## 1 Introduction  
The transportation of natural gas to its destination is a very acute issue worldwide. To solve this issue, specialists used various methods of transportation: motor transport [1], tankers [2], railways [3], and main gas pipelines [4]. The latter method is currently the most acceptable due to its cost-effectiveness, which can be attributed to the following advantages: high speed of delivery to plants and storage points, wide geographical coverage, transporting the product over long distances, ensuring uninterrupted deliveries regardless of climatic conditions, and minimal resource losses during transit. However, there are also risks of emergencies during transportation by gas pipelines due to various reasons: corrosion of pipe material, stress concentration along structural elements, structural defects [5; 6; 7; 8; 9], and external impacts on the structural parts [10; 11; 12; 13; 14], which, as a result of the internal pressure impacts, are subject to destruction [15; 16; 17; 18] and leading to accidents [19; 20; 21; 22]. Since the middle of the 20 th century, several studies have generally been devoted to investigating the issue of the destruction of main and conventional gas pipelines, on the basis of which a lot of design norms and codes were adopted [23; 24; 25; 26; 27; 28; 29; 30]. Back in 1970, the problem of crack occurrences along pipelines and ways of stopping them were studied [31]. In 1980, full-scale investigations on the rupture of large-diameter pipes were carried out, where the emphasis was placed on the method of manufacture and mechanics of the pipe material [32; 33]. In the studies performed in 1990 [34; 35], the issue of mainline crack propagation, which is induced by the gas motion, was established. It was stated that the problem of main crack motion consists of three subproblems: analysis of the stress-strain state of the structure, gas propagation through the pipeline and the corresponding crack, and fracture mechanics. The development of a calculation program was described, which consists of three modules: stress state analysis, gas dynamics, and fracture modeling. Approaches to prevent the rapid crack movements were discussed. Particularly in [PERSON] and [PERSON] [36] and [PERSON] et al. [37], the extended finite-element method was utilized to model the stress state close to the cracks, which, in turn, demonstrated its evaluation accuracy and reliability. During the decade 2000-2010, a number of works along this research direction were carried out, where, in [PERSON] et al. [38], the finite-element approach was specifically applied for modeling the fracture of pipelines. Based on their calculations, the crack tip opening angle was determined. This parameter was experimentally determined for each material. At the critical value of this parameter, crack growth occurs. [PERSON] and [PERSON] [39] discussed some methods to stop crack development. The use of wire and composite wraps to prevent crack movement was analyzed. [PERSON] et al. [40] described a numerical procedure for modeling the gas dynamic processes that are commonly observed when the gas flows out of a pipeline. Conversely, in [PERSON] et al. [41] and [PERSON] et al. [42], experimental and numerical studies were executed on bending sections of gas pipelines under internal operating pressure to determine the critical points. Their outcomes showed that fatigue failure occurs in the bending area under repeated loading. In the previous decade, studies were conducted to investigate the crack formation in large-diameter gas pipelines, where a computational approach for determining the mainline crack movement was proposed by [PERSON] et al. [43]. The commercial software LS-DYNA R-12.1.0 was used to calculate the stress state and crack propagation, while another software was implemented for dynamic issues along gas pipelines. The dependence on the strain rate was emphasized when analyzing the fracture of the entire structure. Near the crack tip, the plastic strain of the material was considered.