Semi-probabilistic design of rockfall protection layers

Increasing rockfall activity in the European Alps raises the need for designing systems protecting Alpine infrastructure. So far, layout of rockfall protection layers was carried out in a quasi-deterministic manner. This paper is concerned with the extension towards a semi-probabilistic design of the thickness of gravel layers covering steel pipelines. Quantities with little scatter such as geometric dimensions and elasto-plastic material constants of steel and gravel are treated as deterministic. By contrast, strongly scattering quantities such as the indentation resistance of gravel, R, and rockfall characteristics including boulder mass m and height of fall h (f) are considered as probabilistic variables. While 5 and 95% quantiles of R (obtained from statistical evaluation of a series of real-scale impact tests onto gravel) represent probability-based interval bounds for designing the gravel layer thickness, the lack of statistical data from rare rockfall events motivates to follow the philosophy of EUROCODE 1, i.e., to define a design rockfall: m = 10,500 kg and h (f) = 80 m. Based on this input, a standard burying depth of steel pipelines (H = 1 m) is assessed, by comparing estimates of (i) boulder penetration depth into gravel and of (ii) the maximum impact force, respectively, with corresponding quantities related to a suitable real-scale impact test. This comparison shows the need to increase the height of the gravel overburden. In order to prove that a gravel layer thickness H = 2.7 m is sufficient to prevent the pipeline from inelastic deformations when the structure is hit by the design rockfall, several structural analyses with different values for R are carried out. This is done by means of a validated Finite Element model. As a by-product of the proposed semi-probabilistic design procedure, three different deformation modes of the hit pipeline are identified.