EXCEL-BASED TOOL FOR THE

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E

XCEL

-

BASED TOOL FOR THE

E

XCEL BASED TOOL FOR THE

RISK ANALYSIS OF ROCK

-

FALL

PROTECTION GALLERIES

Matthias Schubert

ETH Zürich, IBK, Group Risk & Safety

03.12.2008

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Overview

• Methodology

• Detachment process

• Falling process

• Failure gallery

• Consequences

• Software demonstration

©-M. Schubert

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Introduction

• The knowledge of the risk enables the strategic planning

of risk reduction measures and the budget planning.

• The currently used methodologies in the field of natural

hazards have principle drawbacks :

• Strong simplification

Æ

restricted informative value

• Probabilistic modeling knowledge required

Æ

High

• Probabilistic modeling knowledge required

Æ

High

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Introduction

• Generic models can close this gap

• Such models enables:

• The efficient assessment of risks – and automatic

ti

f

h

d

generation of hazard maps

• Use in the strategic planning (land use, investment in

Use in the strategic planning (land use, investment in

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Modeling of the detachment process

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System Exposures

• The relevant parameter is the volume of a detached rock

volume

V

or rock mass.

volume

V

or rock mass.

• Rockfall is an uncertain process – impossible to predict

the time and extend of the next event.

• The relevant rock-fall parameter can be described as a

random variable

V

.

• Typically described by its annual exceedance frequency

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Uncertainties in the modeling

It is reasonable to distinguish:

• Aleatoric uncertainties

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Th

d

f

b d

ib d b

Uncertainties in rock-fall exposure

• The exceedance frequency can be described by , e.g.:

• Include the epistemic uncertainties by modeling the

parameters (

A,B

) as a random vector

θ

=[

a,b

]

T

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Modeling of the rockfall exposure

•

For protection structures the annual maximum rockfall

event is of interest.

•

Derivation of the distribution

f

V

(

v

)

of the annual maximum

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The falling process

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Uncertainties in rockfall trajectories

• Once a rock is released its trajectory is mainly determined

by the topography, its mode of motion and its material

characteristics.

• Result of the trajectory

Result of the trajectory

simulation: energy/velocity at

the impact location.

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Generic characterization of the Slope

• Generic description of the

topography

• Description of the

geologic zones

• Massif Central

• Helvetic Nappes

• Penninic Nappes

• 18.612 different combinations have

been pre-calculated

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Generic characterization of the slope

• Results of the trajectory

Results of the trajectory

simulation are stored in a

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Calculation of the probability

f f il

f th

ll

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Cusion layer

From: Schellenberg K (2008) ON THE DESIGN OF ROCKFALL PROTECTION GALLERIES Dissertation ETH Zürich From: Schellenberg, K., (2008), ON THE DESIGN OF ROCKFALL PROTECTION GALLERIES, Dissertation, ETH Zürich.

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Shear force

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Bending of the global system

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Development of vulnerability curves

• Such deterministic (mechanical) models of assets can be

d

l

b l

used to develop vulnerability curves.

• Here the model from Schellenberg (2008) is used

• Here, the model from Schellenberg (2008) is used

• Vulnerability curves represent the conditional failure (or

damage) probability of an asset (conditional on the

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1 C ,Y, P ] g] 6000 7000 8000 10 20 30 40 50 2000 4000 6000 8000 100000 0.5 Pr [F |M ,V, C M a ss [ k g cushion= 40 [cm] plate= 70 [cm] SIA161:1993 2000 3000 4000 5000 6000 0 10 0 2000 Velocity [m/s] Mass [kg] 0 5 10 15 _{Velocity [m/s]}20 25 30 35 40 45 1 8000 9000 100000 0.5 P r [F |M ,V ,C ,Y ,P ] M a ss [ k g ] plate= 70 [cm] SIA161:1993 3000 4000 5000 6000 7000 0 10 20 30 40 50 0 2000 4000 6000 8000 Velocity [m/s] Mass [kg] _{Velocity [m/s]} cushion= 55 [cm] 0 5 10 15 20 25 30 35 40 45 2000 9000 0.5 1 [F |M ,V,C ,Y,P] SIA161 1993 M a ss [ k g ] 4000 5000 6000 7000 8000 0 10 20 30 40 50 0 2000 4000 6000 8000 100000 Velocity [m/s] Mass [kg] Pr [ cushion= 100 [cm] plate= 70 [cm] SIA161:1993 Velocity [m/s] M 0 5 10 15 20 25 30 35 40 45 2000 3000 4000

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Calculation of the failure probability

• The Bayesian network is used to

calculate the unconditional probability

p

y

of failure:

• Mean value

• Distribution

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Vehicle impact

• The probability of an vehicle impact in free-flowing traffic:

p

y

p

g

• Direct hit

P b bilit f

d i

P

[D] 1 0

Probability of dying

Pr

[D]=1.0

• Indirect hit

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Probability of dying

Adapted from: Evans, L. (1994). "Driver injury and fatality risk in two-car crashes versus mass ratio inferred using Newtonian mechanics." Accident Analysis & Prevention 26(5): 609-616.

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6. O

UTLOOK

• Possible extensions and further developments:

• Free roads

• Areas

• Implementing methodology in GIS

• Perform large scale risk assessments

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E