Project 2: Risk assessment for
geohazards
Project Manager: Unni Eidsvig (NGI)
Subproject 2: Case studies
The following case
studies and applications of the Integrated Risk Assessment Framework are
presented here:
Case study 1: Rock slopes
Case study 2: Slopes in clays
Case study 3: Snow avalanches
Case study 4: Tsunamis
Case study 1: Rock Slopes
When the Integrated
Risk Assessment Framework is implemented for rock slopes it takes the
form illustrated here.
Figure 1 Risk
assessment framework for rock slopes
Data collection
Data collection involves obtaining relevant data for geology, geometry,
strength, groundwater condition, dynamic loads and elements at risk.
Hazard assessment
Hazards assessment is composed of the following consecutive stages:
- Kinematic analysis:
The basic aim of this stage is to determine discontinuity sets which
governs the slope instability
- Numerical modeling:
This stage is for understanding the possible failure mechanism and
better determination of failure surface and slope geometry. Continuum
models are more appropriate for weak rock conditions while
discontinuum models are more suitable for competent rock situations.
The outputs of this stage are volume of rock mass to slide, geometry
of slip surface and depth of slide for weak rock and number of blocks
to slide and volume of sliding rock for competent rock.
- Sensitivity
analysis: This stage is for evaluation of model’s sensitivity to input
parameters. Here the sensitivity of Mohr-Coulomb and/or Barton-Bandis
failure criteria which are most frequently used failure criteria for
rock slopes can also be compared.
- Uncertainty
analysis: Prior to probabilistic modeling, uncertainty analysis is
essential in order to obtain more realistic slope failure
probabilities. The uncertainties associated with most sensitive
parameters are quantified and analyzed in this stage.
- Probabilistic
modeling: Failure probability for the considered rock slope can be
evaluated based on Monte Carlo simulation (MCS) or First Order
Reliability Method (FORM).
- Evaluation of slide
magnitude: The magnitude of the hazard can be assessed by constructing
probability of failure (Pf) versus possible rock block volumes.
Vulnerability
assessment
The vulnerability assessment in this case diminishes to 2-dimension as
the scale is small scale. Then vulnerability can be assessed in a (n x
m) matrix, where n is the type of elements at risk and m is number of
rock blocks to slide.
Risk assessment
Risk assessment starts with the computation of total and specific risk.
Case study 2: Slopes in clay
The zone assessed in
this study is located in an urban area on the Southern coast of Norway,
extending about 1 km along the banks of a river in the vicinity of a
fjord.
The quaternary geology
description indicates that the soils in the area are normally
consolidated. Typical soil profiles display river sand layer at the
surface with marine deposits down to bedrock. The transition from marine
deposits to sand/gravel deposits is lower than the river water level,
which means that the clay deposits are exposed to river erosion. The
sensitivity tests of the clay, indicates “quick clay” behaviour.
Figure 2 Model of the
area under investigation
Hazard assessment
To quantify hazard, a
scenario-based second-moment probabilistic limit equilibrium approach is
implemented. The spatial variability of undrained shear strength is
accounted for in the slope stability analyses. Spatial variability of
soil strength, river water level and river bed erosion were shown to
influence hazard and expected risk levels significantly.
Probabaility distributions of calculated
3-D factor of safety for "01yr" scenarios
Vulnerability
assessment
Vulnerability and elements at risk are estimated with a second-moment
approach. Values for vulnerability are obtained from published data and
engineering judgement. Categories of elements at risk are considered in
the study.
Risk assessment
Risk estimates are obtained based on hazard, vulnerability and the
potential loss associated with the elements at risk. The uncertainty in
risk estimates is quantified using first-order second-moment
approximation.
Case study 3: Snow avalanches
Figure 4
Avalanches constitute
a considerable natural hazard in snow-covered mountain areas. They are
fast moving masses of snow and debris on (steep) mountain slopes, which
can cause catastrophic destruction. During precipitation and/or storm
periods, snow accumulates on slopes. When the snow amount increases,
snow weight may exceed the shear resistance at some critical snow depth
and a slide will be released. In addition, external loads can contribute
to the release of a slab, like a skier or loading by explosives as done
for temporal mitigation. Also the reduction of the strength, for example
due to rapid warming or rain, can cause an avalanche release. During
their descent, avalanches may reach velocity up to 100 m s-1; the
flowing density is thought to range typically between 30 to 300 kg m-3.
Thus, impact pressures can be as high as several hundred kPa.
Two case studies for
avalanches have been performed where hazard, vulnerability and risk are
estimated:
1) A case
regarding the risk to a building in an avalanche path
2) A study
concerning the risk to traffic on a major mountain road.
Here the first of
these case studies is presented.
Risk to a
building in an avalanche path
A farm is
located at the foot of an avalanche path at about 30 masl.
Hazard assessment
The hazard is
comprised of two parts: the probability for release and the probability
for run-out of a snow avalanche.
Input parameters are:
-
Meteorology parameter: precipitation,
-
Slide release parameters, see table below
|
Random variable |
Distribution |
|
Thickness (or height) of slab, D |
Beta |
|
Slope angle, y |
Lognormal |
|
Shear strength of sliding plane,
ts |
Lognormal |
|
Width of slide, B |
Normal |
|
Length of slide, L |
Normal |
|
Density
of snow, r |
Lognormal |
|
Additional load Wext |
|
In
the hazard assessment, the following models for release and run-out are
used:
1. Release model: A
simple snow slab avalanche model is used for predicting the release, see
figure below. The release probability is denoted P release. The
probability of sliding, Pslide is found by integrating Prelease over all
snowdepths.
Figure 5
Snow-slab
avalanche definitions, coordinate system and acting forces (Lackinger,
1989).
2. Run-out model: An
energy line approach combined with Monte Carlo simulation is used for
run-out prediction. Based on simple energy considerations, the energy
line approach allows to determine the run out length and to give an
estimate on the velocity along the track:
Kinetic energy = loss of potential energy – energy
loss due to friction
The run out probability is denoted Ptravel
The avalanche hazard at
farm location is given by the probability of the avalanche occurrence
times the probability that the avalanche actually reaches the location:
H = Pslide∙Ptravel
Vulnerability assessment
Vulnerability curves for both constant flow density and velocity
dependent density are given in the figure below.
Figure 6 Cumulative
vulnerability curve versus avalanche speed (red solid line velocity
dependent density; red dashed line constant flow density). The blue
lines show corresponding specific loss curve for a monumental buildings.
The vulnerability of a
building is defined by integrating the probability of a specific loss
over all speeds.
Risk assessment
Building
The risk to a building is given by the product of hazard and the
vulnerability of the specific building
Inhabitants
The individual risk to a person is given by the product of hazard,
vulnerability and the exposure of the respective person.
The risk estimation
process is illustrated in the figure below.
Figure 7 llustration
of the steps in the risk assessment
Case study 4: Tsunamis
The scope of the study
is to quantify the risk associated with a rock slide at Åknes, which has
the potential to generate a tsunami. The Åknes rock slope is located in
Storfjorden in Western Norway. The area has been subject to a large
number of rockslides during post glacial time. In 1934 a rock slide hit
the fjord near Tafjord, also in the Storfjorden area, and caused a
disastrous tsunami which killed 41 people.
Data collection
Data has been collected from available literature about historical
rockslides in the Storfjorden area. Data for vulnerability has been
collected from sources containing fatality rates from tsunamis in
western Norway, from the December 2004 Indian Ocean tsunami and from the
July 2006 Java tsunami.
Hazard assessment
The Åknes threat is not the rockslide itself but its tsunamigenic
potential. This means that the hazard is comprised of two parts:
-
The probability of a rockslide at Åknes.
-
The probability of generating a tsunami caused by the Åknes rockslide.
The probability is
calculated from frequency of previous rockslides in the Storfjorden area
and from expert judgement.
Figure 1 The diagram
shows the number of rock-avalanche events and the volume distribution in
the entire Storfjorden, Blikra et al. (2005).
The tsunami generated
by the rockslide is calculated by numerical simulation using the linear
shallow water equations. Several rock volumes are considered in the
analysis. Corresponding run-up heights are calculated for four different
locations.
Vulnerability
assessment
In this study vulnerability to people is studied.
The quantitative vulnerability models for people are
based on historic data from statistics of previous tsunami disasters.
This is obtained in two steps:
- A
review of life’s losses caused by earlier tsunamis.
- A
formulation of a continuous model relating inundation height with
life’s losses.
Vulnerability curves
are proposed for vulnerability as a function of inundation height, these
curves, are shown in the figure below.
Figure 2 Empirical
quantification of vulnerability as a function of inundation height
Risk assessment
Two approaches are proposed for quantifying risk at the prescribed
locations in Storfjorden. An ‘implicit’ approach I, based on the
principle that the expected risk value equals the product of the
expected value of hazard, vulnerability and losses, including an
implicit relaxation on the dependencies between multi-threats; and the
Bayesian network approach BN, which relates the causal
dependencies between the threats and other relevant risk factors.
|
