Computational Mechanics

, Volume 42, Issue 2, pp 327–336 | Cite as

Semi-probabilistic design of rockfall protection layers

  • Bernhard PichlerEmail author
  • Christian Hellmich
  • Josef Eberhardsteiner
  • Herbert A. Mang
Original Paper


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.


Semi-probabilistic design Rockfall Impact Gravel Validation 

List of symbols


acceleration of boulder


outer pipe diameter


characteristic size of boulder


gravitational acceleration


Young’s modulus of steel


impact energy


maximum impact force


F related to the design rockfall


F related to a real-scale impact test


height of gravel overburden


height of fall


dimensionless impact function


I related to the design rockfall


boulder mass


statistical sample size


indentation resistance of gravel


5% quantile of R


95% quantile of R


co-ordinate following the inner surface of the pipe




pipe thickness


boulder volume


impact velocity


boulder penetration depth at maximum impact force


w related to the design rockfall


boulder penetration depth after completed impact


X related to the design rockfall


X measured in a real-scale impact test


impact duration


Poisson’s ratio of steel


mass density of boulder


mass density of gravel


equivalent von Mises stress


uniaxial yield stress of steel


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Copyright information

© Springer Verlag 2007

Authors and Affiliations

  • Bernhard Pichler
    • 1
    Email author
  • Christian Hellmich
    • 1
  • Josef Eberhardsteiner
    • 1
  • Herbert A. Mang
    • 1
  1. 1.Institute for Mechanics of Materials and StructuresVienna University of Technology (TU Wien)ViennaAustria

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