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Semi-probabilistic design of rockfall protection layers

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Abstract

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.

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Abbreviations

a :

acceleration of boulder

d :

outer pipe diameter

d c :

characteristic size of boulder

g :

gravitational acceleration

E :

Young’s modulus of steel

E imp :

impact energy

F :

maximum impact force

F D :

F related to the design rockfall

F exp :

F related to a real-scale impact test

H :

height of gravel overburden

h f :

height of fall

I :

dimensionless impact function

I D :

I related to the design rockfall

m :

boulder mass

n :

statistical sample size

R :

indentation resistance of gravel

R 5% :

5% quantile of R

R 95% :

95% quantile of R

s :

co-ordinate following the inner surface of the pipe

t :

time

t p :

pipe thickness

V :

boulder volume

v 0 :

impact velocity

w :

boulder penetration depth at maximum impact force

w D :

w related to the design rockfall

X :

boulder penetration depth after completed impact

X D :

X related to the design rockfall

X exp :

X measured in a real-scale impact test

Δt :

impact duration

ν:

Poisson’s ratio of steel

ρ b :

mass density of boulder

ρ g :

mass density of gravel

σ vM :

equivalent von Mises stress

σ y :

uniaxial yield stress of steel

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Authors and Affiliations

  1. Institute for Mechanics of Materials and Structures, Vienna University of Technology (TU Wien), Karlsplatz 13/202, A-1040, Vienna, Austria

    Bernhard Pichler, Christian Hellmich, Josef Eberhardsteiner & Herbert A. Mang

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  1. Bernhard Pichler
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  2. Christian Hellmich
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  3. Josef Eberhardsteiner
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  4. Herbert A. Mang
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Correspondence to Bernhard Pichler.

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Pichler, B., Hellmich, C., Eberhardsteiner, J. et al. Semi-probabilistic design of rockfall protection layers. Comput Mech 42, 327–336 (2008). https://doi.org/10.1007/s00466-007-0207-5

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  • DOI: https://doi.org/10.1007/s00466-007-0207-5

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