## 2 Materials and Methods  
### Critical Infrastructure and Earthquake-Related Geohazards  
As it has been mentioned, CI is considerably vulnerable to earthquake events and earthquake-related geohazards due to the inertial distress caused by strong ground shaking (Transient Ground Displacements--TGDs) and/or kinematic distress caused by Permanent Ground Displacements (PGDs). Nevertheless, it should be stressed that none of the earthquake excitation components along the three directions are expected to significantly threaten an onshore buried gas pipeline, regardless of the earthquake type and resulting seismic waves. High-pressure natural gas pipelines are characterized by low mass; thus, their dynamic response is significantly different from that of typical above-ground structures, where high vertical forces (i.e., gravitational forces) in conjunction with high seismic accelerations lead to significant inertial forces and structural failures. Hence, onshore buried gas pipelines are mainly distressed kinematically due to PGDs and External Loading (EL), especially when the fault rupture reaches the ground surface (i.e., in the case of shallow earthquakes). There is no doubt that the structural impact of PGDs can be detrimental for specific types of pipelines (e.g., water and oil) under certain local site conditions. Nonetheless, the distress of high-pressure gas pipelines due to PGDs and EL is more challenging and has a high probability of occurrence during their lifetime. Consequently, they play a key role in the design and optimal route selection [23]. The impact of earthquake-related geohazards, such as slope instabilities, soil liquefaction phenomena, and seismic fault ruptures at the ground surface, on CI is of paramount importance. This is evidenced by the fact that several international guidelines and standards have been developed for the seismic design of pipelines by combining existing analytical and numerical methodologies [24] (e.g., ASCE guidelines [25], American Lifelines Alliance [26], and Eurocode 8 [27]). The main goals of these standards are to (a) evaluate the performance of a pipeline subjected to earthquake-related geohazards, (b) establish pipe strain limits for pipe-soil interaction corresponding to different loading scenarios, and (c) propose several mitigation measures. Slope instabilities are natural geological events that are often triggered by seismic or other dynamic loads (if any), fluctuations in the level of the groundwater table, soil erosion phenomena, etc., and can cause sudden or gradual mass movements on the ground surface [28]. Earthquake-related landslides are widely recognized as one of the most unpredictable and destructive geohazards that may directly or indirectly affect the structural integrity of CI located in or near mountainous or hilly areas. Considering that it is not always technically and economically feasible for a CI to completely avoid potentially unstable slopes characterized by large inclinations, earthquake-related landslides may result in excessive EL (e.g., structural distress of the CI due to debris sliding), PGDs (e.g., exposure and/or spanning of the CI), or a combination of these actions across the alignment of the CI [29; 30; 31]. As a consequence, landslide-related incidents may lead to ruptures and leaks that may have severe environmental impacts, as well as long periods of service disruption [32; 33]. In the mountainous regions of the Andes, nearly 50% of CI failures have been attributed to landslides [34], while the European Gas Pipeline Incident Data Group reported that 85% of gas pipeline accidents due to geological reasons in Europe from 2004 to 2013 occurred due to landslide-induced tension or buckling [35]. In parallel, soil liquefaction phenomena, which can occur as a result of repeated cyclic motions in saturated loose cohesionless soils, also play a key role in the structural response of CI.