for modeling hydraulic fracturing process in gravity dam is studied. The governing equation of XFEM for hydraulic fracture modeling is derived by building the virtual work principle of the fracture problem considering water pressure loading on the crack surface. Then the implement method of XFEM for hydraulic fracture modeling is deduced,such as numerical integration of discontinuous functions reflecting discontinuity of the crack surface,crack growth criteria,integral method of stress intensity factors,and the modeling method of crack propagation. Finally,the feasibility and superiority of this method are exhibited through numerical analysis of the Xiangjiaba gravity dam with XFEM. Comparing with classical FEM,the crack growth in the gravity dam can be modeled by XFEM without making the crack surface associated to the mesh,without setting dense mesh near the crack tip and without remeshing after crack growth. Thus the disadvantages of hydraulic fracturing analysis with FEM are avoided and the pre-processing work is simplified.
引文
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[14]方修君,金峰,王进廷.基于扩展有限元法的Koyna重力坝地震开裂过程模拟[J].清华大学学报(自然科学版),2008,48(12):2065-2069.
[15]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.
[16]Melenk J M,Babu-ka I.The partition of unity finite element method:Basic theory and application[sJ].Comput-e r Methods in Applied Mechanics and Engineering,1996(139):289-314.
[17]Duarte C A,Oden J T.An H-P adaptive method using clouds[J].Computer Methods in Applied Mechanics andE ngineering,1996(139):237-262.
[18]董玉文,余天堂,任青文.直接计算应力强度因子的扩展有限元法[J].计算力学学报,2008,25(1):72-77.
[2]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.
[3]Belytschko T,Black T.Elastic crack growth in finite elements with minimal remeshing[J].International Journalf or Numerical Method in Engineering,1999(45):601-620.
[4]Mo-s N,Dolbow J,Belytschko T.A finite element method for crack growth without remeshing[J].InternationalJ ournal for Numerical Method in Engineering,1999(46):131-150.
[5]Karihaloo B L,Xiao Q Z.Modeling of stationary and growing cracks in FE framework without remeshing:as tate-of-the-art review[J].Computers and Structures,2003(81):119-129.
[6]Stefano M,Umberto P.Extended finite element method for quasi-brittle fracture[J].International Journal for Nu-m erical Methods in Engineering,2003(58):103-126.
[7]Legrain G,Mo-s N,Verron E.Stress analysis around crack tips in finite strain problems using the extended finitee lement method[J].International Journal for Numerical Methods in Engineering,2005(63):290-314.
[8]Zi G,Belytschko T.New crack-tip elements for XFEM and applications to cohesive cracks[J].InternationalJ ournal for Numerical Methods in Engineering,2003(57):2221-2240.
[9]Unger J F,Eckardt S,K-nke C.Modeling of Cohesive Crack Growth in Concrete Structures with the Extended Fi-n ite Element Method[J].Computer Methods in Applied Mechanics and Engineering,2007(196):4087-4100.
[10]Günther M,Peter D.Energy-based modeling of cohesive and cohesionless cracks via X-FEM[J].ComputerM ethods in Applied Mechanics and Engineering,2007(196):2338-2357.
[11]Dolbow J,Mo-s N,Belytschko T.An extended finite element method for crack growth with frictional contac[tJ].C omputer Methods in Applied Mechanics and Engineering,2001(190):6825-6846.
[12]Elguedj T,Gravouil A,Combescure A.A mixed augmented Lagrangian-extended finite element method for mod-e lling elastic-plastic fatigue crack growth with unilateral contac[tJ].International Journal for Numerical Methodsi n Engineering,2007(71):1569-1597.
[13]杜效鹄,段云岭,王光纶.重力坝断裂数值分析研究[J].水利学报,2005,36(9):1035-1042.
[14]方修君,金峰,王进廷.基于扩展有限元法的Koyna重力坝地震开裂过程模拟[J].清华大学学报(自然科学版),2008,48(12):2065-2069.
[15]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.
[16]Melenk J M,Babu-ka I.The partition of unity finite element method:Basic theory and application[sJ].Comput-e r Methods in Applied Mechanics and Engineering,1996(139):289-314.
[17]Duarte C A,Oden J T.An H-P adaptive method using clouds[J].Computer Methods in Applied Mechanics andE ngineering,1996(139):237-262.
[18]董玉文,余天堂,任青文.直接计算应力强度因子的扩展有限元法[J].计算力学学报,2008,25(1):72-77.
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