Loading of a gravel-buried steel pipe subjected to rockfall

Increasing rockfall activity in the European Alps has raised the need for designing protection systems for Alpine infrastructure. This paper is concerned with protection of steel pipelines by a gravel overburden of height H. Rockfall-induced loading of such pipes is estimated by means of a three-dimensional, quasi-static, elasto-plastic finite-element (FE) model. Maximum impact forces F and corresponding penetration depths w are estimated based on dimensionless formulas, related to real scale impact tests onto gravel layers. The forces F are applied as surface loads onto the FE model, at a distance (H-w) from the pipe. Material behavior of gravel is represented by a cap model, which is based on pressure-independent linear elasticity and associated plasticity. Related material parameters are identified from acoustic and static material tests. The structural FE model is validated by comparing FE-predicted stresses in the pipe with stresses determined in a real-scale structural experiment. This is reasonable only because the real-scale test is independent of the experiments used for identification of the material parameters used as input for the structural FE model. Satisfactory FE predictions motivate use of the FE model for estimating the loading of the steel pipe in untested scenarios, concerning, e.g., different heights of overburden, or different impact intensities. These estimates show some efficiency of gravel protection systems for modest rockfall, with impact energies well below 3,500 kJ.