## 2 Materials and Methods
### Critical Infrastructure and Earthquake-Related Geohazards
During a strong earthquake, where the shear strength of the soil degrades significantly, liquefaction-induced PGDs, such as ground oscillation, loss of bearing capacity, subsidence,lateral spreading, and buoyancy, may affect the structural performance of the crossing or adjacent CI. Buoyancy (which leads to the uplift of a buried CI approximately equal to its burial depth) and lateral spreading (which mobilizes the full passive pressure against the CI, thus resulting in a lateral movement of the CI) are the most critical effects on CI. Extensive distractions of CI caused by soil liquefaction phenomena have been documented in various earthquakes, including the 1964 Niigata Earthquake, 1983 Nihonkai-Chubu Earthquake, 1993 Kushiro-Oki Earthquake, 1994 Hokkaido-Toho-Oki Earthquake, and 2004 Niigata-ken Chuetsu Earthquake [36]. Finally, the problem of pipe-fault intersection has been adequately investigated with analytical [37; 38; 39; 40], numerical [23; 41; 42], and experimental [43; 44] methodologies. Nonetheless, the research effort, as well as the provisions of the aforementioned international standards, have focused on the intersection of the pipeline with single faults, treating them rather unrealistically as individual entities. Consequently, the presence of secondary faulting in the same region (which might also lead to unexpected failures of an adjacent or crossing CI) is usually ignored. Secondary faults, defined as subsidiary ruptures to a lesser extent in the proximity of the main fault, are mainly attributed to stress redistributions and/or heterogeneities in rock properties and can produce displacements comparable to those of the main fault [45; 46]. Secondary faults can have multiple orientations (i.e., parallel or intersecting the main fault), while they can be activated either concurrently (i.e., during the same tectonic episode) or during different tectonic episodes [47; 48]. The present study focused on a specific case where secondary faults intersect the tips of the main fault unilaterally, and their orientation is perpendicular to the main fault (Figure 1). It should be noted that both faults are assumed to rupture simultaneously, and that the displacements produced by both faults are of the same magnitude. The presence of such secondary ruptures has been recorded in several earthquakes, such as the 1992 M\({}_{\rm w}\) 7.3 Landers (USA), the 2010 M\({}_{\rm w}\) 7.2 El Mayor (Mexico), the 2016 M\({}_{\rm w}\) 6.5 Norcia (Italy), and the 2019 M\({}_{\rm w}\) 6.4 and 7.1 California (USA), causing damage to structures and infrastructure [49; 50; 51]. Figure 1: The complex geohazard of secondary seismic faulting perpendicular to the main fault. Simultaneous main and secondary fault rupture and: (**a**) pipe-main-fault intersection, (**b**) pipe-secondary-fault intersection, and (**c**) pipe-main-and-secondary-fault intersection. Figure 1a depicts a pipeline that perpendicularly crosses the main fault, parallel to and far away from the secondary fault. This constitutes a common case that has also been included in all seismic norms and guidelines used for the design of pipelines. On the other hand, Figure 1b shows a pipeline that is aligned parallel to the main fault but crosses a secondary fault. This constitutes a realistic scenario in engineering practice where a pipeline is aligned parallel to an active tectonic fault in order to prevent crossing it without properly assessing the presence and potential impact of secondary faults. Although this pipeline routing is hypothetically safer, recent studies by the authors' group revealed that in such cases, the pipeline may even have the same risk as if it intersected the main fault [52; 53]. Lastly, Figure 1c illustrates the potential scenario in which a pipeline crosses both the main and the secondary fault. It should be noted that in such cases, the design standards (e.g., Eurocode 8 [27]) suggest that a suitable intersection angle of the pipeline with the (main) fault should be chosen in order to minimize pipe distress.