盾构隧道动力有效应力分析方法研究
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摘要
耦合场分割算法是求解Biot动力固结方程的一种有效的方法,它能够充分利用现有程序资源,并且在土介质渗透系数较小时能够有效地解决统一算法中容易出现的病态矩阵问题。然而,目前已经提出的Biot方程分割算法都是基于有限元离散方程形式的,难以直接应用于现在软件的二次开发。在对瞬态热传导方程和孔压消散方程的对比研究的基础上,推导一种能够在结构–温度耦合场分析软件(也可以在单独的结构场软件和温度场软件)上实现的Biot方程多次迭代串行分割算法,即在求解Biot方程的第n+1荷载步时,预先将孔压消散方程中的耦合项(未知量)用某种形式的预测值(已知量)代替,使孔压消散方程中的未知量只剩下节点孔压,从而可独立求解;再代入Biot方程的第1式,求出节点位移;如此循环迭代,即能以解耦的形式完成Biot方程的求解过程。这种方法对不同维数的问题、不同单元类型以及动力或静力问题都适用,并且额外编程量很少,十分便于推广应用和充分利用现有资源。数值算例结果表明,这种方法具有良好的精度和计算稳定性。最后,利用这种方法对武汉长江盾构隧道横断面进行动力有效应力分析,并对该工程地基的液化危险性进行评价。
Partitioned solution procedures could be effectively used to solve Biot′s equations,which can depict the coupled soil-pore fluid systems.With this method,the existing finite element analysis software could be utilized adequately,while the problem of ill-conditioned matrix,emerging in monolithical approach when the coefficient of permeability of the soil is comparatively small,can be settled successful.The partitioned approaches of Biot′s equations are all based on the discrete form by finite element method,which will lead to the difficulties when employing them in the redevelopment of existing programs.After comparing the transient heat conduction equation and the pore pressure dissipation equation,a new multi-iteration serial partitioned solution procedure is proposed,in which a certain predicted known value is substituted for the coupled unknown item in pore pressure dissipation equation.With the only one unknown parameter,the nodal pore pressure is left in the equation and could be figured out easily.Subsequently,the solution from the above step is incorporated into the second equation and the other variable,the nodal displacement could be calculated separately.And then,all the load steps could be solved in uncoupled form iteration.With little additional procedures,this method could be easily realized in thermo-structural analysis programme(or independent).This differential equation based method,suitable for two or three-dimensional problems and for static or dynamic problems as well as various element types,is proposed.As demonstrated with numerical examples,this approach could give comparatively precise results and has good computational stability.Subsequently,this approach was applied to the transverse dynamic response analysis of Wuhan Yangtze River Tunnel.
Partitioned solution procedures could be effectively used to solve Biot′s equations,which can depict the coupled soil-pore fluid systems.With this method,the existing finite element analysis software could be utilized adequately,while the problem of ill-conditioned matrix,emerging in monolithical approach when the coefficient of permeability of the soil is comparatively small,can be settled successful.The partitioned approaches of Biot′s equations are all based on the discrete form by finite element method,which will lead to the difficulties when employing them in the redevelopment of existing programs.After comparing the transient heat conduction equation and the pore pressure dissipation equation,a new multi-iteration serial partitioned solution procedure is proposed,in which a certain predicted known value is substituted for the coupled unknown item in pore pressure dissipation equation.With the only one unknown parameter,the nodal pore pressure is left in the equation and could be figured out easily.Subsequently,the solution from the above step is incorporated into the second equation and the other variable,the nodal displacement could be calculated separately.And then,all the load steps could be solved in uncoupled form iteration.With little additional procedures,this method could be easily realized in thermo-structural analysis programme(or independent).This differential equation based method,suitable for two or three-dimensional problems and for static or dynamic problems as well as various element types,is proposed.As demonstrated with numerical examples,this approach could give comparatively precise results and has good computational stability.Subsequently,this approach was applied to the transverse dynamic response analysis of Wuhan Yangtze River Tunnel.
引文
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[14]赵维炳,施健勇.软土固结与流变[M].南京:河海大学出版社,1996.(ZHAO Weibing,SHI Jianyong.Consolidation and rheology of soft soil[M].Nanjing:Hohai University Press,1996.(in Chinese))
[15]李培振.结构–地基动力相互作用体系的振动台试验及计算模拟分析[博士学位论文][D].上海:同济大学,2002.(LI Peizhen.Shaking table test and numerical simulation of structure-soil dynamic system[Ph.D.Thesis][D].Shanghai:Tongji University,2002.(in Chinese))
[2]徐志英,沈珠江.地震液化的有效应力二维动力分析方法[J].华东水利学院学报,1981,9(3):1–14.(XU Zhiying,SHEN Zhujiang.2D dynamic soil liquefaction analysis based on effective stress principle[J].Journal of East China Technical University of Water Resources,1981,9(3):1–14.(in Chinese))
[3]BLOM F J.A monolithical fluid-structure interaction algorithm applied to the piston problem[J].Computer Methods in Applied Mechanics and Engineering,1998,167(3/4):369–391.
[4]PARK K C,FELIPPA C A.Partitioned analysis of coupled systems[C]//BELYTSCHKO T,HUGHES T J R ed.Computational Methods for Transient Analysis.North-Holland:[s.n.],1983:157–219.
[5]FELIPPA C A,PARK K C.Synthesis tools for structural dynamics and partitioned analysis of coupled systems[C]//IBRAHIMBEGOVIC A,BRANK B ed.Multi-physics and Multi-scale Computer Models in Nonlinear Analysis and Optimal Design of Engineering Structures under Extreme Conditions.Ljubljana,Slovenia:[s.n.],2004:50–110.
[6]FELIPPA C A,PARK K C.Staggered transient analysis procedures for coupled-field mechanical systems:formulation[J].Computer Methods in Applied Mechanics and Engineering,1980,24(1):61–111.
[7]HUANG M S,ZIENKIEWICZ O C.New unconditionally stable staggered solution procedures for coupled soil-pore fluid dynamic problems[J].International Journal for Numerical Methods in Engineering,1998,43(6):1 029–1 052.
[8]PREVOST J H.Partitioned solution procedure for simultaneous integration of coupled-field problems[J].Communications in Numerical Methods in Engineering,1997,13(4):239–247.
[9]HUANG M S,WU S M,ZIENKIEWICZ O C.Incompressible or nearly incompressible soil dynamic behaviour—a new staggered algorithm to circumvent restrictions of mixed formulation[J].Soil Dynamics and Earthquake Engineering,2001,21(2):169–179.
[10]王栋,栾茂田.广义Biot固结方程隐–隐式解法的推广及应用[J].世界地震工程,2002,18(1):23–26.(WANG Dong,LUAN Maotian.Extension and application of implicit-implicit staggered solution procedure for generalized Biot′s consolidation equation[J].World Earthquake Engineering,2002,18(1):23–26.(in Chinese))
[11]谢康和,周健.岩土工程有限元分析理论与应用[M].北京:科学出版社,2002.(XIE Kanghe,ZHOU Jian.Theory and application of finite element analysis in geotechnical engineering[M].Beijing:Science Press,2002.(in Chinese))
[12]BAJKOWSKI J,HAC M.Influence of coupled thermal-structural loads on stresses in elements of machines[C]//International Conference on Numerical Methods in Continuum Mechanics.Liptovsky,Slovak Republic:[s.n.],2000:19–24.
[13]周健,孔戈,张刚,等.基于耦合场分割算法的ANSYS二次开发及其应用[J].地震工程与工程振动,2006,26(2):73–79.(ZHOU Jian,KONG Ge,ZHANG Gang,et al.ANSYS redevelopment and its application based on partitioned solution procedures of coupled mechanical systems[J].Earthquake Engineering and Engineering Vibration,2006,26(2):73–79.(in Chinese))
[14]赵维炳,施健勇.软土固结与流变[M].南京:河海大学出版社,1996.(ZHAO Weibing,SHI Jianyong.Consolidation and rheology of soft soil[M].Nanjing:Hohai University Press,1996.(in Chinese))
[15]李培振.结构–地基动力相互作用体系的振动台试验及计算模拟分析[博士学位论文][D].上海:同济大学,2002.(LI Peizhen.Shaking table test and numerical simulation of structure-soil dynamic system[Ph.D.Thesis][D].Shanghai:Tongji University,2002.(in Chinese))
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