Direct and inverse problems of pipeline bending

The paper considers the static linear pipe bending at river crossings and ravines under the gravity of the pipe and transported fluid. It is assumed that the parts of the pipeline on either sides of the sagging part are embedded into the ground with same properties. A simple model of the ground elasticity is used which entails a replacement of its distributed spring system with a certain rigidity in the longitudinal and transverse directions of the pipeline. The fluid speed is not considered. The internal pressure difference exerts an unbalanced lateral force directed towards the convexity of the curved axial line. The impact on the axial extension bend of the pipe produced by the axially symmetric deformation is also taken into consideration. The direct problem is to determine the deflection for the given size, stiffness and strength characteristics of the pipe and ground. To simplify the problem, the case of a high internal pressure and shallow pipe occurrence in the ground is considered. The dependence of bending is determined based on the stiffness of the ground and pipeline, as well as on the internal pressure. The pressure growth results in the bending increase. In particular, the critical value of the internal pressure is determined when the bending increases without limit in the linear problem. The inverse problem is to determine the relative stiffness of the ground under the instrumental determination of the pipeline bending or deformation of its outer fibers. It is achieved using the method of the pipeline additional loading by the concentrated power and determination of an appropriate instrumental bending or deformation. In particular, the loading and corresponding measurements are carried out at the midpoint of the pipeline span. The critical value of the relative ground stiffness is determined, below which the bending starts to increase without limit.