混凝土强度尺寸效应的实验研究
|
摘要
尺寸效应是准脆性材料的一个普遍性质,混凝土作为一种准脆性材料也存在尺寸效应。混凝土强度的尺寸效应是指混凝土的强度不仅由材料的性质决定,还会随着试件或构件的尺寸的大小而变化,而不是一个定值。随着混凝土材料的运用越来越广泛,结构高度和跨度的增加,混凝土结构尺寸也越来越大,但受到试验研究条件的和认识水平的限制,目前我们大尺寸试件的设计还是参考小尺寸试件研究成果而建立的设计理念和方法、计算公式等,当它们用于现代实际工程中时,将缺乏科学依据的推导。虽然我们在混凝土强度尺寸效应的研究领域中取得一些成绩,但还没有一个统一的衡量尺寸效应的标准或指标,目前为止还没有把尺寸效应考虑到行业规范和标准中去。针对上述情况,本文开展了以下几个方面工作：
(1)本文进行了混凝土抗压强度和劈裂抗拉强度两方面的尺寸效应实验研究,抗压试验考虑了立方体、棱柱体和圆柱体三种试件形式；劈裂受拉试验考虑了立方体和圆柱体两种试件形式。
(2)混凝土抗压强度的尺寸效应实验中,各种试件形式考察了边长或直径为150mm、250mm、350mm、450mm四组不同试件尺寸。实验结果表明,无论哪种试件形式混凝土的抗压强度都存在尺寸效应,且随着试件尺寸的增加,混凝土抗压强度在减小。同时采用Bazant基于应力重分布的尺寸效应公式及其修正式和Carpinteri多种分形理论尺寸效应公式拟合了实验结果,两种理论均能较好的说明实验结果。
(3)混凝土劈裂受拉强度的尺寸效应实验中考察了边长为150mm、250mm、350mm、450mm、550mm、750mm六组不同立方体试件尺寸和直径为150mm、250mm、350mm、450mm、550mm五种圆柱体试件尺寸。实验结果显示,混凝土的劈裂受拉强度存在尺寸效应,且随着试件尺寸的增加,混凝土抗压强度在减小,但无论试件形式如何当劈裂面积达时1000mm2时,尺寸效应接近消失,劈拉强度趋近一个定值。同时采用Weibull统计尺寸效应理论分析了实验结果,研究表明混凝土劈裂受拉强度与劈裂面积存在很好的相关性。
(4)通过对试件形式对混凝土强度尺寸效应影响的比较,发现无论是混凝土的抗压强度实验还是劈裂抗拉强度试验,试件的形式对混凝土的强度尺寸效应存在影响,虽然在大体趋势上表现相同,但是在具体尺寸上试件形状对混凝土强度的尺寸效应的影响有差异。
Size effect is a general property of quasi-brittle materials. Concrete as a quasi-brittle materials, there is also size effect happening. The size effect of concrete strength is affected not only by the property of the material, but also by the size of specimen, which is not a constant value. With more and more concrete materials being widely used, and the increase of structure height and span, the sizes of the concrete structures are also increased. However, the designing concepts, methods and formulas of large-size specimens are also based on the research findings of the small-size specimens currently because of the limitation of understandings and experimental conditions. This will be lack of scientific proof when they are used in modern practical projects. Although we have got some achievements in the research field of the size effect of concrete strength, there is no uniform standard or index to judge the size effect. And we still haven't taken the size effect into account in the codes of conduct so far. According to the above problems, the several main aspects of theoretical and experimental research are as follows:
(1) The size effect of concrete compressive strength and splitting tensile strength are considered in this experimental research of this article. The concrete compressive strength test considered cube, prism and cylinder these three specimen form. While the splitting tensile test only considered cube and cylinder these two kinds of specimens.
(2) In the size effect test of concrete compressive, four groups of cubes and prism with side length of 150mm,250mm,350mm,450mm,and four groups of cylinders with diameter of 150mm,250mm,350mm,450mm were considered respectively. The results show that size effect exists in all the three forms of concrete specimens of compressive strength and that the concrete compressive strength decrease with the increase of specimens'size. The author also use Bazant's size effect formula and modified formula based on the stress distribution and Carpinteri fractal size effect formula to fitting the experimental results, which fits well.
(3) In the size effect test of concrete splitting tensile strength, six groups of cube specimens with side lengths of 150mm,250mm,350mm,450mm,550mm,750mm, and five cylinder specimens with diameters of 150mm、250mm、350mm、450mm、550mm were considered respectively. The result show that size effect exists in the concrete splitting tensile strength and that the concrete splitting tensile strength decrease as its size increase. But no matter what the specimens'form is, when the splitting area reaches 1000mm2, the size effect almost disappears, and splitting tensile strength reaches a constant value. At the same time, using Weibull's statistical size effect theory to analysis experimental results, a good correlation can be found between splitting tensile strength of concrete and splitting area.
(4) By comparing the influence of the specimens'form on the size effect of concrete strength, the specimens'form affect the concrete strength, which can be found on the concrete compressive strength test and the splitting test. Although the general trends perform the same, the influences that the different shapes acted at the size effect of concrete strength perform differently.
(1)本文进行了混凝土抗压强度和劈裂抗拉强度两方面的尺寸效应实验研究,抗压试验考虑了立方体、棱柱体和圆柱体三种试件形式；劈裂受拉试验考虑了立方体和圆柱体两种试件形式。
(2)混凝土抗压强度的尺寸效应实验中,各种试件形式考察了边长或直径为150mm、250mm、350mm、450mm四组不同试件尺寸。实验结果表明,无论哪种试件形式混凝土的抗压强度都存在尺寸效应,且随着试件尺寸的增加,混凝土抗压强度在减小。同时采用Bazant基于应力重分布的尺寸效应公式及其修正式和Carpinteri多种分形理论尺寸效应公式拟合了实验结果,两种理论均能较好的说明实验结果。
(3)混凝土劈裂受拉强度的尺寸效应实验中考察了边长为150mm、250mm、350mm、450mm、550mm、750mm六组不同立方体试件尺寸和直径为150mm、250mm、350mm、450mm、550mm五种圆柱体试件尺寸。实验结果显示,混凝土的劈裂受拉强度存在尺寸效应,且随着试件尺寸的增加,混凝土抗压强度在减小,但无论试件形式如何当劈裂面积达时1000mm2时,尺寸效应接近消失,劈拉强度趋近一个定值。同时采用Weibull统计尺寸效应理论分析了实验结果,研究表明混凝土劈裂受拉强度与劈裂面积存在很好的相关性。
(4)通过对试件形式对混凝土强度尺寸效应影响的比较,发现无论是混凝土的抗压强度实验还是劈裂抗拉强度试验,试件的形式对混凝土的强度尺寸效应存在影响,虽然在大体趋势上表现相同,但是在具体尺寸上试件形状对混凝土强度的尺寸效应的影响有差异。
Size effect is a general property of quasi-brittle materials. Concrete as a quasi-brittle materials, there is also size effect happening. The size effect of concrete strength is affected not only by the property of the material, but also by the size of specimen, which is not a constant value. With more and more concrete materials being widely used, and the increase of structure height and span, the sizes of the concrete structures are also increased. However, the designing concepts, methods and formulas of large-size specimens are also based on the research findings of the small-size specimens currently because of the limitation of understandings and experimental conditions. This will be lack of scientific proof when they are used in modern practical projects. Although we have got some achievements in the research field of the size effect of concrete strength, there is no uniform standard or index to judge the size effect. And we still haven't taken the size effect into account in the codes of conduct so far. According to the above problems, the several main aspects of theoretical and experimental research are as follows:
(1) The size effect of concrete compressive strength and splitting tensile strength are considered in this experimental research of this article. The concrete compressive strength test considered cube, prism and cylinder these three specimen form. While the splitting tensile test only considered cube and cylinder these two kinds of specimens.
(2) In the size effect test of concrete compressive, four groups of cubes and prism with side length of 150mm,250mm,350mm,450mm,and four groups of cylinders with diameter of 150mm,250mm,350mm,450mm were considered respectively. The results show that size effect exists in all the three forms of concrete specimens of compressive strength and that the concrete compressive strength decrease with the increase of specimens'size. The author also use Bazant's size effect formula and modified formula based on the stress distribution and Carpinteri fractal size effect formula to fitting the experimental results, which fits well.
(3) In the size effect test of concrete splitting tensile strength, six groups of cube specimens with side lengths of 150mm,250mm,350mm,450mm,550mm,750mm, and five cylinder specimens with diameters of 150mm、250mm、350mm、450mm、550mm were considered respectively. The result show that size effect exists in the concrete splitting tensile strength and that the concrete splitting tensile strength decrease as its size increase. But no matter what the specimens'form is, when the splitting area reaches 1000mm2, the size effect almost disappears, and splitting tensile strength reaches a constant value. At the same time, using Weibull's statistical size effect theory to analysis experimental results, a good correlation can be found between splitting tensile strength of concrete and splitting area.
(4) By comparing the influence of the specimens'form on the size effect of concrete strength, the specimens'form affect the concrete strength, which can be found on the concrete compressive strength test and the splitting test. Although the general trends perform the same, the influences that the different shapes acted at the size effect of concrete strength perform differently.
引文
[1]张立军,安明喆.混凝土强度的尺寸效应评述.煤炭工程[J],2005,10：51-53.
[2]W.Weibull.Phenomenon of Rupturein Solids[J].Proc Royal Swedish Inst of Engineering Researeh.1939(153):1-55.
[3]Zdenek P. Bazant, Statistical size effect in quasi-brittle structures:I.Is Weibull theory applicable? Redistribution subject to ASCE license or copyright.
[4]何淅淅,徐积善.混凝土拉、压剪强度尺寸效应研究[J].福州大学学报(自然科学版)增刊,1996,51-57.
[5]徐积善,何淅淅.混凝土构件体积(尺寸)效应及抗裂塑性系数γ值的初步分析研究[J].力学学报,1986(4).
[6]Bazant Z P. Scaling of Quasi-brittle Fracture:Asympototic Analysis[J]. International Journal of Fracture,1997, Vol-83, No.1,19-40.
[7]Bazant Z P, Xiang Yuxin. Size Effect in Compression Fracture:Splitting Crack Band Propagation [J]. Journal of Engineering Mechanics, ASCE, Vol.123, No.2,1997.
[8]Zdenek p.Bazant.Scaling theory for quasibaittle structural failure.PNAS,2004,vol.101,37.
[9]Zdenek p.Bazant,Arash Yavari.Is the cause of size effect on structural stength fractal or energetic-statistical? Engineering Fracture Mechsnics,2005,72:1-31.
[10]Bazant Z P, Xiang Yuxin. Size Effect in Compression Fracture:Splitting Crack Band Propagation [J]. Journal of Engineering Mechanics, ASCE, Vol.123, No.2,1997.
[11]黄海燕.凝土尺寸效应理论研究与断裂参数分析(学位论文).河海大学,2004,14-40.
[12]Carpinteri,B.Chiaia,andG.Ferro.Multifractal scaling law for the nominal strength variation of concrete structures,in Size Effect In Concrete Structure,eds.H.Mihashi, H.Okamura,Z.P.Bazant, E&FNSon,1994.
[13]钱觉时,黄煜镔.混凝土强度尺寸效应的研究进展[J].混凝土与水泥制品,2003年第3期,1-5.
[14]A.Carpinteri, B.Chiaia. Multifractal scaling laws in the breaking behaviors of disordered materials, Chaos, Solitons&Fraetals.1997,8(2):135-150.
[15]Sabins,G.M.,and Mirza,S.M.,"Size effects in Model Concretes?", Journal of the Structural Division,ASCE,Vol.105,No.ST6,1979
[16]程娟,郭向阳.混凝土静载荷力学特性的尺寸效应研究[J].预拌混凝土,36-37.
[17]王岩.高强混凝土立方强度尺寸效应的分析计算[J].数学的实践与认识,2006,36(8),144-148.
[18]Semsi Yqzaci,Gozde Inan Sezer.The effect of cylindrical specimen size on the compressive strength of concrete[J].Building and Environment,2007,42:2417-2420.
[19]王泽云.不同强度等级混凝土尺寸效应的讨论[J].四川建筑科学研究,2005,31(1),95-97.
[20]Malhotra V.M.,Effect of specimen size on tensile strength of concrete[J].ACI Journal, Vol.67,No.6,1970.
[21]姜福田.混凝土力学性能与测定(第一版),中国铁道出版社,1989.
[22]宣国良.混凝土圆柱体劈拉强度的尺寸效应[J].河海大学学报,1996,24(2)：92-97.
[23]R.Gettu,2.P.Bazant, M.E.Karr.Fracture properties and brittleness of high-strength conerete. ACI Materials Journal.1990(87):608-618.
[24]P.C.Perdikaris, A.Romeo.Effect of size and compressive strength on the fracture energy of plain conerete.In Proceedings of the first international conference on fracture mechanies of conerete structures, FRAMCOS, edited by 2.P.Bazant, Breekenridge, USA,1992:550-555.
[25]2.P.Bazant, M.T.Kazemi. Size effect on diagonal shear failure of beams without stirrups. ACI Structural Journal.1991(88):268-276.
[26]G.M.Sabnis, S.M.Mirza. Size effect in model coneretes? Journal of Structure.1979 (105):1007-1020.
[27]钱觉时,杨再富等.粗集料对混凝土抗压强度测试结果的影响[J].中国科技论文在线.
[28]杨成球,吴政.全级配混凝土强度尺寸效应及变形特性研究[J].大连理工学报(增刊1),1997,129-134.
[29]杨忠义.全级配混凝土强度的尺寸效应研究[J].水电站设计,2008,24(3)：11-14.
[30]李嘉进.试件尺寸和骨料粒径对混凝土强度的影响[J].水电站设计,1991,7(3)：20-27.
[31]Siddik Sener.Size effect tests of hige strength concrete[J].Journal of materials in civil engineering.1997,46-48.
[32]Seong-Tae Yi,Eun-Ik Yang,and ect.Effect of specimen sizes,specimen shapes,and placement dieections on compressive strength of concrete[J].Nuclear Engneering and Design,2006,236:115-127.
[32]中华人民共和国住房和城乡建设部.JG 237-2008,混凝土试模[S].中国标准出版社,2008.
[33]中国建筑科学研究院.GB／T 50081—2002,普通混凝土力学性能试验方法标准[S].北京：中国建筑工业出版社,2003.
[34]Kim, J.K., Eo, S.H.,1990. Size effect in concrete specimens with dissimilar initial cracks. Mag. Concrete Res.42 (153),233-238.
[35]Bazant, Z.P.,1987. Fracture energy of heterogeneous material and similitude. In:EM-RILEM International Conference on Fracture of Concrete and Rock, pp.390-402.
[36]Bazant, Z.P.,1993. Size effect in tensile and compressive quasibrittle failures. In:JCI International Workshop on Size Effect in Concrete Structures, pp.141-160.
[37]Bazant, Z.P., Xiang, Y.,1997. Size effect in compression fracture:splitting crack band propagation. J. Eng. Mech. ASCE 123 (2),162-172.
[38]Kim, J.H.J., Yi, S.T., Kim, J.K.,2004. Size effect of concrete members applied with flexural compressive stresses. Int. J. Fracture 126 (1),79-102.
[39]Kim, J.K., Yi, S.T., Park, C.K., Eo, S.H.,1999. Size effect on compressive strength of plain and spirally reinforced concrete cylinders. ACI Struct. J.96 (1),88-94.
[40]Senog-Tae Yi,Eun-IK Yang ect.Effect of specimen sizes, specimen shapes, and placement directions on compressive strength of concrete.Nuclear Engineering and Design236(2006),115-127.
[41]尹健,周士琼.高性能混凝土的轴心抗拉强度与劈裂抗拉强度试验研究[J].长沙铁道学院学报,2001
[42]Bazant Z P, Gettu R, Jirasek M et al. RILEM TC QFS 'Quasibrittle fracture scaling and size effect'-Final report [J]. Materials and Structures, vol.37,2004,547-568.
[43]杜修力,张伟建,符佳,李振宝.钢筋混凝土构件的尺寸效应研究进展及展望[J].建筑科学与工程学报,vol.26(3),2009,14-18.
[44]Alberto Carpinteri, Bernardino Chiaia, Giuseppe Ferro. Size effects on nominal tensile strength of concrete structures:multifractality of material ligaments and dimensional transition from order to disorder [J]. Materials and Structures,1995, vol.28,311-317.
[45]Rocco C, Guinea GV, Planas J, Elices M. Review of the splitting-test standards from a fracture mechanics point of view [J]. Cement and Concrete Research, vol.31,2001,73-82.
[46]Tang T. Effects of load-distributed width on split tension of unnotched and notched cylindrical specimens [J]. Journal of Testing and Evaluation,1994, vol.22(5),401-409.
[47]Olesen J F, Ostergaard L, Stang H. Nonlinear fracture mechanics and plasticity of the split cylinder test [J]. Materials and Structures, vol.39,2006,421-432.
[48]南京水利科学研究院.SL352—2006,水工混凝土试验规程[S].北京：中国电力出版社,2006.
[49]VI Kadlecek Sr, S Modry, and VI Kadlecek Jr. Size effect of test specimens on tensile splitting strength of concrete:general relation [J]. Materials and Structures, vol.35,2002,28-34.
[50]姜福田.混凝土抗拉强度测定中的几个问题[J].水力发电.1986,vol.9,25-30.
[51]朱尔玉.大骨料混凝土多轴强度理论及本构关系的实验研究[D].大连：大连理工大学,1996.
[52]李玉君.全级配混凝土力学特性的实验研究[D].大连：大连理工大学,1993.
[53]钱觉时,杨在富,黄煜镔等.高强混凝土强度尺寸效应的试验研究[J],华中科技大学学报,2004,vol21(1),1-4.
[54]A. Kanos, A.E. Giannakopoulos, P.C. Perdikaris. Size effect on concrete splitting tensile strength and modulus of elasticity.Measuring, Monitoring and Modeling Concrete Properties[M],2006, Netherlands: Springer,239-246.
[55]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,2004,vol.21(3),29-34
[56]黄煜镔.混凝土脆性与力学参数的尺寸效应及其相互关系的研究[D].重庆：重庆大学.2002.
[57]王怀亮.复杂应力状态下大骨料混凝土力学特性的试验研究和分析[D].大连：大连理工大学,2006.
[58]冷发光,丁威等.尺寸效应对混凝土耐久性研究[J].水泥与混凝土,：大连理工大学,2006.
[59]中华人民共和国建设部.GB 50010—2002,混凝土结构设计规范[S].北京：中国建筑工业出版社,2002.
[60]Semsi Yazici, Gozde Inan Sezer. The effect of cylindrical specimen size on the compressive strength of concrete [J]. Building and Environment,2007,2417-2420.
[61]B.Trunk and F.H.Wittmann. Influence of size on fracture energy of concrete[J]. Materials and Structures, vol.34,2001,260-265.
[62]Review of the splittting-test standarda form a fracture mechanics point of view[J]. Cement and Concrete Research, vol.31,2001,73-82.
[63]Zdenek P. Bazant. Size effect[J]. Internatinal Journal of Solids and Structures, vol.37,2000,69-80.
[2]W.Weibull.Phenomenon of Rupturein Solids[J].Proc Royal Swedish Inst of Engineering Researeh.1939(153):1-55.
[3]Zdenek P. Bazant, Statistical size effect in quasi-brittle structures:I.Is Weibull theory applicable? Redistribution subject to ASCE license or copyright.
[4]何淅淅,徐积善.混凝土拉、压剪强度尺寸效应研究[J].福州大学学报(自然科学版)增刊,1996,51-57.
[5]徐积善,何淅淅.混凝土构件体积(尺寸)效应及抗裂塑性系数γ值的初步分析研究[J].力学学报,1986(4).
[6]Bazant Z P. Scaling of Quasi-brittle Fracture:Asympototic Analysis[J]. International Journal of Fracture,1997, Vol-83, No.1,19-40.
[7]Bazant Z P, Xiang Yuxin. Size Effect in Compression Fracture:Splitting Crack Band Propagation [J]. Journal of Engineering Mechanics, ASCE, Vol.123, No.2,1997.
[8]Zdenek p.Bazant.Scaling theory for quasibaittle structural failure.PNAS,2004,vol.101,37.
[9]Zdenek p.Bazant,Arash Yavari.Is the cause of size effect on structural stength fractal or energetic-statistical? Engineering Fracture Mechsnics,2005,72:1-31.
[10]Bazant Z P, Xiang Yuxin. Size Effect in Compression Fracture:Splitting Crack Band Propagation [J]. Journal of Engineering Mechanics, ASCE, Vol.123, No.2,1997.
[11]黄海燕.凝土尺寸效应理论研究与断裂参数分析(学位论文).河海大学,2004,14-40.
[12]Carpinteri,B.Chiaia,andG.Ferro.Multifractal scaling law for the nominal strength variation of concrete structures,in Size Effect In Concrete Structure,eds.H.Mihashi, H.Okamura,Z.P.Bazant, E&FNSon,1994.
[13]钱觉时,黄煜镔.混凝土强度尺寸效应的研究进展[J].混凝土与水泥制品,2003年第3期,1-5.
[14]A.Carpinteri, B.Chiaia. Multifractal scaling laws in the breaking behaviors of disordered materials, Chaos, Solitons&Fraetals.1997,8(2):135-150.
[15]Sabins,G.M.,and Mirza,S.M.,"Size effects in Model Concretes?", Journal of the Structural Division,ASCE,Vol.105,No.ST6,1979
[16]程娟,郭向阳.混凝土静载荷力学特性的尺寸效应研究[J].预拌混凝土,36-37.
[17]王岩.高强混凝土立方强度尺寸效应的分析计算[J].数学的实践与认识,2006,36(8),144-148.
[18]Semsi Yqzaci,Gozde Inan Sezer.The effect of cylindrical specimen size on the compressive strength of concrete[J].Building and Environment,2007,42:2417-2420.
[19]王泽云.不同强度等级混凝土尺寸效应的讨论[J].四川建筑科学研究,2005,31(1),95-97.
[20]Malhotra V.M.,Effect of specimen size on tensile strength of concrete[J].ACI Journal, Vol.67,No.6,1970.
[21]姜福田.混凝土力学性能与测定(第一版),中国铁道出版社,1989.
[22]宣国良.混凝土圆柱体劈拉强度的尺寸效应[J].河海大学学报,1996,24(2)：92-97.
[23]R.Gettu,2.P.Bazant, M.E.Karr.Fracture properties and brittleness of high-strength conerete. ACI Materials Journal.1990(87):608-618.
[24]P.C.Perdikaris, A.Romeo.Effect of size and compressive strength on the fracture energy of plain conerete.In Proceedings of the first international conference on fracture mechanies of conerete structures, FRAMCOS, edited by 2.P.Bazant, Breekenridge, USA,1992:550-555.
[25]2.P.Bazant, M.T.Kazemi. Size effect on diagonal shear failure of beams without stirrups. ACI Structural Journal.1991(88):268-276.
[26]G.M.Sabnis, S.M.Mirza. Size effect in model coneretes? Journal of Structure.1979 (105):1007-1020.
[27]钱觉时,杨再富等.粗集料对混凝土抗压强度测试结果的影响[J].中国科技论文在线.
[28]杨成球,吴政.全级配混凝土强度尺寸效应及变形特性研究[J].大连理工学报(增刊1),1997,129-134.
[29]杨忠义.全级配混凝土强度的尺寸效应研究[J].水电站设计,2008,24(3)：11-14.
[30]李嘉进.试件尺寸和骨料粒径对混凝土强度的影响[J].水电站设计,1991,7(3)：20-27.
[31]Siddik Sener.Size effect tests of hige strength concrete[J].Journal of materials in civil engineering.1997,46-48.
[32]Seong-Tae Yi,Eun-Ik Yang,and ect.Effect of specimen sizes,specimen shapes,and placement dieections on compressive strength of concrete[J].Nuclear Engneering and Design,2006,236:115-127.
[32]中华人民共和国住房和城乡建设部.JG 237-2008,混凝土试模[S].中国标准出版社,2008.
[33]中国建筑科学研究院.GB／T 50081—2002,普通混凝土力学性能试验方法标准[S].北京：中国建筑工业出版社,2003.
[34]Kim, J.K., Eo, S.H.,1990. Size effect in concrete specimens with dissimilar initial cracks. Mag. Concrete Res.42 (153),233-238.
[35]Bazant, Z.P.,1987. Fracture energy of heterogeneous material and similitude. In:EM-RILEM International Conference on Fracture of Concrete and Rock, pp.390-402.
[36]Bazant, Z.P.,1993. Size effect in tensile and compressive quasibrittle failures. In:JCI International Workshop on Size Effect in Concrete Structures, pp.141-160.
[37]Bazant, Z.P., Xiang, Y.,1997. Size effect in compression fracture:splitting crack band propagation. J. Eng. Mech. ASCE 123 (2),162-172.
[38]Kim, J.H.J., Yi, S.T., Kim, J.K.,2004. Size effect of concrete members applied with flexural compressive stresses. Int. J. Fracture 126 (1),79-102.
[39]Kim, J.K., Yi, S.T., Park, C.K., Eo, S.H.,1999. Size effect on compressive strength of plain and spirally reinforced concrete cylinders. ACI Struct. J.96 (1),88-94.
[40]Senog-Tae Yi,Eun-IK Yang ect.Effect of specimen sizes, specimen shapes, and placement directions on compressive strength of concrete.Nuclear Engineering and Design236(2006),115-127.
[41]尹健,周士琼.高性能混凝土的轴心抗拉强度与劈裂抗拉强度试验研究[J].长沙铁道学院学报,2001
[42]Bazant Z P, Gettu R, Jirasek M et al. RILEM TC QFS 'Quasibrittle fracture scaling and size effect'-Final report [J]. Materials and Structures, vol.37,2004,547-568.
[43]杜修力,张伟建,符佳,李振宝.钢筋混凝土构件的尺寸效应研究进展及展望[J].建筑科学与工程学报,vol.26(3),2009,14-18.
[44]Alberto Carpinteri, Bernardino Chiaia, Giuseppe Ferro. Size effects on nominal tensile strength of concrete structures:multifractality of material ligaments and dimensional transition from order to disorder [J]. Materials and Structures,1995, vol.28,311-317.
[45]Rocco C, Guinea GV, Planas J, Elices M. Review of the splitting-test standards from a fracture mechanics point of view [J]. Cement and Concrete Research, vol.31,2001,73-82.
[46]Tang T. Effects of load-distributed width on split tension of unnotched and notched cylindrical specimens [J]. Journal of Testing and Evaluation,1994, vol.22(5),401-409.
[47]Olesen J F, Ostergaard L, Stang H. Nonlinear fracture mechanics and plasticity of the split cylinder test [J]. Materials and Structures, vol.39,2006,421-432.
[48]南京水利科学研究院.SL352—2006,水工混凝土试验规程[S].北京：中国电力出版社,2006.
[49]VI Kadlecek Sr, S Modry, and VI Kadlecek Jr. Size effect of test specimens on tensile splitting strength of concrete:general relation [J]. Materials and Structures, vol.35,2002,28-34.
[50]姜福田.混凝土抗拉强度测定中的几个问题[J].水力发电.1986,vol.9,25-30.
[51]朱尔玉.大骨料混凝土多轴强度理论及本构关系的实验研究[D].大连：大连理工大学,1996.
[52]李玉君.全级配混凝土力学特性的实验研究[D].大连：大连理工大学,1993.
[53]钱觉时,杨在富,黄煜镔等.高强混凝土强度尺寸效应的试验研究[J],华中科技大学学报,2004,vol21(1),1-4.
[54]A. Kanos, A.E. Giannakopoulos, P.C. Perdikaris. Size effect on concrete splitting tensile strength and modulus of elasticity.Measuring, Monitoring and Modeling Concrete Properties[M],2006, Netherlands: Springer,239-246.
[55]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,2004,vol.21(3),29-34
[56]黄煜镔.混凝土脆性与力学参数的尺寸效应及其相互关系的研究[D].重庆：重庆大学.2002.
[57]王怀亮.复杂应力状态下大骨料混凝土力学特性的试验研究和分析[D].大连：大连理工大学,2006.
[58]冷发光,丁威等.尺寸效应对混凝土耐久性研究[J].水泥与混凝土,：大连理工大学,2006.
[59]中华人民共和国建设部.GB 50010—2002,混凝土结构设计规范[S].北京：中国建筑工业出版社,2002.
[60]Semsi Yazici, Gozde Inan Sezer. The effect of cylindrical specimen size on the compressive strength of concrete [J]. Building and Environment,2007,2417-2420.
[61]B.Trunk and F.H.Wittmann. Influence of size on fracture energy of concrete[J]. Materials and Structures, vol.34,2001,260-265.
[62]Review of the splittting-test standarda form a fracture mechanics point of view[J]. Cement and Concrete Research, vol.31,2001,73-82.
[63]Zdenek P. Bazant. Size effect[J]. Internatinal Journal of Solids and Structures, vol.37,2000,69-80.