基于倒角处拉应变的玄武岩纤维约束矩形截面混凝土轴压峰值应力计算模型

刘小方; 段昕智; 欧阳利军

doi:10.13801/j.cnki.fhclxb.20220930.001

基于倒角处拉应变的玄武岩纤维约束矩形截面混凝土轴压峰值应力计算模型

doi: 10.13801/j.cnki.fhclxb.20220930.001

刘小方^{1, 2},
段昕智^{1, 2},
欧阳利军^3, ,

1.
上海市市政规划设计研究院有限公司，上海 200031
2.
上海城市路域生态工程技术研究中心，上海201418
3.
上海理工大学　环境与建筑学院，上海 200093

基金项目: 桥隧工程系列超高性能混凝土技术研究(CTKY-ZDXM-2018-003)；国家自然科学基金(51708349)

详细信息

通讯作者:
欧阳利军，博士，副教授，硕士生导师，研究方向为工程结构加固理论和复合材料在土木工程中的应用　E-mail: ouyang@usst.edu.cn

中图分类号: TB332
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- 文章访问数: 561
- HTML全文浏览量: 204
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-31
- 修回日期: 2022-08-30
- 录用日期: 2022-09-04
- 网络出版日期: 2022-10-08
- 刊出日期: 2022-11-01

Axial ultimate compressive stress model of BFRP-confined rectangular concrete based on tensile strain at rounded corners

LIU Xiaofang^{1, 2},
DUAN Xinzhi^{1, 2},
OUYANG Lijun^{3
, ,}

1.
Shanghai Municipal Engineering Design Institute (Group) CO., LTD., Shanghai 200031, China
2.
Shanghai Urban Road Area Ecological Engineering Technology Research Center, Shanghai 201418, China
3.
School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China

Funds: Research on ultra-high performance concrete technology of bridge and tunnel engineering series (CTKY-ZDXM-2018-003); National Natural Science Foundation of China (51708349)

摘要

摘要: 对54个玄武岩纤维增强树脂基复合材料(BFRP)约束的矩形截面混凝土试件进行了轴压试验，探究了BFRP约束层数、倒角半径和截面长宽比对BFRP拉应变折减系数的影响规律。试验结果表明，依据矩形截面侧边拉应变和环向平均拉应变确定的BFRP拉应变折减系数会高估BFRP的约束效率。基于BFRP约束矩形截面混凝土时倒角处的纤维拉应变，建议了BFRP拉应变折减系数的计算方法，同时依据该计算方法和试验数据，通过构建柱状膜结构静水压力平衡模型建立了BFRP约束矩形截面混凝土轴压峰值应力计算模型。基于收集的大量试验数据，对比分析了本文建议的纤维增强树脂基复合材料(FRP)约束矩形截面混凝土轴压峰值应力计算模型和典型轴压峰值应力计算模型的预测结果，验证了典型计算模型的合理性，发现本文建议的FRP约束矩形截面混凝土轴压峰值应力计算模型的预测精度较高。
- 玄武岩纤维 /
- 混凝土 /
- 轴压性能 /
- 峰值应力 /
- 拉应变折减系数
Abstract: This paper presents an experimental study on the axial compressive behavior of 54 rectangular prisms confined with basalt fiber-reinforced polymer (BFRP). The influences of the BFRP layers, corner radius and aspect ratio on the tensile strain reduction factors of BFRP were investigated. The test results show that the tensile strain reduction factors calculated based on tensile strains in sides and average tensile strain of lateral BFRP sheets will overestimate confinement efficiency. Based on tensile strains at the corners, a computing method of tensile strain reduction factors of BFRP sheets was proposed. According to the proposed computing method of tensile strain reduction factors and experimental data in this paper, the hydrostatic pressure balance equation of the cylindrical BFRP membrane was used to build an axial ultimate compressive stress model of BFRP-confined rectangular concrete. Based on a large collection of test data, predicted results of the proposed model and the existing typical models were compared and analyzed. The rationality of the existing typical models was verified. The prediction accuracy of the proposed axial ultimate compressive stress model is higher than the existing typical models.
- basalt fiber /
- concrete /
- axial compressive behavior /
- ultimate stress /
- tensile strain reduction factor

HTML全文

图 1 玄武岩纤维增强树脂基复合材料(BFRP)约束后的矩形截面混凝土试件

b—Width; h—Height; R—Corner radius

Figure 1. Concrete prisms confined with basalt fiber-reinforced polymer (BFRP) sheets

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图 2 试件修复和加固过程

Figure 2. Repairing and wrapping process of specimens

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图 3 应变片布置

R1, T1, M1, M2, T2 and R2—Number of FRP strain measuring points

Figure 3. Strain gauges arrangement

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图 4 位移计布置

Figure 4. Displacement meters arrangement

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图 5 BFRP约束混凝土试件破坏形态

Figure 5. Failure modes of specimens confined with BFRP

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图 6 BFRP约束矩形截面混凝土约束层数-拉应变折减系数关系曲线

Figure 6. BFRP layers-strain reduction factor curves for rectangular sections concrete confined with BFRP

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图 7 BFRP约束矩形截面混凝土倒角半径-拉应变折减系数关系曲线

Figure 7. Corner radius-BFRP strain reduction factor curves for rectangular sections concrete confined with BFRP

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图 8 BFRP约束矩形截面混凝土倒角半径率-拉应变折减系数$k_{\text{εcr}}$关系曲线

Figure 8. Corner radius ratio-BFRP strain reduction factor $k_{\text{εcr}} $ curves for rectangular sections concrete confined with BFRP

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图 9 BFRP约束矩形截面混凝土长宽比-拉应变折减系数关系曲线

Figure 9. Aspect ratio-BFRP strain reduction factor curves for rectangular sections concrete confined with BFRP

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图 10 BFRP约束矩形截面混凝土不同倒角半径试件截面纤维布侧向应变分布

Figure 10. Distribution of FRP lateral strains of specimens with different corner radii for rectangular sections concrete confined with BFRP

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图 11 BFRP约束矩形截面混凝土不同长宽比试件截面纤维布侧向应变分布

Figure 11. Distribution of FRP lateral strains of specimens with different aspect ratios for rectangular sections concrete confined with BFRP

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图 12 BFRP约束矩形截面时有效约束区域

Figure 12. Effective confinement region in rectangular section confined with BFRP

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图 13 BFRP拉应变折减系数拟合曲线

A—Variate for tensile strain reduction factor of BFRP

Figure 13. Fitted curve of strain reduction factors of BFRP

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图 14 倒角处BFRP微截面张力平衡模型

Figure 14. Micro tension equilibrium model of FRP rounded corners

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图 15 BFRP约束矩形截面混凝土轴压峰值应力拟合曲线

f_cc—Ultimate stress of confined concrete; f_co—Ultimate stress of unconfined concrete; f_l,e—Effective confinement stress

Figure 15. Fitted curve of axial ultimate stress for rectangular sections concrete confined with BFRP

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图 16 FRP约束矩形截面混凝土轴压典型峰值应力计算模型预测值与试验值对比

Figure 16. Comparison of results predicted by typical axial ultimate compressive stress models and test results for rectangular sections concrete confined with FRP

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图 17 选取的FRP约束矩形截面混凝土轴压典型峰值应力计算模型预测效果比较

Figure 17. Prediction performance comparison of selected axial ultimate compressive stress models for rectangular sections concrete confined with FRP

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表 1 试件基本参数

Table 1. Details of specimens

Corner radius/mm	Number of confinement layer	Section dimension/mm (Aspect ratio)
Corner radius/mm	Number of confinement layer	100×100 (1.0)	83×124.5 (1.5)	75×150 (2.0)
20	3	A10 R20 L3-1	A15 R20 L3-1	A20 R20 L3-1
		A10 R20 L3-2	A15 R20 L3-2	A20 R20 L3-2
		A10 R20 L3-3	A15 R20 L3-3	A20 R20 L3-3
	4	A10 R20 L4-1	A15 R20 L4-1	A20 R20 L4-1
		A10 R20 L4-2	A15 R20 L4-2	A20 R20 L4-2
		A10 R20 L4-3	A15 R20 L4-3	A20 R20 L4-3
	5	A10 R20 L5-1	A15 R20 L5-1	A20 R20 L5-1
		A10 R20 L5-2	A15 R20 L5-2	A20 R20 L5-2
		A10 R20 L5-3	A15 R20 L5-3	A20 R20 L5-3
30	3	A10 R30 L3-1	A15 R30 L3-1	A20 R30 L3-1
		A10 R30 L3-2	A15 R30 L3-2	A20 R30 L3-2
		A10 R30 L3-3	A15 R30 L3-3	A20 R30 L3-3
	4	A10 R30 L4-1	A15 R30 L4-1	A20 R30 L4-1
		A10 R30 L4-2	A15 R30 L4-2	A20 R30 L4-2
		A10 R30 L4-3	A15 R30 L4-3	A20 R30 L4-3
	5	A10 R30 L5-1	A15 R30 L5-1	A20 R30 L5-1
		A10 R30 L5-2	A15 R30 L5-2	A20 R30 L5-2
		A10 R30 L5-3	A15 R30 L5-3	A20 R30 L5-3
Notes：Number following letter A represents aspect ratio; Number following letter R represents corner radius; Number following letter L represents FRP layers; The last number represents sequence number of specimens with same condition.

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表 2 BFRP力学性能

Table 2. Mechanical properties of BFRP

Type	Ultimate tensile stress/MPa	Elastic modulus/GPa	Ultimate tensile strain/%	Thickness /mm	Density /(g·m⁻²)
BF3300	2303	105	2.18	0.121	341

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表 3 混凝土配合比

Table 3. Proportions of concrete mix

Strength grade of concrete	Sand ratio	Amount of each composition/(kg·m⁻³)
Strength grade of concrete	Sand ratio	Cement	Gravel	Sand	Water
C40	0.32	451	1206	568	185

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表 4 BFRP约束矩形截面混凝土轴压试验结果

Table 4. Test results of rectangular sections concrete confined with BFRP

Specimen	f_cc/MPa	ε_cu	R1	T1	M1	M2	T2	R2	ε_h,max
A10 R20 L3-1	61.72	0.01416	–	0.02074	0.01657	0.01678	0.01753	0.01417	0.02074
A10 R20 L3-2	60.03	0.01348	0.01352	0.01731	0.01744	0.01679	0.01731	0.01308	0.01744
A10 R20 L3-3	60.23	0.01368	0.01352	0.01709	0.01635	–	0.01043	0.01330	0.01709
A10 R20 L4-1	69.15	0.01654	–	0.01992	0.01591	0.01635	0.01788	0.01308	0.01992
A10 R20 L4-2	71.60	0.01923	0.01308	0.01709	0.01679	0.01657	0.01809	0.01373	0.01809
A10 R20 L4-3	67.18	0.01586	0.01264	–	0.01635	0.01613	0.01788	0.01308	0.01788
A10 R20 L5-1	79.02	0.02265	0.01308	0.01684	0.01635	0.01613	–	0.01330	0.01684
A10 R20 L5-2	78.55	0.02024	0.01264	0.01666	0.01591	0.01570	0.01688	0.01243	0.01688
A10 R20 L5-3	77.93	0.01944	0.01221	0.01644	0.01548	–	0.01666	0.01221	0.01666
A10 R30 L3-1	65.44	0.01511	0.01395	0.01709	–	0.01657	0.01731	0.01373	0.01731
A10 R30 L3-2	66.18	0.01612	0.01439	0.01753	0.01722	0.01766	0.02071	–	0.02071
A10 R30 L3-3	65.91	0.01551	0.01352	0.01731	0.01679	0.01679	0.01731	0.01417	0.01731
A10 R30 L4-1	77.79	0.01991	0.01373	0.01709	0.01635	0.01635	0.01734	0.01308	0.01734
A10 R30 L4-2	76.57	0.01865	0.01330	0.01688	0.01657	0.01613	0.01709	0.01373	0.01709
A10 R30 L4-3	78.57	0.02043	-	0.02017	0.01679	0.01722	0.01784	0.01373	0.02017
A10 R30 L5-1	87.43	0.02315	0.01264	–	0.01570	0.01591	0.01662	0.01308	0.01662
A10 R30 L5-2	87.81	0.02394	0.01308	0.01709	0.01657	0.01657	–	0.01352	0.01709
A10 R30 L5-3	86.92	0.02324	0.01286	0.01667	0.01613	0.01591	0.01666	0.01330	0.01667
A15 R20 L3-1	53.64	0.01186	0.01134	0.01453	0.01384	0.01809	0.01853	0.01155	0.01853
A15 R20 L3-2	53.47	0.01153	–	0.00050	0.01384	0.01788	0.01831	0.01134	0.01831
A15 R20 L3-3	51.94	0.01099	–	0.00513	0.01367	0.01766	0.01809	0.01112	0.01809
A15 R20 L4-1	60.96	0.01394	0.01112	0.01385	0.01341	0.01744	0.01833	0.01090	0.01833
A15 R20 L4-2	61.73	0.01426	0.01134	0.01509	0.01363	0.01766	0.01809	–	0.01809
A15 R20 L4-3	60.20	0.01387	0.01090	0.01466	0.01319	0.01722	0.01788	0.01046	0.01788
A15 R20 L5-1	67.11	0.01661	0.01068	0.01365	0.01297	0.01657	0.01744	0.01090	0.01744
A15 R20 L5-2	66.27	0.01623	0.01003	0.01344	0.01275	0.01744	0.01788	0.01025	0.01788
A15 R20 L5-3	68.80	0.01696	0.01003	0.01449	0.01319	–	0.01766	0.01090	0.01766
A15 R30 L3-1	60.34	0.01317	0.01330	0.01431	0.01417	–	0.02093	–	0.02093
A15 R30 L3-2	57.97	0.01234	0.01243	0.01388	0.01330	0.01744	0.01809	0.01264	0.01809
A15 R30 L3-3	58.36	0.01283	0.01286	0.01389	–	0.01788	0.01831	0.01308	0.01831
A15 R30 L4-1	67.34	0.01586	0.01177	0.01382	0.01330	0.01722	0.01809	0.01286	0.01809
A15 R30 L4-2	69.45	0.01614	0.01199	0.01409	0.01373	0.01766	0.02071	–	0.02071
A15 R30 L4-3	66.43	0.01531	0.01155	0.01379	0.01286	0.01679	–	0.01243	0.01679
A15 R30 L5-1	74.62	0.01852	0.01068	0.01343	0.01264	0.01657	0.02093	–	0.02093
A15 R30 L5-2	75.07	0.01886	0.01155	0.01365	0.01286	0.01679	0.01744	0.01199	0.01744
A15 R30 L5-3	76.57	0.01899	0.01177	–	0.01308	0.01700	0.01766	0.01243	0.01766
A20 R20 L3-1	46.78	0.00916	0.00850	0.01309	0.01210	–	–	0.00828	0.01309
A20 R20 L3-2	47.81	0.01013	0.00916	0.01331	0.01232	0.02027	0.01831	0.00872	0.02027
A20 R20 L3-3	47.90	0.01016	0.00916	0.01331	0.01254	0.01984	0.02071	–	0.02071
A20 R20 L4-1	55.54	0.01211	0.00850	0.01309	0.01210	0.02006	0.02049	–	0.02049
A20 R20 L4-2	52.03	0.01123	0.00763	0.01309	0.01166	0.01918	0.01809	0.00828	0.01918
A20 R20 L4-3	52.44	0.01169	–	0.02027	0.01188	0.01962	0.01809	0.00872	0.02027
A20 R20 L5-1	58.08	0.01331	0.00719	–	0.01101	0.01875	0.01831	0.00763	0.01875
A20 R20 L5-2	58.98	0.01353	0.00763	0.01231	–	0.01962	0.02115	–	0.02115
A20 R20 L5-3	59.28	0.01389	0.00807	0.01253	0.01188	–	0.01875	0.00850	0.01875
A20 R30 L3-1	50.90	0.01055	0.01068	0.01253	0.01247	–	0.01809	0.01112	0.01809
A20 R30 L3-2	52.16	0.01123	–	0.02049	0.01269	0.02049	0.01875	0.01134	0.02049
A20 R30 L3-3	50.09	0.01014	0.01068	0.01231	0.01225	0.02006	0.01862	0.01090	0.02006
A20 R30 L4-1	58.47	0.01316	0.01046	0.01209	0.01225	0.02006	–	0.01090	0.02006
A20 R30 L4-2	57.54	0.01248	0.01003	0.01166	0.01182	0.01962	0.01809	0.01046	0.01962
A20 R30 L4-3	58.08	0.01294	0.01025	0.01388	0.01203	0.01984	0.02093	–	0.02093
A20 R30 L5-1	63.73	0.01467	–	0.02115	0.01094	0.01875	0.01744	0.00894	0.02115
A20 R30 L5-2	68.55	0.01573	0.01025	–	0.01203	0.01984	0.01809	0.01003	0.01984
A20 R30 L5-3	64.73	0.01493	0.01068	0.01166	0.01182	0.01962	0.01766	0.00981	0.01962
Notes: f_cc—Ultimate stress; ε_cu—Ultimate strain; ε_h,max—Maximal strain of FRP.

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