由小尺寸试件确定混凝土的断裂韧度与拉伸强度
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摘要
该文利用骨料最大粒径dmax=10 mm,试件高度W依次为60 mm、80 mm、100 mm、140 mm、160 mm,厚度B=40 mm的小尺寸三点弯曲梁试件,来确定无尺寸效应的混凝土断裂韧度KIC与拉伸强度ft。区别于现有尺寸效应模型关注于"绝对尺寸W",该文提出"相对尺寸W/dmax"的概念,分析了骨料颗粒对有限尺寸试件断裂破坏的影响机理,进而将骨料最大粒径dmax与离散度参数?引入修正的边界效应模型的解析表达式中,发展建立了离散颗粒断裂模型,进而给出了由实验室条件下小尺寸试件(W=60 mm～160 mm和B=40 mm)的峰值荷载Pmax同时确定混凝土材料参数—KIC和ft的实用方法。进而分析了不同试件组合和不同峰值荷载时裂缝扩展量取值对材料参数确定的影响规律,建立了混凝土材料破坏的完整曲线,给出了满足线弹性断裂力学条件的混凝土试件理论最小尺寸,并基于确定的材料参数对各试件的峰值荷载进行了成功预测。。
A simple method is presented for determining the material parameters of concrete KIC and ft using the small specimens in laboratory,in which the maximum aggregate of the concrete dmax=10 mm,the specimens depth W=60 mm,80 mm,100 mm,140 mm and 160 mm,and the specimens width B=40 mm.Compared to existing size effect models,only linked to specimen size W,the concept "relative size W/dmax" is proposed.The roles of aggregate size on fracture of finite size specimens were analyzed,and the maximum aggregate dmax and discrete number β are included in the analytic solution expression of the improved Boundary Effect Model,named discrete particle fracture model.The different combination conditions of tested specimens and different fictitious crack growth at peak loading are adopted to determine the influence law of KIC and ft.The whole fracture failure curves of the concrete material are obtained.The theoretical minimum concrete specimen size meeting the condition of linear elastic fracture mechanics is obtained.And the peak loads of every specimens are predicted successfully based on the determined material parameters.
A simple method is presented for determining the material parameters of concrete KIC and ft using the small specimens in laboratory,in which the maximum aggregate of the concrete dmax=10 mm,the specimens depth W=60 mm,80 mm,100 mm,140 mm and 160 mm,and the specimens width B=40 mm.Compared to existing size effect models,only linked to specimen size W,the concept "relative size W/dmax" is proposed.The roles of aggregate size on fracture of finite size specimens were analyzed,and the maximum aggregate dmax and discrete number β are included in the analytic solution expression of the improved Boundary Effect Model,named discrete particle fracture model.The different combination conditions of tested specimens and different fictitious crack growth at peak loading are adopted to determine the influence law of KIC and ft.The whole fracture failure curves of the concrete material are obtained.The theoretical minimum concrete specimen size meeting the condition of linear elastic fracture mechanics is obtained.And the peak loads of every specimens are predicted successfully based on the determined material parameters.
引文
[1]ASTM E399-12e2,Standard test method for linear-elastic plane-strain fracture toughness testing of high strength metallic materials[S].Philadelphia:American Society for Testing and Material,2013.
[2]DL/T 5332-2005,水工混凝土断裂试验规程[S].北京:中国电力出版社,2006.DL/T 5332-2005,Norm for fracture test of hydraulic concrete[S].Beijng:China Electric Power Press,2006.(in Chinese)
[3]CB/T 50152-2012,混凝土结构试验方法标准[S].北京:中国建筑工业出版社,2012.CB/T 50152-2012,Standard for test method of concrete structures[S].Beijing:Chinese Building Press,2012.(in Chinese)
[4]SL 352-2006,水工混凝土试验规程[S].北京:中国水利水电出版社,2006.SL 352-2006,Test code for hydraulic concrete[S].Beijing:Chinese Water&Power Press,2006.(in Chinese)
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[7]郑建军,周欣竹.混凝土断裂能尺寸效应的细观方法[J].水利学报,2001,61(10):54-57.Zheng Jianjun,Zhou Xinzhu.A mesoscopic approach for the size effect on fracture energy of concrete[J].Journal of Hydraulic Engineering,2001,61(10):54-57.(in Chinese)
[8]曹亮,王向东.三点弯曲试件混凝土尺寸效应公式的修正[J].河海大学学报(自然科学版),2007,35(1):63-66.Cao Liang,Wang Xiangdong.Modification of size effect formula of fracture toughness of concrete for three-point bending specimens[J].Journal of Hohai University(Natural Sciences),2007,35(1):63-66.(in Chinese)
[9]王学志,毕重,张小刚,等.碾压混凝土断裂韧度尺寸效应的试验研究[J].武汉理工大学学报,2007,29(6):54-57.Wang Xuezhi,Bi Zhong,Zhang Xiaogang,et al.Experimental investigation on size effect formula for fracture toughness of RCC[J].Journal of Wuhan University of Technology,2007,29(6):54-57.(in Chinese)
[10]Wang X Z,Xu Z C,Bi Z,et al.Experimental investigation on size effect formulae suitable for common concrete nominal fracture toughness[C].International Conference of Logistics Engineering and Management,Chengdu,2010:1424-1430.
[11]管俊峰.钢筋混凝土结构仿真模型试验理论与应用研究[D].大连:大连理工大学,2010.Guan Junfeng.Research on theory and application of simulation model test for reinforced concrete structure[D].Dalian:Dalian University of Technology,2010.(in Chinese)
[12]Guan J F,Zhao S B,Huang C K.Crack elongation and its width of large depth reinforced concrete beams[J].Journal of harbin institute of technology(New Series),2010,17(5):631-635.
[13]管俊峰,赵顺波,李晓克,等.钢筋混凝土梁裂缝宽度试验与计算方法研究[J].中国公路学报,2011,24(5):74-81,88.Guan Junfeng,Zhao Shunbo,Li Xiaoke,et al.Experiment and calculation method of crack width of reinforced concrete beams[J].China Journal of Highway and Transport,2011,24(5):74-81,88.(in Chinese)
[14]Ba?ant Z P,Kazemi M T.Determination of fracture energy,process zone length,and brittleness number from size effect with application to rock and concrete[J].International Journal of Fracture,1990,44(2):111-131.
[15]Carpinteri A.Fractal nature of material microstructure and size effects on apparent mechanical properties[J].Mechanics of Materials,1994,18(2):89-101.
[16]Karihaloo B L,Abdalla H M,Xiao Q Z.Size effect in concrete beams[J].Engineering Fracture Mechanics,2003,70(7/8):979-993.
[17]Wang Y S,Hu X Z,Li L,et al.Determination of tensile strength and fracture toughness of concrete using notched3-p-b specimens[J].Engineering Fracture Mechanics,2016,160(7):67-77.
[18]管俊峰,胡晓智,王玉锁,等.用边界效应理论考虑断裂韧性和拉伸强度对破坏的影响[J].水利学报,2016,47(10):1298-1306.Guan Junfeng,Hu Xiaozhi,Wang Yusuo,et al.Effect of fracture toughness and tensile strength on fracture based on boundary effect theory[J].Journal of Hydraulic Engineering,2016,47(10):1298-1306.(in Chinese)
[19]Wang Y S,Hu X Z.Determination of strength and toughness of granite using notched three-point-bend samples[J].Rock Mechanics and Rock Engineering,2017,50(1):17-28.
[20]管俊峰,王强,胡晓智,等.考虑骨料尺寸的混凝土岩石边界效应断裂模型[J].工程力学,2017,34(12):22-30.Guan Junfeng,Wang Qiang,Hu Xiaozhi,et al.Boundary effect fracture model for concrete and granite considering aggregate size[J].Engineering Mechanics,2017,34(12):22-30.(in Chinese)
[21]Guan J F,Hu X Z,Li Q B.In-depth analysis of notched3-p-b concrete fracture[J].Engineering Fracture Mechanics,2016,165(10):57-71.
[22]Hu X Z,Guan J F,Wang Y S,et al.Comparison of boundary and size effect models based on new developments[J].Engineering Fracture Mechanics,2017,175(4):146-167.
[23]Guan J F,Hu X Z,Yao X H,et al.Fracture of 0.1 and 2m long mortar beams under three-point-bending[J].Materials&Design,2017,133(11):363-375.
[24]李冬,金浏,杜修力,等.骨料级配对二维模型混凝土单轴抗拉强度影响的理论研究[J].工程力学,2017,34(6):64-72.Li Dong,Jin Liu,Du Xiuli,et al.A theoretical study on the influence of aggregate gradation on the tensile strength of 2-demensional model concrete[J].Engineering Mechanics,2017,34(6):64-72.(in Chinese)
[25]王璀瑾,董伟,王强,等.混凝土I型裂缝扩展准则比较研究[J].工程力学,2016,33(5):89-96.Wang Cuijin,Dong Wei,Wang Qiang,et al.Acomparative study on propagation criterion of concrete mode I crack[J].Engineering Mechanics,2016,33(5):89-96.(in Chinese)
[26]卿龙邦,王妥,管俊峰,等.有限尺寸混凝土试件允许损伤尺度的解析研究[J].工程力学,2017,34(1):213-218.Qing Longbang,Wang Tuo,Guan Junfeng,et al.Analytical study on permissible damage scale of cracks in finite size concrete specimens[J].Engineering Mechanics,2017,34(1):213-218.(in Chinese)
[27]Dong W,Zhou X M,Wu Z M,et al.Investigating crack initiation and propagation of concrete in a restrained shrinkage circular/elliptical ring test[J].Materials&Structures,2017,50(1):1-13.
[28]Hu X Z,Wittmann F.Size effect on toughness induced by crack close to free surface[J].Engineering Fracture Mechanics,2000,65(2):209-221.
[29]Hu X Z,Duan K.Influence of fracture process zone height on fracture energy of concrete[J].Cement and Concrete Research,2004,34(8):1321-1330.
[30]Hu X Z,Duan K.Size effect and quasi-brittle fracture:the role of FPZ[J].International Journal of Fracture,2008,154(1):3-14.
[31]Hu X Z,Duan K.Mechanism behind the size effect phenomenon[J].Journal Engineering Mechanics,ASCE,2010,136(1):60-68.
[32]Tada H I,Paris P C,Irwin G R.The analysis of cracks handbook[M].New York:ASME Press,2000.
[33]李晓东,董伟,吴智敏,等.小尺寸混凝土试件双K断裂参数试验研究[J].工程力学,2010,27(2):166-171,185.Li Xiaodong,Dong Wei,Wu Zhimin,et al.Experimental investigation on double-K fracture parameters for small size specimens of concrete[J].Engineering Mechanics,2010,27(2):166-171,185.(in Chinese)
[34]赵燕茹,王磊,韩霄峰,等.冻融条件下玄武岩纤维混凝土断裂韧度研究[J].工程力学,2017,34(9):92-101.Zhao Yanru,Wang Lei,Han Xiaofeng,et al.Fracture toughness of basalt-fiber reinforced concrete subjected to cyclic freezing and thawing[J].Engineering Mechanics,2017,34(9):92-101.(in Chinese)
[35]Jenq Y S,Shah S P.Two parameter fracture model for concrete[J].Journal Engineering Mechanics-ASCE,1985,111(10):1227-1241.
[36]管俊峰,李庆斌,吴智敏.采用峰值荷载法确定全级配水工混凝土断裂参数[J].工程力学,2014,31(8):8-13.Guan Junfeng,Li Qingbin,Wu Zhimin.Determination of fully-grade hydraulic concrete fracture parameters by Peak-load method[J].Engineering Mechanics,2014,31(8):8-13.(in Chinese)
[37]Karihaloo B L,Nallathambi P.Effective crack model for the determination of fracture toughness(Ke IC)of Concrete[J].Engineering Fracture Mechanics,1990,35(4/5):637-645.
[38]Zhang P,Gao J X,Dai X B,et al.Fracture behavior of fly ash concrete containing silica fume[J].Structural Engineering&Mechanics,2016,59(2):261-275.
[39]Qing L B,Cheng Y H.The fracture extreme theory for determining the effective fracture toughness and tensile strength of concrete[J].Theoretical and Applied Fracture Mechanics,2018,96(8):461-467.
[2]DL/T 5332-2005,水工混凝土断裂试验规程[S].北京:中国电力出版社,2006.DL/T 5332-2005,Norm for fracture test of hydraulic concrete[S].Beijng:China Electric Power Press,2006.(in Chinese)
[3]CB/T 50152-2012,混凝土结构试验方法标准[S].北京:中国建筑工业出版社,2012.CB/T 50152-2012,Standard for test method of concrete structures[S].Beijing:Chinese Building Press,2012.(in Chinese)
[4]SL 352-2006,水工混凝土试验规程[S].北京:中国水利水电出版社,2006.SL 352-2006,Test code for hydraulic concrete[S].Beijing:Chinese Water&Power Press,2006.(in Chinese)
[5]徐世烺.混凝土断裂韧度的概率统计分析[J].水利学报,1984,15(10):51-58.Xu Shilang.Probabilistic statistical analysis of fracture toughness of concrete[J].Journal of Hydraulic Engineering,1984,15(10):51-58.(in Chinese)
[6]徐世烺,赵国藩.巨型试件断裂韧度和高混凝土坝裂缝评定的断裂韧度准则[J].土木工程学报,1991,24(2):1-9.Xu Shilang,Zhao Guofan.Concrete fracture toughness of huge specimens and criterion of fracture toughness for judging cracks in high concrete dam[J].China Civil Engineering Journal,1991,24(2):1-9.(in Chinese)
[7]郑建军,周欣竹.混凝土断裂能尺寸效应的细观方法[J].水利学报,2001,61(10):54-57.Zheng Jianjun,Zhou Xinzhu.A mesoscopic approach for the size effect on fracture energy of concrete[J].Journal of Hydraulic Engineering,2001,61(10):54-57.(in Chinese)
[8]曹亮,王向东.三点弯曲试件混凝土尺寸效应公式的修正[J].河海大学学报(自然科学版),2007,35(1):63-66.Cao Liang,Wang Xiangdong.Modification of size effect formula of fracture toughness of concrete for three-point bending specimens[J].Journal of Hohai University(Natural Sciences),2007,35(1):63-66.(in Chinese)
[9]王学志,毕重,张小刚,等.碾压混凝土断裂韧度尺寸效应的试验研究[J].武汉理工大学学报,2007,29(6):54-57.Wang Xuezhi,Bi Zhong,Zhang Xiaogang,et al.Experimental investigation on size effect formula for fracture toughness of RCC[J].Journal of Wuhan University of Technology,2007,29(6):54-57.(in Chinese)
[10]Wang X Z,Xu Z C,Bi Z,et al.Experimental investigation on size effect formulae suitable for common concrete nominal fracture toughness[C].International Conference of Logistics Engineering and Management,Chengdu,2010:1424-1430.
[11]管俊峰.钢筋混凝土结构仿真模型试验理论与应用研究[D].大连:大连理工大学,2010.Guan Junfeng.Research on theory and application of simulation model test for reinforced concrete structure[D].Dalian:Dalian University of Technology,2010.(in Chinese)
[12]Guan J F,Zhao S B,Huang C K.Crack elongation and its width of large depth reinforced concrete beams[J].Journal of harbin institute of technology(New Series),2010,17(5):631-635.
[13]管俊峰,赵顺波,李晓克,等.钢筋混凝土梁裂缝宽度试验与计算方法研究[J].中国公路学报,2011,24(5):74-81,88.Guan Junfeng,Zhao Shunbo,Li Xiaoke,et al.Experiment and calculation method of crack width of reinforced concrete beams[J].China Journal of Highway and Transport,2011,24(5):74-81,88.(in Chinese)
[14]Ba?ant Z P,Kazemi M T.Determination of fracture energy,process zone length,and brittleness number from size effect with application to rock and concrete[J].International Journal of Fracture,1990,44(2):111-131.
[15]Carpinteri A.Fractal nature of material microstructure and size effects on apparent mechanical properties[J].Mechanics of Materials,1994,18(2):89-101.
[16]Karihaloo B L,Abdalla H M,Xiao Q Z.Size effect in concrete beams[J].Engineering Fracture Mechanics,2003,70(7/8):979-993.
[17]Wang Y S,Hu X Z,Li L,et al.Determination of tensile strength and fracture toughness of concrete using notched3-p-b specimens[J].Engineering Fracture Mechanics,2016,160(7):67-77.
[18]管俊峰,胡晓智,王玉锁,等.用边界效应理论考虑断裂韧性和拉伸强度对破坏的影响[J].水利学报,2016,47(10):1298-1306.Guan Junfeng,Hu Xiaozhi,Wang Yusuo,et al.Effect of fracture toughness and tensile strength on fracture based on boundary effect theory[J].Journal of Hydraulic Engineering,2016,47(10):1298-1306.(in Chinese)
[19]Wang Y S,Hu X Z.Determination of strength and toughness of granite using notched three-point-bend samples[J].Rock Mechanics and Rock Engineering,2017,50(1):17-28.
[20]管俊峰,王强,胡晓智,等.考虑骨料尺寸的混凝土岩石边界效应断裂模型[J].工程力学,2017,34(12):22-30.Guan Junfeng,Wang Qiang,Hu Xiaozhi,et al.Boundary effect fracture model for concrete and granite considering aggregate size[J].Engineering Mechanics,2017,34(12):22-30.(in Chinese)
[21]Guan J F,Hu X Z,Li Q B.In-depth analysis of notched3-p-b concrete fracture[J].Engineering Fracture Mechanics,2016,165(10):57-71.
[22]Hu X Z,Guan J F,Wang Y S,et al.Comparison of boundary and size effect models based on new developments[J].Engineering Fracture Mechanics,2017,175(4):146-167.
[23]Guan J F,Hu X Z,Yao X H,et al.Fracture of 0.1 and 2m long mortar beams under three-point-bending[J].Materials&Design,2017,133(11):363-375.
[24]李冬,金浏,杜修力,等.骨料级配对二维模型混凝土单轴抗拉强度影响的理论研究[J].工程力学,2017,34(6):64-72.Li Dong,Jin Liu,Du Xiuli,et al.A theoretical study on the influence of aggregate gradation on the tensile strength of 2-demensional model concrete[J].Engineering Mechanics,2017,34(6):64-72.(in Chinese)
[25]王璀瑾,董伟,王强,等.混凝土I型裂缝扩展准则比较研究[J].工程力学,2016,33(5):89-96.Wang Cuijin,Dong Wei,Wang Qiang,et al.Acomparative study on propagation criterion of concrete mode I crack[J].Engineering Mechanics,2016,33(5):89-96.(in Chinese)
[26]卿龙邦,王妥,管俊峰,等.有限尺寸混凝土试件允许损伤尺度的解析研究[J].工程力学,2017,34(1):213-218.Qing Longbang,Wang Tuo,Guan Junfeng,et al.Analytical study on permissible damage scale of cracks in finite size concrete specimens[J].Engineering Mechanics,2017,34(1):213-218.(in Chinese)
[27]Dong W,Zhou X M,Wu Z M,et al.Investigating crack initiation and propagation of concrete in a restrained shrinkage circular/elliptical ring test[J].Materials&Structures,2017,50(1):1-13.
[28]Hu X Z,Wittmann F.Size effect on toughness induced by crack close to free surface[J].Engineering Fracture Mechanics,2000,65(2):209-221.
[29]Hu X Z,Duan K.Influence of fracture process zone height on fracture energy of concrete[J].Cement and Concrete Research,2004,34(8):1321-1330.
[30]Hu X Z,Duan K.Size effect and quasi-brittle fracture:the role of FPZ[J].International Journal of Fracture,2008,154(1):3-14.
[31]Hu X Z,Duan K.Mechanism behind the size effect phenomenon[J].Journal Engineering Mechanics,ASCE,2010,136(1):60-68.
[32]Tada H I,Paris P C,Irwin G R.The analysis of cracks handbook[M].New York:ASME Press,2000.
[33]李晓东,董伟,吴智敏,等.小尺寸混凝土试件双K断裂参数试验研究[J].工程力学,2010,27(2):166-171,185.Li Xiaodong,Dong Wei,Wu Zhimin,et al.Experimental investigation on double-K fracture parameters for small size specimens of concrete[J].Engineering Mechanics,2010,27(2):166-171,185.(in Chinese)
[34]赵燕茹,王磊,韩霄峰,等.冻融条件下玄武岩纤维混凝土断裂韧度研究[J].工程力学,2017,34(9):92-101.Zhao Yanru,Wang Lei,Han Xiaofeng,et al.Fracture toughness of basalt-fiber reinforced concrete subjected to cyclic freezing and thawing[J].Engineering Mechanics,2017,34(9):92-101.(in Chinese)
[35]Jenq Y S,Shah S P.Two parameter fracture model for concrete[J].Journal Engineering Mechanics-ASCE,1985,111(10):1227-1241.
[36]管俊峰,李庆斌,吴智敏.采用峰值荷载法确定全级配水工混凝土断裂参数[J].工程力学,2014,31(8):8-13.Guan Junfeng,Li Qingbin,Wu Zhimin.Determination of fully-grade hydraulic concrete fracture parameters by Peak-load method[J].Engineering Mechanics,2014,31(8):8-13.(in Chinese)
[37]Karihaloo B L,Nallathambi P.Effective crack model for the determination of fracture toughness(Ke IC)of Concrete[J].Engineering Fracture Mechanics,1990,35(4/5):637-645.
[38]Zhang P,Gao J X,Dai X B,et al.Fracture behavior of fly ash concrete containing silica fume[J].Structural Engineering&Mechanics,2016,59(2):261-275.
[39]Qing L B,Cheng Y H.The fracture extreme theory for determining the effective fracture toughness and tensile strength of concrete[J].Theoretical and Applied Fracture Mechanics,2018,96(8):461-467.