Cyclic compression test and stress-strain constitutive relationship of polypropylene fiber coral seawater concrete
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摘要: 为研究聚丙烯纤维珊瑚海水混凝土(PPF/CAC)在循环受压荷载作用下的力学行为，以聚丙烯纤维体积分数和加载方式为变化参数，设计了20个圆柱体试件进行单轴受压以及单轴循环受压试验。试验观察了PPF/CAC的破坏形态，获取了应力-应变全曲线及峰值应力应变、塑性应变等重要指标，深入分析了PPF/CAC在单轴循环受压作用下的应力-应变行为和损伤演化。结果表明：与单调加载相比，循环加载试件的强度退化了1.21%~3.67%，聚丙烯纤维能有效延缓强度退化；聚丙烯纤维体积分数为0.15%时珊瑚混凝土的峰值应力和峰值应变增幅最大，分别为10.45%和6.45%，改性效果最好；此外，聚丙烯纤维体积分数的增加可显著降低塑性应变的积累，提高弹性刚度比。本文根据试验结果定义了滞回曲线的四个特征点：卸载点、公共点、残余点和终点，并建立了残余应变、公共点应变和终点应变与卸载应变的关系。最后，提出了PPF/CAC在循环荷载作用下的应力-应变本构方程和损伤本构模型，且基于损伤演化规律简化后的应力-应变本构方程可以有效地预测其在循环荷载作用下的应力-应变行为。Abstract: The stress-strain characteristics and damage evolution of polypropylene fiber coral seawater concrete (PPF/CAC) under uniaxial cyclic compression were studied. A total of 20 samples with different fiber volume fractions were tested. The failure form of PPF/CAC was observed in the test, and the stress-strain curve, peak stress-strain, plastic strain and other important indexes were obtained. The results show that the strength of specimens under cyclic loading is reduces by 1.21%-3.67% compared with that under monochrome loading, and the degradation can be slowed down with the increase of fiber content. The peak stress and peak strain increases are the largest when the polypropylene fiber volume fraction is 0.15%, which are 10.45% and 6.45%, respectively. In addition, the increase of PPF volume fraction can significantly reduce the accumulation of plastic strain and increase the elastic stiffness ratio. According to the test results, four characteristic points of hysteresis curve are defined: unloading point, common point, residual point and end point. And the relationship between residual strain, common point strain and end point strain and unloading strain is established. Finally, the stress-strain constitutive equation and damage constitutive model of PPF/CAC under cyclic load are proposed, and the simplified stress-strain constitutive equation based on the damage evolution law can effectively predict the stress-strain behavior of PPF/CAC under cyclic load.
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Key words:
- polypropylene fiber /
- coral sea concrete /
- cyclic compression /
- stress-strain /
- constitutive equation
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图 9 每组PPF/CAC试件平均应力-应变曲线
Figure 9. Average stress-strain curve of each group of PPF/CAC specimens
图 10 PPF/CAC循环受压全过程示意图
Figure 10. The whole process diagram of PPF/CAC specimen under cyclic compression
图 14 PPF/CAC试件残余应变xp与卸载应变xu关系
Figure 14. Relation between residual strain xp and unloading strain xu of PPF/CAC specimens
图 15 PPF/CAC试件公共点应变xc与残余应变xu的关系
Figure 15. Relationship between common point strain xc and residual strain xu of PPF/CAC specimens
图 16 PPF/CAC试件终点应变xe与残余应变xu的关系
Figure 16. Relationship between terminal strain xe and residual strain xu of PPF/CAC specimens
图 17 PPF/CAC归一化应力-应变曲线及模型验证
Figure 17. Normalized stress-strain curves of PPF/CAC and model validation
图 18 PPF/CAC试件在循环加载下的损伤指数变化
Figure 18. Change of damage index of PPF/CAC specimens under cyclic loading
图 19 PPF/CAC试件损伤指数df的拟合结果
Figure 19. Fitting result of damage index df of PPF/CAC specimens
表 1 试件配合比及设计参数(kg/m3)
Table 1. Sample fit ratio and design parameters
Specimen number Cement Coarse aggregate Fine aggregate Water water reducer VPPF/% 0%PPF/CAC 530 672 753 252 10.6 - 0.1%PPF/CAC 530 672 753 252 10.6 0.10 0.15%PPF/CAC 530 672 753 252 10.6 0.15 0.2%PPF/CAC 530 672 753 252 10.6 0.20 0.25%PPF/CAC 530 672 753 252 10.6 0.25 Notes: VPPF—Polypropylene fiber volume content. 
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表 2 珊瑚骨料的物理性能
Table 2. Mechanical and physical parameters of coral aggregate
Coral aggregate Bulk density /(kg·m−3) Performance density/(kg·m−3) Water content/% Water absorption/% 1 h 24 h Coarse aggregate 878 1846 2.3 8.5 9.6 Fine aggregate 1285 2701 2.4 3.45 3.70
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表 3 聚丙烯纤维基本物理性能
Table 3. Basic physical properties of polypropylene fibers
Physical property PPF Fiber appearance d/mm 0.048 
l/mm 19 Tensile strength/MPa ＞550 Density/(g·cm−3) 0.91 Elasticity modulus/GPa 6.5 Elongation at break/% 15 Notes: d—Diameter of fiber; l—Length of fiber.
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表 4 经典混凝土残余应变计算公式
Table 4. Residual strain calculation formula of classical concrete
Constitutive model name Residual strain formula Karsan[27] model $ {x_{\text{p}}} = 0.145 x_{\text{u}}^2 + 0.127{x_{\text{u}}} $ Bahn and Hsu[28] model $ {x_{\text{p}}} = {c_{\text{p}}}{({x_{\text{u}}})^{{n_{\text{p}}}}} $ Biao Li[16] Linear function model $ {x_{\text{p}}} = G{x_{\text{u}}} + H $ Notes: xp—Remanent strain; xu—Unloading strain; cp, np, G and H—Model parameter.
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表 5 第i次循环荷载下PPF/CAC试件的损伤指数
Table 5. Damage index of PPF/CAC specimens under i cycle load
Specimen df4 df5 df6 df7 df8 df9 df10 df11 df12 df13 df14 df15 0%PPF/CAC 0.350 0.556 0.645 0.723 0.759 0.796 0.815 0.834 0.856 0.867 0.881 0.892 0.1%PPF/CAC 0.310 0.471 0.568 0.642 0.671 0.739 0.761 0.784 0.802 0.811 0.825 0.821 0.15%PPF/CAC 0.287 0.416 0.526 0.597 0.637 0.671 0.710 0.725 0.746 0.759 0.774 0.789 0.2%PPF/CAC 0.243 0.364 0.468 0.544 0.576 0.624 0.655 0.667 0.686 0.714 0.725 0.736 0.25%PPF/CAC 0.184 0.302 0.390 0.446 0.513 0.570 0.627 0.656 0.667 0.700 0.703 0.704 Notes: The data in the table are the average values of the three specimens in each group, dfi—Damage index under i cycle load.
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