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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

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.

Keywords

Semi-probabilistic design Rockfall Impact Gravel Validation 

List of symbols

a

acceleration of boulder

d

outer pipe diameter

dc

characteristic size of boulder

g

gravitational acceleration

E

Young’s modulus of steel

Eimp

impact energy

F

maximum impact force

FD

F related to the design rockfall

Fexp

F related to a real-scale impact test

H

height of gravel overburden

hf

height of fall

I

dimensionless impact function

ID

I related to the design rockfall

m

boulder mass

n

statistical sample size

R

indentation resistance of gravel

R5%

5% quantile of R

R95%

95% quantile of R

s

co-ordinate following the inner surface of the pipe

t

time

tp

pipe thickness

V

boulder volume

v0

impact velocity

w

boulder penetration depth at maximum impact force

wD

w related to the design rockfall

X

boulder penetration depth after completed impact

XD

X related to the design rockfall

Xexp

X measured in a real-scale impact test

Δt

impact duration

ν

Poisson’s ratio of steel

ρb

mass density of boulder

ρg

mass density of gravel

σvM

equivalent von Mises stress

σy

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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