PSI - Issue 44

Gianfranco De Matteis et al. / Procedia Structural Integrity 44 (2023) 681–688 Gianfranco De Matteis et al. / Structural Integrity Procedia 00 (2022) 000–000

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2. Application of nonlinear analysis to existing reinforced concrete bridges 2.1. Definition of mechanical properties of materials

To date, several SFs are available in the literature (Cervenka, 2008), developed with the aim of extending the partial factors SF, usually applied at a sectional level in design codes for new and existing structures, to global verifications within the NLA approach. Among the others, EC2 refers to a design resistance R d , derived with a NLA in which the mean values are the representative properties of concrete and steel. In detail, EC2 indicates that: • for reinforcing steel, the steel mean yield strength f ym has to be estimated starting from the characteristic one according to f ym = 1.1 · f yk . Also, k·f yk , corresponding at the ultimate characteristic strain, should be replaced with k·f ym = 1.1 · k f yk ; • for prestressing steel, the steel mean yield strength f pm has to be estimated starting from the characteristic one with the expression f pm = 1.1 · f pk ; • for concrete, the mean strength f cm may be calculated with the expression f cm = 1.1 ·γ s / γ c ·f ck , where γ s and γ c are the partial factors of steel and concrete, respectively. Therefore, f cm = 1.1·1.15/1.5 ·f ck = 0.85 · f ck . This SF clearly refers to new RC bridges for which the design values of material strengths (i.e., the characteristics values) are established, and from which the estimates of the mean values are obtained consistently with the SF. As for the concrete and reinforcing steel, it is interesting to evaluate how the estimated mean values are approximated. To this scope, Fig. 1a reports the ratio f ym / f yk by varying the Coefficient of Variation (CV), obtained for reinforcing steel, and by assuming a normal distribution for the Probability Density Function (PDF) for three values of f yk (300 MPa, 350 MPa, 600 MPa). In addition, Fig. 1b shows the ratio ln( f cm )/ln( f ck ) depending on the CV and considering a log-normal PDF. Again, three values of f ck are considered: 20 MPa, 30 MPa and 40 MPa. In the same graphs, the ratios estimated with the EC2 SF are reported, too.

(a)

(b)

Fig. 1. Ratio of mean to characteristic strength for (a) steel, and (b) concrete at different levels of CV.

As it is easy to note, the mean values estimated with the EC2 SF are always lower than the ones resulting from a normal (steel) and log-normal (concrete) PDF. This means that the EC2 SF underestimates the mean values, for any CV, starting from the design characteristic values. On the contrary, if one would apply the EC2 SF for NLA of an existing RC bridge, the design values would be unknown while the mean values (derived from in-situ tests) would be directly available. In this case, however, the CV will be higher than that of new structures, leading to an overestimation of the characteristic values of steel and concrete strengths. Thus, to keep the same safety margin for existing bridges as those recommended by EC2 for new structures, it is suggested to perform a sufficient number of material tests allowing for the estimation of the characteristic values of the in-site material properties distribution and then define the design strength based on these latter values.