引入流体方程的离散颗粒–连续土体耦合方法研究
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摘要
为了将只适用于固体的离散颗粒–连续土体耦合方法应用至饱和土体,构建流体与离散颗粒–连续土体的耦合框架,此框架要求流体方程具有边界网格移动能力,并且流体方程分别与离散颗粒和连续土体耦合时具有统一的形式。然后建立新的流体方程组,此流体方程组基于任意拉格朗日–欧拉描述以实现流体边界网格移动控制,并且在离散颗粒和连续土体区域以不同方式提取的流固耦合力可以纳入统一的流体方程进行计算。为了保证流体微分方程有限元离散后的稳定性,基于特征线分离方法对建立的流体方程进行分离分步,然后基于标准伽辽金离散获得其有限元格式。最后通过模拟可液化场地中地下管线地震响应的离心机试验,表明引入流体方程后的离散颗粒–连续土体耦合方法可以有效描述离散颗粒与地下结构的非连续动力接触作用,同时有效降低离散元的模拟规模,并且可以兼顾地下结构移动时流体的边界移动问题。
For the approach of coupled discrete-continuous solids for solid phase to be extended to saturated soil,a theoretical framework of coupling the fluid with the discrete-continuous solids was established. The unified dynamic equations for the fluid-phase were established based on the ALE(arbitrary Lagrangian Eulerian)description which controlled the moving boundaries and meshes conveniently. The interaction forces between the fluid and the solid derived in the discrete and continuous domains separately were incorporated in these fluid equations in a unified form. The dynamic equations of fluid were split based on the algorithm of splitting the characteristic curves to obtain the proper forms suitable for the application of the standard Galerkin discretization procedure. The proposed method was applied to simulate the underground structure buried in the liquefiable soil under seismic excitation. The results of the simulation demonstrated that the proposed method depicted effectivelythe non-continuous contacts between the particles and the underground structure,reduced the number of particles for simulation and considered the moving boundaries for fluid-phase caused by underground structure as well.
For the approach of coupled discrete-continuous solids for solid phase to be extended to saturated soil,a theoretical framework of coupling the fluid with the discrete-continuous solids was established. The unified dynamic equations for the fluid-phase were established based on the ALE(arbitrary Lagrangian Eulerian)description which controlled the moving boundaries and meshes conveniently. The interaction forces between the fluid and the solid derived in the discrete and continuous domains separately were incorporated in these fluid equations in a unified form. The dynamic equations of fluid were split based on the algorithm of splitting the characteristic curves to obtain the proper forms suitable for the application of the standard Galerkin discretization procedure. The proposed method was applied to simulate the underground structure buried in the liquefiable soil under seismic excitation. The results of the simulation demonstrated that the proposed method depicted effectivelythe non-continuous contacts between the particles and the underground structure,reduced the number of particles for simulation and considered the moving boundaries for fluid-phase caused by underground structure as well.
引文
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[18]BRAESS H,WRIGGERS P.Arbitrary Lagrangian Eulerian finite element analysis of free surface flow[J].Computer Methods in Applied Mechanics and Engineering,2000,190(1/2):95–109.
[19]SUNG J,CHOI H G,YOO J Y.Time-accurate computation of unsteady free surface flows using an ALE-segregated equal-order FEM[J].Computer Methods in Applied Mechanics and Engineering,2000,190(11/12):1 425–1 440.
[20]SOULI M,ZOLESIO J P.Arbitrary Lagrangian-Eulerian and free surface methods in fluid mechanics[J].Computer Methods in Applied Mechanics and Engineering,2001,191(3/5):451–466.
[21]RABIER S,MEDALE M.Computation of free surface flows with aprojection FEM in a moving mesh framework[J].Computer Methods in Applied Mechanics and Engineering,2003,192(41/42):4 703–4721.
[22]LO D C,YOUNG D L.Arbitrary Lagrangian-Eulerian finite element analysis of free surface flow using velocity-vorticity formulation[J].Journal of Computational Physics,2004,195(1):175–201.
[23]ERGUN S.Fluid flow through packed columns[J].Chemical Engineering Progress,1952,48(2):89–94.
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[25]CUNDALL P A.PFC user manual[M].Minneapolis,Minnesota:Itasca Consulting Group Inc.,2004:7–11.
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[31]ZIENKIEWICZ O C,TAYLOR R L,NITHIARASU P.The finite element method for fluid dynamics[M].6th ed.Singapore:Elsevier(Singapore)Pte Ltd.,2009:79–105.
[32]LING H I,MOHRI Y,KAWABATA T,et al.Centrifuge modeling of seismic behavior of large-diameter pipe in liquefiable soil[J].Journal of Geotechnical and Geoenvironmental Engineering,2003,129(12):1 092–1 101.
[33]ARULMOLI K,MURALEETHARAN K K,HOSSAIN M M,et al.VELACS verification of liquefaction analysis by centrifuge studies laboratory testing program soil data report[R].Irvine,Canada:The Earth Technology Corporation,1992.
[34]HOOMANS B P B,KUIPERS J A M,BRIELS W J,et al.Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed:A hard-sphere approach[J].Chemical Engineering Science,1996,51(1):99–118.
[2]JIN W,ZHOU J.A coupled micro-macro method for pile penetration analysis[C]//Proceedings of the 2010 Geo-Shanghai International Conference.Shanghai:Geotechnical Special Publication,2010:234–239.
[3]周健,邓益兵,贾敏才.基于颗粒单元接触的二维离散–连续耦合分析方法[J].岩土工程学报,2010,32(10):1 479–1 484.(ZHOU Jian,DENG Yibing,JIA Mincai.Coupling method of two-dimensional discontinuum-continuum based on contact between particle and element[J].Chinese Journal of Geotechnical Engineering,2010,32(10):1 479–1 484.(in Chinese))
[4]陈建峰,郑希,李辉利,等.软土地基加筋土挡墙二维离散–连续耦合模拟[J].土木工程学报,2011,44(增):33–36.(CHEN Jianfeng,ZHENG Xi,LI Huili,et al.Coupling discontinuum-continuum simulation of a geogrid-reinforced soil retaining wall(RSW)on soft soil[J].China Civil Engineering Journal,2011,44(Supp.):33–36.(in Chinese))
[5]周健,金炜枫.基于耦合方法的挡土墙地震响应的数值模拟[J].岩土力学,2010,31(12):3 949–3 957.(ZHOU Jian,JIN Weifeng.Coupled approach based simulation of a retaining wall under seismic excitation[J].Rock and Soil Mechanics,2010,31(12):3 949–3 957.(in Chinese))
[6]金炜枫,周健.列车振动下隧道与土体响应的双尺度耦合模拟[J].岩石力学与工程学报,2011,30(5):1 016–1 024.(JIN Weifeng,ZHOU Jian.Two-scale coupled simulation of tunnel-soil vibrations under train excitation[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(5):1 016–1 024.(in Chinese))
[7]金炜枫,周健,张姣.基于离散–连续耦合方法的地下结构在地震中破坏过程模拟[J].固体力学学报,2013,34(1):93–102.(JIN Weifeng,ZHOU Jian,ZHANG Jiao.Collapse simulation of the subway structure during the earthquake based on the two-scale coupled method[J].Chinese Journal of Solid Mechanics,2013,34(1):93–102.(in Chinese))
[8]ZEGHAL M,SHAMY U E.A continuum-discrete hydromechanical analysis of granular deposit liquefaction[J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(14):1 361–1 381.
[9]SHAMY U E,ZEGHAL M.A micro-mechanical investigation of the dynamic response and liquefaction of saturated granular soils[J].Soil Dynamics and Earthquake Engineering,2007,27(8):712–729.
[10]ZEGHAL M,SHAMY U E.Liquefaction of saturated loose and cemented granular soils[J].Powder Technology,2008,184(2):254–265.
[11]AMSDEN A A,HIRT C W.An arbitrary Lagrangian-Eulerian computer program for fluid flow at all speeds[R].Los Alamos:Los Alamos Scientific Laboratory,1973.
[12]LIU W K,GVILDYS J.Fluid-structure interaction of tanks with an eccentric core barrel[J].Computer Methods in Applied Mechanics and Engineering,1986,58(1/2):51–77.
[13]HUGHES T J R,LIU W K,ZIMMERMANN T K.LagrangianEulerian finite element formulation for incompressible viscous flows[J].Computer Methods in Applied Mechanics and Engineering,1981,29(3/4):329–349.
[14]HUERTA A,LIU W K.Viscous flow with large free surface motion[J].Computer Methods in Applied Mechanics and Engineering,1988,69(3/4):277–324.
[15]NAVTI S E,RAVINDRAN K,TAYLOR C,et al.Finite element modelling of surface tension effects using a Lagrangian-Eulerian kinematic description[J].Computer Methods in Applied Mechanics and Engineering,1997,147(1/2):41–60.
[16]HUSHIJIMA S.Three-dimensional arbitrary Lagrangian-Eulerian numerical prediction method for non-linear free surface oscillation[J].International Journal for Numerical Methods in Fluids,1998,26(5):605–623.
[17]ZHOU J G,STANSBY P K.An arbitrary Lagrangian-Eulerian(ALES)model with non-hydrostatic pressure for shallow water flows[J].Computer Methods in Applied Mechanics and Engineering,1999,178(1/2):199–214.
[18]BRAESS H,WRIGGERS P.Arbitrary Lagrangian Eulerian finite element analysis of free surface flow[J].Computer Methods in Applied Mechanics and Engineering,2000,190(1/2):95–109.
[19]SUNG J,CHOI H G,YOO J Y.Time-accurate computation of unsteady free surface flows using an ALE-segregated equal-order FEM[J].Computer Methods in Applied Mechanics and Engineering,2000,190(11/12):1 425–1 440.
[20]SOULI M,ZOLESIO J P.Arbitrary Lagrangian-Eulerian and free surface methods in fluid mechanics[J].Computer Methods in Applied Mechanics and Engineering,2001,191(3/5):451–466.
[21]RABIER S,MEDALE M.Computation of free surface flows with aprojection FEM in a moving mesh framework[J].Computer Methods in Applied Mechanics and Engineering,2003,192(41/42):4 703–4721.
[22]LO D C,YOUNG D L.Arbitrary Lagrangian-Eulerian finite element analysis of free surface flow using velocity-vorticity formulation[J].Journal of Computational Physics,2004,195(1):175–201.
[23]ERGUN S.Fluid flow through packed columns[J].Chemical Engineering Progress,1952,48(2):89–94.
[24]WEN C Y,YU Y H.Mechanics of fluidization[J].Chemical Engineering Progress Symposium Series,1966,62:100–111.
[25]CUNDALL P A.PFC user manual[M].Minneapolis,Minnesota:Itasca Consulting Group Inc.,2004:7–11.
[26]NITHIARASU P.An arbitrary Lagrangian Eulerian(ALE)formulation for free surface flows using the characteristic-based split(CBS)scheme[J].International Journal for Numerical Methods in Fluids,2005,48(12):1 415–1 428.
[27]BROOKS A N,HUGHES T J R.Streamline upwind/Petrove-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier-strokes equations[J].Computer Methods in Applied Mechanics and Engineering,1982,32(1/3):199–259.
[28]HUGHES T J R,FRANCA L P,HULBERT G M.A new finite element formulation for computation fluid dynamics:VIII.The Galerkin/least-squares method for advective-diffusive equations[J].Computer Methods in Applied Mechanics and Engineering,1989,73(5):173–189.
[29]ZIENKIEWICZ O C,CODINA R.A general algorithm for compressible and incompressible flow—Part I.The split,characteristic-based scheme[J].International Journal for Numerical Methods in Fluids,1995,20(8/9):869–885.
[30]ZIENKIEWICZ O C,SAI B V K S,MORGAN K,et al.A general algorithm for compressible and incompressible flow—Part II.Tests on the explicit form[J].International Journal for Numerical Methods in Fluids,1995,20(8/9):887–913.
[31]ZIENKIEWICZ O C,TAYLOR R L,NITHIARASU P.The finite element method for fluid dynamics[M].6th ed.Singapore:Elsevier(Singapore)Pte Ltd.,2009:79–105.
[32]LING H I,MOHRI Y,KAWABATA T,et al.Centrifuge modeling of seismic behavior of large-diameter pipe in liquefiable soil[J].Journal of Geotechnical and Geoenvironmental Engineering,2003,129(12):1 092–1 101.
[33]ARULMOLI K,MURALEETHARAN K K,HOSSAIN M M,et al.VELACS verification of liquefaction analysis by centrifuge studies laboratory testing program soil data report[R].Irvine,Canada:The Earth Technology Corporation,1992.
[34]HOOMANS B P B,KUIPERS J A M,BRIELS W J,et al.Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed:A hard-sphere approach[J].Chemical Engineering Science,1996,51(1):99–118.
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