Bond-slip constitutive relation between FRP bars and coral aggregate seawater concrete
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摘要: 纤维增强树脂复合材料(Fiber reinforced polymer，FRP)具有优良的抗腐蚀性能，用其代替普通钢筋能够很好地解决钢筋锈蚀问题。同时我国的珊瑚和海水资源丰富，用其代替传统砂石骨料是解决海岛建设中传统材料稀缺问题的有效方法之一。FRP筋与珊瑚骨料海水混凝土之间的粘结性能是决定其是否能像普通钢筋混凝土一样在实际工程中应用的重要因素之一。目前，关于FRP筋全珊瑚骨料海水混凝土结构的界面粘结性能研究很少，尤其是理论方面。于是，通过试验和数值模拟验证了简化双线性模型的合理性，并在此基础上推导了FRP筋全珊瑚骨料海水混凝土的界面粘结应力τ(x)和相对滑移量s(x)表达式，绘制了界面相对滑移和界面粘结应力的分布图。将采用表达式所得到的理论解与试验和模拟结果进行对比分析，其结果表明：通过理论计算所得的理论解与试验结果吻合度较高；FRP筋直径和粘结长度的增加会导致界面粘结应力和相对滑移的分布更加不均匀；珊瑚骨料混凝土强度的改变对界面粘结应力和相对滑移的分布影响不大；玻璃纤维增强树脂复合材料(GFRP)筋和玄武岩纤维增强树脂复合材料(BFRP)筋珊瑚骨料海水混凝土的界面粘结应力和相对滑移的分布相类似，与碳纤维增强树脂复合材料(CFRP)筋珊瑚骨料海水混凝土相比，前者的分布更加均匀。
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关键词:
- 全珊瑚骨料海水混凝土 /
- FRP筋 /
- 粘结性能 /
- 本构模型 /
- 理论计算方法
Abstract: Since fiber reinforced polymer (FRP) has excellent corrosion resistance, it can be used to replace ordi-nary steel bars to solve the problem of steel corrosion. Because of the abundant coral and seawater resources in China, using coral instead of traditional sand aggregate is one of the effective methods to solve the problem of scarcity of traditional materials in island construction. Bonding property between FRP bars and coral aggregate seawater concrete is one of the important factors to determine whether FRP reinforced coral aggregate seawater concrete structure can be applied in practical engineering like ordinary reinforced concrete structure. At present, there is little research on the interfacial bonding property of FRP reinforced coral aggregate seawater concrete structure, especially in theory. Therefore, the rationality of the simplified bilinear model will be verified by experiments and numerical simulation. Based on the experiments and numerical simulation, the expressions of interfacial bonding stress and relative slip of FRP reinforced coral aggregate seawater concrete will be derived, and then the distribution maps of interfacial bonding stress and relative slip will be plotted. The theoretical solution obtained by the expression will be compared with the experimental and numerical simulation solution. The results show that the theoretical solution obtained by theoretical calculation is in good agreement with the experimental results. The increase of FRP bar diameter and bonding length will lead to more non-uniform distribution of interfacial bonding stress and relative slip. The change of coral aggregate concrete strength has little effect on the distribution of interfacial bonding stress and relative slip. The interfacial bond stress and relative slip distribution of glass fiber reinforced polymer (GFRP) and basalt fiber reinforced polymer (BFRP) reinforced coral aggregate seawater concrete are similar, and are more uniform than that of carbon fiber reinforced polymer (CFRP) coral aggregate concrete. -
图 1 FRP筋全珊瑚骨料海水混凝土试件设计示意图
Figure 1. Schematic diagram of FRP reinforced full coral aggregate seawater concrete specimen design
PVC—Polyvinyl chloride
图 4 FRP筋全珊瑚骨料海水混凝土试件破坏形态
Figure 4. Failure mode of FRP reinforced full coral aggregate seawater concrete specimen
图 5 BFRP筋全珊瑚骨料海水混凝土试件的荷载-滑移曲线
Figure 5. Load-slip curves of BFRP reinforced full coral aggregate seawater concrete specimens
图 6 全珊瑚/骨料海水混凝土的真实应力-塑性应变曲线
Figure 6. True stress-plastic strain curve of full coral aggregate seawater concrete
图 7 FRP筋全珊瑚骨料海水混凝土结构的粘结滑移本构模型
Figure 7. Bond slip constitutive model of FRP reinforced full coral aggregate seawater concrete structure
K—Crack initiation bond stiffness; G—Interfacial fracture energy; τu—Bonding stress at the peak slip point; su—Slip value at the peak slip point
图 9 FRP筋与全珊瑚骨料海水混凝土界面单元应力云图
Figure 9. Stress nephogram of the interface element of FRP bars and full coral aggregate seawater concrete
图 10 FRP筋/全珊瑚骨料海水混凝土构件微分单元的受力状态
Figure 10. Force state of differential element of FRP reinforced full coral aggregate seawater concrete specimen
τ—Bonding stress; σf—Tensile stress of FRP bars; σc—Stress of coral concrete
图 11 FRP筋全珊瑚骨料海水混凝土界面粘结应力的分布
Figure 11. Distribution of bond stress at the interface between FRP bars and full coral aggregate seawater concrete
图 12 FRP筋全珊瑚骨料海水混凝土界面滑移的分布
Figure 12. Distribution of slip at the interface between FRP bars and full coral aggregate seawater concrete
表 1 纤维增强树脂复合材料(FRP)筋全珊瑚骨料海水混凝土构件参数
Table 1. Parameters of fiber reinforced polymer (FRP) reinforced full coral aggregate seawater concrete
Specimen number d/mm Fiber reinforced polymer (FRP) l/mm Coral concrete strength BFRP(d8)/C40-2.5d 8 BFRP 2.5d C40 BFRP(d8)/C40-5d 8 BFRP 5.0d C40 BFRP(d8)/C40-7.5d 8 BFRP 7.5d C40 BFRP(d10)/C40-2.5d 10 BFRP 2.5d C40 BFRP(d10)/C40-5d 10 BFRP 5.0d C40 BFRP(d10)/C40-7.5d 10 BFRP 7.5d C40 BFRP(d12)/C40-2.5d 12 BFRP 2.5d C40 BFRP(d12)/C40-7.5d 12 BFRP 7.5d C40 CFRP(d12)/C40-5d 12 CFRP 5.0d C40 BFRP(d12)/C40-5d 12 BFRP 5.0d C40 GFRP(d12)/C40-5d 12 GFRP 5.0d C40 BFRP(d12)/C30-5d 12 BFRP 5.0d C30 BFRP(d12)/C35-5d 12 BFRP 5.0d C35 Notes: d—Diameter of FRP bars; C—Coral concrete strength grade; l—Bond length; BFRP—Basalt fiber reinforced polymer; CFRP—Carbon fiber reinforced polymer; GFRP—Glass fiber reinforced polymer. 
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表 2 变形FRP筋材料性能参数
Table 2. Performance parameters of deformed FRP bars
Reinforcement
typeDiameter/
mmYield strength/
MPaStandard value of ultimate
strength/MPaElastic modulus/
GPaElongation/
%BFRP 12 – 1405 53.6 2.63 GFRP 12 – 1021 54.8 1.87 CFRP 12 – 1815 104.5 1.78
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表 3 人工海水化学成分(g/L)
Table 3. Chemical composition of artificial seawater (g/L)
NaCl MgCl2 Na2SO4 CaCl2 KCl NaHCO3 22.16 5.265 3.861 1.082 0.745 0.207
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表 4 全珊瑚骨料海水混凝土配合比设计
Table 4. Full coral aggregate seawater concrete mix design
Concrete
typeCement/
(kg·m−3)Coarse aggregate/
(kg·m−3)Fine aggregate/
(kg·m−3)Water consumption/
(kg·m−3)Water reducing
agent/(kg·m−3)28-day cube compressive
strength/MPaCoral concrete 540 560 710 220 7.5 41.2
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表 5 FRP筋全珊瑚骨料海水混凝土试件拉拔试验结果
Table 5. Drawing test results of FRP reinforced full coral aggregate seawater concrete specimen
Group
numberSpecimen
numberAverage value
of ultimate
load/kNUltimate load slip amount/mm Average value
of ultimate bond
strength/MPaFailure
modeLa1 BFRP(d8)/C40-2.5d 21.77 2.84 43.32 Pulling-out failure La2 BFRP(d8)/C40-5d 34.68 2.62 34.51 Pulling-out failure La3 BFRP(d8)/C40-7.5d 39.48 2.96 26.19 Pulling-out failure
(one pulling-out-splitting failure)Lb1 BFRP(d10)/C40-2.5d 28.39 3.75 36.16 Pulling-out failure Lb2 BFRP(d10)/C40-5d 44.05 3.51 28.06 Pulling-out failure
(one splitting failure)Lb3 BFRP(d10)/C40-7.5d 45.88 2.03 19.48 Splitting failure Lc1 BFRP(d12)/C40-2.5d 40.12 4.19 35.49 Pulling-out failure
(two splitting failure)Lc3 BFRP(d12)/C40-7.5d 48.93 — 14.43 Splitting failure Ld1 CFRP(d12)/C40-5d 10.48 1.30 4.64 Pulling-out failure Ld2 BFRP(d12)/C40-5d 30.52 1.81 13.50 Pulling-out failure Ld3 GFRP(d12)/C40-5d 29.57 2.03 13.08 Pulling-out failure Le1 BFRP(d12)/C30-5d 49.39 3.86 21.85 Pulling-out failure
(one splitting failure)Le2 BFRP(d12)/C35-5d 61.00 5.00 26.98 Splitting failure
(one pulling-out failure)
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表 6 FRP筋全珊瑚骨料海水混凝土试件的计算值与试验值对比
Table 6. Comparison of calculated and experimental values of FRP reinforced full coral aggregate seawater concrete specimens
Group number Ptest/kN Pcal/kN Error/% δtest/mm δcal/mm Error/% La1 21.77 21.44 1.53 2.84 2.60 8.51 La2 34.68 33.84 2.42 2.62 2.40 8.32 La3 39.48 38.83 1.64 2.96 2.82 4.61 Lb1 28.39 27.94 1.57 3.75 3.47 7.54 Lb2 44.05 43.49 1.26 3.51 3.20 8.76 Lb3 45.88 43.23 5.77 2.03 1.87 8.12 Lc1 40.12 39.31 2.01 4.19 3.92 6.48 Lc3 57.87 54.67 5.53 – 2.30 – Ld1 10.84 10.64 1.86 1.30 1.20 7.64 Ld2 29.57 28.29 4.32 1.81 1.71 5.34 Ld3 30.52 29.47 3.41 2.03 1.96 3.21 Le1 49.39 46.31 6.23 3.86 3.61 6.52 Le2 55.23 51.30 7.12 5.00 4.76 4.87 Notes: Ptest—Average value of the ultimate load obtained from the test; δtest—Slip value corresponding to the ultimate load obtained in the test; δcal—Slip value corresponding to the ultimate load obtained by numerical simulation.
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