Reliability-based Analysis And Design Of Development Length Of Glass Fiber Reinforced Polymer Rods In Concrete

Fiber reinforced polymer (FRP) rods have been regarded as a good solution to durability problems exists in conventional steel reinforced concrete structures. The very essential part of designing FRP-rein forced concrete members is the determination of the development of FRP rods in concrete. Due to distinct differences in material properties, surface geometry, etc., between FRP rods and reinforcing bars, the specifications on the development length of reinforcing bars should be applied directly to FRP rods.Some proposed methods are available so far on this subject, among which the semi-empirical-semi-theoretical method (hereafter called SEST method) and the regression method are commonly used.As the definitions of the two methods, the SEST method is empirical to some extent and the bond resistance between FRP rod and concrete is sometimes overestimated.Design provisions from the combination of these two methods by using probabilistic concepts would be more reasonable and acceptable.And,the provisions would be much more helpful for code-written work and further extensive engineering practice of FRP-reinforced concrete structures.Reliability assessment was carried out on the ultimate limit state of bond of GFRP rod in concrete developed by the SEST method.From the assessment, the value of factor K is proposed to be 0.030 and the relation between additional target reliability index and factor K is established as well.The coefficient of variations (C.O.V.) of concrete strength,GFRP strength and computational uncertainty factor were found to be main influencing factors through the accompanied parametric study. The effect of the C.O.V. of GFRP strength with assumed cumulative density function (CDF) of the Weibull distribution is more significant on factor K than that of the C.O.V.of GFRP strength with assumed normal CDF. K-factor method is only applicable for splitting bond failure mode, i.e.concrete cover is not less than 60mm and the diameter of GFRP rod is not less than 19.1mm.The formulae of bond capacity of GFRP rod in concrete for splitting bond failure mode and pull-out bond failure mode were developed respectively, by the statistical analysis on collected test data. The design tables and design formulae for ld/db and ls/db for splitting failures and ld/db for pull-out failures were put forward by reliability analysis.As for splitting failures, the splice length of GFRP rod in concrete was suggested to be 2.3 times bigger than that of development length.In this case, concrete cover might not be greater than 3.15 times diameter. For other values of GFRP strength, the values of ld/db and ls/db can be estimated by linear interpolation.The effects of the mean of concrete strength, the mean and C.O.V. of concrete cover, the mean of two assumed CDF of GFRP strength and the mean-to-nominal value of the computational uncertainty factor were found be significant on the value of ld/db and ls/db in this case.As for pull-out failures, the value of factor Kp is proposed to be 0.0738 from the analysis.The C.O.V. of GFRP strength and the computational uncertainty factor have put much influence on the value of factor Kp. The effect of the C.O.V. of GFRP strength with assumed CDF of the Weibull distribution is more significant than that of the C.O.V. of GFRP strength with assumed CDF of the normal distribution.In addition, the relationships between the additional target reliability index and the ratios of ld/db and ls/db for splitting failures and the factor Kp for pull-out failures were developed.Accompanied by these relationships, the relation between the ratios of ld/db and ls/db for splitting failure and the strength utilization factor of GFRP rod is also established.An example given in the end of this paper is helpful for understanding how to design the development length of GFRP rod in concrete.A new time-dependent reliability bond design methodology for GFRP rod in concrete was put forward with the durability considerations of bond resistances and pull-out forces resulted from concrete strength, GFRP strength and bond behavior of GFRP rod in concrete. It can be seen from the example analysis in this part that the SEST method and the regression method can provide acceptable initial development length of GFRP rod in concrete if only splitting failure could be expected to occur in whole design service life of concrete structures. The C.O.V.s of concrete strength and GFRP strength, and the time-variant model of concrete strength have put many significant effects on changing tendency of reliability indexes from the two methods.Other variables only put influence on the reliability index at the same time instant, with no effect on changing tendency. If only pull-out failures are expected to occur, the proposed initial development length can not meet the requirements of durability during design service life of concrete structures. The effect of diameter of GFRP rod is very substantial on the changing tendency of time-dependent reliability level.The effects of other variables are negligible.Note that the investigation in this paper is only focused on a specific bond failure mode throughout design service life, without the consideration of the shift in failure mode. This is due to the fact that the shifting point between splitting bond failure and pull-out bond failure is very uncertain.Once the shifting point is known, the combination of the two proposed analytical method can be applied.