基于SPH-FEM耦合方法的落石冲击拱形钢筋混凝土棚洞数值模拟
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摘要
与框架钢筋混凝土棚洞相比,拱形钢筋混凝土棚洞具有自重小、跨度大的优点,其常用砂土垫层来耗散冲击能量。针对有限元法(FEM)模拟拱棚洞砂土材料超大变形问题时所存在的困难,建立了有限元(FEM)与光滑粒子流体动力学(SPH)的耦合数值计算方法。利用SPH粒子模拟落石冲击区域的大变形砂土,为提高计算效率和精度,非冲击区域砂土用有限元单元模拟,并将混凝土、钢筋、岩石、冲击锤等划分成Lagrange标准有限元网格;然后基于耦合SPH-FEM方法建立了落石冲击拱形钢筋混凝土棚洞数值模型。研究结果表明:随着冲击能量的增大,冲击力峰值和拱中点位移峰值也逐渐增大;与足尺冲击试验结果对比,冲击力峰值和拱中点位移峰值最大误差均没有超过10%,验证了数值耦合模型的准确性;数值耦合模型形象再现了砂土成坑的物理过程,砂土垫层耗能占初始冲击动能的85%以上,说明砂垫层是一种很好的缓冲耗能材料。SPH-FEM耦合方法显示出了模拟拱形钢筋混凝土棚洞冲击问题的有效性。
Compared with frame reinforced concrete(RC) hangar tunnels, arch RC ones have advantages of small self-weight and large span, and sand cushion is commonly used by the latter to dissipate impact energy. Aiming at the existing difficulty of using FEM to simulate arch hangar tunnel's sand materials with super-large deformation, the smooth particle hydrodynamics-finite element method(SPH-FEM) coupled method was proposed. SPH particles were used to simulate large deformation sand cushion in rock-fall impact area to improve computation efficiency and accuracy, finite elements were used to simulate sand cushion in non-impact area. Concrete, reinforcement, rock and ram hammers, etc. were divided into Lagrange standard finite element meshes. Based on the SPH-FEM coupled method, the numerical model for rock-fall impacting an arch RC hangar tunnel was established. The numerical simulation results showed that with increase in impact energy, impact force peak and displacement peak at arch middle point gradually increase; compared with full-scale impact test results, maximum errors of impact force peak and displacement peak at arch middle point are less than 10%, so the correctness of the numerical coupled model is verified; the numerical coupled model vividly reproduces a physical process of sand pit-forming, sand cushion's energy-dissipating occupies more than 85% of initial impact kinetic energy, so sand cushion is a very good material for buffering and energy-dissipating; the SPH-FEM coupled method is an effective means to simulate rock-fall impacting arch RC hangar tunnels.
Compared with frame reinforced concrete(RC) hangar tunnels, arch RC ones have advantages of small self-weight and large span, and sand cushion is commonly used by the latter to dissipate impact energy. Aiming at the existing difficulty of using FEM to simulate arch hangar tunnel's sand materials with super-large deformation, the smooth particle hydrodynamics-finite element method(SPH-FEM) coupled method was proposed. SPH particles were used to simulate large deformation sand cushion in rock-fall impact area to improve computation efficiency and accuracy, finite elements were used to simulate sand cushion in non-impact area. Concrete, reinforcement, rock and ram hammers, etc. were divided into Lagrange standard finite element meshes. Based on the SPH-FEM coupled method, the numerical model for rock-fall impacting an arch RC hangar tunnel was established. The numerical simulation results showed that with increase in impact energy, impact force peak and displacement peak at arch middle point gradually increase; compared with full-scale impact test results, maximum errors of impact force peak and displacement peak at arch middle point are less than 10%, so the correctness of the numerical coupled model is verified; the numerical coupled model vividly reproduces a physical process of sand pit-forming, sand cushion's energy-dissipating occupies more than 85% of initial impact kinetic energy, so sand cushion is a very good material for buffering and energy-dissipating; the SPH-FEM coupled method is an effective means to simulate rock-fall impacting arch RC hangar tunnels.
引文
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[17] 王玉锁,王涛,周良.跨中受落石冲击的拱形护桥明洞力学响应[J].隧道建设,2018,38(1):22-32.WANG Yusuo,WANG Tao,ZHOU Liang.Mechanical responses of arched protection shed of bridge under rock-fall impaction on midspan of rooftop[J].Tunnel Construction,2018,38(1):22-32.
[18] 罗杰,肖建春,马克俭,等.半球壳冲击土壤的SPH-FEM耦合分析方法[J].振动与冲击,2017,36(17):195-199.LUO Jie,XIAO Jianchun,MA Kejian,et al.SPH-FEM coupled method for analyzing a hemispherical shell impact soil[J].Journal of Vibration and Shock,2017,36(17):195-199.
[19] 王玉锁,李俊杰,李正辉,等.落石冲击力评定的离散元颗粒流数值模拟[J].西南交通大学学报,2016,51(1):22-29.WANG Yusuo,LI Junjie,LI Zhenghui,et al.Assessment of rockfall impact force by particle flow code numerical simulation based on discrete element model[J].Journal of Southwest Jiaotong University,2016,51(1):22-29.
[20] 庞勇,刘才山.低速刚性体冲击密实散体介质的动力学实验与理论研究[C]//中国力学大会暨钱学森诞辰100周年纪念大会.哈尔滨,2011.
[21] 黄雨,郝亮,野々山人.SPH方法在岩土工程中的研究应用进展[J].岩土工程学报,2008,30(2):256-262.HUANG Yu,HAO Liang,NONOYAMA Hideto.The state of the art of SPH method applied in geotechnical engineering[J].Chinese Journal of Geotechnical Engineering,2008,30(2):256-262.
[22] 陈书宇,陈成光.混凝土本构模型及其动态有限元算法研究[J].力学季刊,1998(2):109-117.CHEN Shuyu,CHEN Chengguang.The research of the constitutive model of concrete using the dynamic finite element method[J].Shanggai Journal of Mechanics,1998(2):109-117.
[23] 王政,倪玉山,曹菊珍,等.冲击载荷下混凝土本构模型构建研究[J].高压物理学报,2006,20(4):337-344.WANG Zheng,NI Yushan,CAO Juzhen,et al.Building of a constitutive model for concrete under dynamic impact[J].Chinese Journal of High Pressure Physics,2006,20(4):337-344.
[24] LIU G R,LIU M B.Smoothed particle hydrodynamics-a meshfree particle method[M].New Jersey:World Scientific Publishing Company,2003.
[25] LS-DANY Theroy Manual[S].07/22/17 (r:8697):LS-DYNA Dev.
[26] 林晓东,卢义玉,汤积仁,等.基于SPH-FEM耦合算法的磨料水射流破岩数值模拟[J].振动与冲击,2014,33(18):170-176.LIN Xiaodong,LU Yiyu,TANG Jiren,et al.Numerical simulation of abrasive water jet breaking rock with SPH-FEM coupling algorithm[J].Journal of Vibration and Shock,2014,33(18):170-176.
[27] 张志春,强洪夫,高巍然.一种新型SPH-FEM耦合算法及其在冲击动力学问题中的应用[J].爆炸与冲击,2011,31(3):243-249.ZHANG Zhichun,QIANG Hongfu,GAO Weiran.A new coupled SPH-FEM algorithm and its application to impact dynamics[J].Explosion and Shock Waves,2011,31(3):243-249.
[28] JSCE.Standard specification for design and construction of concrete structures-2007 “design”[S].[in Japanese].
[29] MOUTOUSSAMY L,HERVE G,BARBIER F.Qualification of Constrained_Lagrange_In_Solid command for steel/concrete interface modeling[C].LS-DYNA European User Conference,2011.
[30] KISHI N,BHATTI A Q.An equivalent fracture energy concept for nonlinear dynamic response analysis of prototype RC girders subjected to falling-weight impact loading[J].International Journal of Impact Engineering,2010,37(1):103-113.
[2] 阳友奎,原振华,杨涛.柔性防护系统及其工程设计与应用[M].北京:科学出版社,2015.
[3] BHATTI A Q,KISHI N.An application of impact response analysis on small-scale RC arch-type beams without stirrups[J].Construction and Building Materials Journal,2011,25(10):3972-3976.
[4] 刘成清,陈林雅,陈驰,等.柔性钢棚洞结构在落石灾害防治中的应用研究[J].西南交通大学学报,2015,50(1):110-117.LIU Chengqing,CHEN Linya,CHEN Chi,et al.Application of flexible shed-tunnel structure to rock-fall hazard prevention[J].Journal of Southwest Jiaotong University,2015,50(1):110-117.
[5] 王爽,周晓军,罗福君,等.拱形棚洞受落石冲击的模型试验研究[J].振动与冲击,2017,36(12):215-222.WANG Shuang,ZHOU Xiaojun,LUO Fujun,et al.An experimental study on the performance of an arch shaped shed tunnel due to the impact of rockfall[J].Journal of Vibration and Shock,2017,36(12):215-222.
[6] MOUGIN J P,PERROTIN P,MOMMESSIN M,et al.Rock fall impact on reinforced concrete slab:an experimental approach[J].International Journal of Impact Engineering,2005,31(2):169-183.
[7] KISHI N,KONNO H,IKEDA K,et al.Prototype impact tests on ultimate impact resistance of PC rock-sheds[J].International Journal of Impact Engineering,2002,27(9):969-985.
[8] DELHOMME F,MOMMESSIN M,MOUGIN J P,et al.Behavior of a structurally dissipating rock-shed:experimental analysis and study of punching effects[J].International Journal of Solids & Structures,2005,42(14):4204-4219.
[9] KISHI N,KONNO H.Numerical analysis model for three layer absorbing system under falling weight impact loading[J].JSCE Journal of Structural Engineering,2003,49(A):1323-1332.
[10] BHATTI A Q,KHATOON S,MEHMOOD A,et al.Numerical study for impact resistant design of full scale arch type reinforced concrete structures under falling weight impact test[J].Journal of Vibration & Control,2011,18(9):1275-1283.
[11] 刘茂.基于弹塑性修正Hertz接触理论的落石冲击力计算方法[J].中国地质灾害与防治学报,2012,23(3):21-27.LIU Mao.Calculation of impact force of falling rock based on elastoplastic modified hertz contact theory[J].The Chinese Journal of Geological Hazard and Control,2012,23(3):21-27.
[12] 易伟,余斌,刘秧,等.滚石冲击力计算方法研究[J].山地学报,2016,34(3):310-316.YI Wei,YU Bin,LIU Yang,et al.Research on calculation method of rockfall impact force[J].Mountain Research,2016,34(3):310-316.
[13] 王林峰,唐红梅,陈洪凯.消能棚洞的落石冲击计算及消能效果研究[J].中国铁道科学,2012,33(5):40-46.WANG Linfeng,TANG Hongmei,CHEN Hongkai.Study on the calculation method for rockfall impact and energy dissipation effect of energy dissipation shed tunnel[J].China Railway Science,2012,33(5):40-46.
[14] MONTANI S,DESCOEUDRES F,LABIOUSE V.Experimental study of rock sheds impacted by rock blocks[J].Structural Engineering International,1996,6(3):171-175.
[15] KAWAHARA S,MURO T.Effects of dry density and thickness of sandy soil on impact response due to rockfall[J].Journal of Terramechanics,2006,43(3):329-340.
[16] 王爽,周晓军,姜波,等.落石冲击下隧道大跨度棚洞的动力响应数值分析与抗冲击研究[J].爆炸与冲击,2016,36(4):548-556.WANG Shuang,ZHOU Xiaojun,JIANG Bo,et al.Numerical analysis of dynamic response and impact resistance of a large-span rock shed in a tunnel under rockfall impact[J].Explosion and Shock Waves,2016,36(4):548-556.
[17] 王玉锁,王涛,周良.跨中受落石冲击的拱形护桥明洞力学响应[J].隧道建设,2018,38(1):22-32.WANG Yusuo,WANG Tao,ZHOU Liang.Mechanical responses of arched protection shed of bridge under rock-fall impaction on midspan of rooftop[J].Tunnel Construction,2018,38(1):22-32.
[18] 罗杰,肖建春,马克俭,等.半球壳冲击土壤的SPH-FEM耦合分析方法[J].振动与冲击,2017,36(17):195-199.LUO Jie,XIAO Jianchun,MA Kejian,et al.SPH-FEM coupled method for analyzing a hemispherical shell impact soil[J].Journal of Vibration and Shock,2017,36(17):195-199.
[19] 王玉锁,李俊杰,李正辉,等.落石冲击力评定的离散元颗粒流数值模拟[J].西南交通大学学报,2016,51(1):22-29.WANG Yusuo,LI Junjie,LI Zhenghui,et al.Assessment of rockfall impact force by particle flow code numerical simulation based on discrete element model[J].Journal of Southwest Jiaotong University,2016,51(1):22-29.
[20] 庞勇,刘才山.低速刚性体冲击密实散体介质的动力学实验与理论研究[C]//中国力学大会暨钱学森诞辰100周年纪念大会.哈尔滨,2011.
[21] 黄雨,郝亮,野々山人.SPH方法在岩土工程中的研究应用进展[J].岩土工程学报,2008,30(2):256-262.HUANG Yu,HAO Liang,NONOYAMA Hideto.The state of the art of SPH method applied in geotechnical engineering[J].Chinese Journal of Geotechnical Engineering,2008,30(2):256-262.
[22] 陈书宇,陈成光.混凝土本构模型及其动态有限元算法研究[J].力学季刊,1998(2):109-117.CHEN Shuyu,CHEN Chengguang.The research of the constitutive model of concrete using the dynamic finite element method[J].Shanggai Journal of Mechanics,1998(2):109-117.
[23] 王政,倪玉山,曹菊珍,等.冲击载荷下混凝土本构模型构建研究[J].高压物理学报,2006,20(4):337-344.WANG Zheng,NI Yushan,CAO Juzhen,et al.Building of a constitutive model for concrete under dynamic impact[J].Chinese Journal of High Pressure Physics,2006,20(4):337-344.
[24] LIU G R,LIU M B.Smoothed particle hydrodynamics-a meshfree particle method[M].New Jersey:World Scientific Publishing Company,2003.
[25] LS-DANY Theroy Manual[S].07/22/17 (r:8697):LS-DYNA Dev.
[26] 林晓东,卢义玉,汤积仁,等.基于SPH-FEM耦合算法的磨料水射流破岩数值模拟[J].振动与冲击,2014,33(18):170-176.LIN Xiaodong,LU Yiyu,TANG Jiren,et al.Numerical simulation of abrasive water jet breaking rock with SPH-FEM coupling algorithm[J].Journal of Vibration and Shock,2014,33(18):170-176.
[27] 张志春,强洪夫,高巍然.一种新型SPH-FEM耦合算法及其在冲击动力学问题中的应用[J].爆炸与冲击,2011,31(3):243-249.ZHANG Zhichun,QIANG Hongfu,GAO Weiran.A new coupled SPH-FEM algorithm and its application to impact dynamics[J].Explosion and Shock Waves,2011,31(3):243-249.
[28] JSCE.Standard specification for design and construction of concrete structures-2007 “design”[S].[in Japanese].
[29] MOUTOUSSAMY L,HERVE G,BARBIER F.Qualification of Constrained_Lagrange_In_Solid command for steel/concrete interface modeling[C].LS-DYNA European User Conference,2011.
[30] KISHI N,BHATTI A Q.An equivalent fracture energy concept for nonlinear dynamic response analysis of prototype RC girders subjected to falling-weight impact loading[J].International Journal of Impact Engineering,2010,37(1):103-113.
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