Présentation Dr Suzane Lacasse (Directrice Technique NGI) - SCG Ouest Québec

Approche fiabiliste pour un
dimensionnement plus robuste
Suzanne Lacasse
Institut de géotechnique norvégien (NGI) Oslo Norvège
Société canadienne de géotechnique
Section Ouest du Québec
2018-06-07

Design approaches
• “Working stress" design (WSD) approach based on an
overall factor of safety has been used for a long time.
• Modern design codes are based on the LRFD approach
(Load and Resistance Factor Design) in North America
and the characteristic values and “partial safety factors”
approach in Europe.
• Reliability-based design (RBD) using a target annual
failure probability or target reliability index.
- More rigorous, more “complete”
- Accounts for the uncertainty in the analysis
parameters and their correlation(s) explicitly.
- Will give you a more robust design.
Level I
Level II
Level III

Reliability-Based Design (RBD)
• All predictions are subject to uncertainties.
• Realistically, safety (or serviceability) can be assured
only in terms of the probability that the available
strength (resistance, capacity) will be adequate to
withstand the lifetime maximum load.
Robustness (“robustesse”):
Ability to accommodate what is unforeseen

• Concepts de base, dimensionnement fiabiliste
• Cas d’études
• Barrage en enrochement
• Jacket pétrolier offshore
• Facteur de sécurité et écoulement (runout), argiles
sensibles
• Evaluations qualitatives
• Risque acceptable
• “Stress testing”, multi-dangers à Hong Kong
• Conclusions
Contour de la présentation

Risk assessment and management
[ISO-3100:2009]
RISQUE:
“Risk is the effect of
uncertainty on objectives.”
“Le risque est l’effet des
incertitudes sur les objectifs à
atteindre”.
DECISION-MAKING:
ISO 2015:2394
Need to do «risk-informed
decisions»
«Prendre des décisions en
connaissant les risques.»

Deterministic analysis
Model
(mathematical
idealization)
Soil properties
Loads and
drainage conditions
Geometry, etc.
Safety factor
Acceptance criterion:
FS ≥ FSacceptable

Model
(idealization
including
uncertainty)
Soil properties
Loads and drainage
conditions
Geometry etc.
Safety margin
Probability of failure (Pf)
Reliability index (β), …
Probabilistic analysis
Acceptance criterion:
β ≥ βacceptable
Pf < Pf tolerable/acceptable

Factor of safety and
probability of failure
We need to be aware that Pf is never zero!
Pf

• Cas d’études
sensibles
• “Stress testing”, multi-dangers à Hong Kong
• ConclusionsEvaluations qualitatives

Risk assessment of embankment dam
Dravladalsvatndammen

Dravladalsvatndammen: Rockfill hydropower dam
Built 1971-72
Dam height 29 m
Dam length 780 m
Reservoir volume58 million m3
Central inclined moraine core
1 Moraine core
2 Filter
3 Transition
Rockfill is quarried rock

In an event tree, the events at a
node should be defined such that
they are mutually exclusive
(cannot occur simultaneously).
Event tree analysis (ETA)
A "What happens if " type of analysis
Initiation continuation progression to failure
/yr
[Hartford & Baecher 2003]

Event tree analysis (ETA)
Probabilities at a node of the event tree
● Statistical estimates based on observations, test results etc.
● Engineering calculations with models based on physical
processes.
● Expert judgment developed through evaluated experience.
Usually done by an expert team
“The collective judgment of experts, structured within a
process of debate, can yield as good an assessment of
probabilities as mathematical analyses” [Vick 2002].

Probability Verbal description of probabilities
≈ 0.0 – 0.005
Mean= 0.1%
Virtually impossible,
due to known physical conditions or process that can be described and
specified with almost complete confidence
0.005 – 0.02
(1%)
Very unlikely,
although the possibility cannot be ruled out on the basis of physical or
other reasons
0.02 – 0.33
(10%)
Unlikely,
but it could happen
0.33 – 0.66
(50%)
As likely as not (unknown),
with no reason to believe that one possibility is more or less likely
than the other
0.66 – 0.98
(90%)
Likely,
but it may not happen
0.98 – 0.995
(99%)
Very likely,
but not completely certain
0.995 – ≈ 1.0
(99.9%)
Virtually certain,
due to know physical conditions or process that can be described and
specified with almost complete confidence
How to quantify and describe the uncertainties?

Spillway approach
The spillway approach of the
dam could be blocked by ice
and hard-packed snow in the
winter time.
Spillway
Spillway tunnel entrance
Approach channel

Failure mode screening
Weaknesses in the dam
Internal erosion
Slides in the upstream and/or
downstream slopes
Rockslide in reservoir
Plane of weakness in bedrock
foundation
Operator error
External triggers
Flood (summer)/extreme
snows (winter)
Earthquake
Melting of glacier (flood)
Sabotage
Meteor impact, plane crash

Example event tree analysis
Dravladalvatndammen
Overløps
-
problemer
vinter
0.9
0.1
Overløp ikke
fylt med snø
Overløp fylt
med snø
Ikke hardpakket
snø eller is som
blokkerer
Hardpakket snø
eller is som
blokkerer
0.05
0.95
Vannstand
<954m
Vannstand >
954m
0.1
0.9
0.9
0.1
Kraftstasjonen
går
Kraftstasjonen
går ikke
0.9
0.1
Bypass åpnet
Bypass ikke
åpen
Bunntappeluke
åpen
Bunntappeluke
ikke åpen
0.5
0.5
0.9
0.1
Flom som ikke
fører til
overtopping
Flom som
forårsaker
overtopping
Ikke dambrudd
Dambrudd
0.1
0.9
0.5
0.5
Bunntappeluke
åpen
Bunntappeluke
ikke åpen
Flom som ikke
fører til
overtopping
Flom som
forårsaker
overtopping
0.02
0.98
Ikke dambrudd
Dambrudd
0.1
0.9
0.5/år
1.3·10
-8
/år
2.3·10
-7
/år
ΣP
brudd
=2.4
⋅
10
-7
/år
Hendelse:
Flom på vinterhalvåret (is og
hardpakket snø i overløpet)

Tid på året og
hendelser
Snø i overløp?
Is og hardpakket
snø?
Vannstand i
magasinet?
Går kraftstasjonen? Er bypass åpen?
Er bunntappeluke
åpen?
Flom som fører til
overtopping?
Omfatter
vinterhalvåret,
P = 0.5
Hendelser:
Overløpsproblemer
kombinert med
flom
(Fig E.3)
-
Forårsaket av
snøsig inn i
overløpet
-17 m akkumulert
snø årlig i
Dravladalen
.
-
Siden 2012:
Overbygg med tette
sidevegger over
eksisterende
flomløp, som
fungerer bra
- Is og hardpakket
snø kan tette
overløpet
-
Ikke høyt
vanninnhold i
snøen, som er en
forutsetning for
isdannelse
-
Lite sannsynlig
med tine/fryse
prosesser-
Kun delvis
blokkering
-
Vannstand høyest i
desember,
synker
fra januar til juni-
Sannsynlighet for
vannstand over
nivå 954m i April: 5
- 10%.
-
Benytter 10% som
representativt for
sannsynligheten
på vinteren
-
Nivå under 954m:
tilstrekkelig fribord i
magasinet
Merk: Nivå 954m er
3m under
HRV=957m
.
-
Konservative
sannsynligheter
basert på
driftserfaring
-
Konsensus fra
workshopen
-
Konservative
sannsynligheter
basert på
driftserfaring
-
Konsensus fra
workshopen
-Bypass er en
energidreper som
gjør det mulig å
tappe forbi vann
dersom
kraftstasjonen står
.
Den kan ikke nyttes
samtidig med
kraftstasjonen,
derfor vurderes
ikke
kombinasjoenen av
kraftstasjon og
bypass.
-
Bunntappeluken
er testet
-
Åpning er
avhengig av
fremkommelighet
av personell og
strøm
-
Samlet slukeevne i
kraftstasjon og
bunntappeluke er
45 m
3
/s
-10 årsflom 40m
3
/s,
sannsynlighet 0.1
-
Hvis
kraftstasjonen går
(nedre forgrening)
vil kun flommer
større enn 50års
flommen
(sannsynlighet 0.02)
forårsake
overtopping
Example event tree analysis
Dravladalvatndammen

Dam Dravladalen
Results before rehabilitation
Event Most probable failure mechanism
Prob. of
failure, Pf
Seismic Overtopping due to settlement of dam < 1,5 x 10-6/yr
Hydraulic
Overtopping due to plugging (hard snow,
ice) of spillway and tunnel
3 x 10-3/yr
Internal
erosion
Damage and failure of downstream fill and
toe
5 x 10-4
(lifetime)
Sabotage Overtopping due to bombing of dam crest < 1 x 10-5/yr

31 March 2000
Ice and hard snow blocking spillway

Dravladalsvatndammen - rehabilitation
Early 2000s
• New toe to increase drainage capacity
• New leakage measurement system
• New fill protection system downstream
• Higher crest and new crest protection
• New spillway
2008 – 2012
• New fill thickness and fill protection upstream
• Structure to keep open the spillway during very snowy/windy winter
seasons
• Increase drainage capacity in tunnel
• Instrumentation of upstream slope and crest, automatic measurement of
leakage

Ice and hard snow blocking spillway?
Protective cover built over the spillway
approach to mitigate risk of blockage of
drainage due to snow drift.
(Photos: Statkraft)
2 March 2012

Ice and hard snow blocking spillway?
31 March 2000
24 March 2015

Dam Dravladalen
Results after rehabilitation
Potential trigger for failure
Annual prob. of
failure, Pf annual
Internal erosion due to leakage 5 ∙ 10-6
Flooding
Ice and hard snow blocking spillway
(winter)
2 ∙ 10-7
Glacier melting inn water reservoir
(summer)
5 ∙ 10-6
Earthquake 9 ∙ 10-8
Total probability of failure (geo) 1 ∙ 10-5
Sabotage* 2 ∙ 10-5
* Large uncertainty

Once per 1.000.000 yr
Annual failure probability, other dams
Once per 1.000 yr
Dam Dravladalen
(2016)
Dam Dravladalen
before rehabilitation

 The first risk analysis identified a new, and so far
ignored, mode of failure.
 The best estimate of the annual probability of failure
today for Dam Dravladalen after rehabilitation is 10-5
(once pr 100.000 years), and is now lower than
reported probabilities of failure for dams worldwide.
 The rehabilitation reduced the estimated probability of
failure significantly.
 Uncertainties around sabotage/terrorism are large and
can well be higher than 10-5 per year. New precautionary
measures.
Added value of reliability analyses

 ETA looks at all potential failure modes in a systematic
manner.
 ETA can be reused and adjusted through the entire
lifetime of the dam.
 Reliability analyses provide means to compare the safety
of a facility with other facilities and the efficiency of
different mitigation measures.
 Probabilistic risk analysis in dam engineering has been
coined as a «systematic application of engineering
judgment» [Vick 2002; Høeg 1996].
Added value of reliability analyses

Motivation
• Guidelines require the same level of safety for the new
CPT-based pile capacity design methods as for the older
API method.
• The designer is required to select an "appropriate" safety
factor when using the newer CPT-methods.
• The designer can choose to:
1) be conservative and apply a "high" safety factor or
2) document the level of safety (through the
calculation of the reliability index (or “probability of
failure")).

Safety evaluated with partial safety factors:
γl ⋅ Char Load ≤ Char Capacity/γm
~

FORM/SORM approach to derive partial
safety factors corresponding to a target Pf =
10-4/yr

Undrained
shear strength,
Su
UU
Site A
“clay site”
0 200 400 600
Undrained shear strength, suUU (kPa)
100
80
60
40
20
0
Depthbelowseafloor,m
Mean
Mean ± 1 SD
Characteristic
0.25po'

Consequence for required
pile penetration depths at 3 sites
Method
Required pile penetration depths
Site A
(clay)
Site B
(sand)
Site C
(clay and sand)
NGI-05
90 m to
75 m
51 m to
27 m
45 m to
36 m
Reduction of the deterministic pile penetration depth
(NGI-05 CPT method), because it was documented
that Pf < 10-4/yr.

Failure in strain-softening clay
Shear deformations, PLAXIS [Jostad 2014]
Perfectly plastic
Strain-softening

Lessons from back-calculations of earlier
failures and finite element modelling
• Limit equilibrium analysis cannot find the critical
mechanism of failure and cannot model progressive
failure nor ensure strain compatibility.
• If limit equilibrium analysis is used, and they will continue
to be used, we need to account for strain-softening and
progressive failure.
• How can we find a factor that will be representative of the
strain-softening behaviour? Selected to apply a
correction factor on the safety factor
γMstrain-softening
= γM ∙ Fsoftening

Monte-Carlo simulations to obtain Fsoftening

Required reduction in peak undrained shear strength
if LE analysis is used [Jostad et al 2013]
Mean
2,5% simulations
12% simulations
Requiredreductioninpeaksu

Significant factors in analysis
(Jostad et al 2015; Dolva et al 2016)

Correction factor on the safety factor
γMstrain-softening
= γM ∙ Fsoftening

Landslide
risk
analysis
through
scenarios
(After
Corominas et
al., 2014;
SafeLand
project)
ISO 2394:2016 Need for “risk-informed decisions”

LANDSLIDE RUNOUT
Visco-plastic model
with Herschel-Bulkley rheology ('BING CLAW‘)
• Extension of NGI’s Bing
model
• Depth-averaged model
in two horizontal
dimensions
• Implemented with
finite volume method
in Eulerian coordinates
Rotation speed (rps)
(Grue et al 2017)
Torque(mNm)
(Locat and Demers, 2018)

Herschel-Bulkley model
Constant velocity profile for the plug and parabolic
velocity profile for the shear layer.
Plug
layer
Shear
layer

Visco-plastic model parameters
• 𝑛𝑛 : fluid index (0 < 𝑛𝑛 ≤ 1)
• Strain rate, ̇𝛾𝛾𝑟𝑟 =
𝜏𝜏𝑦𝑦
𝜇𝜇
1
𝑛𝑛
• Remolding varies exponentially with the accumulated
bottom shear
• 3 parameters to describe behaviour:
𝜏𝜏𝑦𝑦,0 : initial yield stress
𝜏𝜏𝑦𝑦,∞ : remoulded yield stress
𝛤𝛤 : remoulding parameter

Visco-plastic model parameters
Random variable Mean SD CoV PDF
Initial yield stress 𝜏𝜏𝑦𝑦,0 (kPa) 20 2 10% LN
Residual yield stress 𝜏𝜏𝑦𝑦,∞ (kPa) 0.5 0.05 10% LN
Gamma 𝛤𝛤 0.02 0.01 50% LN

Influence of Γ-value on averaged yield stress
0 100 200 300 400 500
Accmulated yield shear strain
0
0.5
1
1.5
2
Yieldstrength,Pa
10
4
= 0.05
= 0.03
= 0.01
−−− Γ = 0.01
−−− Γ = 0.05
−−− Γ = 0.03

What does Γ- mean?
Replaces the remoulding index vs normalised energy and Ip
(Flon (1982); Tavenas et al, 1983; Yong and Tang , 1983)

Runout distance = f(Γ)
0
400
800
1 200
1 600
0 0,01 0,02 0,03 0,04 0,05 0,06
Runoutdistance(m)
Remolding rate Γ
Measured

Observed vs calculated runout distance

400
600
800
1000
1200
1400
1600
0 0,02 0,04 0,06 0,08 0,1
Runoutdistance(m)
Gamma
1000 Monte Carlo simulations of landslide
movement, Phase 2 - Runout distance

Max = 1413
Min = 590
Mean = 1122
SD = 188
COV = 0.168
N = 1000
500 700 900 1100 1300 1500
Runout distance, in m
0
40
80
120
160
200Frequency
1000 Monte Carlo simulations of landslide
movement, Phase 2 - Runout distance

Average
deposit
height
Max = 5.2
Min = 1.3
Mean = 3.7
SD = 0.9
COV = 0.236
N = 1000
0.5 1.5 2.5 3.5 4.5 5.5
Deposit height, in m
0
30
60
90
120
150
Frequency

6 m
Measured
Runout Measured Use in design (Mean + 1 SD)
Distance 1200 m 1122 to 1310 m
Ave deposit thickness 4 3.7 to 4.6 m
Max deposit height 6 5.2 to 6.3 m

Kattmarka slide • Retrogressive slide with 5 phases
• Initiated at phase 1 area by rock blasting
• Main slide movement for 10 minutes
• Volume of 300,000-500,000 𝑚𝑚3
in an
area of 300 m x 100 m
• Remolded yield strength is 0.6-1 kPa

Back-calculation of the Kattmarka slide

Added value
 One of very few models for runout in sensitive clays (and tailings)
 A good prediction of maximum runout is of great significance for
reducing and mitigating landslide risk.
 New numerical model to predict landslide runout in sensitive clays:
 Reasonably good prediction of Stage 2 of the Rissa landslide. Used
for 9 landslides so far.
 Challenge: finding representative analysis parameters for strength
reduction.
 Improvements underway
 Include non-sensitive topsoil riding above the sliding sensitive clay.
 Dedicated laboratory and theoretical studies to provide a priori
criteria for choosing 𝛤𝛤.

• Cas d’études
sensibles
• Structures linéaires
• Protection de la collection au musée Viking
• Conclusions

• GIS-based
• Risk matrix (hazards
and consequences)
along railway
corridors
• Qualitative method
Risk assessment for railways (for Bane Nor)
Hazard analysis
 average slope angle
 slope direction (rel.to railway)
 soil type
 area of exposed slope
 earlier sliding evidence
 drainage capacity
 potential erosion
Consequence analysis
elements at risk
 terrain conditions at time of
potential derailment
 impact speed
 accessibility for rescue

Efficient risk
assessment for linear
infrastructure
Illustrative risk map [Hefre
et al 2016].
• hazard class
• consequence class
• risk class

Value added of
risk qualification
• Simple
• Cost-efficient tool for
continuous risk assessment
on a regional scale
• Great potential for use in all
large scale linear
infrastructures
• Important method for
prioritising risk-reducing
measures

Extension of Viking Ship Museum (Oslo)

i Traffic
Sheetpiling
Digging of
trenches for
attenuation
barrier

Risk matrix
• Project phases
• 1 Design and planning
• 2 Preparation work
• 3 Pre-excavation for sheetpiling
• 4 Sheetpiling
• 5 Excavation, construction pit
• 6 Shoring and stiffeners
• 7 Local conditions, environment
Sources of uncertainty
1 Material
2 Design
3 Execution
4 Environmental loads (natural)
5 External loads
6 Extreme rainfall
10 High groundwater
11 Fallout on excavated slopes
Consequences
H Health damage or fatality
M Environment
F Progress in execution
Ø Economy
[Engen & Langford 2016; Kalsnes et al 2016]

5
4 1:3-FØ, 4-FØ
3 2:3-FØ
2
3:1-FØ, 2-FØ
5:4-Ø, 9-HF
2:1-FØ, 2-HM
4:1-Ø, 2-Ø
7:2-MØ
1:1-FØ
5:11-HFØ, 12-FØ
6:1-F, 2-HØ, 3-FØ, 4-FØ,
5-FØ
7:1-MØ
1 2:4-MFØ
5:10-FØ
6:7-FØ
1:2-HMFØ
5:2-MFØ, 3-HMFØ, 5-
Ø, 7-H, 8-H
1 2 3 4 5
Probability
Consequence
Each matrix cell
1:3—FØ
Constr. Phase : Uncertainty
—Consequences
Probabilityclassestimate
Consequence class
Risk matrix
Excavation

Risk matrix
Damage to the Viking ship collection
Consequence class
Probabilityofdamageclass

Whitman, 1984
Risk acceptance
How much risk are we willing to accept?

Acceptable risk: Requirements [GEO, 2008)
Detailed
study

F-N curves and acceptable risk
The F-N plot
is one useful
vehicle for
comparing
calculated
probabilities
with, e.g.,
observed
frequencies
of failure of
comparable
facilities.

F-N diagram for geohazards USA 1900- 2013
(Abedinisohi 2014)
• Curves from Baecher. Del i 2

Extreme events
1 10
10-1
100 1000 10000
10-3
10-5
10-7
10-9
10-11
Ånnualfailureprobability
Number of fatalities or damage costs
Unacceptable
Acceptable
Stress testing:
Subject the system to
extreme scenarios
Focus on the
identification of the
weakest links in a
system and to make
the system more
robust at these links.

Critical facilities designed to withstand events with
Pf of 10-4 - 10-6 / yr are not 100% safe. The risk is
often governed by low-probability - high impact
extreme events that occur very
rarely. There is, however, usually
not enough data to make statistical
estimates of the probabilities (also
a central concern in UN’s IPCC
SREX Report 2012)
Emerging solution:
“Stress testing"
Emerging approach

0.01
0.1
1
10
100
1000
0 0.1 0.2 0.3 0.4 0.5
Storm-basedlandslidedensity(nos./km2)
Normalized maximum rolling 24-h rainfall
June 2008 storm
in Hong Kong
Typhoon
Morokot in 2009
Correlation between natural terrain landslides and rainfall in Hong
(Zhang et al 2017)

Stress-testing for evaluating the Hong Kong
slope safety system
Stress
scenarios
Develop critical rainstorm scenarios under the
changing climate (earlier experience)
Impact,
system
response
and risks
Evaluate sizes, locations and impact areas of
landslides, debris flows, and flash floods.
Evaluate response of «slope safety system».
Assess consequences of multi-hazard events (No.
of people and No. of buildings affected)
Manage-
ment
strategies
Mitigation: Find “bottlenecks” and develop
strategies to improve performance
Assess effectiveness of proposed strategies
Quantify changes in risk profile due to mitigation

Input layers for the cell-based regal landslide analysis (Zhang et al 2017)

Landslides, debris flows and floods on north Hong Kong
Island, extreme storm of 85% PMP (Zhang et al 2017).

Hazard intensity for flooding due to landslide-dam
breach (Zhang et al 2017)

Stress testing results
• Four scenarios: 29%, 44%, 65% and 85% PMP
• Number of slope failures and debris flows (and
consequences) increased abruptly from 44 to 65 %
PMP
• From 65 to 85% PMP, impact (increase in
landslides/debris flows) was less distinct.

Stress tests were imposed by WENRA on all nuclear power
plants in Europe in 2011 and 2012 in the aftermath of
Tōhoku earthquake and Fukushima Dai-ichi accident.
Japan,
11 March 2011

Conclusions
• Natural and man-made hazards will continue to happen
despite our best efforts to prevent them. Society must
learn to live with landslide and other risks.
• Quantitative Risk Assessment (QRA) is a useful tool for
evaluating risk, comparing alternatives and evaluating the
need for mitigation. But it needs to be “dynamic”.
• Vulnerability is increasingly important in risk management.
Vulnerability “belongs” to several disciplines and addresses
many types of assets.
• Risk and probability tools have reached a degree of
maturity that make them effective to use in practice. They
provide more insight than deterministic analyses alone.
They help reduce uncertainty and focus on safety and cost-
effectiveness.

The role of our profession
Hazard and risk assessment, management and
governance requires a strong component of
communication.
Our role is not only to act as scientists and engineers
providing judgment on factors of safety. Our role has
evolved to providing input in the evaluation of hazard,
vulnerability and risk associated with landslides. Our
profession should be increasingly perceived as
reducing risk and protecting people.

Perspectives
Need for a cultural shift
Hazard
Response
Reactive
Science-driven
Response management
Single agencies
Planning for communities
Consequence
Preparedness & risk reduction
Proactive
Multi-disciplinary
Risk management
«Everyone’s business»
Planning with communities

Uncertainties
In all
geotechnical
assessments,
one needs to
deal with
uncertainties,
either
implicitly or
explicitly.
E18 expressway in Norway, February 2015
Slide in sensitive clay causing bridge collapse
[Photo: SVV 2015]

Probabilistic analyses and RBD complete the picture by
making explicit the uncertainties and their effects;
Deterministic analyses and design with a factor
of safety give an impression of certainty;
For robust and improved geo-design,
we need both.

“Le doute est un état mental
désagréable, mais la certitude
est ridicule.”
Voltaire
(1694-1778)
“A woman's guess is much more
accurate than a man's certainty”.
"L'intuition d'une femme vaut toujours
plus que la certitude d'un homme."
Rudyard Kipling
(1865-1936)

Présentation Dr Suzane Lacasse (Directrice Technique NGI) - SCG Ouest Québec

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