如美观测廊道流固耦合多体接触分析
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摘要
渗流作用下的多体接触问题在水利工程中普遍存在,现有的接触面单元方法存在诸多缺陷。基于计算接触力学的框架和计算程序,通过Lagrange乘子法引入接触界面孔压连续条件,发展了基于流固耦合理论的计算接触力学方法;对如美观测廊道进行流固耦合情况下的多体接触应力变形分析。分析结果表明,计算接触力学方法具有有效处理非协调计算网格的能力,可有效解决如美观测廊道三维形态复杂,以及廊道块体与坝体尺寸相差悬殊所带来的有限元计算网格划分的巨大困难。计算所得观测廊道位移的计算结果分布合理,且能很好地捕捉块体间大规模脱开和滑移等不连续变形。由于进行了计算网格的局部加密,可在混凝土廊道边壁内计算得到较为准确合理的应力分布。
Problems of multi-body contact with seepage are common in hydraulic engineering, but traditional joint element-based methods have a number of shortcomings. In this paper, we develop a new algorithm of multi-body contact with consolidation using a Lagrange multiplier method to handle the pore pressure continuity condition at contact interfaces, based on the computational contact mechanics and fluid-solid coupling. This algorithm is applied to a stress-deformation analysis of the observation galleries in the earth core of the Rumei dam. Numerical calculations show that it is capable of handling nonconforming meshes and effectively solves the enormous difficulties in mesh generation arising from the complicated 3 D form of the galleries and the huge dimensional differences between the gallery blocks and dam body. The calculated gallery displacements are reasonable, and the behaviors of discontinuous deformation such as the separation and sliding between the gallery blocks are captured. By refining the local gallery mesh, we can further achieve better results and a higher accuracy in the calculations of stress distribution over the gallery blocks.
Problems of multi-body contact with seepage are common in hydraulic engineering, but traditional joint element-based methods have a number of shortcomings. In this paper, we develop a new algorithm of multi-body contact with consolidation using a Lagrange multiplier method to handle the pore pressure continuity condition at contact interfaces, based on the computational contact mechanics and fluid-solid coupling. This algorithm is applied to a stress-deformation analysis of the observation galleries in the earth core of the Rumei dam. Numerical calculations show that it is capable of handling nonconforming meshes and effectively solves the enormous difficulties in mesh generation arising from the complicated 3 D form of the galleries and the huge dimensional differences between the gallery blocks and dam body. The calculated gallery displacements are reasonable, and the behaviors of discontinuous deformation such as the separation and sliding between the gallery blocks are captured. By refining the local gallery mesh, we can further achieve better results and a higher accuracy in the calculations of stress distribution over the gallery blocks.
引文
[1]GOODMAN R E,TAYLOR R L,BREKKE T L.A model for the mechanics of jointed rock[J].Journal of Soil Mechanics and Foundations Division,1968,94(3):637-659.
[2]QIAN X X,YUAN H N,LI Q M,et al.Comparative study on interface elements,thin-layer elements,and contact analysis methods in the analysis of high concrete-faced rockfill dams[J].Journal of Applied Mathematics,2013,2013(19):4499-4588.
[3]WRIGGERS P.Computational contact mechanics[M].German:Springer-Verlag Berlin Heidelberg,2006.
[4]张丙印,师瑞锋,王刚.高面板堆石坝面板脱空问题的接触力学分析[J].岩土工程学报,2003,25(3):361-364.ZHANG Bingyin,SHI Ruifeng,WANG Gang.Contact analysis of separation between concrete slab and cushion layer in high concrete face rock-fill dam[J].Chinese Journal of Geotechnical Engineering,2003,25(3):361-364.(in Chinese)
[5]周墨臻,张丙印,张宗亮,等.超高面板堆石坝面板挤压破坏机理及数值模拟方法研究[J].岩土工程学报,2015,37(8):1426-1432.ZHOU Mozhen,ZHANG Bingyin,ZHANG Zongliang,et al.Mechanisms and simulation methods for extrusion damage of concrete faces of high concrete-faced rockfill dams[J].Chinese Journal of Geotechnical Engineering,2015,37(8):1426-1432.(in Chinese)
[6]ZHOU M Z,ZHANG B Y,PENG C,et al.Threedimensional numerical analysis of concrete-faced rockfill dam using dual-mortar finite element method with mixed tangential contact constraints[J].International Journal for Numerical&Analytical Methods in Geomechanics,2016,40(15):2100-2122.
[7]介玉新,许延春,李广信.固结计算中接触面渗流问题的模拟[J].工程力学学报,2007,24(S1):104-107.JIE Yuxin,XU Yanchun,LI Guangxin.Simulating of seepage through interface in consolidation analysis[J].Engineering Mechanics,2007,24(S1):104-107.(in Chinese)
[8]SEGURA J M,CAROL I.Coupled HM analysis using zero-thickness interface elements with double nodes.Part I:Theoretical model[J].International Journal for Numerical&Analytical Methods in Geomechanics,2008,32(18):2083-2101.
[9]CERFONTAINE B,DIEUDONNéA C,RADU J P,et al.3D zero-thickness coupled interface finite element:Formulation and application[J].Computers and Geotechnics,2015,69:124-140.
[10]SABETAMAL H,NAZEM M,SLOAN S W,et al.Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method[J].International Journal for Numerical&Analytical Methods in Geomechanics,2016,40(1):25-61.
[11]BIOT M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[12]LADE P V,DE BOER R.The concept of effective stress for soil,concrete and rock[J].Geotechnique,1997,47(1):61-78.
[13]DOCA T,PIRES F M A,Cesar de Sa J M A.A frictional mortar contact approach for the analysis of large inelastic deformation problems[J].International Journal of Solids&Structures,2014,51(9):1697-1715.
[14]BELYTSCHKO T,NEAL M O.Contact-impact by the pinball algorithm with penalty and Lagrangian methods[J].International Journal for Numerical Methods in Engineering,1991,31(3):547-572.
[15]WOHLMUTH B I.A mortar finite element method using dual spaces for the Lagrange multiplier[J].SIAM Journal on Numerical Analysis,2001,36(6):995-1012.
[16]POPP A,WALL W A.Dual mortar methods for computational contact mechanics-overview and recent developments[J].Gamm-mitteilungen,2014,37(1):66-84.
[17]HüEBER S,WOHLMUTH B I.A primal-dual active set strategy for non-linear multibody contact problems[J].Computer Methods in Applied Mechanics and Engineering,2005,194(27):3147-3166.
[18]GITTERLE M,POPP A,GEE M W,et al.Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization[J].International Journal for Numerical Methods in Engineering,2010,84(5):543-571.
[19]POPP A,SEITZ A,GEE M W,et al.Improved robustness and consistency of 3D contact algorithms based on a dual mortar approach[J].Computer Methods in Applied Mechanics&Engineering,2013,264(3):67-80.
[20]周墨臻,张丙印,王伟.高面板堆石坝软缝接触计算模型及其数值实现[J].岩石力学与工程学报,2016,35(S1):2803-2810.ZHOU Mozhen,ZHANG Bingyin,WANG Wei.Algorithm and simulation methods for the soft longitudinal joint of the concrete faces in high concretefaced rockfill dams[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(S1):2803-2810.(in Chinese)
[2]QIAN X X,YUAN H N,LI Q M,et al.Comparative study on interface elements,thin-layer elements,and contact analysis methods in the analysis of high concrete-faced rockfill dams[J].Journal of Applied Mathematics,2013,2013(19):4499-4588.
[3]WRIGGERS P.Computational contact mechanics[M].German:Springer-Verlag Berlin Heidelberg,2006.
[4]张丙印,师瑞锋,王刚.高面板堆石坝面板脱空问题的接触力学分析[J].岩土工程学报,2003,25(3):361-364.ZHANG Bingyin,SHI Ruifeng,WANG Gang.Contact analysis of separation between concrete slab and cushion layer in high concrete face rock-fill dam[J].Chinese Journal of Geotechnical Engineering,2003,25(3):361-364.(in Chinese)
[5]周墨臻,张丙印,张宗亮,等.超高面板堆石坝面板挤压破坏机理及数值模拟方法研究[J].岩土工程学报,2015,37(8):1426-1432.ZHOU Mozhen,ZHANG Bingyin,ZHANG Zongliang,et al.Mechanisms and simulation methods for extrusion damage of concrete faces of high concrete-faced rockfill dams[J].Chinese Journal of Geotechnical Engineering,2015,37(8):1426-1432.(in Chinese)
[6]ZHOU M Z,ZHANG B Y,PENG C,et al.Threedimensional numerical analysis of concrete-faced rockfill dam using dual-mortar finite element method with mixed tangential contact constraints[J].International Journal for Numerical&Analytical Methods in Geomechanics,2016,40(15):2100-2122.
[7]介玉新,许延春,李广信.固结计算中接触面渗流问题的模拟[J].工程力学学报,2007,24(S1):104-107.JIE Yuxin,XU Yanchun,LI Guangxin.Simulating of seepage through interface in consolidation analysis[J].Engineering Mechanics,2007,24(S1):104-107.(in Chinese)
[8]SEGURA J M,CAROL I.Coupled HM analysis using zero-thickness interface elements with double nodes.Part I:Theoretical model[J].International Journal for Numerical&Analytical Methods in Geomechanics,2008,32(18):2083-2101.
[9]CERFONTAINE B,DIEUDONNéA C,RADU J P,et al.3D zero-thickness coupled interface finite element:Formulation and application[J].Computers and Geotechnics,2015,69:124-140.
[10]SABETAMAL H,NAZEM M,SLOAN S W,et al.Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method[J].International Journal for Numerical&Analytical Methods in Geomechanics,2016,40(1):25-61.
[11]BIOT M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[12]LADE P V,DE BOER R.The concept of effective stress for soil,concrete and rock[J].Geotechnique,1997,47(1):61-78.
[13]DOCA T,PIRES F M A,Cesar de Sa J M A.A frictional mortar contact approach for the analysis of large inelastic deformation problems[J].International Journal of Solids&Structures,2014,51(9):1697-1715.
[14]BELYTSCHKO T,NEAL M O.Contact-impact by the pinball algorithm with penalty and Lagrangian methods[J].International Journal for Numerical Methods in Engineering,1991,31(3):547-572.
[15]WOHLMUTH B I.A mortar finite element method using dual spaces for the Lagrange multiplier[J].SIAM Journal on Numerical Analysis,2001,36(6):995-1012.
[16]POPP A,WALL W A.Dual mortar methods for computational contact mechanics-overview and recent developments[J].Gamm-mitteilungen,2014,37(1):66-84.
[17]HüEBER S,WOHLMUTH B I.A primal-dual active set strategy for non-linear multibody contact problems[J].Computer Methods in Applied Mechanics and Engineering,2005,194(27):3147-3166.
[18]GITTERLE M,POPP A,GEE M W,et al.Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization[J].International Journal for Numerical Methods in Engineering,2010,84(5):543-571.
[19]POPP A,SEITZ A,GEE M W,et al.Improved robustness and consistency of 3D contact algorithms based on a dual mortar approach[J].Computer Methods in Applied Mechanics&Engineering,2013,264(3):67-80.
[20]周墨臻,张丙印,王伟.高面板堆石坝软缝接触计算模型及其数值实现[J].岩石力学与工程学报,2016,35(S1):2803-2810.ZHOU Mozhen,ZHANG Bingyin,WANG Wei.Algorithm and simulation methods for the soft longitudinal joint of the concrete faces in high concretefaced rockfill dams[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(S1):2803-2810.(in Chinese)