## 4 Global Sensitivity Analysis  
This section presents the results of the global sensitivity analysis (GSA) conducted to quantify the uncertainty (variance) of the model prediction \(y=g(x_{1},x_{2},\ldots,x_{m})\), attributed to each input random variable \(x_{i}\). This method has the advantage of considering the sensitivity over the entire input space, including the nonlinear interaction effects between the system variables, allowing us to identify those parameters that have the greatest influence on the model output. The adopted GSA procedure is based on the Sobol's variance decomposition method, in which the total variance of model output \(V=Var(y)\) is decomposed into component variances resulting from individual parameters \(V_{i}\) and their interactions \(V_{ijk}\)[38]. Specifically, the first-order Sobol index \(S_{i}\) of an input variable \(x_{i}\) represents the fraction of the output variance attributed to \(x_{i}\) (\(S_{i}=V_{i}/V\)), while the higher order Sobol indices \(S_{ijk}\) indicate the impact of input parameter interactions on the output results (\(S_{ijk}=V_{ijk}/V\)). Finally, the total-order index \(S_{TI}\) quantifies the overall effects of one input parameter \(x_{i}\) including its interactions with all other variables on the model output, and is defined as the sum of all sensitivity indices involving \(x_{i}\) (\(S_{TI}=S_{i}+\Sigma_{i\
eq j}S_{ij}+\Sigma_{i\
eq j\
eq k}S_{ijk}+\ldots\)). To accurately estimate the first-order and total Sobol indices this study performs a double-loop Monte Carlo integration procedure [39]. The estimated influence of the input random variables on the achievement of the pipeline performance limit states, based on Sobol's sensitivity indexes, is shown in Figure 12.  
The soil block length \(L_{b}\) is the most influential parameter, with a first-order sensitivity index \(S_{i}\) of 51.2% and 38.1% for the NOL and PIL limit states, respectively, and a total sensitivity index \(S_{TI}\) greater than 72% for both performance limit states. This is evident, since the length of the PGD zone \(L_{b}\) controls the pipeline deformation demand, where each limit state is achieved provided that the soil block length value exceeds the corresponding critical threshold (\(L_{b}\geq L_{\sigma i}\)). Figure 12: The comparison of the first-order and total-order sensitivity indices of the system input parameters for the (**a**) NOL and (**b**) PIL performance limit states. The second most significant variable is the soil friction reaction per unit pipe length \(f_{s}\), with a first-order sensitivity index \(S_{i}\) of 7.8% and 8.7% for the NOL and PIL limit states, respectively, and a total sensitivity index \(S_{Ti}\) greater than 32% for both damage levels. The third most influential parameter for the PIL limit state is the soil displacement \(\delta\), with an associated first-order sensitivity index \(S_{i}\) of 12.8% and a total sensitivity index \(S_{Ti}\) of 33.2%. Interestingly, the pipeline operating temperature is the third most influential parameter for the NOL limit state, with a first-order sensitivity index \(S_{i}\) and a total sensitivity index \(S_{Ti}\) of 1.6% and 15.2%, respectively. This is consistent with the sensitivity analysis results reported in [25], quantifying the effect of uncertainties of the pipeline system subjected to longitudinal PGD, including the significant impact of operational loads. While the first-order sensitivity indices for the internal pressure \(P_{i}\), are negligible (\(S_{i}<1\%\)), the total sensitivity index \(S_{Ti}\) reaches 10.7% and 5.5% for the NOL and PIL limit states, respectively, highlighting the considerable interaction effects of \(P_{i}\) with the other input variables. The least influential input random variables are the pipe yield strength \(\sigma_{y}\) and relative soil-pipe displacement at friction sliding \(u_{0}\), with an associated total sensitivity index \(S_{Ti}\) less than 4.5% and 0.3%, respectively.