多轴加载状态下混凝土损伤特性研究
|
摘要
混凝土结构的安全性、耐久性与维修加固已成为混凝土结构研究的重要研究方向,其中建立一种简便高效的损伤评估方法,对遭受损伤的新建和改建建筑物进行检测鉴定和评估是工程实践中迫切需要解决的问题。为了描述混凝土试件在经历各种荷载作用下,微裂纹萌生、扩展、汇集而造成材料的损伤过程,本文利用Najar损伤理论对混凝土在多轴加载条件下的损伤特性进行了比较深入的研究。
首先,本文对混凝土开裂破坏的机理、损伤理论和各种类型的混凝土损伤模型进行了深入分析和综述,在此基础上,从能量损伤的角度出发,基于经典Najar损伤理论,利用高精度的Simpson积分方法建立了损伤模型及损伤演变方程。
其次,本文重点是将单轴加载条件下的混凝土损伤模型推广应用到三轴受压状态,对单轴和多轴加载状态下混凝土损伤进行分析,为建立多轴加载条件下的混凝土损伤本构模型奠定理论基础。主要考虑的加载方式包括:单轴压缩、单轴拉伸、恒定单侧压比例加载,恒定不等双侧压比例加载,三轴比例加载及三向等压加载。结果表明,混凝土在多轴受压和单轴受压作用下的损伤有相似的发展趋势。各种类型加载历史下混凝土损伤都随着应变的增大而增大,且初始加载阶段损伤发展较快,加载末段损伤发展缓慢并趋于稳定值。但是,在相同应变历史条件下,三轴受压下的损伤值比单压下的损伤值明显偏小,而且随着侧压比例的增大损伤进一步减小,说明侧压有效限制了混凝土损伤的发展。另外,三向等比例加载状态下混凝土损伤近似沿直线增长,且损伤增长速率非常小,说明这种加载状态对于充分发挥混凝土受压特性是最有利的。
最后,本文还以三轴比例加载为例,推演了峰值应力处损伤与峰值应变的关系,在一定加载比例范围内,可以利用混凝土峰值应变快速推演得到混凝土的损伤。
The structural safety, durability and evaluation of damage in concrete under various loading patterns are of primary interest in every country. A simple and efficient method for the early and regular engineering measurement of damage, as well as for quality assurance during and after the construction of new structures and of reconstruction processes, is urgently required. Generally, it can be stated that the process of progressive cracking is the primary cause of the behavior of concrete observed under compression and subsequent failure. The density of fine cracking caused by the loading history is therefore a measure of material integrity, and is defined in the present work as damage.
Firstly, the damage mechanism under various loading patterns, the theory of continuum damage mechanics and multiform damage constitutive models of concrete are investigated. Based on the damage theory by Najar, the damage model has been developed using the Simpson integral method.
Secondly, the damage model of concrete under uniaxial compression has been applied to triaxial compressive state, to analysis damage evolvement of concrete under variety triaxial loading pattern, which is the most important part of the dissertation. In this paper, loading patterns include uniaxial compression, uniaxial tension, biaxial proportional compression, triaxial proportional compression and triaxial equi-compression. The damage evolution rule of concrete under triaxial and uniaxial compression shows the similar tendency. With the increase in the strain of the loading history, the incremental speed of damage becomes less and less, and finally the damage approaches a stable extreme value. Experienced the same axial strain loading history, the damage value of concrete is lower than that under uniaxial compression, and the damage of concrete in axial direction is reduced gradually with the increase in lateral pressures, which means that the lateral pressures can reduce the damage effectively. In addition, under triaxial equi-compression loading history, the damage of concrete is found to be in linear dependence relationship with the increase of axial strain, which means that kind of loading pattern could develop the compressive feature of concrete adequately.
Finally, the relationship between the damage and the peak strain under the condition of triaxial proportional compression is investigated. It is concluded that the damage of concrete subjected triaxial proportional compression can be determined by the peak strain of the loading histories conveniently and accurately.
首先,本文对混凝土开裂破坏的机理、损伤理论和各种类型的混凝土损伤模型进行了深入分析和综述,在此基础上,从能量损伤的角度出发,基于经典Najar损伤理论,利用高精度的Simpson积分方法建立了损伤模型及损伤演变方程。
其次,本文重点是将单轴加载条件下的混凝土损伤模型推广应用到三轴受压状态,对单轴和多轴加载状态下混凝土损伤进行分析,为建立多轴加载条件下的混凝土损伤本构模型奠定理论基础。主要考虑的加载方式包括:单轴压缩、单轴拉伸、恒定单侧压比例加载,恒定不等双侧压比例加载,三轴比例加载及三向等压加载。结果表明,混凝土在多轴受压和单轴受压作用下的损伤有相似的发展趋势。各种类型加载历史下混凝土损伤都随着应变的增大而增大,且初始加载阶段损伤发展较快,加载末段损伤发展缓慢并趋于稳定值。但是,在相同应变历史条件下,三轴受压下的损伤值比单压下的损伤值明显偏小,而且随着侧压比例的增大损伤进一步减小,说明侧压有效限制了混凝土损伤的发展。另外,三向等比例加载状态下混凝土损伤近似沿直线增长,且损伤增长速率非常小,说明这种加载状态对于充分发挥混凝土受压特性是最有利的。
最后,本文还以三轴比例加载为例,推演了峰值应力处损伤与峰值应变的关系,在一定加载比例范围内,可以利用混凝土峰值应变快速推演得到混凝土的损伤。
The structural safety, durability and evaluation of damage in concrete under various loading patterns are of primary interest in every country. A simple and efficient method for the early and regular engineering measurement of damage, as well as for quality assurance during and after the construction of new structures and of reconstruction processes, is urgently required. Generally, it can be stated that the process of progressive cracking is the primary cause of the behavior of concrete observed under compression and subsequent failure. The density of fine cracking caused by the loading history is therefore a measure of material integrity, and is defined in the present work as damage.
Firstly, the damage mechanism under various loading patterns, the theory of continuum damage mechanics and multiform damage constitutive models of concrete are investigated. Based on the damage theory by Najar, the damage model has been developed using the Simpson integral method.
Secondly, the damage model of concrete under uniaxial compression has been applied to triaxial compressive state, to analysis damage evolvement of concrete under variety triaxial loading pattern, which is the most important part of the dissertation. In this paper, loading patterns include uniaxial compression, uniaxial tension, biaxial proportional compression, triaxial proportional compression and triaxial equi-compression. The damage evolution rule of concrete under triaxial and uniaxial compression shows the similar tendency. With the increase in the strain of the loading history, the incremental speed of damage becomes less and less, and finally the damage approaches a stable extreme value. Experienced the same axial strain loading history, the damage value of concrete is lower than that under uniaxial compression, and the damage of concrete in axial direction is reduced gradually with the increase in lateral pressures, which means that the lateral pressures can reduce the damage effectively. In addition, under triaxial equi-compression loading history, the damage of concrete is found to be in linear dependence relationship with the increase of axial strain, which means that kind of loading pattern could develop the compressive feature of concrete adequately.
Finally, the relationship between the damage and the peak strain under the condition of triaxial proportional compression is investigated. It is concluded that the damage of concrete subjected triaxial proportional compression can be determined by the peak strain of the loading histories conveniently and accurately.
引文
[1]唐春安,朱万成.混凝土损伤与断裂-数值试验[M].北京:科学出版社,2003.
[2]马怀发,陈厚群,黎保馄.混凝土细观力学研究进展及评述[J].中国水利水电科学研究院学报. 2004, 2 (2):124-130.
[3]谢和平.岩石、混凝土损伤力学[M].徐州:中国矿业大学出版社,1990.
[4]余天庆,钱济成.损伤理论及其应用[M].北京:国防工业出版社,1993. YU Tian-qing, Qian Ji-cheng. Damage theory and application[M].Beijing:National Defence Industry Press, 1993.
[5]李兆霞.损伤力学及其应用[M].北京:科学出版社,2002.
[6] Kaplan M.F.Crack propagation and fracture of concrete[J].ACI,1961,58:591-610.
[7] Dougill,J.W.,et al.Journal of Engineering Mechanics[J].ASCE,1976,102:333.
[8] Krajcinovic,D.Constitutive equation for damaging platerials[J].J.Appl.Mech, 1983,50:355-360.
[9] Gao Lubin,Cheng Qingguo.An Anisotropic damage constitutive model for concrete and itsapplications[M].Applied Mechnics,International Academic publisher,Beijing, 1988:578-583.
[10]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997.
[11] Li.Z X.Viscoplastic damage model applied to cracking of gravity dam.Theo.and Appl[C].FracMech.1995:165-170.
[12] Li Z X,Xiao L G.Finite element analysis of local damage and post-failure behavior forstrain-sofening solid[C].Int.J of Frac.1996,80(1):85-95
[13]杨廷毅.混凝土损伤断裂过程研究[M].浙江大学出版社,1993.
[14]杨光松.损伤力学与复合材料损伤[M].国防工业出版社,1995.
[15]陈建兵,李杰.混凝土结构非线性随机损伤状态的演化分析[J].东南大学学报,2002.32(5):756-759.
[16]任青文,徐道远等.复杂条件下的高拱坝(300米级)建设中的应用基础研究,国家自然科学基金委员会,1997:1-53.
[17]刘华,蔡正敏,杨菊生等.混凝土结构三维损伤开裂破坏全过程非线性有限元分析[J].工程力学,1999,4:45-51.
[18] Noh.Sam-Yong,Kratzig,wilfried.B,Meskourid.konsiantin.Numerical simulation of service ability,damage evolution and failure of reinforced concrete shells. Computer and structures, 2003,81(5):843-857.
[19]张强勇,朱维申,金亚兵.弹塑性损伤模型在某地下厂房中的应用[J].岩石力学与工程学报,1999,18(6):654-657.
[20]余天庆.混凝土的分段线性损伤模型.岩石、混凝土断裂及强度,1985(2) YU Tian-qing. Linear segment damage model of concrete[J].Fracture and Capacity of Crack and Concrete,1985(2)
[21]何明,徐道远等.混凝土的损伤模型[J].福州大学学报,1994(4).
[22]钱济成,周建方.混凝土的两种损伤模型及其应用[J].河海大学学报,1989(3).
[23] Loland K E. continuous damage model for load response esti-mation of concrete [J].Cement and Concrete Research,1980(10):392-492.
[24] Mazarz J. Application de la mecanique de la mecanique de l’endommagement au comportement non linearie et a la rupturedu beton de structure[D]. Paris:These de Doctorat d’EtatU-niv, 1984.
[25]钱济成,周建方.混凝土分段曲线损伤模型及其应用[J].河海大学学报,1989(3):40-47. QIAN Ji-cheng, ZHOU Jian-fang. Segment curve model ofconcrete damage and application [J]. Journal of Hehai University,1989(3): 40-47.
[26] Supartono F, Sidoroff F. Anisotropic damage modeling for brittle elastic materials[C]∥Symposium of franc-poland,1984.
[27] Krajcinovic D,Lemaitre J. Continuum damage mechanics theory and applications[M]. New York: Springer- Verilag,1987:233-294.
[28]徐道远,符晓陵.高强混凝土损伤-断裂模型及其在大体积混凝土结构中的应用.河海大学,1995年3月.
[29]楼志文.损伤力学基础[M].西安交通大学出版社,1991.
[30] L.M.卡恰诺夫(杜善义、王殿富译)连续介质损伤力学引论.哈尔滨工业大学出版社,1989.
[31] RabotnovYN.Creeprupture.Ptoe.12thInt.Cong,Appl.Meeh.IUTAM,1968.
[32]徐定华,徐敏.混凝土材料学概论[M].北京:中国标准出版社.2002.
[33] Sidoroff F Description of anisotropic damage application to elasticity. IUTAM Colloqumm,Physical Nonlinearities in structural analysis,1981.
[34] Meier, R. W .,Gerstle, K. H. and KO. H. -Y.,Effects of multiaxial compressive loading on the residual tensile strength of plain concrete [R], report submitted to the New Mexico Engineering Research Institute, University of New Mexico, Albuquerque. N. M.,1981.
[35] A. Delibes Liniers, Microcracking of concrete under compression and its influence on tensile strength[J]. Material and Structures. 1987,20,111一116.
[36] D. J. Cook ancf P. Chindaprasirt, Influence of loading history upon the tensile properties of concrete [J].Mag. Concrete Res. 33(116), September 1981.154160.
[37] Ravindra Gettu,Antonio Aguado,and Marcel O. F. Oliveira, Damage in high-strengthconcrete due to monotonic and cyclic compression-a study based on splitting tensile strength[J].ACI Material Journal, Vol. 93, No. 6,November-December 1996, 519523.
[38] D. J. Cook and P. Chindaprasirt, Influence of lowing history upon the compressivee propertiesofconcrete[J]. Mag. Concrete Res. 32(111),June 1980. 89-100.
[39] K.E. Loland, Continuous Damage Model for Load-response Estimation of Concrete. Cement and Concrete Research. Pergamon Press,Ltd1980,Vo1.10:395-402.
[40] J. Mazars, Continuous Damage Theory-Application to Concrete. Journal of Enginee- ring.1980,115(2):345-365.
[41] Jan G.M. van Mier, Influenceof Damage OrientationCement and Concrete Distribution on The Multiaxial Stress Behaviors of Concrete. Research.Press, Ltd.1980.
[42] D. Krajcinovio, CxU. Fonseka, The Continuous Damage Theory of Brittle Materials. Journal of Applied Mechanics, ASME,1981,vo1.48:809-815.
[43]徐道远,王向东,朱为玄等.基于全曲线的混凝土损伤定量分析[J],岩石力学与工程学报,2001(专辑):1428-1431.
[44] Sinha B P, Gerstle K H, Tulin L Cz Stress-Strain Relations for Concrete Under Cyclic Loading. ACI Journal, February 1964,61(2):195-211.
[45]董毓利,谢和平,赵鹏.循环受压硷全过程声发射实验及其本构关系.实验力学,1996.11 (2): 216-221.
[46] Hsieh S S.A plastic-Fracture Model for Concrete. International Journal of Solids and Structures,1982, vo1.18(3):181-197.
[47]董毓利,谢和平,李世平.不同围压下混凝土受压弹塑性损伤本构模型的研究[J].煤炭学报,1996,21(3):265-270.
[48]李杰,吴建营.混凝土弹塑性损伤本构模型研究[J].土木工程学报,2005,38,(9): 14-27.
[49]尹双增.断裂·损伤理论及应用[M].北京:清华大学出版社,1992.353-356.
[50] Krajcinovic D, Silva G. Statistic aspects of the continuous damage theory[J]. International Journal of Solids & Struc-tures,1982,18(17):551-562.
[51]余志武,丁发兴.混凝土受压力学性能统一计算方法[J].建筑结构学报,2003,24(4): 41-46.
[52]丁发兴,余志武.混凝土受拉力学性能统一计算方法[J].华中科技大学学报(城市科学版),2004,21(3):29-34.
[53]蔡四维,蔡敏.混凝土的损伤断裂[M].北京:人民交通出版社,1999.94-110.
[54]逯静洲.三轴受压混凝土损伤特性理论与试验研究[D].大连理工大学博士学位论文,2001.
[55]逯静洲,林皋,王哲,肖诗云.三向等压荷载历史后混凝土超声波探伤方法研究[J].应用基础与工程科学学报,2005(3):313-319.
[56]王哲.混凝土弹塑性损伤本构关系的研究[R].大连理工大学海岸与近海工程国家重点实验室报告.1997, 6.
[57]王哲.内时理论的推广及其在混凝土中的应用[D].大连理工大学博士学位论文,1993.
[58]李京爽,王哲.混凝土一种假三轴塑性本构模型[J].北京交通大学学报,2005,29(4):49-53.
[2]马怀发,陈厚群,黎保馄.混凝土细观力学研究进展及评述[J].中国水利水电科学研究院学报. 2004, 2 (2):124-130.
[3]谢和平.岩石、混凝土损伤力学[M].徐州:中国矿业大学出版社,1990.
[4]余天庆,钱济成.损伤理论及其应用[M].北京:国防工业出版社,1993. YU Tian-qing, Qian Ji-cheng. Damage theory and application[M].Beijing:National Defence Industry Press, 1993.
[5]李兆霞.损伤力学及其应用[M].北京:科学出版社,2002.
[6] Kaplan M.F.Crack propagation and fracture of concrete[J].ACI,1961,58:591-610.
[7] Dougill,J.W.,et al.Journal of Engineering Mechanics[J].ASCE,1976,102:333.
[8] Krajcinovic,D.Constitutive equation for damaging platerials[J].J.Appl.Mech, 1983,50:355-360.
[9] Gao Lubin,Cheng Qingguo.An Anisotropic damage constitutive model for concrete and itsapplications[M].Applied Mechnics,International Academic publisher,Beijing, 1988:578-583.
[10]余寿文,冯西桥.损伤力学[M].北京:清华大学出版社,1997.
[11] Li.Z X.Viscoplastic damage model applied to cracking of gravity dam.Theo.and Appl[C].FracMech.1995:165-170.
[12] Li Z X,Xiao L G.Finite element analysis of local damage and post-failure behavior forstrain-sofening solid[C].Int.J of Frac.1996,80(1):85-95
[13]杨廷毅.混凝土损伤断裂过程研究[M].浙江大学出版社,1993.
[14]杨光松.损伤力学与复合材料损伤[M].国防工业出版社,1995.
[15]陈建兵,李杰.混凝土结构非线性随机损伤状态的演化分析[J].东南大学学报,2002.32(5):756-759.
[16]任青文,徐道远等.复杂条件下的高拱坝(300米级)建设中的应用基础研究,国家自然科学基金委员会,1997:1-53.
[17]刘华,蔡正敏,杨菊生等.混凝土结构三维损伤开裂破坏全过程非线性有限元分析[J].工程力学,1999,4:45-51.
[18] Noh.Sam-Yong,Kratzig,wilfried.B,Meskourid.konsiantin.Numerical simulation of service ability,damage evolution and failure of reinforced concrete shells. Computer and structures, 2003,81(5):843-857.
[19]张强勇,朱维申,金亚兵.弹塑性损伤模型在某地下厂房中的应用[J].岩石力学与工程学报,1999,18(6):654-657.
[20]余天庆.混凝土的分段线性损伤模型.岩石、混凝土断裂及强度,1985(2) YU Tian-qing. Linear segment damage model of concrete[J].Fracture and Capacity of Crack and Concrete,1985(2)
[21]何明,徐道远等.混凝土的损伤模型[J].福州大学学报,1994(4).
[22]钱济成,周建方.混凝土的两种损伤模型及其应用[J].河海大学学报,1989(3).
[23] Loland K E. continuous damage model for load response esti-mation of concrete [J].Cement and Concrete Research,1980(10):392-492.
[24] Mazarz J. Application de la mecanique de la mecanique de l’endommagement au comportement non linearie et a la rupturedu beton de structure[D]. Paris:These de Doctorat d’EtatU-niv, 1984.
[25]钱济成,周建方.混凝土分段曲线损伤模型及其应用[J].河海大学学报,1989(3):40-47. QIAN Ji-cheng, ZHOU Jian-fang. Segment curve model ofconcrete damage and application [J]. Journal of Hehai University,1989(3): 40-47.
[26] Supartono F, Sidoroff F. Anisotropic damage modeling for brittle elastic materials[C]∥Symposium of franc-poland,1984.
[27] Krajcinovic D,Lemaitre J. Continuum damage mechanics theory and applications[M]. New York: Springer- Verilag,1987:233-294.
[28]徐道远,符晓陵.高强混凝土损伤-断裂模型及其在大体积混凝土结构中的应用.河海大学,1995年3月.
[29]楼志文.损伤力学基础[M].西安交通大学出版社,1991.
[30] L.M.卡恰诺夫(杜善义、王殿富译)连续介质损伤力学引论.哈尔滨工业大学出版社,1989.
[31] RabotnovYN.Creeprupture.Ptoe.12thInt.Cong,Appl.Meeh.IUTAM,1968.
[32]徐定华,徐敏.混凝土材料学概论[M].北京:中国标准出版社.2002.
[33] Sidoroff F Description of anisotropic damage application to elasticity. IUTAM Colloqumm,Physical Nonlinearities in structural analysis,1981.
[34] Meier, R. W .,Gerstle, K. H. and KO. H. -Y.,Effects of multiaxial compressive loading on the residual tensile strength of plain concrete [R], report submitted to the New Mexico Engineering Research Institute, University of New Mexico, Albuquerque. N. M.,1981.
[35] A. Delibes Liniers, Microcracking of concrete under compression and its influence on tensile strength[J]. Material and Structures. 1987,20,111一116.
[36] D. J. Cook ancf P. Chindaprasirt, Influence of loading history upon the tensile properties of concrete [J].Mag. Concrete Res. 33(116), September 1981.154160.
[37] Ravindra Gettu,Antonio Aguado,and Marcel O. F. Oliveira, Damage in high-strengthconcrete due to monotonic and cyclic compression-a study based on splitting tensile strength[J].ACI Material Journal, Vol. 93, No. 6,November-December 1996, 519523.
[38] D. J. Cook and P. Chindaprasirt, Influence of lowing history upon the compressivee propertiesofconcrete[J]. Mag. Concrete Res. 32(111),June 1980. 89-100.
[39] K.E. Loland, Continuous Damage Model for Load-response Estimation of Concrete. Cement and Concrete Research. Pergamon Press,Ltd1980,Vo1.10:395-402.
[40] J. Mazars, Continuous Damage Theory-Application to Concrete. Journal of Enginee- ring.1980,115(2):345-365.
[41] Jan G.M. van Mier, Influenceof Damage OrientationCement and Concrete Distribution on The Multiaxial Stress Behaviors of Concrete. Research.Press, Ltd.1980.
[42] D. Krajcinovio, CxU. Fonseka, The Continuous Damage Theory of Brittle Materials. Journal of Applied Mechanics, ASME,1981,vo1.48:809-815.
[43]徐道远,王向东,朱为玄等.基于全曲线的混凝土损伤定量分析[J],岩石力学与工程学报,2001(专辑):1428-1431.
[44] Sinha B P, Gerstle K H, Tulin L Cz Stress-Strain Relations for Concrete Under Cyclic Loading. ACI Journal, February 1964,61(2):195-211.
[45]董毓利,谢和平,赵鹏.循环受压硷全过程声发射实验及其本构关系.实验力学,1996.11 (2): 216-221.
[46] Hsieh S S.A plastic-Fracture Model for Concrete. International Journal of Solids and Structures,1982, vo1.18(3):181-197.
[47]董毓利,谢和平,李世平.不同围压下混凝土受压弹塑性损伤本构模型的研究[J].煤炭学报,1996,21(3):265-270.
[48]李杰,吴建营.混凝土弹塑性损伤本构模型研究[J].土木工程学报,2005,38,(9): 14-27.
[49]尹双增.断裂·损伤理论及应用[M].北京:清华大学出版社,1992.353-356.
[50] Krajcinovic D, Silva G. Statistic aspects of the continuous damage theory[J]. International Journal of Solids & Struc-tures,1982,18(17):551-562.
[51]余志武,丁发兴.混凝土受压力学性能统一计算方法[J].建筑结构学报,2003,24(4): 41-46.
[52]丁发兴,余志武.混凝土受拉力学性能统一计算方法[J].华中科技大学学报(城市科学版),2004,21(3):29-34.
[53]蔡四维,蔡敏.混凝土的损伤断裂[M].北京:人民交通出版社,1999.94-110.
[54]逯静洲.三轴受压混凝土损伤特性理论与试验研究[D].大连理工大学博士学位论文,2001.
[55]逯静洲,林皋,王哲,肖诗云.三向等压荷载历史后混凝土超声波探伤方法研究[J].应用基础与工程科学学报,2005(3):313-319.
[56]王哲.混凝土弹塑性损伤本构关系的研究[R].大连理工大学海岸与近海工程国家重点实验室报告.1997, 6.
[57]王哲.内时理论的推广及其在混凝土中的应用[D].大连理工大学博士学位论文,1993.
[58]李京爽,王哲.混凝土一种假三轴塑性本构模型[J].北京交通大学学报,2005,29(4):49-53.