循环荷载作用下超高性能混凝土的轴拉力学性能及本构关系模型

杲晓龙; 王俊颜; 郭君渊; 刘超

doi:10.13801/j.cnki.fhclxb.20201218.002

循环荷载作用下超高性能混凝土的轴拉力学性能及本构关系模型

doi: 10.13801/j.cnki.fhclxb.20201218.002

杲晓龙^{1, 2,},
王俊颜^1, ,,
郭君渊^1,,
刘超^2,

1.
同济大学　先进土木工程材料教育部重点实验室，上海 201804
2.
同济大学　土木工程学院，上海 201804

基金项目: 浙江省交通运输厅科技计划项目(2019-GCKY-01)

详细信息

通讯作者:
王俊颜，博士，特聘研究员，博士生导师，研究方向为超高性能混凝土及其结构　 E-mail：14529@tongji.edu.cn

中图分类号: TU528
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出版历程
- 收稿日期: 2020-11-12
- 录用日期: 2020-12-08
- 网络出版日期: 2020-12-18
- 刊出日期: 2021-11-01

Axial tensile mechanical properties and constitutive relation model of ultra-high performance concrete under cyclic loading

GAO Xiaolong^{1, 2
,},
WANG Junyan^{1
, ,},
GUO Junyuan^1
,,
LIU Chao^2
,

1.
Key Laboratory of Advanced Civil Engineering Materials of the Ministry of Education, Tongji University, Shanghai 201804, China
2.
College of Civil Engineering, Tongji University, Shanghai 201804, China

摘要

摘要: 对具有不同拉伸应变特性(应变强化和应变软化)的超高性能混凝土(Ultra high performance concrete, UHPC)进行了单调和循环荷载作用下的直接拉伸试验。试验结果表明：应变强化UHPC基体开裂后进入多点微裂纹分布的应变强化段，达到极限抗拉强度后进入单缝开裂的应变软化段；应变软化UHPC基体开裂后直接进入单缝开裂的应变软化段；循环荷载下两种类型UHPC的轴拉应力-应变曲线包络线与单调荷载下的应力-应变曲线基本一致；基于刚度退化过程建立了两种类型UHPC的轴拉损伤演化方程，根据实测应力-应变曲线和试件的裂缝分布形态建立了两种类型UHPC的轴拉本构关系模型，与试验结果基本吻合；采用能量法研究了应变强化UHPC两阶段轴拉本构关系在数值计算时的等效方法。最后，通过无筋应变强化UHPC抗弯试验梁的数值模拟对本文建立的应变强化UHPC轴拉本构关系模型和损伤演化方程及相关假定进行了验证，结果表明本文建立的应变强化UHPC轴拉本构模型能较好地预测UHPC弯拉构件的极限承载力，轴拉损伤变量能在宏观层面上较好地反应试件的裂缝分布状态。
- 超高性能混凝土(UHPC) /
- 直接拉伸试验 /
- 循环荷载 /
- 轴拉本构模型 /
- 数值模拟
Abstract: The direct tensile tests under monotonic and cyclic loading were conducted on the ultra high performance concrete (UHPC) with different tensile strain characteristics (strain hardening and strain softening). The test results reflect that the strain hardening UHPC enters the stage of strain hardening with multi-point microcrack distribution after the cracking of UHPC matrix, and it enters the strain softening section with single seam cracking after reaching the ultimate tensile strength. The strain softening UHPC enters the strain softening stage with single seam crack after the cracking of UHPC matrix. The envelope of axial tensile stress-strain curves of the two types UHPC under cyclic load are generally consistent with that curves under monotonic load. Based on the stiffness degradation process, the axial tensile damage evolution equations of two types of UHPC were established. Based on the measured stress-strain curves and the crack distribution of the specimens, the axial tensile constitutive relation models of the two UHPCs were established. The test data are satisfactorily approximate to the proposed models. The equivalent method for the strain hardening UHPC with two-stage axial tensile constitutive relation in numerical calculation was studied by using energy method. Finally, the proposed axial tensile constitutive relation model and damage evolution equation of strain hardening UHPC were verified according to the numerical simulation of unreinforced strain strengthened UHPC flexural test beam. The results reveal that the proposed axial tensile constitutive model could precisely predict the ultimate bearing capacity of UHPC flexural-tensile members, and the axial tensile damage variables could generally reflect the crack distribution of the specimens.
- ultra high performance concrete(UHPC) /
- direct tensile test /
- cyclic loading /
- axial tensile constitutive model /
- numerical simulation

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图 1 UHPC轴拉试件

Figure 1. UHPC specimen for direct tensile test

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图 2 轴拉试验加载装置

Figure 2. Setup of direct tensile test

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图 3 循环试验加载制度

Figure 3. Cyclic loading procedures

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图 4 循环荷载条件下UHPC典型的轴拉应力-应变曲线

Figure 4. Typical axial tensile stress-strain curves of UHPC under cyclic load

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图 5 循环荷载条件下和单调荷载条件下UHPC轴拉应力-应变曲线对比

Figure 5. Comparison of axial tensile stress-strain curves of UHPC under cyclic and monotonic loading

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图 6 不同拉伸荷载阶段应变强化UHPC试件表面裂缝分布情况

Figure 6. Distribution of surface cracks for strain hardening UHPC specimens at different tensile loading stages

${\varepsilon _{\rm{t}}} $—Tensile strain

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图 7 不同拉伸荷载阶段应变软化UHPC试件表面裂缝分布情况

Figure 7. Distribution of surface cracks for strain softening UHPC specimens at different tensile loading stages

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图 8 UHPC轴拉损伤变量变化曲线

Figure 8. Variation curves of tensile damage variable of UHPC

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图 9 应变强化UHPC轴拉本构模型

Figure 9. Axial tension constitutive model for strain hardening UHPC

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图 10 应变强化UHPC试验曲线与模型曲线的对比

Figure 10. Comparison between test curve and model curve for strain hardening UHPC

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图 11 应变软化UHPC轴拉本构模型

Figure 11. Axial tension constitutive model for strain softening UHPC

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图 12 应变软化UHPC试验曲线与模型曲线的对比

Figure 12. Comparison between test curve and model curve for strain softening UHPC

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图 13 不同单元特征长度时UHPC有限元计算结果和本构关系曲线对比

Figure 13. Comparison between numerical simulation results and constitutive relation curves of UHPC with different element characteristic length

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图 14 应变强化UHPC拉伸过程中能量耗散模型

Figure 14. Energy dissipation model for strain hardening UHPC under direct tensile loading

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图 15 UHPC单元能量计算结果与真实解对比

Figure 15. Comparison of unite energy between calculation results and real solution of UHPC

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图 16 UHPC梁的加载装置和截面尺寸(Unit: mm)

Figure 16. Setup and section dimensions for UHPC beam (Unit: mm)

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图 17 UHPC梁的有限元模型

Figure 17. Finite element model for UHPC beam

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图 18 不同单元特征长度时UHPC梁荷载-跨中挠度曲线的有限元计算结果和试验对比

Figure 18. Comparison of load-span deflection curve between finite element calculation results and test results of UHPC beam with different element characteristic length

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图 19 UHPC梁破坏状态的有限元计算结果和试验结果的对比

Figure 19. Comparison of failure mode for UHPC beam between finite element calculation results and test results

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表 1 超高性能混凝土(UHPC)基体配合比(kg/m³)

Table 1. Mix proportions of ultra high performance concrete (UHPC) matrix(kg/m³)

Cement	Silica fume	Ground quartz	Quartz sand	Water	Superplasticizer
745	223.5	223.5	998.3	179.0	13.1

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表 2 钢纤维特征参数

Table 2. Properties of the steel fibres

Fiber shape	Tensile strength/MPa	Elastic modulus/GPa	Length/mm	Diameter/μm	Density/(kg·m⁻³)
Straight smooth	2500	200	16	200	7850

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表 3 两种类型UHPC的基本力学性能

Table 3. Basic mechanical properties of two types of UHPC

Specimen type	f_c/MPa (Cov)	E_c/GPa (Cov)
Strain softening UHPC	127.8 (0.032)	47.4 (0.031)
Strain hardening UHPC	135.2 (0.044)	48.9 (0.026)
Notes: f_c─Compressive strength; E_c─Elastic modulus.

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表 4 应变强化(SH)UHPC轴拉应力-应变曲线特征参数

Table 4. Characteristic parameters of axial tensile stress-strain curve of strain hardening (SH) UHPC

Specimen	Monotonic loading				Cyclic loading
Specimen	f_te/MPa	ε_te/10⁻⁴	f_tu/MPa	ε_tu/10⁻³	f_te/MPa	ε_te/10⁻⁴	f_tu/MPa	ε_tu/10⁻³
SH1	9.62	2.2	11.71	4.11	9.75	2.1	12.08	3.49
SH2	9.76	2.1	11.28	3.72	9.42	2.3	11.65	4.55
SH3	8.71	2.3	12.01	3.82	10.19	2.1	12.18	4.45
Mean	9.36	2.2	11.67	3.89	9.79	2.2	11.97	4.16
Cov	0.06	0.6	0.03	0.05	0.04	0.7	0.02	0.14
Notes: f_te─Elastic ultimate tensile strength; ε_te─Elastic ultimate tensile strain; f_tu─Ultimate tensile strength; ε_tu─Ultimate tensile strain.

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表 5 应变软化(SS)UHPC轴拉应力-应变曲线特征参数

Table 5. Characteristic parameters of axial tensile stress-strain curve of strain softening (SS) UHPC

Specimen	Monotonic loading				Cyclic loading
Specimen	f_te/MPa	ε_te/10⁻⁴	f_tee/MPa	f_tee/f_te	f_te/MPa	ε_te/10⁻⁴	f_tee/MPa	f_tee/f_te
SS1	9.09	2.2	8.45	0.93	9.01	2.4	8.32	0.92
SS2	9.28	2.8	8.83	0.95	8.69	2.2	8.52	0.98
SS3	9.47	2.2	−	−	9.47	3.1	8.51	0.89
Mean	9.28	2.4	8.64	0.94	9.06	2.6	8.45	0.93
Cov	0.02	1.6	0.03	0.02	0.04	1.9	0.01	0.04
Notes: f_tee─Equivalent tensile strength.

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表 6 UHPC轴拉损伤演化方程中的参数

Table 6. Parameters for the evolution equation of axial tensile damage of UHPC

	a₀	t₀	a₁	t₁	b
Strain hardening UHPC	0.1048	3.1381	0.8541	0.0739	−0.0118
Strain softening UHPC	0.2037	3.3832	0.8076	0.0763	−0.0162

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表 7 UHPC梁极限承载力的有限元计算和试验结果对比

Table 7. Comparison of ultimate bearing capacity between finite element calculation results and test results of UHPC beam

Beam	P_u,test/kN	P_u,FEA/kN	P_u,test/P_u,FEA
Numerical (10 mm)	127.23	131.27	0.97
Numerical (20 mm)	127.23	126.73	1.01
Numerical (30 mm)	127.23	120.81	1.05
Notes: P_u,test─Ultimate bearing capacity obtained from experiment results；P_u,FEA─Ultimate bearing capacity obtained from numerical simulation results.

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