Long-term development length of GFRP bar in concrete under coupling effect of seawater immersion and sustained load
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摘要: 为了获得海水浸泡与持续荷载耦合作用下玻璃纤维增强树脂复合材料(Glass fiber-reinforced polymer,GFRP)筋的长期锚固长度计算公式,首先搜集了81个拔出破坏的GFRP筋混凝土梁式试件的数据,提出了GFRP筋的短期锚固长度计算公式。然后测试了在海水浸泡与持续荷载耦合作用下GFRP筋拉拔试件的粘结强度,结合强度预测理论,得到了粘结强度折减系数。采用粘结强度折减系数及基于他人试验获得的GFRP筋抗拉强度折减系数修正了短期锚固长度计算公式,最终建立了海水浸泡与持续荷载耦合作用下适用于拔出破坏的GFRP筋长期锚固长度计算公式。研究结果表明:GFRP筋的长期锚固长度变化主要是由粘结强度和抗拉强度的减小造成的。经过海水浸泡与持续荷载耦合作用50年后,当环境的年平均温度为8℃、13℃、18℃、23℃和28℃时,GFRP筋的粘结强度折减系数分别为0.60、0.60、0.56、0.56和0.52。相应的GFRP筋抗拉强度折减系数分别为0.63、0.56、0.49、0.42和0.35。
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关键词:
- 纤维增强树脂复合材料(FRP) /
- 海洋环境 /
- 持续荷载 /
- 粘结强度 /
- 锚固长度
Abstract: To obtain the long-term development length equation of the glass fiber-reinforced polymer (GFRP) bar under the coupling effect of seawater immersion and sustained load, a short-term development length equation was proposed first according to the collected 81 GFRP bar-reinforced concrete beam with pullout failure. Then, the bond strength of the pullout specimen under the coupling effect of seawater immersion and sustained load was tested, and the bond strength reduction factor was obtained with a prediction theory. Based on the bar’s bond strength reduction factor and the tensile strength reduction factor deduced from others’ tests, the short-term development length equation was modified. Finally, the long-term development length equation of the GFRP bar for the beam with pullout failure was established. The results show that the change in the long-term development length of the GFRP bar is mainly caused by the reductions in bond strength and tensile strength. After the coupling effect of seawater immersion and sustained load for 50 years, when the annual average temperatures of the environment are 8℃, 13℃, 18℃, 23℃ and 28℃, the bar’s bond strength retentions are 0.60, 0.60, 0.56, 0.56 and 0.52, respectively. The corresponding tensile strength retentions of the GFRP bar are 0.63, 0.56, 0.49, 0.42 and 0.35, respectively. -
图 8 GFRP筋抗拉强度保留率与时间的对数之间的关系
T—Temperatures; tD—Design service days; tS—Service days at T1 corresponding to the tensile strength retention at design service days at T3; δ1—Tensile strength reduction at T1 for 365 days; δ2—Tensile strength reduction at T1 from 365 days to design service days; δ3—Percentage loss of tensile strength as the temperature rises from T1 to T3; α—Angle between the tensile strength reduction curve at T1 and the horizontal line
Figure 8. Relation between GFRP bar’s tensile strength retention and logarithmic time
表 1 玻璃纤维增强树脂复合材料(GFRP)筋混凝土梁式构件粘结试验数据
Table 1. Data from the bond test of concrete beam reinforced with glass fiber-reinforced polymer (GFRP) bars
Data sources Specimen $ f_{\text{c}}' $/MPa db/mm C/mm le/mm u/MPa Surface condition [2] 46 B3 B2 27.6 19 48 76 17.1 WH 46 B6 B2 27.6 19 48 152 9.3 46 B12 B2 39.2 19 48 305 5.6 86 B12 B2 47.7 19 48 305 5.7 46 B16 B4 39.2 19 86 406 5.4 86 B16 B4 47.7 19 86 406 5.2 49 B4 B2 27.6 29 73 102 15.2 49 B8 B2 27.6 29 73 203 8.5 49 B22 B2 39.7 29 73 559 4.2 89 B22 B2 44.8 29 73 559 4.0 49 B26 B4 39.7 29 132 660 3.9 89 B26 B4 47.3 29 132 660 3.8 [3] G-10-0-100 33.3 10 38 150 0.8 WH+SC G-19-0-190 33.3 19 38 285 3.4 [5] I 30-1-f 24.1 16 50 40 18.49 WH+SC I 30-1-s 24.1 16 50 40 14.88 I 30-2-s 24.1 16 50 80 14.88 [12] G8 Sf/4.5-11-4.5-5-1/C30 29.1 8 36 40 11.0 SC G8 Sf/4.5-11-4.5-10-1/C30 29.1 8 36 80 7.8 G8 Sf/4.5-11-4.5-20-1/C20 17.3 8 36 160 5.1 G8 Sf/4.5-11-4.5-10-1/C40 41.4 8 36 80 7.6 G8 Sf/4.5-11-4.5-10-0/C20 17.3 8 36 80 5.0 G8 Sf/2.5-15-4.5-10-1/C30 29.1 8 20 80 8.5 G8 Sf/4.5-11-2.5-10-1/C30 29.1 8 20 80 7.5 G8 Sf/4.5-11-3.5-10-1/C30 29.1 8 28 80 8.2 G6 Sf/4.5-17.7-4.5-10-1/C30 29.1 6 36 60 13.6 G12 Sf/4.5-11-4.5-10-1/C30 29.1 12 36 120 6.1 G8 Sf/4.5-3.75-4.5-10-1/C30 29.1 8 15 80 5.8 G8 Sf/4.5-7-4.5-10-1/C30 29.1 8 28 80 8.8 G8 WO/4.5-11-4.5-10-1/C30 29.1 8 36 80 11.4 WO G8 WO/4.5-11-4.5-20-1/C20 17.3 8 36 160 8.8 G8 WO/4.5-11-4.5-10-1/C20 17.3 8 36 80 9.3 G8 WO/4.5-11-4.5-10-1/C35 37.3 8 36 80 14.7 G8 WO/4.5-11-4.5-10-1/C40 41.4 8 36 80 11.8 G8 WO/4.5-11-4.5-10-0/C20 17.3 8 36 80 9.3 G8 WO/4.5-11-2.5-10-1/C30 29.1 8 20 80 11.4 G8 WO/4.5-11-3.5-10-1/C30 29.1 8 28 80 11.5 G12 WO/4.5-11-4.5-10-1/C30 29.1 12 54 120 10.2 G8 WO/4.5-7-4.5-10-1/C30 29.1 8 28 80 11.5 G12 WW/4.5-11-4.5-10-1/C30 29.1 12 54 120 11.4 WW G8 R/4.5-11-4.5-10-1/C30 29.1 8 36 80 15.1 R G8 R/4.5-11-4.5-20-1/C20 17.3 8 36 160 9.6 G8 R/4.5-11-4.5-10-1/C20 17.3 8 36 80 10.7 G8 R/4.5-11-4.5-10-1/C40 41.4 8 36 80 17.4 G8 R/4.5-11-4.5-10-0/C20 17.3 8 36 80 11.1 G8 R/2.5-15-4.5-10-1/C30 29.1 8 20 80 15.8 G8 R/4.5-11-2.5-10-1/C30 29.1 8 20 80 13.8 G8 R/4.5-11-3.5-10-1/C30 29.1 8 28 80 16.0 G8 R/4.5-3.75-4.5-10-1/C30 29.1 8 15 80 12.8 G8 R/4.5-7-4.5-10-1/C30 29.1 8 28 80 15.6 G6 R/4.5-17.7-4.5-10-1/C30 29.1 6 27 60 13.1 G12 R/4.5-11-4.5-10-1/C30 29.1 12 54 120 10.7 [14] – 31 12.7 50 76.2 11.3 WH+SC – 31 15.9 50 95.4 10.6 – 31 19.1 50 114.6 7.1 – 31 25.4 50 152.4 7.0 – 31 19.1 50 305.6 5.3 – 31 25.4 50 406.4 5.1 – 31 12.7 50 127 10.6 – 31 15.9 50 159 7.3 – 31 19.1 50 191 6.6 – 31 25.4 50 254 6.4 – 31 12.7 50 127 12.3 – 31 15.9 50 159 10.8 – 31 25.4 50 254 7.4 WH [15] T1.25 L15 52 12 15 180 2.9 WH T1.25 L20 52 12 15 240 1.7 T2 L15 52 12 25 180 2.7 T2 L20 52 12 25 240 1.7 T1.25 L20-C 52 12 15 240 1.9 T2 L20-C 52 12 25 240 2.2 [16] GS-12-5.1 32.2 12 50 60 14.8 SC GS-12-5.2 32.2 12 50 60 14.5 GS-12-5.3 32.2 12 50 60 12.7 GS-16-5.1 31.9 16 50 80 11.7 GS-16-5.2 31.9 16 50 80 10.3 GS-16-5.3 31.9 16 50 80 12.1 GS-18-5.1 32.2 18 50 90 10.0 GS-18-5.2 32.2 18 50 90 11.6 GS-18-5.3 32.2 18 50 90 11.8 Notes: $ f_{\text{c}}' $—Compressive strength of the concrete cylinder with a size of 150 mm×300 mm; db—Bar diameter; C—Smaller of the distance from the concrete surface to the center of the bar and 1/2 of the spacing between the adjacent bars; le—Embedment length of the GFRP bar in the concrete; u—Bond strength of the GFRP bar; WH—Wrapped in a helical pattern; SC—Sand coated; WO—Wound; WW—Widely-spaced and tight wrapping; R—Ribbed; For the specimen name in reference [2], First number—Compressive strength of concrete, Second number—Bar diameter, Third number—Embedment length, Fourth number—Ratio of the clear concrete cover to the bar diameter, First letter B—Beam specimen, Second letter B—Bar is casted at the bottom of the beam; For the specimen name in reference [3], G—Specimen with GFRP bar, First number—Bar diameter, Second number—Concrete mix, Third number—Embedment length; For the specimen name in reference [5], I—First test method, First number—Compressive strength of concrete, Second number—Embedment length, f—GFRP bar, s—Steel bar; For the specimen name in reference [12], the letters and numbers represents the GFRP bar, bar diameter, surface properties of bar, side concrete cover, bar span, bottom concrete cover, embedment length, stirrup effect, strength class of concrete, respectively; For the specimen name in reference [15], R—GFRP ribbed bar, First number—Ratio of the concrete cover to the clear spacing between the splices, L and the second number—Splice length, C—Steel confinement; For the specimen name in reference [16], GS—GFRP bar with sand-coated surface, First number—Bar diameter, Second number—Embedment length, Third number—Specimen number among three identical specimens. 表 2 GFRP筋混凝土梁式构件粘结性能参数的取值范围
Table 2. Parameter ranges of bond performance of concrete beam reinforced with GFRP bars
Parameter $ f_{\text{c}}' $/MPa db/mm C/db le/db u/MPa Maximum 52.0 29.0 6.0 22.8 22.1 Minimum 17.3 6.0 1.3 2.5 0.8 Average 32.2 13.8 3.4 11.0 9.5 Standard deviation 8.7 6.6 1.0 5.2 4.5 表 3 混凝土立方体抗压强度和圆柱体抗压强度的关系
Table 3. Relationship between cube and cylinder compressive strengths of concrete
fcu/MPa $ f_{\text{c}}' $/MPa 10 8 15 12 20 16 25 20 30 25 37 30 45 35 50 40 55 45 60 50 67 55 75 60 85 70 95 80 105 90 115 100 Note: fcu—Compressive strength of the concrete cube with a side length of 150 mm. 表 4 GFRP筋混凝土拉拔试件的粘结强度
Table 4. Bond strength of GFRP-reinforced concrete pullout specimen
Specimen Immersion
time/daysSustained
loadBond strength Average
/MPaRetention
/%P0 N 0 No 26.4 100.0 P90 N 90 No 27.7 104.9 P90 L 90 Yes 27.2 103.0 P180 N 180 No 25.8 97.7 P180 L 180 Yes 25.6 97.0 P270 N 270 No 24.4 92.4 P270 L 270 Yes 23.5 89.0 Notes: The naming method of all the specimens follows the form of “PAB”. P—Pullout specimen; A—Immersion time; B—Sustained load applied on the specimen, where L and N indicate the specimens with and without sustained load, respectively. 表 5 GFRP筋粘结强度折减系数计算结果
Table 5. Calculation of reduction factors of GFRP bar’s bond strength
Annual average temperature/℃ nmo nT nSL nd Seawater immersion Seawater immersion + Sustained load R10 1/ηb R10 1/ηb 8 1 0.0 2.7 0 11 0.65 13 0.60 13 0.0 0.65 0.60 18 0.5 0.61 0.56 23 0.5 0.61 0.56 28 1.0 0.58 0.52 Notes: nmo, nT, nSL, nd—Parameters related to the humidity, temperature, structure’s design service life and bar diameter, respectively; R10—Standard reduction of bond strength in percent per decade; ηb—Parameter related to the reduction factor of the GFRP bar’s bond strength. 表 6 GFRP筋的抗拉强度试验数据
Table 6. Test data of GFRP bar’s tensile strength
Specimen Tensile strength Average/MPa Retention/% BC 1054 100.0 B/32/21/0 1032 97.9 B/32/42/0 1007 95.5 B/32/63/0 1036 98.3 B/55/21/0 966 91.7 B/55/42/0 980 93.0 B/55/63/0 948 89.9 B/40/21/20 915 86.8 B/40/42/20 865 82.0 B/40/63/20 781 74.1 B/55/21/20 724 68.7 B/55/42/20 773 73.4 B/55/63/20 617 58.6 Notes: BC—Control specimen. The naming method of all the conditioned specimens follows the form of “B/a1/a2/a3”, in which B is GFRP bar, a1 is olution temperature in ℃, a2 is immersion time in day, and a3 is sustained load level in %. 表 7 GFRP筋抗拉强度折减系数计算结果
Table 7. Calculation of reduction factors of GFRP bar’s tensile strength
Annual average temperature/℃ tY β Seawater immersion Seawater immersion + Sustained load δ1 ρ $ {r_{32 {\text{-}} {T_3}}} $ ηt δ1 ρ $ {r_{40 {\text{-}} {T_3}}} $ ηt 8 50 1 0.07 −0.0573 0.02 0.93 0.41 −0.23 0.01 0.63 13 0.05 0.91 0.03 0.56 18 0.11 0.89 0.06 0.49 23 0.24 0.87 0.11 0.42 28 0.54 0.85 0.22 0.35 Notes: tY—Design service life of structures; β—Humidity coefficient; δ1—Reduction of GFRP bar’s tensile strength after 365 days at the temperature of T1; ρ—Slope of the time-dependent tensile strength curve of GFRP bar; $ {r_{32 - {T_3}}} $—Time conversion factor under seawater immersion; $ {r_{40 - {T_3}}} $—Time conversion factor under the coupling effect of seawater immersion and sustained load; ηt—Parameter related to the reduction factor of the GFRP bar’s tensile strength. 表 8 GFRP筋长期粘结强度计算公式总结
Table 8. Summary of long-term bond strength equations of GFRP bar
Annual average temperature/°C Long-term bond strength equations Seawater immersion Seawater immersion + Sustained load 8 $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.131 + 0.204\dfrac{C}{{{d_{\text{b}}}}} + 4.906\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.121 + 0.188\dfrac{C}{{{d_{\text{b}}}}} + 4.528\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ 13 $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.131 + 0.204\dfrac{C}{{{d_{\text{b}}}}} + 4.906\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.121 + 0.188\dfrac{C}{{{d_{\text{b}}}}} + 4.528\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ 18 $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.123 + 0.192\dfrac{C}{{{d_{\text{b}}}}} + 4.604\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.113 + 0.176\dfrac{C}{{{d_{\text{b}}}}} + 4.226\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ 23 $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.123 + 0.192\dfrac{C}{{{d_{\text{b}}}}} + 4.604\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.113 + 0.176\dfrac{C}{{{d_{\text{b}}}}} + 4.226\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ 28 $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.117 + 0.182\dfrac{C}{{{d_{\text{b}}}}} + 4.377\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ $\dfrac{u}{{\sqrt {f_{\text{c}}'} }} = - 0.105 + 0.163\dfrac{C}{{{d_{\text{b}}}}} + 3.924\dfrac{{{d_{\text{b}}}}}{{{l_{\text{e}}}}}$ 表 9 GFRP筋的长期锚固长度计算公式总结
Table 9. Summary of long-term development length equations of GFRP bar
Annual average temperature/°C Long-term development length equations Seawater immersion Seawater immersion + Sustained load 8 ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.93 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 19.624\right)/\left(0.816\dfrac{C}{{{d_{\text{b}}}}} - 0.524\right)$ ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.63 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 18.112\right)/\left(0.752\dfrac{C}{{{d_{\text{b}}}}} - 0.484\right)$ 13 ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.91 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 19.624\right)/\left(0.816\dfrac{C}{{{d_{\text{b}}}}} - 0.524\right)$ ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.56 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 18.112\right)/\left(0.752\dfrac{C}{{{d_{\text{b}}}}} - 0.484\right)$ 18 ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.89 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 18.416\right)/\left(0.768\dfrac{C}{{{d_{\text{b}}}}} - 0.492\right)$ ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.49 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 16.904\right)/\left(0.704\dfrac{C}{{{d_{\text{b}}}}} - 0.452\right)$ 23 ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.87 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 18.416\right)/\left(0.768\dfrac{C}{{{d_{\text{b}}}}} - 0.492\right)$ ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.42 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 16.904\right)/\left(0.704\dfrac{C}{{{d_{\text{b}}}}} - 0.452\right)$ 28 ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.85 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 17.508\right)/\left(0.728\dfrac{C}{{{d_{\text{b}}}}} - 0.468\right)$ ${l_{\text{d}}} = {d_{\text{b}}} \left(\dfrac{{0.35 f_{{\text{fu}}}^*}}{{\sqrt {f_{\text{c}}'} }} - 15.696\right)/\left(0.652\dfrac{C}{{{d_{\text{b}}}}} - 0.420\right)$ Note: $f_{{\text{fu}}}^*$—Guaranteed tensile strength of the GFRP bar. 表 10 GFRP筋的长期与短期锚固长度之比
Table 10. Ratios of GFRP bar’ long-term and short-term development lengths
Annual average temperature/°C Conditions for long-term length Seawater immersion Seawater immersion + Sustained load 8 1.43 1.05 13 1.40 0.93 18 1.46 0.88 23 1.43 0.75 28 1.47 0.67 -
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