In accordance with the specifications dictated by the production process, the transportation of oil and gas via subsea pipelines requires operation at elevated temperatures and pressures. These operational conditions induce significant thermal stresses within the pipeline materials, potentially affecting the structural integrity and service life of the pipeline system (Cai and Grognec in Ocean Eng 244, 2022 [1]). Constrained by seabed soil, submarine pipelines cannot freely deform to release internal stresses, particularly due to thermal expansion. As pipeline length increases, these stresses accumulate. Once they exceed the soil’s resistance, sudden deformation occurs, leading to vertical or lateral thermal buckling. This buckling results from compressive axial forces surpassing the pipeline’s critical threshold, causing instability and potentially compromising the pipeline's structural integrity (Liu et al. in J Coastal Res 73, 391–398, 2015 [2]).