几何与非几何相似试件确定混凝土韧度及强度

管俊峰; 鲁猛; 王昊; 姚贤华; 李列列; 张敏; 胡圣能

doi:10.6052/j.issn.1000-4750.2020.08.0573

几何与非几何相似试件确定混凝土韧度及强度

doi: 10.6052/j.issn.1000-4750.2020.08.0573

华北水利水电大学土木与交通学院，河南，郑州 450045

基金项目: 国家自然科学基金面上项目(51779095)；河南省高校科技创新人才支持计划资助项目(20HASTIT013)；华北水利水电大学研究生教育创新计划基金项目(YK2020-11)

详细信息

作者简介:
鲁　猛(1995−)，男，河南周口人，硕士生，从事混凝土断裂力学研究(E-mail: 1263759120@qq.com)

王　昊(1995−)，男，河南郑州人，硕士生，从事混凝土断裂力学研究(E-mail: 664967240@qq.com)

姚贤华(1976−)，男，河南襄城人，实验师，博士，从事混凝土材料性能方面研究(E-mail: yaoxianhua@ncwu.edu.cn)

李列列(1983−)，男，山西临汾人，讲师，博士，从事混凝土损伤与断裂力学研究(E-mail: 13370912@qq.com)

张　敏(1981−)，女，河南驻马店人，讲师，博士，从事混凝土材料与结构方面研究(E-mail: zhangmin888@163.com)

胡圣能(1979−)，男，河南信阳人，副教授，博士，硕导，从事混凝土材料与结构方面研究(E-mail: hsn@ncwu.edu.cn)

通讯作者:
管俊峰(1980−)，男，河南许昌人，教授，博士，博导，从事混凝土断裂力学研究(E-mail: junfengguan@ncwu.edu.cn)

中图分类号: TU528；TU501
计量
- 文章访问数: 101
- HTML全文浏览量: 10
- PDF下载量: 19
- 被引次数: 0
出版历程
- 收稿日期: 2020-08-18
- 修回日期: 2020-12-07
- 网络出版日期: 2021-03-17
- 刊出日期: 2021-09-13

DETERMINATION OF THE FRACTURE TOUGHNESS AND TENSILE STRENGTH OF CONCRETE USING GEOMETRICALLY AND NON-GEOMETRICALLY SIMILAR SPECIMENS

School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou, He’nan 450045, China

摘要

摘要: 几何相似与非几何相似试件，分别为尺寸效应与边界效应模型的推荐试件型式。考虑尺寸效应和边界效应模型的各自特点与优势，提出了改进的混凝土离散颗粒断裂模型。基于几何相似与非几何相似两类试件的断裂试验，确定出混凝土的材料参数——断裂韧度与拉伸强度，并与试验强度值及由尺寸效应模型确定的断裂韧度进行了比较。结果表明：当韧带高度(W−a₀)与骨料代表尺寸d_i的比值约为10时，对应的断裂韧度与拉伸强度的确定曲线的相关系数最佳，且与试验强度值、尺寸效应模型断裂韧度计算值吻合较好。采用几何相似、非几何相似、几何与非几何相似试件确定的混凝土材料参数，分别建立了不同情况下混凝土断裂破坏设计预测曲线，其±20%即可涵盖全部试验数据。基于统计归纳，可取虚拟裂缝扩展量Δa_fic=nd_i和特征裂缝长度$a_\infty ^ *$=0.5d_i，进而建立了峰值荷载与断裂韧度、峰值荷载与拉伸强度的解析关系式，实现了由实测峰值荷载直接确定出混凝土的断裂韧度与拉伸强度的目的，预测值的±15%可涵盖所有试验数据。基于解析公式，预测了满足线弹性断裂的大尺寸真实结构的峰值状态。
- 混凝土 /
- 几何相似 /
- 非几何相似 /
- 尺寸效应 /
- 边界效应 /
- 断裂韧度 /
- 拉伸强度
Abstract: Geometrically similar specimens and non-geometrically similar specimens are respectively recommended for the size effect model (SEM) and the boundary effect model (BEM). Considering the individual characteristics and advantages of the SEM and BEM, it proposed an improved discrete particle fracture model for concrete. The fracture tests of two types of specimens with geometrical and non-geometrical similarity are used to determine the material parameters of concrete, that is, the fracture toughness and tensile strength. The determined strengths are compared with the experimental strengths. The determined fracture toughness is compared with the values determined by the SEM. The results show that when the ratio of the ligament length (W−a₀) to the representative size of aggregate d_i is approximately 10, the correlation coefficient of the determination curves for the fracture toughness and tensile strength is the best. The determined fracture toughness and tensile strength are in good agreement with the experimental strengths and the fracture toughness from the SEM. Based on the determined concrete material parameters using the geometrically similar, the non-geometrically similar, and the geometrically and non-geometrically similar specimens, the corresponding design curves of concrete under different conditions are established. The design curves can cover all test data by ±20%. Based on a statistical analysis, the fictitious crack growth length Δa_fic=nd_i and the characteristic crack length $a_\infty ^ *$=0.5d_i can be taken. Then the analytical relations between the peak load and fracture toughness and between the peak load and tensile strength are established. The purpose of directly determining the fracture toughness and tensile strength of concrete using the experimental peak loads is achieved. ±15% of the predicted curves can cover all the experimental data. Based on the analytical formulas, the peak loads of large-scale real concrete structures that exhibit linear elastic fracture can be predicted.
- concrete /
- geometrically similar /
- non-geometrically similar /
- size effect /
- boundary effect /
- fracture toughness /
- tensile strength

HTML全文

图 1 试件尺寸与裂缝长度对断裂特性的影响

Figure 1. Effect of specimen size and crack length on fracture characteristics

下载: 全尺寸图片幻灯片

图 2 试件高度W与裂缝长度对几何结构参数a_e的影响

Figure 2. Variation of a_e with W and α for geometrically and non-geometrically similar specimens

下载: 全尺寸图片幻灯片

图 3 几何相似与非几何相似试件的几何结构参数a_e随试件高度W与缝高比α变化的变化规律

Figure 3. Variation of a_e with W and α for geometrically and non-geometrically similar specimens

下载: 全尺寸图片幻灯片

图 4 试件尺寸、裂缝长度、骨料颗粒的相互影响

Figure 4. Interaction of specimen size, crack length, and aggregate

下载: 全尺寸图片幻灯片

图 5 有限尺寸试件的离散颗粒断裂模型

Figure 5. Discrete particle fracture model for limited size of concrete specimens

下载: 全尺寸图片幻灯片

图 6 SEM中σ_N与BEM中σ_n的比较

Figure 6. Comparison between σ_N of SEM and σ_n of BEM

下载: 全尺寸图片幻灯片

图 7 由几何相似试件确定d_max=19 mm混凝土的K_IC与f_t

Figure 7. Determination of K_IC and f_t using geometrically similar concrete specimens with d_max=19 mm

下载: 全尺寸图片幻灯片

图 8 由非几何相似试件确定d_max=19 mm的混凝土的断裂韧度K_IC与拉伸强度f_t

Figure 8. Determination of K_IC and f_t using non-geometrically similar concrete specimens with d_max=19 mm

下载: 全尺寸图片幻灯片

图 9 由几何相似与非几何相似试件确定d_max=19 mm的混凝土的断裂韧度K_IC与拉伸强度f_t

Figure 9. Determination of K_IC and f_t using geometrically similar and non-geometrically similar concrete specimens with d_max=19 mm

下载: 全尺寸图片幻灯片

图 10 由几何相似试件确定d_max=25 mm的混凝土的断裂韧度K_IC与拉伸强度f_t

Figure 10. Determination of K_IC and f_t using geometrically similar concrete specimens with d_max=25 mm

下载: 全尺寸图片幻灯片

图 11 由非几何相似试件确定d_max=25 mm的混凝土的断裂韧度K_IC与拉伸强度f_t

Figure 11. Determination of K_IC and f_t using non-geometrically similar concrete specimens with d_max=25 mm

下载: 全尺寸图片幻灯片

图 12 由几何相似与非几何相似试件确定d_max=25 mm的混凝土的断裂韧度K_IC与拉伸强度f_t

Figure 12. Determination of K_IC and f_t using geometrically similar and non-geometrically similar concrete specimens with d_max=25 mm

下载: 全尺寸图片幻灯片

图 13 构建d_max=19 mm混凝土的断裂破坏曲线

Figure 13. Fracture curves of concrete with d_max=19 mm

下载: 全尺寸图片幻灯片

图 14 构建d_max=25 mm混凝土的断裂破坏曲线

Figure 14. Fracture curves of concrete with d_max=25 mm

下载: 全尺寸图片幻灯片

图 15 构建d_max=19 mm和d_max=25 mm混凝土的断裂破坏曲线

Figure 15. Fracture curves of concrete with d_max=19 mm and d_max=25 mm

下载: 全尺寸图片幻灯片

图 16 基于几何与非几何相似试件对d_max=19 mm混凝土的P_max、K_IC、f_t进行预测

Figure 16. Predicting P_max, K_IC and f_t of concrete with d_max=19 mm using geometrically and non-geometrically similar specimens

下载: 全尺寸图片幻灯片

图 17 基于几何与非几何相似试件对d_max=25 mm混凝土的P_max、K_IC、f_t进行预测

Figure 17. Predicting P_max, K_IC and f_t of concrete with d_max=25 mm using geometrically and non-geometrically similar specimens

下载: 全尺寸图片幻灯片

图 18 基于d_max=19 mm和d_max=25 mm的几何与非几何相似试件对混凝土的P_max、K_IC、f_t进行预测

Figure 18. Predicting P_max, K_IC and f_t of concrete with d_max=19 mm and 25 mm using geometrically and non-geometrically similar specimens

下载: 全尺寸图片幻灯片

表 1 d_max=19 mm混凝土试件尺寸与实测P_max

Table 1. Detailed dimensions of concrete specimens with d_max=19 mm and experimental P_max

分组	编号	高度W/ mm	跨度S/ mm	宽度B/ mm	初始裂缝 a₀/mm	峰值荷载 P_max/kN
几何相似	D19-0.3-1	57	142.5	57	17.1	3.22
	D19-0.3-2	57	142.5	57	17.1	3.16
	D19-0.3-3	57	142.5	57	17.1	3.26
	D19-0.3-4	114	285	57	34.2	5.24
	D19-0.3-5	114	285	57	34.2	5.46
	D19-0.3-6	114	285	57	34.2	5.48
	D19-0.3-7	228	570	57	68.4	7.84
	D19-0.3-8	228	570	57	68.4	8.12
	D19-0.3-9	228	570	57	68.4	9.00
	D19-0.3-10	456	1140	57	136.8	13.71
	D19-0.3-11	456	1140	57	136.8	14.70
	D19-0.3-12	456	1140	57	136.8	13.51
非几何相似	D19-0.1-1	142.5	1410.75	57	14.25	2.24
	D19-0.1-2	142.5	1410.75	57	14.25	2.17
	D19-0.1-3	142.5	1410.75	57	14.25	2.19
	D19-0.2-1	142.5	1410.75	57	28.5	1.77
	D19-0.2-2	142.5	1410.75	57	28.5	1.71
	D19-0.2-3	142.5	1410.75	57	28.5	1.74
	D19-0.4-1	142.5	1410.75	57	57	1.10
	D19-0.4-2	142.5	1410.75	57	57	1.05
	D19-0.4-3	142.5	1410.75	57	57	1.09
	D19-0.6-1	142.5	1410.75	57	85.5	0.48
	D19-0.6-2	142.5	1410.75	57	85.5	0.50
	D19-0.6-3	142.5	1410.75	57	85.5	0.49

下载: 导出CSV

表 2 d_max=25 mm混凝土试件尺寸与实测P_max

Table 2. Detailed dimensions of concrete specimens with d_max=25 mm and experimental P_max

分组	编号	高度W/ mm	跨度S/ mm	宽度B/ mm	初始裂缝 a₀/mm	峰值荷载 P_max/kN
几何相似	D25-0.3-1	75	187.5	75	22.5	5.10
	D25-0.3-2	75	187.5	75	22.5	5.01
	D25-0.3-3	75	187.5	75	22.5	4.86
	D25-0.3-4	150	375	75	45	8.01
	D25-0.3-5	150	375	75	45	7.63
	D25-0.3-6	150	375	75	45	7.91
	D25-0.3-7	300	750	75	90	14.20
	D25-0.3-8	300	750	75	90	13.27
	D25-0.3-9	300	750	75	90	13.85
非几何相似	D25-0.1-1	142.5	1410.75	57	14.25	2.27
	D25-0.1-2	142.5	1410.75	57	14.25	2.39
	D25-0.1-3	142.5	1410.75	57	14.25	2.31
	D25-0.2-1	142.5	1410.75	57	28.5	1.77
	D25-0.2-2	142.5	1410.75	57	28.5	1.87
	D25-0.2-3	142.5	1410.75	57	28.5	1.82
	D25-0.4-1	142.5	1410.75	57	57	1.09
	D25-0.4-2	142.5	1410.75	57	57	1.14
	D25-0.4-3	142.5	1410.75	57	57	1.04
	D25-0.6-1	142.5	1410.75	57	85.5	1.41
	D25-0.6-2	142.5	1410.75	57	85.5	1.41
	D25-0.6-3	142.5	1410.75	57	85.5	1.41

下载: 导出CSV

参考文献(37)

[1]	Li Qingbin, Guan Junfeng, Wu Zhimin, et al. Fracture behavior of site-casting dam concrete [J]. ACI Material Journal, 2015, 112(1): 11 − 20.
[2]	Li Qingbin, Guan Junfeng, Wu Zhimin, et al. Equivalent maturity for ambient temperature effect on fracture parameters of site-casting dam concrete [J]. Construction and Building Materials, 2016, 120(9): 293 − 308.
[3]	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. doi: 10.6052/j.issn.1000-4750.2013.03.0205 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) doi: 10.6052/j.issn.1000-4750.2013.03.0205
[4]	管俊峰, 李庆斌, 吴智敏, 等. 现场浇筑大坝混凝土起裂断裂韧度研究[J]. 水利学报, 2014, 45(12): 1487 − 1492. Guan Junfeng, Li Qingbin, Wu Zhimin, et al. Initial fracture toughness of site-casting dam concrete [J]. Journal of Hydraulic Engineering, 2014, 45(12): 1487 − 1492. (in Chinese)
[5]	管俊峰, 李庆斌, 吴智敏. 现场浇筑大坝混凝土与湿筛混凝土起裂韧度换算关系研究[J]. 水利学报, 2016, 47(11): 1435 − 1441. Guan Junfeng, Li Qingbin, Wu Zhimin. Conversion relationship between initial fracture toughness of site-casting and sieved concrete [J]. Journal of Hydraulic Engineering, 2016, 47(11): 1435 − 1441. (in Chinese)
[6]	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. doi: 10.3321/j.issn:0559-9350.1984.10.007 Xu Shilang. Probabilistic statistical analysis of fracture toughness of concrete [J]. Journal of Hydraulic Engineering, 1984, 15(10): 51 − 58. (in Chinese) doi: 10.3321/j.issn:0559-9350.1984.10.007
[7]	徐世烺, 赵国藩, 刘毅, 等. 三点弯曲梁法研究混凝土断裂能及其试件尺寸影响[J]. 大连理工大学学报, 1991, 31(1): 79 − 86. Xu Shilang, Zhao Guofan, Liu Yi, et al. Fracture energy of concrete and its variational trend in size effect studied by using three point-bending beams [J]. Journal of Dalian University of Technology, 1991, 31(1): 79 − 86. (in Chinese)
[8]	Hillerborg A. Results of three comparative test series for determining the fracture energy GF of concrete [J]. Materials and Structures, 1985, 18(5): 407 − 413. doi: 10.1007/BF02472416
[9]	Wittmann F H, Mihashi H, Nomura N. Size effect on fracture energy of concrete [J]. Engineering Fracture Mechanics, 1990, 35(1/3): 107 − 115.
[10]	钱觉时, 范英儒, 袁江. 三点弯曲法测定砼断裂能的尺寸效应[J]. 重庆建筑大学学报, 1995, 17(2): 1 − 8. Qian Jueshi, Fan Yingru, Yuan Jiang. The size effect of the fracture energy of concrete tested by three point bending [J]. Journal of Chongqing Jianzhu University, 1995, 17(2): 1 − 8. (in Chinese)
[11]	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]. 大连理工大学学报, 1997, 37(增刊 1): 131 − 136. Yang Chengqiu, Wu Zheng. Investigation of size effect on strength and deformation behaviour of full mix concrete [J]. Journal of Dalian University of technology, 1997, 37(Suppl 1): 131 − 136. (in Chinese)
[12]	吴智敏, 徐世烺, 王金来, 等. 三点弯曲梁法研究砼双K断裂参数及其尺寸效应[J]. 水力发电学报, 2000(4): 16 − 24. doi: 10.3969/j.issn.1003-1243.2000.04.002 Wu Zhimin, Xu Shilang, Wang Jinlai, et al. Double-K fracture parameter of concrete and its size effect by using three-point bending beam method [J]. Journal of Hydroelectric Engineering, 2000(4): 16 − 24. (in Chinese) doi: 10.3969/j.issn.1003-1243.2000.04.002
[13]	Zhao Z F, Kwon S H, Shah S P. Effect of specimen size on fracture energy and softening curve of concrete: Part I. Experiments and fracture energy [J]. Cement and Concrete Research, 2008, 38(8/9): 1049 − 1060. doi: 10.1016/j.cemconres.2008.03.017
[14]	Hoover C G, Bažant Z P, Vorel J, et al. Comprehensive concrete fracture tests: description and results [J]. Engineering Fracture Mechanics, 2013, 114(12): 92 − 103.
[15]	胡少伟, 胡亮. 混凝土Ⅱ型断裂韧度尺寸效应的试验研究[J]. 水利学报, 2014, 45(增刊 1): 57 − 63. Hu Shaowei, Hu Liang. Experimental research on size effect of mode Ⅱ fracture toughness of concrete [J]. Journal of Hydraulic Engineering, 2014, 45(Suppl 1): 57 − 63. (in Chinese)
[16]	Çağlar Y, Şener S. Size effect tests of different notch depth specimens with support rotation measurements [J]. Engineering Fracture Mechanics, 2016, 157(5): 43 − 55.
[17]	Ghasemi M, Ghasemi M R, Mousavi S R. Studying the fracture parameters and size effect of steel fiber-reinforced self-compacting concrete [J]. Construction and Building Materials, 2019, 201(5): 447 − 460.
[18]	Rong H, Dong W, Zhang X, et al. Size effect on fracture properties of concrete after sustained loading [J]. Materials and Structures, 2019, 52(1): 1 − 12. doi: 10.1617/s11527-018-1302-0
[19]	Yu K Q, Ding Y, Zhang Y X. Size effects on tensile properties and compressive strength of engineered cementitious composites [J]. Cement and Concrete Composites, 2020, 113(10): 103691.
[20]	Bažant Z P. Size effect in blunt fracture: Concrete, rock, metal [J]. Journal of Engineering Mechanics, 1984, 110(4): 518 − 535. doi: 10.1061/(ASCE)0733-9399(1984)110:4(518)
[21]	Hoover C G, Bažant Z P. Universal size-shape effect law based on comprehensive concrete fracture tests [J]. Journal Engineering Mechanics, 2014, 140(3): 473 − 479. doi: 10.1061/(ASCE)EM.1943-7889.0000627
[22]	Hu X Z, Wittmann F. Size effect on toughness induced by crack close to free surface [J]. Engineering Fracture Mechanics, 2000, 65(2-3): 209 − 221. doi: 10.1016/S0013-7944(99)00123-X
[23]	Hu X Z. An asymptotic approach to size effect on fracture toughness and fracture energy of composites [J]. Engineering Fracture Mechanics, 2002, 69(5): 555 − 564. doi: 10.1016/S0013-7944(01)00102-3
[24]	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.
[25]	Guan Junfeng, Hu Xiaozhi, Li Qingbin. In-depth analysis of notched 3-p-b concrete fracture [J]. Engineering Fracture Mechanics, 2016, 165(10): 57 − 71.
[26]	Guan Junfeng, Hu Xiaozhi, Yao Xianhua, et al. Fracture of 0.1 and 2 m long mortar beams under three-point-bending [J]. Materials & Design, 2017, 133(11): 363 − 375.
[27]	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)
[28]	管俊峰, 胡晓智, 李庆斌, 等. 边界效应与尺寸效应模型的本质区别及相关设计应用[J]. 水利学报, 2017, 48(8): 955 − 967. Guan Junfeng, Hu Xiaozhi, Li Qingbin, et al. Essential difference and design application of boundary effect model and size effect model [J]. Journal of Hydraulic Engineering, 2017, 48(8): 955 − 967. (in Chinese)
[29]	Guan Junfeng, Hu Xiaozhi, Xie Chaopeng, et al. Wedge-splitting tests for tensile strength and fracture toughness of concrete [J]. Theoretical and Applied Fracture Mechanics, 2018, 93(2): 263 − 275.
[30]	管俊峰, 姚贤华, 白卫峰, 等. 由小尺寸试件确定混凝土的断裂韧度与拉伸强度[J]. 工程力学, 2019, 36(1): 70 − 79, 87. Guan Junfeng, Yao Xianhua, Bai Weifeng, et al. Determination of fracture toughness and tensile strength of concrete using small specimens [J]. Engineering Mechanics, 2019, 36(1): 70 − 79, 87. (in Chinese)
[31]	Guan Junfeng, Li Changming, Juan Wang, et al. Determination of fracture parameter and prediction of structural fracture using various concrete specimen types [J]. Theoretical and Applied Fracture Mechanics, 2019, 100(4): 114 − 127.
[32]	管俊峰, 宋志锴, 姚贤华, 等. 采用无缝试件确定混凝土岩石的断裂韧度[J]. 工程力学, 2020, 37(3): 36 − 45, 107. Guan Junfeng, Song Zhikai, Yao Xianhua, et al. Determination of fracture toughness of concrete and rock using unnotched specimens [J]. Engineering Mechanics, 2020, 37(3): 36 − 45, 107. (in Chinese)
[33]	ASTM E399−90, Standard test method for plane-strain fracture toughness testing of metallic materials [S]. Philadelphia: American Society for Testing and Materials, 1990.
[34]	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.
[35]	BS EN ISO 12737: 1999, Metallic materials—Determination of plane-strain fracture toughness [S]. London: British Standards Institution, 1999.
[36]	Guan Junfeng, Yuan Peng, Hu Xiaozhi, et al. Statistical analysis of concrete fracture using normal distribution pertinent to maximum aggregate size [J]. Theoretical and Applied Fracture Mechanics, 2019, 101(5): 236 − 253.
[37]	Sadrmomtazia A, Lotfi-Omrana O, Nikbinb I M. Influence of cement content and maximum aggregate size on the fracture parameters of magnetite concrete using WFM, SEM and BEM [J]. Theoretical and Applied Fracture Mechanics, 2020, 107(6): 102482.