考虑混凝土软化效应的钢筋与混凝土粘结强度计算模型

兰官奇; 王毅红; 刘乐; 刘喜; 宋梅梅

doi:10.6052/j.issn.1000-4750.2021.06.0433

考虑混凝土软化效应的钢筋与混凝土粘结强度计算模型

doi: 10.6052/j.issn.1000-4750.2021.06.0433

兰官奇^1, ,,
王毅红^2,,
刘乐^3,,
刘喜^2,,
宋梅梅^1,

1.
西安石油大学机械工程学院，陕西，西安 710065
2.
长安大学建筑工程学院，陕西，西安 710061
3.
中联西北工程设计研究院有限公司，陕西，西安 710077

基金项目: 陕西省自然科学基础研究计划资助项目(2022JQ-301)；西部绿色建筑国家重点实验室开放基金项目(LSKF202217)；国家自然科学基金项目(51878054)；陕西省自然科学基础研究计划一般项目(青年)(2021JQ-605)

详细信息

作者简介:
王毅红(1955−)，女，山东人，教授，博士，主要从事混凝土结构基本理论及其应用研究(E-mail: wangyh@chd.edu.cn)

刘　乐(1994−)，男，陕西人，硕士，主要从事混凝土结构设计相关方面研究(E-mail: 1738677491@qq.com)

刘　喜(1986−)，男，陕西人，副教授，博士，主要从事工程结构抗震与防灾方面研究(E-mail: lliuxii@163.com)

宋梅梅(1988−)，女，陕西人，讲师，博士，主要从事高性能混凝土材料方面研究(E-mail: songmeimei2016@163.com)

通讯作者:
兰官奇(1991−)，男，陕西人，讲师，博士，主要从事混凝土结构基本理论及其应用研究(E-mail: 201202@xsyu.edu.cn)

中图分类号: TU375
计量
- 文章访问数: 352
- HTML全文浏览量: 192
- PDF下载量: 92
- 被引次数: 0
出版历程
- 收稿日期: 2021-06-07
- 修回日期: 2021-08-28
- 网络出版日期: 2021-09-17
- 刊出日期: 2022-09-01

A MODEL OF CALCULATING THE BOND STRENGTH BETWEEN REBARS AND CONCRETE CONSIDERING THE SOFTENING EFFECT OF CONCRETE

LAN Guan-qi^{1
, ,},
WANG Yi-hong^2
,,
LIU Le^3
,,
LIU Xi^2
,,
SONG Mei-mei^1
,

1.
Xi'an Shiyou University, School of Mechanical Engineering, Xi’an, Shaanxi 710065, China
2.
Chang'an University, School of Civil Engineering, Xi’an, Shaanxi 710061, China
3.
China United Northwest Institute Co., Ltd, Xi’an, Shaanxi 710077, China

摘要

摘要: 通过钢筋与混凝土拉式粘结试验，测试了高强度带肋钢筋与不同强度等级混凝土的粘结强度，分析了带肋钢筋与混凝土的粘结受力机理；采用双线性软化本构对开裂区的软化行为进行描述，建立了综合考虑开裂区及未开裂区混凝土影响的粘结强度理论计算模型；研究了开裂区不同径向位移分布对计算结果的影响，并将计算结果与试验结果进行对比，验证了计算模型的有效性。结果表明：模型采用基于等效弹性假设的开裂区径向位移分布时，计算值与试验值最为吻合，但却过高的估计了低强度混凝土试件的粘结强度；为确保有足够的安全储备，建议采用弹性假设作为开裂区混凝土径向位移分布。
- 钢筋混凝土 /
- 粘结锚固 /
- 破坏机理 /
- 粘结强度 /
- 力学模型 /
- 计算方法
Abstract: The bond strength between high-strength rebars and concrete with different strengths was tested by pull-out tests. The bonding mechanism between rebars and concrete was analyzed. The bilinear softening constitutive model was used to describe the softening behavior of concrete in the cracked zone, and the theoretical calculation model of the bond strength considering the influence of concrete in cracked and non-cracking zones were established. The effects of different radial displacement distributions in the cracked zone on the calculation results are studied. The validity of the calculation model was verified by comparing the calculated results with the experimental results. The results show that the computational model has the best accuracy when the radial displacement distribution in the fracture zone is assumed to be equivalently elastic. However, the bond strength of low-strength concrete specimens was overestimated under this assumption. It is suggested that the elastic assumption be used as the radial displacement distribution of concrete in the cracked zone to ensure adequate safety reserves.
- reinforced concrete /
- bonding /
- failure mechanisms /
- bond strength /
- analytical models /
- computational methods

HTML全文

图 1 试件尺寸　/mm

Figure 1. Specimen size

下载: 全尺寸图片幻灯片

图 2 加载装置

Figure 2. Loading device

下载: 全尺寸图片幻灯片

图 3 钢筋与混凝土粘结锚固受力机理

Figure 3. Mechanisms of bonding and anchoring between rebar and concrete

下载: 全尺寸图片幻灯片

图 4 简化计算模型

Figure 4. Simplified analytical model

下载: 全尺寸图片幻灯片

图 5 考虑开裂区混凝土软化的计算模型

Figure 5. Computational model considering softening of concrete in cracked zone

下载: 全尺寸图片幻灯片

图 6 混凝土的软化效应

Figure 6. Softening effect of concrete

下载: 全尺寸图片幻灯片

图 7 不同软化曲线形式

Figure 7. Different forms of softening curve

下载: 全尺寸图片幻灯片

图 8 开裂区混凝土径向位移的不同假设

Figure 8. Different hypotheses of radial displacement of concrete in cracked zone

下载: 全尺寸图片幻灯片

表 1 拉式粘结试验结果

Table 1. Bond test results

试件编号	钢筋直径/mm	锚固长度/mm	保护层厚度/mm	混凝土抗压强度/MPa	混凝土抗拉强度/MPa	粘结强度均值/MPa	粘结强度标准差/MPa
T16-7d-C30	16	115	92	40.69	3.03	18.65	3.41
T16-7d-C40	16	115	92	50.32	3.41	24.94	1.83
T16-7d-C50	16	115	92	56.02	3.62	25.79	1.52

下载: 导出CSV

表 2 粘结强度的理论计算值

Table 2. Calculation value of bond strength

试件编号	参数C₁/mm	按假设①计算		按假设②计算		按假设③计算
试件编号	参数C₁/mm	r_u1/mm	${\tau} _{ {\text{u1} } }^{\text{c} }$/MPa	r_u2/mm	${\tau} _{ {\text{u2} } }^{\text{c} }$/MPa	r_u3/mm	${\tau} _{ {\text{u3} } }^{\text{c} }$/MPa
T16-7d-C30	−174.97	69.85	24.55	52.96	18.54	57.33	21.10
T16-7d-C40	168.11	69.04	27.34	51.97	20.49	56.58	23.44
T16-7d-C50	−164.15	68.55	28.84	51.38	21.52	56.13	24.69
A18-10d-C40^[2]	−209.56	73.93	10.48	57.95	8.71	61.11	9.30
A18-10d-C50^[2]	−207.28	73.66	11.41	57.62	9.36	60.86	10.08
A18-10d-C60^[2]	−204.05	73.28	12.72	57.16	10.27	60.51	11.18
B18-20d-C60^[21]	−208.86	73.85	10.77	57.85	8.91	61.04	9.54
B18-20d-C80^[21]	−204.73	73.59	11.66	57.53	9.53	60.79	10.29
B18-20d-C100^[21]	−201.50	72.98	13.76	56.79	11.00	60.23	12.05
注：1) 为便于对比分析，所收集数据试件编号按照本文试件编号规则重新赋予编号，例如A18-10d-C40含义为钢筋公称直径为18 mm、锚固长度为10 d、混凝土强度等级为C40的试件；2) 每组收集数据为3个试件实测值的平均值；3) 相同强度等级混凝土实测强度值存在差异，所收集数据中详细试验参数见相应文献；4) r_u1、r_u2、r_u3分别为假设①、②、③下计算得到的裂缝深度；5) ${\tau} _{ {\text{u1} } }^{\text{c} } $、${\tau} _{ {\text{u2} } }^{\text{c} } $、${\tau} _{ {\text{u3} } }^{\text{c} } $分别为假设①、②、③下计算得到的粘结强度。

下载: 导出CSV

表 3 粘结强度理论计算值与试验值的对比

Table 3. Comparisons between calculated and experimental values of bond strength

试件编号	试验值${\tau} _{\text{u} }^{\text{t} }$/MPa	${ {{\tau} _{ {\text{u1} } }^{\text{c} } } \mathord{/ {\vphantom { {{\tau} _{ {\text{u1} } }^{\text{c} } } {{\tau} _{\text{u} }^{\text{t} } } }} } {{\tau} _{\text{u} }^{\text{t} } } }$	${ {{\tau} _{ {\text{u2} } }^{\text{c} } } \mathord{/ {\vphantom { {{\tau} _{ {\text{u2} } }^{\text{c} } } {{\tau} _{\text{u} }^{\text{t} } } }} } {{\tau} _{\text{u} }^{\text{t} } } }$	${ {{\tau} _{ {\text{u3} } }^{\text{c} } } \mathord{/ {\vphantom { {{\tau} _{ {\text{u3} } }^{\text{c} } } {{\tau} _{\text{u} }^{\text{t} } } }} } {{\tau} _{\text{u} }^{\text{t} } } }$
T16-7d-C30	18.65	1.33	1.00	1.15
T16-7d-C40	24.94	1.10	0.82	0.95
T16-7d-C50	25.79	1.16	0.87	0.99
A18-10d-C40	8.92	1.17	0.98	1.04
A18-10d-C50	10.45	1.09	0.90	0.96
A18-10d-C60	11.56	1.10	0.89	0.97
B18-20d-C60	10.31	1.04	0.86	0.93
B18-20d-C80	11.50	1.01	0.83	0.89
B18-20d-C100	12.45	1.11	0.88	0.97
注：${ { {\tau} _{ {\text{u1} } }^{\text{c} } } \mathord{/ {\vphantom { { {\tau} _{ {\text{u1} } }^{\text{c} } } { {\tau} _{\text{u} }^{\text{t} } } } } } { {\tau} _{\text{u} }^{\text{t} } } } $、${ {{\tau} _{ {\text{u2} } }^{\text{c} } } \mathord{/ {\vphantom { {{\tau} _{ {\text{u2} } }^{\text{c} } } {{\tau} _{\text{u} }^{\text{t} } } }} } {{\tau} _{\text{u} }^{\text{t} } } } $、${ {{\tau} _{ {\text{u3} } }^{\text{c} } } \mathord{/ {\vphantom { {{\tau} _{ {\text{u3} } }^{\text{c} } } {{\tau} _{\text{u} }^{\text{t} } } }} } {{\tau} _{\text{u} }^{\text{t} } } } $分别为假设①、②、③下计算得到的粘结强度与试验实测粘结强度的比值。

下载: 导出CSV

参考文献(21)

[1]	徐有邻, 沈文都, 汪洪. 钢筋砼粘结锚固性能的试验研究[J]. 建筑结构学报, 1994, 15(3): 26 − 37. doi: 10.3321/j.issn:1000-6869.1994.03.001 Xu Youlin, Shen Wendu, Wang Hong. Experimental research on bonding and anchoring performance of reinforced concrete [J]. Journal of Building Structures, 1994, 15(3): 26 − 37. (in Chinese) doi: 10.3321/j.issn:1000-6869.1994.03.001
[2]	李艳艳, 李晓清, 苏恒博. 600 MPa高强钢筋与混凝土的粘结锚固性能试验研究[J]. 土木建筑与环境工程, 2017, 39(2): 19 − 25. Li Yanyan, Li Xiaoqing, Su Hengbo. Experimental analysis of bond – anchorage properties between 600 MPa high strength reinforcement and concrete [J]. Journal of Civil, Architectural and Environmental Engineering, 2017, 39(2): 19 − 25. (in Chinese)
[3]	Mousavi S S, Dehestani M, Mousavi K K. Bond strength and development length of steel bar in unconfined self-consolidating concrete [J]. Engineering Structures, 2017, 131: 587 − 598. doi: 10.1016/j.engstruct.2016.10.029
[4]	袁鹏, 陈万祥, 郭志昆, 等. 中低加载速率下BFRP筋-混凝土粘结性能研究[J]. 工程力学, 2021, 38(5): 131 − 142. doi: 10.6052/j.issn.1000-4750.2020.06.0377 Yuan Peng, Chen Wanxiang, Guo Zhikun, et al. Study on bond behavior of BFRP bars and concrete under medium and low loading rates [J]. Engineering Mechanics, 2021, 38(5): 131 − 142. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.06.0377
[5]	林红威, 赵羽习, 郭彩霞, 等. 锈胀开裂钢筋混凝土粘结疲劳性能试验研究[J]. 工程力学, 2020, 37(1): 98 − 107. doi: 10.6052/j.issn.1000-4750.2019.01.0038 Lin Hongwei, Zhao Yuxi, Guo Caixia, et al. Fatigue of the bond behavior of corroded reinforced concrete with corrosion-induced cracks [J]. Engineering Mechanics, 2020, 37(1): 98 − 107. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.01.0038
[6]	熊能, 顾冬生. 钢筋粘结滑移弯矩-转角计算模型[J]. 工程力学, 2019, 36(12): 98 − 105. doi: 10.6052/j.issn.1000-4750.2018.12.0696 Xiong Neng, Gu Dongsheng. A calculation model for the slip moment-rotation of reinforcement bond [J]. Engineering Mechanics, 2019, 36(12): 98 − 105. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.12.0696
[7]	Goto Y. Cracks formed in concrete around deformed tension bars [J]. ACI Journal, 1971, 68(4): 244 − 251.
[8]	Tepfers R. Cracking of concrete cover along anchored deformed reingorced bars [J]. Magazine of Concrete Research, 1979, 31(106): 3 − 12. doi: 10.1680/macr.1979.31.106.3
[9]	Nielsen C V, Bicanic N. Radial fictitious cracking of thick-walled cylinder due to bar pull-out [J]. Magazine of Concrete Research, 2002, 54(3): 215 − 221. doi: 10.1680/macr.2002.54.3.215
[10]	Hillerborg A, Modeer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements [J]. Cement & Concrete Research, 1976, 6(6): 773 − 781.
[11]	Cattaneo S, Rosati G. Bond between steel and self-consolidating concrete: Experiments and modeling [J]. Aci Structural Journal, 2009, 106(4): 540 − 550.
[12]	Den Uijl J A, Bigaj A J. A bond model for ribbed bars based on concrete confinement [J]. Heron, 1996, 41(3): 201 − 226.
[13]	Wang X, Liu X. A strain-softening model for steel-concrete bond [J]. Cement & Concrete Research, 2003, 33(10): 1669 − 1673.
[14]	Esfahani M R, Kianoush M R. Development / splice length of reinforcing bars [J]. ACI Structural Journal, 2005, 102(1): 22 − 30.
[15]	GB 50152−92, 混凝土结构试验方法标准[S]. 北京: 中国建筑工业出版社, 1992. GB 50152−92, Standard for test methods of concrete structures [S]. Beijing: China Architecture & Building Press, 1992. (in Chinese)
[16]	赵均海, 汪梦甫. 弹性力学及有限元[M]. 武汉: 武汉理工大学出版社, 2008. Zhao Junhai, Wang Mengfu. Elastic mechanics and finite element method [M]. Wuhan: Wuhan University of Technology Press, 2008. (in Chinese)
[17]	Bazant Z P, Oh B H. Crack band theory for fracture of concrete [J]. Materiaux et Constructions (RILEM), 1983, 16(93): 155 − 177.
[18]	徐世烺. 混凝土断裂力学[M]. 北京: 科学出版社, 2011. Xu Shilang. Fracture mechanics of concrete [M]. Beijing: Science Press, 2011. (in Chinese)
[19]	Xu F, Wu Z, Li W, et al. Analytical bond strength of deformed bars in concrete due to splitting failure [J]. Materials and Structures, 2018, 51(139): 1 − 14.
[20]	过镇海. 钢筋混凝土原理[M]. 北京: 清华大学出版社, 2013. Guo Zhenhai. Reinforced concrete theory [M]. Beijing: Tsinghua University Press, 2013. (in Chinese)
[21]	Xu Q Y, Wang J F, Ding Z D, et al. Experimental investigation and analysis on anchorage performance of 635 MPa hot-rolled ribbed high strength rebars [J]. Structures, 2021, 30: 574 − 584. doi: 10.1016/j.istruc.2020.12.081