# Numerical Simulation Study on the Performance of Buried Pipelines under the Action of Faults
## 1 Introduction  
Pipeline transportation plays an extremely crucial role in the process of oil and gas extraction, transportation, and deployment due to its high transportation efficiency and better safety. According to post-earthquake surveys, the main reason for serious damage to buried steel pipelines for oil and natural gas is the permanent ground action caused by earthquakes, such as fault movements, landslides, and lateral expansion caused by liquefaction. Permanent ground deformation is applied to the pipeline in a quasi-static manner, which may not necessarily be related to high seismic intensity. However, the pipeline may undergo severe deformation within the plastic range, leading to buckling failure or even cracking damage, posing a significant threat to humans and the environment. Damage to this type of pipeline has been reported in many earthquakes, such as the 1971 San Fernando earthquake [1], the 1995 Kobe earthquake [2], the 1999 Kocai earthquake [3], and the 1999 Chi-Chi earthquake [4]. Due to the high degree of overlap between the area through which pipelines must pass and the distribution area of active fault zones, the service life of oil and gas pipelines has suffered from the serious threat of active faults in China [5]. In order to ensure the safety of buried pipelines during permanent strike-slip fault movement, the corresponding deformation and stress state of pipelines should be evaluated. The first researchers to study the response of pipelines under fault displacement were [PERSON] and [PERSON] [6]; this study used a simplified analytical model of a long cable to calculate stresses and strains within its walls. [PERSON] et al. [7] used the finite element method to solve the response of pipelines and soil under the action of faults in a simple and convenient way. [PERSON] et al. [8] proposed a method for evaluating the seismic performance of buried pipelines to estimate the deformation of pipelines induced by ground deformation of pipelines caused by motion, which can provide a good assessment of pipelines in general. [PERSON] et al. [9] proposed a finite element model for analyzing the response of a pipeline under a strike-slip fault, and investigated the effects of fault displacement, dynamic friction coefficient, and other factors on the displacement and strain of the pipeline. Using the continuum modelling approach, [PERSON] et al. [10] presented a parametric analysis of a buried pipeline crossing a strike-slip fault. The proposed modelling procedure can be suitably used to accurately and efficiently analyze the seismic performance of buried pipelines subjected to a similar PGD. [PERSON] et al. [11] conducted an evaluation of the strain response of buried pipelines under an oblique-slip fault. However, the specific boundary conditions and movement characteristics of the oblique-slip fault movement were not given. The behavior of buried steel pipelines subjected to a crossing angle has received significant attention. [PERSON] et al. [12; 13; 14] investigated the mechanical behavior of buried pipelines under the action of strike-slip faults, and derived the critical fault displacements for different damage modes. Assuming that the pipeline passes through the fault plane at different angles, the effects of the crossing angle for several soil and pipe parameters are investigated. In most cases which were analyzed, it is indicated that local buckling is the governing mode of failure for non-positive values of the crossing angle \(\beta\). For pipelines under tension (positive values of \(\beta\)), local buckling does not dominate. As the angle increases, local buckling caused by longitudinal stretching can be avoided, but the pipeline may fail due to excessive axial tensile strain or a flattened cross-section. [PERSON] and [PERSON] [15] used numerical methodology, aiming to determine the optimum crossing angle for a pipeline. [PERSON] et al. [16] made a parametric study on the strain response of an X80 steel pipeline crossing an oblique-slip fault.