Keyword: «gradient descent»

As a result of seasonal thawing and freezing of the surrounding soil, an underground pipeline, laid in the permafrost area, undergoes vertical displacement changes twice a year. Complex deformations occur in some sections, manifesting as multiple arches transitioning into one another without intervals. This article proposes a methodology for assessing the stresses that occur in the pipeline in such sec-tions. An equation describing the vertical position of the underground pipeline, depending on the weight of the soil above and the reactions of the soil below, has been obtained. There is no need to explicitly specify longitudinal forces in the equation, which greatly simplifies field work in data collection. The soil reactions are determined by using the gradient descent method in solving the equation.