## 7 Impact of Climate Change on Structural Reliability
The target reliability index for a reference period of 50 years has been set, as indicated in EN1990 [3], \(\beta_{t}=3.8\), so that the actual reliability index of the structure should satisfy:  
\[\beta(t)\geq\beta_{t}\ \ \ \rightarrow\ \ \beta(t)\geq 3.8\ \ \ \ \ \ \ \ \ \ \forall\ t\leq t_{wn}; \tag{20}\]  
where \(t_{wn}\) is the design working life of the structure itself. In the example, considering a design working life of the construction \(t_{wn}=50\) year, Equation (20) is satisfied when the total degradation does not exceed 9.25%, which implies \(D(50)=0.9075\) and \(a=0.00185\) year\({}^{-1}\), in case of stationary load. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Mean** & **COV** & **PDF** & \(\mathbf{\lambda}\) **(year\({}^{-1}\))** \\ \hline Initial Resistance & 1.05 \(R_{n}\) & 0 & - & - \\ Dead Load & 1.05 \(G_{n}\) & 0 & - & - \\ Variable Load (Snow Load) & 0.60 Q\({}_{n}\) & 0.3 & EV Type I & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical description of structural resistance and loads. Figure 12: FC-time curves for \(\overline{q}\), \(\sigma_{q}\), and \(q_{k}\) of ground snow load in cell 1230. RCP8.5 scenario. As suggested in [24], the hypotheses are that, during the investigated period, no interventions are implemented to restore the initial resistance of the structure, and that the main source of randomness is the variable action. Following the classical load and resistance factor design method (LRFD) [48], the permanent load \(G_{n}\) and the variable load \(Q_{n}\) (snow load in this case), modeled as in Table 2, are combined as in [24] according to the load combination given in ACI standard 318-89 [49], 1.4 \(G_{n}+1.7\)\(Q_{n}\). The resulting total design load is set equal to the reduced design strength, 0.9 \(R_{n}\), leading to the following design Equation:  
\[0.9\ R_{n}=1.4\ G_{n}+1.7\ Q_{n} \tag{21}\]  
where, for simplicity, \(G_{n}\) is set equal to \(Q_{n}\), as it was done in [24]. The results are shown in Figure 13, in the form of \(P_{f}-time\) diagram (a) and \(\beta-time\) diagram (b), where:  
* Results in case of stationary load hypothesis are shown with solid black lines;
* Dashed gray lines refer to non-stationary load and medium emission scenario (RCP4.5);
* Dashed black lines refer to non-stationary load and highest emission scenario (RCP8.5). In the diagrams, the green lines illustrate the variations over time in case the design is based on the maximum characteristic load \(q_{k,env}\) calculated taking into account the effects of climate change, according to the methodology proposed in Section 6.3. In the example, as evident in Figure 12, this characteristic load \(q_{k}\) is higher than that corresponding to the stationary assumption being affected by a factor of change around 1.23 (time window 1971-2010). Inspecting the diagrams, it clearly results that:  
* Apparently, in case of stationary load assumption, the structure satisfies the minimum assumed reliability requirements for its design working life, 50 years, and, in absence of interventions, in 100 years its reliability index decreases till to \(\beta\approx 3.16\);
* On the contrary, adopting \(q_{k,env}\) the reliability index is increased, so that in the example the structural reliability would remain adequate even for 100 years;
* In the RCP4.5 scenario, the structure satisfies minimum reliability requirements for 30 years; its reliability index decreases to \(\beta\approx 3.41\) at the end of the design working life;  
Figure 13: Variation over time of: (**a**) probability of failure \(P_{f^{\prime}}\)(**b**) reliability index \(\beta\).