超高性能纤维增强混凝土单轴本构关系和钢纤维增强作用对其影响

邓金岚; 杨简; 陈宝春; 徐港; 李洋

doi:10.13801/j.cnki.fhclxb.20230613.001

超高性能纤维增强混凝土单轴本构关系和钢纤维增强作用对其影响

doi: 10.13801/j.cnki.fhclxb.20230613.001

邓金岚^{1, 2},
杨简^{1, 2, ,},
陈宝春^{3, 4},
徐港^{1, 2},
李洋^{1, 2}

1.
三峡大学　防灾减灾湖北省重点实验室，宜昌 443002
2.
三峡大学　土木与建筑学院，宜昌 443002
3.
福建理工大学　土木工程学院，福州 350118
4.
福州大学　土木工程学院，福州 350108

基金项目: 磷石膏基高性能水泥基材料制备研究(2022 KJZ09)；基于声发射特征的轻质超高性能混凝土单轴损伤本构关系研究(291219)；国家级地方高校能源和环境材料化学学科创新引智基地(D20015)；土木工程防灾减灾湖北省引智创新示范基地(2021 EJD026)

详细信息

通讯作者:
杨简，博士，讲师，硕士生导师，研究方向为超高性能混凝土、固废资源化利用和钢管节点　E-mail: 845175145@qq.com

中图分类号: TU528.31；TB332
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出版历程
- 收稿日期: 2023-04-17
- 修回日期: 2023-05-25
- 录用日期: 2023-05-26
- 网络出版日期: 2023-06-13
- 刊出日期: 2024-02-01

Uniaxial constitutive relation of ultra-high performance fiber reinforced concrete and the effect of steel fiber reinforcement on it

DENG Jinlan^{1, 2},
YANG Jian^{1, 2
, ,},
CHEN Baochun^{3, 4},
XU Gang^{1, 2},
LI Yang^{1, 2}

1.
Hubei Key Laboratory of Disaster Prevention and Mitigation, China Three Gorges University, Yichang 443002, China
2.
College of Civil Engineering & Architecture, China Three Gorges University, Yichang 443002, China
3.
College of Civil Engineering, Fujian University of Technology, Fuzhou 350118, China
4.
College of Civil Engineering, Fuzhou University, Fuzhou 350108, China

Funds: Research on Phosphogypsum-based High-performance Cement-based Materials (2022 KJZ09); Research on Uniaxial Damage Constitutive Relation of Lightweight Ultra-high Performance Concrete Based on Acoustic Emission Characteristics (291219); The 111 Project of China (D20015); The 111 Project of Hubei Province (2021 EJD026)

摘要

摘要: 超高性能纤维增强混凝土的单轴本构关系是认识其材料特性和非线性结构设计的基础。本文从本构方程函数模型建立的角度梳理了现有超高性能纤维增强混凝土单轴本构关系的相关研究；发现本构关系经验模型适用于结构设计计算，其中轴拉和轴压本构方程式均宜采用有理分式；本构关系简化模型适用于简化受力分析和数值模拟，其中轴拉宜采用三折线模型，轴压宜采用双折线模型；本构关系损伤模型适用于材料特性研究，其损伤演化函数较多采用Weibull分布。此外，还发现现有各种研究所得的本构方程中均不包含纤维相关参数，不能充分体现钢纤维的重要影响。因此，针对3种长径比、6种体积率的超高性能纤维增强混凝土进行轴拉和轴压试验，分析纤维对本构关系的影响。结果表明：超高性能纤维增强混凝土的轴拉和轴压本构关系经验模型均采用有理分式更适合，结合试验与收集的文献数据分析了纤维对经验模型本构方程系数的影响，提出了单轴本构关系经验模型的方程式；还探究了钢纤维参数对单轴损伤本构关系的影响，试验结果表明，钢纤维增强因子与损伤模型的控制系数间存在较强相关性，以试验数据为基础，数值分析得到钢纤维参数与本构方程控制系数间的关系式，进而提出包含钢纤维参数的轴拉和轴压损伤本构方程；并收集文献数据进行验证和修正，结果表明本文提出的本构方程与试验结果更吻合。
- 超高性能纤维增强混凝土 /
- 本构关系 /
- 轴拉 /
- 轴压 /
- 钢纤维 /
- 体积率 /
- 长径比
Abstract: The uniaxial constitutive relation of ultra-high performance fiber reinforced concrete (UHPFRC) is the basis for under-standing its material properties and nonlinear structural design. From the perspective of the constitutive equation function model, this paper reviews the existing research on the uniaxial constitutive relationship of UHPFRC. It was found that the empirical model of constitutive relation is suitable for structural design calculation, and the constitutive equations of uniaxial tension and compression should adopt rational fractions. The simplified model of constitutive relation is suitable for simplified force analysis and numerical simulation. The three-fold line model is suitable for uniaxial tension, and the double-fold line model is suitable for uniaxial compression. The damage model of constitutive relation is suitable for the study of material properties, and the damage evolution function is mostly Weibull distribution. In addition, it is found that the constitutive equations obtained by various existing studies do not contain fiber parameters, which cannot fully reflect the influence of steel fibers. Therefore, uniaxial tension and compression tests were carried out on UHPFRC with three aspect ratios and six volume fractions to analyze the influence of fibers on the constitutive relationship. The results show that the rational fraction is more suitable for the empirical model function of the uniaxial tension and compression constitutive model of UHPFRC. Combined with the test and the collected literature data, the influence of fiber on the coefficient of the empirical model equation was analyzed, and the equation of the empirical model of the uniaxial constitutive relationship was proposed. The influence of steel fiber parameters on the uniaxial damage constitutive relation was also explored. The experimental results show that there is a strong correlation between the steel fiber enhancement factor and the control coefficient of the damage model. Based on the experimental data, the relationship between the parameters of steel fiber and the control coefficient of constitutive equation is obtained by numerical analysis, and then the damage constitutive equations of uniaxial tension and compression including steel fiber variables are proposed. The literature data are collected for verification and correction, indicating that the constitutive relation proposed in this paper is in better agreement with the experimental results.
- ultra-high performance fiber reinforced concrete /
- constitutive relation /
- uniaxial tension /
- uniaxial compression /
- steel fiber /
- volume fraction /
- aspect ratio

HTML全文

图 1 不同长径比的钢纤维

Figure 1. Steel fibers with different aspect ratios

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图 2 试验装置示意图

Figure 2. Diagram of test device

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图 3 UHPFRC轴拉应力-应变曲线

Figure 3. Uniaxial tensile stress-strain curves of UHPFRC

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图 4 UHPFRC轴压应力-应变曲线

Figure 4. Uniaxial compressive stress-strain curves of UHPFRC

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图 5 UHPFRC轴拉本构曲线^{[13-14, 47, 71-82]}

A—Undetermined coefficient

Figure 5. Uniaxial tension constitutive curves of UHPFRC^{[13-14, 47, 71-82]}

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图 6 经验模型的判定系数R²

Figure 6. Determination coefficient R² of empirical model

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图 7 UHPFRC轴拉本构方程控制系数η与纤维增强因子K关系

Figure 7. Relationship between control coefficient η of uniaxial tension constitutive equation and fiber reinforcement factor K of UHPFRC

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图 8 UHPFRC抗拉本构模型与试验数据对比

Figure 8. Comparison between tensile constitutive model and test data of UHPFRC

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图 9 UHPFRC轴压本构方程控制系数与纤维增强因子关系^{[26, 35, 50, 84-95]}

Figure 9. Relationship between control coefficient of uniaxial compression constitutive equation and fiber reinforcement factor of UHPFRC^{[26, 35, 50, 84-95]}

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图 10 UHPFRC抗压本构模型与试验数据对比

Figure 10. Comparison between compressive constitutive model and test data of UHPFRC

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表 1 超高性能纤维增强混凝土(UHPFRC)配合比(质量比)

Table 1. Mix proportion of ultra-high performance fiber reinforced concrete (UHPFRC)(Mass ratio)

Aggregate				Binding material		Superplasticizer
0.212-0.428 mm	0.428-0.850 mm	0.850-1.700 mm	0.038 mm	Cement	Silica fume	Superplasticizer
0.14	0.41	0.53	0.09	1	0.3	0.025

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表 2 A组和B组试验方案

Table 2. Test scheme of group A and group B

Test group	Specimen	Steel fiber volume fraction/vol%	Steel fiber aspect ratio	Test group	Specimen	Steel fiber volume fraction/vol%	Steel fiber aspect ratio
A	C-S0313-1.0vol%	1.0	43	B	T-S0313-3.0vol%	3.0	43
	C-S0313-2.0vol%	2.0	43		T-S0213-0.5vol%	0.5	65
	C-S0313-3.0vol%	3.0	43		T-S0213-1.0vol%	1.0	65
	C-S0213-1.0vol%	1.0	65		T-S0213-1.5vol%	1.5	65
	C-S0213-2.0vol%	2.0	65		T-S0213-2.0vol%	2.0	65
	C-S0213-3.0vol%	3.0	65		T-S0213-2.5vol%	2.5	65
	C-S0220-1.0vol%	1.0	100		T-S0213-3.0vol%	3.0	65
	C-S0220-2.0vol%	2.0	100		T-S0220-0.5vol%	0.5	100
	C-S0220-3.0vol%	3.0	100		T-S0220-1.0vol%	1.0	100
B	T-S0313-0.5vol%	0.5	43		T-S0220-1.5vol%	1.5	100
	T-S0313-1.0vol%	1.0	43		T-S0220-2.0vol%	2.0	100
	T-S0313-1.5vol%	1.5	43		T-S0220-2.5vol%	2.5	100
	T-S0313-2.0vol%	2.0	43		T-S0220-3.0vol%	3.0	100
	T-S0313-2.5vol%	2.5	43
Notes: C—Uniaxial compression test; T—Uniaxial tension test; S0313—Diameter of steel fiber is 0.30 mm and the length is 13 mm; S0213—Diameter of steel fiber is 0.20 mm and the length is 13 mm; S0220—Diameter of steel fiber is 0.20 mm and the length is 20 mm.

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表 3 A值($ A = {E_0}/{E_{\text{c}}} $)的取值范围

Table 3. Value range of A ($ A = {E_0}/{E_{\text{c}}} $)

Function form	Ref.	A value range
Tertiary polynomial	[19]	1.5<A<3
Quartic polynomial	[24]	1.33<A<2.67
Quintic polynomial	[26-27]	1<A<1.67
Sextic polynomial	[22]	1<A<1.5
Rational fraction	[34]	1<A
Notes: E₀—Initial modulus of elasticity; E_c—Secant modulus.

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