混凝土名义强度的尺寸效应研究
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摘要
针对尺寸效应率和边界效应模型在混凝土名义强度的尺寸效应分析中存在分歧等问题,基于幂定律和等效弹性裂缝方法,提出了可综合考虑试件尺寸、初始裂缝长度以及断裂过程区对混凝土名义强度影响的尺寸效应模型.该模型融合了尺寸效应率和边界效应模型在混凝土名义强度尺寸效应分析中的影响因素,而且所需要的经验参数较少、求解方便.结合试验数据以及现有文献中的研究数据,对所提出的尺寸效应模型进行了验证,结果表明:所提出的模型可以较好地描述和预测混凝土材料的准脆性断裂行为,对试件的几何形状没有限制.
In view of the divergence in the size effect analysis of concrete nominal strength between the size effect law and boundary effect model of concrete,a novel size effect model based on a power law and equivalent elastic crack method was proposed.The influence of the specimen size,initial crack length and fracture process zone on the nominal strength of concrete was taken into account in the proposed model simultaneously.The influence factors of size effect law and boundary effect model were included in the proposed model,the few empirical parameters of this model were convenient to determine.The proposed model was verified through the experimental data and research data in the existing literature.The results show that the proposed model can properly describe and predict the quasi-brittle fracture behavior of concrete material,the limit of size or geometry of the specimens will vanish.
In view of the divergence in the size effect analysis of concrete nominal strength between the size effect law and boundary effect model of concrete,a novel size effect model based on a power law and equivalent elastic crack method was proposed.The influence of the specimen size,initial crack length and fracture process zone on the nominal strength of concrete was taken into account in the proposed model simultaneously.The influence factors of size effect law and boundary effect model were included in the proposed model,the few empirical parameters of this model were convenient to determine.The proposed model was verified through the experimental data and research data in the existing literature.The results show that the proposed model can properly describe and predict the quasi-brittle fracture behavior of concrete material,the limit of size or geometry of the specimens will vanish.
引文
[1]苏捷,方志,杨钻.混凝土抗折强度尺寸效应的试验研究[J].工业建筑,2012,42(12):62-66.SU Jie,FANG Zhi,YANG Zuan.Experimental study on the size effect of concrete flexural strength[J].Industrial Construction,2012,42(12):62-66.(in Chinese)
[2]苏捷,方志.普通混凝土与高强混凝土抗压强度的尺寸效应[J].建筑材料学报,2013,16(6):1078-1081,1086.SU Jie,FANG Zhi.Scale effect on cubic compressive strength of ordinary concrete and high-strength concrete[J].Journal of Building Materials,2013,16(6):1078-1081,1086.(in Chinese)
[3]WEIBULL W.A statistical theory of the strength of materials[C]∥Proceedings of the American Mathematical Society.Stockholm,Sweden:Royal Swedish Academy of Engineering and Science,1939,151:1-45.
[4]黄海燕,张子明.混凝土的统计尺寸效应[J].河海大学学报(自然科学版),2004,32(3):291-294.HUANG Haiyan,ZHANG Ziming.Statistical size effect of concrete[J].Journal of Hohai University(Natural Sciences),2004,32(3):291-294.(in Chinese)
[5]BAANT Z P,XI Y,REID S G.Statistical size effect in quasibrittle structures.I.Is Weibull theory applicable[J].Journal of Engineering Mechanics,1991,117(11):2609-2622.
[6]BAANT Z P.Size effect in blunt fracture:Concrete,rock,metal[J].Journal of Engineering Mechanics,1984,110(4):518-535.
[7]黄海燕.混凝土尺寸效应理论研究与断裂参数分析[D].南京:河海大学,2004.HUANG Haiyan.Study on size effects and mechanical parameters of concrete[D].Nanjing:Hohai University,2004.(in Chinese)
[8]倪玉山,张琦.混凝土断裂尺寸效应的研究进展[J].力学进展,1997,27(1):97-105.NI Yushan,ZHANG Qi.Recent advances on fracture size effect for concrete structures[J].Advances in Mechanics,1997,27(1):97-105.(in Chinese)
[9]HU X,WITTMANN F.Size effect on toughness induced by crack close to free surface[J].Engineering Fracture Mechanics,2000,65(2):209-221.
[10]HU X,DUAN K.Size effect:Influence of proximity of fracture process zone to specimen boundary[J].Engineering Fracture Mechanics,2007,74(7):1093-1100.
[11]HU X,DUAN K.Mechanism behind the size effect phenomenon[J].Journal of Engineering Mechanics,2010,136(1):60-68.
[12]YU Q,LE J L,HOOVER C G,et al.Problems with Hu-Duan boundary effect model and its comparison to size-shape effect law for quasi-brittle fracture[J].Journal of Engineering Mechanics,2010,136(1):40-50.
[13]HU X,LIANG L,YANG S.Weibull-strength size effect and common problems with size effect model[C]∥Proceedings of the 8th International Conference on Fracture Mechanics of Concrete and Concrete Structures.Barcelona:International Center for Numerical Methods in Engineering,2013:163-173.
[14]HOOVER C G,BAZANT Z P.Universal size-shape effect law based on comprehensive concrete fracture tests[J].Journal of Engineering Mechanics,2014,140(3):473-479.
[15]AGLAR Y,爦ENER S.Size effect tests of different notch depth specimens with support rotation measurements[J].Engineering Fracture Mechanics,2016,157:43-55.
[16]BAANT Z P,YU Q.Universal size effect law and effect of crack depth on quasi-brittle structure strength[J].Journal of Engineering Mechanics,2009,135(2):78-84.
[17]徐世烺.混凝土断裂力学[M].北京:科学出版社,2011:170-171.XU Shilang.Fracture mechanics of concrete[M].Beijing:Science Press,2011:170-171.(in Chinese)
[18]MOREL S.Size effect in quasibrittle fracture:Derivation of the energetic size effect law from equivalent LEFM and asymptotic analysis[J].International Journal of Fracture,2008,154(1/2):15-26.
[19]MOREL S,LESPINR C,COUREAU J L,et al.Bilinear softening parameters and equivalent LEFM R-curve in quasibrittle failure[J].International Journal of Solids and Structures,2010,47(6):837-850.
[20]XU S,REINHARDT H W.Crack extension resistance and fracture properties of quasi-brittle softening materials like concrete based on the complete process of fracture[J].International Journal of Fracture,1998,92(1):71-99.
[21]XU S L,REINHARDT H W.Determination of double-Kcriterion for crack propagation in quasi-brittle materials,Part I:Experimental investigation of crack propagation[J].International Journal of Fracture,1999,98(2):111-149.
[22]范向前,胡少伟,陆俊.非标准混凝土三点弯曲梁双K断裂韧度试验研究[J].建筑结构学报,2012,33(10):152-157.FAN Xiangqian,HU Shaowei,LU Jun.Experimental researching on the double-K fracture toughness of non-standard three point bending beam[J].Journal of Building Structures,2012,33(10):152-157.(in Chinese)
[23]KARIHALOO B L,ABDALLA H M,XIAO Q Z.Size effect in concrete beams[J].Engineering Fracture Mechanics,2003,70(7/8):979-993.
[2]苏捷,方志.普通混凝土与高强混凝土抗压强度的尺寸效应[J].建筑材料学报,2013,16(6):1078-1081,1086.SU Jie,FANG Zhi.Scale effect on cubic compressive strength of ordinary concrete and high-strength concrete[J].Journal of Building Materials,2013,16(6):1078-1081,1086.(in Chinese)
[3]WEIBULL W.A statistical theory of the strength of materials[C]∥Proceedings of the American Mathematical Society.Stockholm,Sweden:Royal Swedish Academy of Engineering and Science,1939,151:1-45.
[4]黄海燕,张子明.混凝土的统计尺寸效应[J].河海大学学报(自然科学版),2004,32(3):291-294.HUANG Haiyan,ZHANG Ziming.Statistical size effect of concrete[J].Journal of Hohai University(Natural Sciences),2004,32(3):291-294.(in Chinese)
[5]BAANT Z P,XI Y,REID S G.Statistical size effect in quasibrittle structures.I.Is Weibull theory applicable[J].Journal of Engineering Mechanics,1991,117(11):2609-2622.
[6]BAANT Z P.Size effect in blunt fracture:Concrete,rock,metal[J].Journal of Engineering Mechanics,1984,110(4):518-535.
[7]黄海燕.混凝土尺寸效应理论研究与断裂参数分析[D].南京:河海大学,2004.HUANG Haiyan.Study on size effects and mechanical parameters of concrete[D].Nanjing:Hohai University,2004.(in Chinese)
[8]倪玉山,张琦.混凝土断裂尺寸效应的研究进展[J].力学进展,1997,27(1):97-105.NI Yushan,ZHANG Qi.Recent advances on fracture size effect for concrete structures[J].Advances in Mechanics,1997,27(1):97-105.(in Chinese)
[9]HU X,WITTMANN F.Size effect on toughness induced by crack close to free surface[J].Engineering Fracture Mechanics,2000,65(2):209-221.
[10]HU X,DUAN K.Size effect:Influence of proximity of fracture process zone to specimen boundary[J].Engineering Fracture Mechanics,2007,74(7):1093-1100.
[11]HU X,DUAN K.Mechanism behind the size effect phenomenon[J].Journal of Engineering Mechanics,2010,136(1):60-68.
[12]YU Q,LE J L,HOOVER C G,et al.Problems with Hu-Duan boundary effect model and its comparison to size-shape effect law for quasi-brittle fracture[J].Journal of Engineering Mechanics,2010,136(1):40-50.
[13]HU X,LIANG L,YANG S.Weibull-strength size effect and common problems with size effect model[C]∥Proceedings of the 8th International Conference on Fracture Mechanics of Concrete and Concrete Structures.Barcelona:International Center for Numerical Methods in Engineering,2013:163-173.
[14]HOOVER C G,BAZANT Z P.Universal size-shape effect law based on comprehensive concrete fracture tests[J].Journal of Engineering Mechanics,2014,140(3):473-479.
[15]AGLAR Y,爦ENER S.Size effect tests of different notch depth specimens with support rotation measurements[J].Engineering Fracture Mechanics,2016,157:43-55.
[16]BAANT Z P,YU Q.Universal size effect law and effect of crack depth on quasi-brittle structure strength[J].Journal of Engineering Mechanics,2009,135(2):78-84.
[17]徐世烺.混凝土断裂力学[M].北京:科学出版社,2011:170-171.XU Shilang.Fracture mechanics of concrete[M].Beijing:Science Press,2011:170-171.(in Chinese)
[18]MOREL S.Size effect in quasibrittle fracture:Derivation of the energetic size effect law from equivalent LEFM and asymptotic analysis[J].International Journal of Fracture,2008,154(1/2):15-26.
[19]MOREL S,LESPINR C,COUREAU J L,et al.Bilinear softening parameters and equivalent LEFM R-curve in quasibrittle failure[J].International Journal of Solids and Structures,2010,47(6):837-850.
[20]XU S,REINHARDT H W.Crack extension resistance and fracture properties of quasi-brittle softening materials like concrete based on the complete process of fracture[J].International Journal of Fracture,1998,92(1):71-99.
[21]XU S L,REINHARDT H W.Determination of double-Kcriterion for crack propagation in quasi-brittle materials,Part I:Experimental investigation of crack propagation[J].International Journal of Fracture,1999,98(2):111-149.
[22]范向前,胡少伟,陆俊.非标准混凝土三点弯曲梁双K断裂韧度试验研究[J].建筑结构学报,2012,33(10):152-157.FAN Xiangqian,HU Shaowei,LU Jun.Experimental researching on the double-K fracture toughness of non-standard three point bending beam[J].Journal of Building Structures,2012,33(10):152-157.(in Chinese)
[23]KARIHALOO B L,ABDALLA H M,XIAO Q Z.Size effect in concrete beams[J].Engineering Fracture Mechanics,2003,70(7/8):979-993.