## 1 Introduction
Analytical models can be efficiently implemented within a seismic fragility analysis framework to evaluate the structural performance considering the uncertainties of the system parameters. Pipeline fragility assessments require proper consideration of the variability of the physical characteristics of the soil-pipe system, including the material  
Figure 1: Pipeline subjected to longitudinal PGD: (a) 3D view; (b) 2D schematic representation. strength properties, the soil cover depth, and the pipe operational loads such as temperature differences and internal pressure [22; 23; 24; 25]. These uncertainties are considered within a probabilistic framework like the Monte Carlo Simulation (MCS), employing a large number of soil-pipeline system samples, generated by random sampling of the input system parameters, based on their probability distribution. The seismic demands are compared to the structural capacity values associated with a certain performance limit state, allowing to estimate the associated probability of exceedance as a function of the level of seismic intensity measure, IM [26; 27]. The latter is defined by a group of representative seismic ground motion parameters, e.g., the peak ground displacement \(\delta\), and the length of the PGD zone \(L_{b}\). Conversely, the structural limit states are defined on the basis of an adequate Engineering Demand Parameter (EDP), e.g., the peak longitudinal strain, describing the system performance [28; 29]. The analytical fragility relationships represent a useful design tool, allowing us to identify precise locations of pipeline damage, which is fundamental in evaluating pipeline seismic performance and prioritizing resource allocation for mitigative or remedial measures in spatially distributed lifeline systems. To efficiently evaluate the seismic fragility of buried operating steel pipelines under longitudinal PGD, this study developed a new analytical model considering the asymmetric nonlinear response of the operating pipeline for tension and compression. The proposed model was validated through detailed finite element analysis, demonstrating its capacity to accurately evaluate pipeline system response under varying operational and seismic loads. The analytical formulation was further implemented within a fragility function calculation framework based on a Monte Carlo Simulation (MCS), assessing the probability of the pipeline exceeding the performance limit states, conditioned to the ground displacement hazard. Furthermore, to quantify the influence of the uncertain input parameters on the predicted pipeline performance, this study conducted Global Sensitivity Analysis (GSA), based on the Sobol's variance decomposition method, using MCS to calculate the Sobol's sensitivity indices. Figure 2: Pipeline response to longitudinal PGD according to analytical model in [11], assuming symmetric material behavior for tension and compression: (**a**) case I; (**b**) case II. First, this paper presents the methodology adopted to evaluate the seismic fragility of buried pipelines subjected to longitudinal PGD, using an accurate analytical model considering the asymmetric pipeline material behavior for tension and compression under varying service loads. Then, the obtained fragility analysis results are carefully discussed and compared to data reported in other research publications, highlighting the main factors influencing the seismic performance of buried operating pipelines, considering the system uncertainties. Finally, the conclusion section highlights the contributions of the present paper to the state-of-the-art practice and research of pipeline seismic design, suggesting further important perspectives related to the addressed issues.