On the influence of thermally induced radial pipe extension on the axial friction resistance

Abstract

Within the design process of district heating networks, the maximum friction forces between the pipeline and the surrounding soil are calculated from the radial stress state and the coefficient of contact friction. For the estimation of the radial stresses, the soil unit weight, geometric properties such as the pipe's diameter and the depth of embedment, as well as the groundwater level are taken into account. For the coefficient of contact friction, different values are proposed, dependent on the thermal loading condition of the pipeline. Although this is an assumption of practical use, physically the coefficient of friction is a material constant.To revise the interaction behavior of the soil-pipeline system with respect to thermally induced radial pipe extension, a two-dimensional finite element model has been developed. Here, the frictional contact was established using Coulomb's friction law. For the embedment, sand at different states of relative density was considered. This noncohesive, granular material was described by the constitutive model HSsmall, which is able to predict the complex non-linear soil behavior in a realistic manner by stress-dependency of stiffness as well as isotropic frictional and volumetric hardening. In addition to the basic Hardening Soil model, the HSsmall model accounts for an increased stiffness in small strain regions, which is crucial for the presented investigation.After a model validation, a parametric study was carried out wherein a radial pipe displacement was applied due to thermal changes of the transported medium. Different combinations of geometry and soil property were studied. We conclude by presenting a corrective term that enables for an incorporation of thermal expansion effects into the prediction of the maximum friction force.