Bond-slip model of GFRP bars/ECC interface in alkaline-saline or freeze-thaw environments
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摘要: 粘结滑移本构模型可以反映两种材料界面协同工作的性能,国内外对于玻璃纤维增强树脂复合材料(GFRP)筋/普通混凝土的粘结滑移研究较多,对GFRP筋与工程用水泥基复合材料(ECC)的研究较少,尤其是盐碱或冻融环境下。共制作了66个GFRP筋/混凝土拉拔试件,对比了普通环境、盐碱和冻融循环条件下,GFRP筋表面形式、基体类型和混凝土强度等因素变化时,试件的破坏形式、粘结机制及粘结滑移曲线的差异。研究结果表明:带肋GFRP筋/ECC试件主要发生拔出且带缝破坏;冻融循环后的带肋GFRP筋/普通混凝土试件由劈裂破坏变为拔出且带缝破坏;冻融循环使试件的粘结滑移曲线斜率变小;发生拔出破坏和拔出且带缝破坏的试件残余段曲线呈波浪式衰减,且残余应力峰值之间的滑移量约为一个肋间距。与现有粘结滑移模型进行拟合,根据拟合结果和GFRP筋/ECC材料在3种环境下实际粘结滑移特点,提出了包含参数A、B、α的粘结滑移曲线模型,与试验结果拟合相关系数R2均在0.9以上,得到参数A、B、α的取值分别集中在−0.6~0.2,−0.1~0.1和−0.6~−0.3之间。并根据不同学者的试验结果进一步验证了建议模型的可行性和普适性。
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关键词:
- 工程用水泥基复合材料 /
- 玻璃纤维增强复合材料筋 /
- 冻融循环 /
- 盐碱侵蚀 /
- 粘结机制 /
- 粘结滑移模型
Abstract: The bond-slip constitutive model is often used to describe the interface behavior of glass fiber reinforced polymer (GFRP) bars to engineered cementitious composite (ECC). Although significant efforts have been made on the bond-slip relation of GFRP bar to normal concrete, few studies have focused on GFRP bar/ECC interface, particularly in the exposure of some special environments, including alkaline-saline conditions or freeze-thaw cycling. Therefore, this study aims to derive the bond-slip model for GFRP bar to ECC material in these environments through experimental and analytical study. 66 GFRP bar/concrete specimens were designed to gain an understanding of critical factors, including surface treatment of GFRP bars, matrix types and concrete strength, under three different conditions (i.e., ambient environment, alkaline-saline solution, and freeze-thaw cycles), on how to affect the failure modes, bond mechanism and bond-slip curves. The test results show that the pullout failures with cracks mainly occur on ribbed GFRP bar/ECC specimens. After freeze-thaw cycles, ribbed GFRP bar/normal concrete specimens change from splitting failure to pullout failure with cracks; The slope of bond-slip curves decreases. The residual branch curves of the specimens destroyed by pullout failure or pullout failure with crack attenuate in wave mode, and the difference of slips between the peak residual stresses is about a rib spacing of GFRP bar. And the difference of slips between the peak residual stresses is about a rib spacing of GFRP bar. In addition, the bond-slip curves were fitted with the existing bond-slip models. According to the fitting results and the actual bond-slip characteristics of GFRP bar/ECC interface under three different environments, a bond-slip model containing parameters A, B and α was proposed, and the fitting correlation coefficient R2 was above 0.9, and the values of parameters A, B and α were concentrated in the range of −0.6-0.2, −0.1-0.1 and −0.6-−0.3, respectively. In addition, the accuracy and effectiveness of the proposed model were further verified using previous data from the literature. -
图 7 GFRP筋/工程用水泥基复合材料(ECC)粘结滑移曲线的通用模型
Figure 7. Generic response of bond stress-slip relationships of GFRP bars/engineered cementitious composite (ECC) material
$ {\tau _0} $—Bond stress (bond strength) at the beginning of slip; $ {\tau _{\text{u}}} $—Peak bond stress; $ {s_{\text{u}}} $—Slip at peak bond stress; $ {\tau _{\text{r}}} $—Minimum bond stress of the descending branch; $ {s_{\text{r}}} $—Slip corresponding to the minimum bond stress of the descending branch; $ {\tau _{\text{m}}} $—Peak bond stress of the residual branch; $ {s_{\text{m}}} $—Slip at peak bond stress of the residual branch; dr—Spacing between the ribs of GFRP bar
表 1 混凝土配合比及强度测试结果
Table 1. Mix proportions and strength results of concretes
Item Concrete type Cement Fly ash Silica sand Pebble Water Water-
binder
ratioPolyvinyl alcohol
(PVA) fiberDesign compressive strength/MPa Measured compressive strength/MPa E30 ECC 1 0.25 1 − 0.61 0.49 0.038 30 35.72 E50 ECC 1 0.25 1 − 0.41 0.33 0.033 50 57.03 N30 Normal concrete 1 1.22 3.75 4.23 0.82 0.38 − 30 34.70 表 2 三种环境下拟制作的GFRP筋/混凝土拉拔试件
Table 2. GFRP bar/Concrete drawing specimens to be prepared in three environments
Group Number Specimen Type of concrete Compressive strength/MPa Designed condition Surface treatment Number Unconditioned (control) specimens: Group A 1 GFRP(G)/N30-A0 Normal concrete 30 0 Untreated 3 2 GFRP(L)/N30-A0 Normal concrete 30 0 Ribbed 4 3 GFRP(G)/E30-A0 ECC 30 0 Untreated 3 4 GFRP(L)/E30-A0 ECC 30 0 Ribbed 4 5 GFRP(L)/E50-A0 ECC 50 0 Ribbed 4 Specimens
conditioned with alkaline-saline solution: Group B6 GFRP(G)/N30-A60 Normal concrete 30 60 d Untreated 3 7 GFRP(L)/N30-A60 Normal concrete 30 60 d Ribbed 4 8 GFRP(G)/E30-A30 ECC 30 30 d Untreated 3 9 GFRP(G)/E30-A60 ECC 30 60 d Untreated 3 10 GFRP(L)/E30-A30 ECC 30 30 d Ribbed 3 11 GFRP(L)/E30-A60 ECC 30 60 d Ribbed 4 12 GFRP(L)/E30-A90 ECC 30 90 d Ribbed 3 13 GFRP(L)/E50-A60 ECC 50 60 d Ribbed 4 Specimens
conditioned with
freeze-thaw cycles: Group C14 GFRP(L)/N30-F150 Normal concrete 30 150 FT cycles Ribbed 4 15 GFRP(L)/E30-F100 ECC 30 100 FT cycles Ribbed 4 16 GFRP(L)/E30-F150 ECC 30 150 FT cycles Ribbed 5 17 GFRP(L)/E30-F200 ECC 30 200 FT cycles Ribbed 4 18 GFRP(L)/E50-F150 ECC 50 150 FT cycles Ribbed 4 Notes: GFRP(G) in GFRP(G)/N30-A0 means surface treatment of GFRP bar is untreated, N30 means normal concrete with 30 MPa design compressive strength, and A0 means soaked in saline solution for 0 d (day); GFRP(L) in GFRP(L)/E50-F150 means surface treatment of GFRP bar is ribbed, E50 refers to ECC with concrete design compressive strength of 50 MPa, and F150 means 150 FT (freeze-thaw) cycles. 表 3 3种环境下GFRP筋/混凝土试件的拔出试验结果
Table 3. Pull-out test results of GFRP bar/Concrete specimens in 3 kinds of environments
Group Number Specimen sf/mm sl/mm Pmax/kN τmax/MPa Mean τmax/
MPaτSD/MPa Failure
modeUnconditioned (control) specimens: Group A 1 GFRP(G)/N30-A0-1 0.027 0.153 1.840 0.813 0.940 0.220 P GFRP(G)/N30-A0-2 0.033 0.110 2.700 1.194 P GFRP(G)/N30-A0-3 0.096 0.191 1.840 0.813 P 2 GFRP(L)/N30-A0-1 1.472 4.318 34.050 15.053 15.527 1.319 S GFRP(L)/N30-A0-2 0.912 3.492 38.492 17.017 S GFRP(L)/N30-A0-3 0.586 3.078 32.822 14.511 S 3 GFRP(G)/E30-A0-1 0.020 0.359 6.460 2.856 2.716 0.224 P GFRP(G)/E30-A0-2 0.027 0.076 5.560 2.458 P GFRP(G)/E30-A0-3 0.671 0.793 6.410 2.834 P 4 GFRP(L)/E30-A0-1 1.130 4.182 38.898 17.197 16.033 1.008 P-C GFRP(L)/E30-A0-2 1.000 3.004 34.896 15.427 P-C GFRP(L)/E30-A0-3 0.860 4.890 35.006 15.476 P-C 5 GFRP(L)/E50-A0-1 0.832 4.490 49.570 21.915 20.408 1.727 P-C GFRP(L)/E50-A0-2 0.932 4.362 47.014 20.785 P-C GFRP(L)/E50-A0-3 0.996 6.324 41.900 18.524 P-C Specimens conditioned with alkaline-saline solution: Group B 6 GFRP(G)/N30-A60-1 0.020 0.168 2.930 1.295 1.098 0.182 P GFRP(G)/N30-A60-2 0.020 0.134 2.400 1.061 P GFRP(G)/N30-A60-3 0.013 0.059 2.120 0.937 P 7 GFRP(L)/N30-A60-1 0.814 3.320 37.092 16.398 16.616 0.526 S GFRP(L)/N30-A60-2 0.883 3.567 36.720 16.234 S GFRP(L)/N30-A60-3 0.706 2.985 38.941 17.216 S 8 GFRP(G)/E30-A30-1 0.033 0.158 6.860 3.033 2.787 0.248 P GFRP(G)/E30-A30-2 0.023 0.193 5.740 2.538 P GFRP(G)/E30-A30-3 0.013 0.178 6.310 2.790 P 9 GFRP(G)/E30-A60-1 0.151 0.544 7.434 3.286 3.255 0.592 P GFRP(G)/E30-A60-2 0.154 0.460 5.992 2.649 P GFRP(G)/E30-A60-3 0.334 0.490 8.665 3.831 P 10 GFRP(L)/E30-A30-1 1.486 4.252 30.748 13.594 16.068 2.150 P-C GFRP(L)/E30-A30-2 1.226 6.454 39.538 17.480 P-C GFRP(L)/E30-A30-3 1.088 3.302 38.749 17.131 P-C 11 GFRP(L)/E30-A60-1 0.850 1.938 35.268 15.592 15.090 0.585 P-C GFRP(L)/E30-A60-2 2.358 3.548 32.678 14.447 P-C GFRP(L)/E30-A60-3 1.542 2.580 34.454 15.232 P-C 12 GFRP(L)/E30-A90-1 1.410 2.416 33.242 14.696 14.662 0.086 P-C GFRP(L)/E30-A90-2 1.732 2.984 32.944 14.564 P-C GFRP(L)/E30-A90-3 1.508 2.752 33.308 14.725 P-C 13 GFRP(L)/E50-A60-1 1.422 2.468 38.616 17.072 17.284 1.340 P-C GFRP(L)/E50-A60-2 1.676 2.752 36.334 16.063 P-C GFRP(L)/E50-A60-3 1.320 2.908 42.340 18.718 P-C Specimens conditioned with freeze-thaw cycles: Group C 14 GFRP(L)/N30-F150-1 0.494 1.382 3.306 1.462 1.799 0.943 P-C GFRP(L)/N30-F150-2 1.075 1.185 6.480 2.865 P-C GFRP(L)/N30-F150-3 1.862 2.072 2.422 1.071 P-C 15 GFRP(L)/E30-F100-1 1.138 2.966 27.522 12.167 12.345 0.206 P-C GFRP(L)/E30-F100-2 0.912 2.230 27.814 12.296 P-C GFRP(L)/E30-F100-3 0.960 3.010 28.436 12.571 P-C 16 GFRP(L)/E30-F150-1 1.156 2.930 24.220 10.708 9.800 0.807 P-C GFRP(L)/E30-F150-2 1.156 2.726 20.728 9.164 P-C GFRP(L)/E30-F150-3 1.854 2.910 21.554 9.529 P-C 17 GFRP(L)/E30-F200-1 1.312 3.364 15.810 6.990 5.212 2.041 P-C GFRP(L)/E30-F200-2 2.028 3.150 12.810 5.663 P-C GFRP(L)/E30-F200-3 2.466 3.076 6.748 2.983 P 18 GFRP(L)/E50-F150-1 2.068 3.960 20.820 9.204 8.527 0.622 P-C GFRP(L)/E50-F150-2 1.980 3.552 18.054 7.982 P-C GFRP(L)/E50-F150-3 2.060 3.174 18.990 8.395 P Notes: sl—Slip at the load end of GFRP bar; sf—Slip at the free end of GFRP bar; Pmax—Peak load on the specimen in the pull-out test; τmax—Bond stress; τSD—Standard deviation of bond stresses; P—Pullout failure; S—Splitting failure; P-C—Pullout failure with cracks. 表 4 不同粘结滑移模型的GFRP筋/混凝土拟合参数取值
Table 4. Fitting parameters of different bond-slip models for GFRP bar/Concrete
Group Specimen Ascending branch Optimal model Ascending & descending branch Optimal model Malvar mBPE CMR Malvar mBPE F G R2 α R2 λ β R2 F G R2 α p R2 Unconditioned (control) specimens: Group A Load end GFRP(L)/E30-A0-2 1.459 −0.470 0.988 0.777 0.992 1.111 1.570 0.965 mBPE 0.953 0.813 0.899 0.777 0.403 0.958 mBPE GFRP(L)/E50-A0-2 0.970 0.057 0.996 0.994 0.995 1.382 2.605 0.967 Malvar 0.516 0.894 0.925 0.994 0.398 0.854 Malvar GFRP(L)/N30-A0-1 0.865 0.206 0.998 1.034 0.996 1.241 3.300 0.961 Malvar − − − − − − − GFRP(G)/E30-A0-1 1.158 −0.100 0.964 0.811 0.982 0.158 1.299 0.939 mBPE 0.55 1.328 0.906 0.811 0.163 0.673 Malvar Free end GFRP(L)/E30-A0-2 2.923 −2.087 0.661 0.427 0.844 0.782 0.406 0.804 mBPE 3.274 0.870 0.708 0.427 0.119 0.903 mBPE GFRP(L)/E50-A0-2 2.136 −1.172 0.908 0.581 0.953 0.465 0.800 0.896 mBPE 1.313 1.324 0.765 0.581 0.103 0.932 mBPE GFRP(L)/N30-A0-1 0.536 0.563 0.994 1.302 0.990 0.343 7.196 0.956 Malvar − − − − − − − GFRP(G)/E30-A0-1 − − − − − − − − − 35.529 1.272 0.869 0.053 0.008 0.498 Malvar Specimens conditioned with alkaline-saline solution: Group B Load end GFRP(L)/E30-A30-1 1.511 −0.074 0.983 0.664 0.969 1.330 1.648 0.947 Malvar 1.110 0.613 0.980 0.664 0.552 0.976 Malvar GFRP(L)/E30-A60-2 2.072 −0.258 0.976 0.593 0.944 1.205 1.246 0.958 Malvar 1.900 0.354 0.977 0.593 0.477 0.955 Malvar GFRP(L)/E30-A90-3 1.550 −0.420 0.981 0.740 0.975 0.955 1.622 0.966 Malvar 1.144 0.925 0.949 0.740 0.299 0.973 mBPE GFRP(L)/E50-A60-1 1.461 0.360 0.986 0.717 0.959 0.672 1.883 0.979 Malvar 1.364 0.709 0.977 0.717 0.356 0.965 Malvar GFRP(L)/N30-A60-1 0.872 0.167 0.989 1.052 0.988 1.009 3.090 0.954 Malvar − − − − − − − GFRP(G)/E30-A60-1 0.758 0.241 0.973 1.204 0.970 0.163 3.456 0.899 Malvar −0.101 1.787 0.789 1.204 0.162 0.952 mBPE Free end GFRP(L)/E30-A30-1 13.112 −12.250 0.557 0.191 0.758 0.657 0.278 0.734 mBPE 7.508 −0.297 0.867 0.191 0.208 0.926 mBPE GFRP(L)/E30-A60-2 6.192 −6.715 0.433 0.355 0.830 2.251 0.346 0.779 mBPE 4.995 −0.316 0.565 0.355 0.309 0.886 mBPE GFRP(L)/E30-A90-3 2.762 −1.848 0.595 0.489 0.819 1.578 0.425 0.788 mBPE 2.386 0.957 0.719 0.489 0.156 0.924 mBPE GFRP(L)/E50-A60-1 5.838 −4.927 0.745 0.302 0.930 0.849 0.356 0.886 mBPE 3.827 0.441 0.770 0.302 0.194 0.945 mBPE GFRP(L)/N30-A60-1 2.888 −2.255 0.788 0.472 0.938 0.464 0.587 0.899 mBPE − − − − − − − Specimens conditioned with freeze-thaw cycles: Group C Load end GFRP(L)/E30-F100-1 1.784 −0.490 0.975 0.628 0.971 0.996 1.426 0.945 Malvar 1.597 0.714 0.952 0.628 0.313 0.966 mBPE GFRP(L)/E30-F150-2 1.929 −0.903 0.966 0.614 0.981 1.069 1.152 0.933 mBPE 1.750 0.670 0.912 0.614 0.303 0.948 mBPE GFRP(L)/E30-F200-2 4.808 −3.839 0.960 0.379 0.961 1.114 0.692 0.966 CMR 2.674 0.078 0.864 0.379 0.489 0.963 mBPE GFRP(L)/E50-F150-2 2.301 −1.037 0.967 0.540 0.965 1.249 1.132 0.943 Malvar 1.636 0.421 0.974 0.540 0.532 0.965 Malvar GFRP(L)/N30-F150-3 2.374 1.037 0.967 0.463 0.902 0.517 1.397 0.959 Malvar 2.418 0.572 0.968 0.463 0.261 0.920 Malvar Free end GFRP(L)/E30-F100-1 9.612 −9.737 0.649 0.256 0.815 0.548 0.355 0.801 mBPE 9.022 0.052 0.899 0.256 0.109 0.935 mBPE GFRP(L)/E30-F150-2 8.454 −3.300 0.257 0.228 0.828 0.879 0.234 0.781 mBPE 9.592 −0.212 0.891 0.228 0.122 0.929 mBPE GFRP(L)/E30-F200-2 10.493 −12.214 0.808 0.255 0.942 1.106 0.370 0.935 mBPE 4.478 −0.314 0.707 0.255 0.378 0.964 mBPE GFRP(L)/E50-F150-2 10.547 −11.023 0.516 0.226 0.783 1.133 0.280 0.740 mBPE 4.905 −0.109 0.871 0.226 0.269 0.948 mBPE GFRP(L)/N30-F150-3 5.261 −4.351 0.790 0.328 0.872 0.850 0.501 0.836 mBPE 3.399 0.377 0.843 0.328 0.236 0.924 mBPE Note: F, G, α, p, β and λ—Parameters based on curve-fitting. 表 5 典型GFRP筋/混凝土试件与建议模型拟合的参数取值和相关系数R2
Table 5. Fitting parameters and correlation coefficient R2 of typical GFRP bar/Concrete specimens fitted with proposed model
Group Specimen Ascending branch Descending branch Residual branch All branch A R2 B R2 α R2 R2 Unconditioned (control) specimens:
Group ALoad end GFRP(L)/E30-A0-2 −0.155 0.997 0.044 0.928 −0.513 0.993 0.983 GFRP(L)/E50-A0-2 0.096 0.997 0.148 0.892 −0.637 0.933 0.983 GFRP(L)/N30-A0-1 0.109 0.993 − − − − 0.993 GFRP(G)/E30-A0-1 0.033 0.997 0.033 0.998 − − 0.998 Free end GFRP(L)/E30-A0-2 −0.081 0.997 0.003 0.942 −0.448 0.989 0.977 GFRP(L)/E50-A0-2 −0.086 0.992 0.003 0.931 −0.452 0.934 0.981 GFRP(L)/N30-A0-1 0.464 0.982 − − − − 0.982 GFRP(G)/E30-A0-1 −0.175 0.839 0 0.999 − − 0.998 Specimens conditioned with alkaline-saline solution: Group B Load end GFRP(L)/E30-A30-1 −0.445 0.981 0.068 0.987 −0.538 0.986 0.972 GFRP(L)/E30-A60-2 −0.739 0.979 −0.031 0.987 −0.510 0.955 0.984 GFRP(L)/E30-A90-3 −0.259 0.980 −0.042 0.979 −0.478 0.939 0.985 GFRP(L)/E50-A60-1 −0.514 0.976 0.032 0.986 −0.297 0.988 0.983 GFRP(L)/N30-A60-1 0.258 0.991 − − − − 0.991 GFRP(G)/E30-A60-1 0.524 0.998 −0.007 0.891 −0.144 0.911 0.960 Free end GFRP(L)/E30-A30-1 −0.929 0.985 −0.008 0.975 −0.462 0.996 0.991 GFRP(L)/E30-A60-2 −0.528 0.965 −0.012 0.988 −0.459 0.959 0.984 GFRP(L)/E30-A90-3 −0.022 0.992 −0.013 0.984 −0.414 0.948 0.992 GFRP(L)/E50-A60-1 −0.585 0.995 0.007 0.980 − − 0.993 GFRP(L)/N30-A60-1 −0.180 0.999 − − − − 0.999 GFRP(G)/E30-A60-1 0.654 0.986 0.001 0.864 −0.072 0.905 0.946 Specimens conditioned with freeze-thaw cycles: Group C Load end GFRP(L)/E30-F100-1 −0.418 0.987 −0.038 0.983 −0.651 0.932 0.986 GFRP(L)/E30-F150-2 −0.407 0.991 −0.059 0.977 −0.424 0.980 0.992 GFRP(L)/E30-F200-2 −0.459 0.989 −0.070 0.966 −0.535 0.947 0.986 GFRP(L)/E50-F150-2 −0.572 0.991 −0.009 0.959 −0.598 0.957 0.982 GFRP(L)/N30-F150-3 −1.072 0.980 0.045 0.990 −0.266 0.961 0.985 Free end GFRP(L)/E30-F100-1 −0.737 0.994 −0.003 0.985 −0.497 0.932 0.982 GFRP(L)/E30-F150-2 −0.266 0.996 −0.008 0.983 −0.389 0.967 0.993 GFRP(L)/E30-F200-2 −0.327 0.994 −0.010 0.974 −0.501 0.952 0.984 GFRP(L)/E50-F150-2 −0.651 0.997 −0.009 0.972 −0.543 0.946 0.983 GFRP(L)/N30-F150-3 −0.755 0.993 0.031 0.989 −1.672 0.973 0.994 Note: A, B—Parameters based on curve-fitting. -
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