Investigation of Extreme Flood Processes & Uncertainty (IMPACT)

Investigation of Extreme Flood
Processes & Uncertainty (IMPACT)
Identifying Potential Breach Location
WP2: Deliverable D2.4.1
December 2004
Table of contents
1.
INTRODUCTION ..........................................................................................................................3
2.
EXISTING METHODOLOGIES AND POTENTIAL APPROACHES...................................4

2.1. GENERIC APPROACHES ..............................................................................................................4
2.2. UK, DUTCH AND GERMAN APPROACHES...............................................................................4
2.3. AN INTRODUCTION TO PC-RING ................................................................................................5
2.3.1.
AN INTRODUCTION TO THE FAILURE MODES USED IN PC-RING .............................................5
2.3.2.
MAIN STEPS TAKEN IN PC-RING CALCULATIONS ...................................................................6
2.4. AN INTRODUCTION TO THE RASP TIERED METHODOLOGY AND FRAGILITY CURVES .................9
2.4.1
RASP.................................................................................................................................9
LEVEL ...................................................................................................................................................9
2.4.2
RASP and fragility curves...............................................................................................10
3.
LOCAL FACTORS AFFECTING EMBANKMENT PERFORMANCE ..............................12

3.1. AN INTERACTIVE PROBLEM .................................................................................................12
3.1.2.
Internal factors ...............................................................................................................14
3.1.3.
External factors ..............................................................................................................15
3.1.4.
Environmental factors ....................................................................................................16
3.1.5.
Human factors ................................................................................................................17
4.
METHODOLOGY FOR IDENTIFYING POTENTIAL BREACH LOCATION.................18

4.1
CONCLUDING REVIEW .............................................................................................................18
4.1.1
Systems approach ...........................................................................................................18
4.2
CONCLUSIONS .........................................................................................................................18
4.1.1
Local approach...............................................................................................................18
4.3
CONCLUSIONS .........................................................................................................................19
5.
REFERENCES .............................................................................................................................21
APPENDICES ......................................................................................................................................23
APPENDIX A
PC-RING ...............................................................................................................24
AN INTRODUCTION TO PC-RING..........................................................................................................24
INTRODUCTION TO THE FAILURE MODES USED IN PC-RING .................................................................25
Overtopping/overflow.....................................................................................................................26
Erosion of inside slope ...................................................................................................................26
Saturation .......................................................................................................................................27
Instability of the inside slope ..........................................................................................................27
Uplifting and Piping .......................................................................................................................29
Damage of revetment on the outside slope and erosion of the embankment body..........................29
Structures........................................................................................................................................32
STATISTICAL MODELS .........................................................................................................................35
Statistical models of random variables in PC-Ring in general ......................................................35
Statistical models of hydraulic boundary conditions......................................................................35
AVAILABLE CALCULATION METHODS IN PC-RING ..............................................................................38
CALCULATION METHODS AS APPLIED IN PC-RING ..............................................................................38
1. Introduction
Earth embankments form a critical component of many EC countries flood defence systems.
In comparison to other flood defence types (e.g. walls, piling etc), embankments typically
form the greatest percentage of defence type. In the UK alone, it is estimated that there are
approximately 35000km of flood defence embankment all of which require regular
inspection and maintenance to ensure that flood defence performance is maintained at an
acceptable and appropriate level.
With such a maintenance commitment, any systemised approach that will allow maintenance
works to focus on priority areas of embankment will allow more effective use of limited
resources. As specified in the DoW, the objective of this work package is to try and identify
whether the likely mode and location of a breach failure in a long length of embankment can
be established in relative risk terms. This would allow owners of large lengths of flood
embankment to prioritise maintenance works according to the risk of breaching.
This report addresses IMPACT Deliverable D2.4.1 - Breach location methodology / model to
identify the relative risk of breach formation in long lengths of flood defence embankment.
2. Existing methodologies and potential approaches

2.1.
Generic approaches
Before considering what approaches are being developed in Germany, Netherlands and the
UK, it is worth considering some generic issues. When looking at breach location, two scales
of analysis may be considered:
Local:
System:
What local factors are affecting embankment performance

How can you represent embankment performance within a system of
defences, and can relative risk of failure be identified?
Each approach is relevant. The system approach potentially allows the relative risk of failure
of defence lengths to be considered, and hence could permit focussing of attention down to
critical lengths. The local approach allows consideration of a defence length, and
understanding of specific local issues, so permitting effective repair or maintenance works. In
this context, a defence length could comprise a section of defence embankment ranging from
metres to kilometres in length.
Work undertaken in WP6 addresses the issues of local factors. IMPACT partner H-EURAqua
has been collating historic records of embankment failures in Hungary and Czech Republic
for the purpose of analysis to identify typical factors affecting breach. The focus of this report
therefore addresses the system approach to identifying breach location although an overview
of potential approaches is reviewed in Section 4.
2.2.
UK, Dutch and German approaches
Development of a systems based approach for identifying flood risk (and hence the
performance of flood defence structures, hence the risk of breach formation through defence
embankments) is an area where significant progress has been made during the last few years.
The countries most active in developing these system risk based approaches are the UK,
Netherlands and Germany.
In the UK the Environment Agency / Defra joint research programme on flood defence
continues to fund a series of research development projects, building on an original project
called RASP: Risk Assessment of flood and coastal defences for Strategic Planning. This
project aimed to develop tiered methodologies for the risk assessment of flood defence system
performance. RASP used and built upon reliability-based design tools developed for dike
rings in the Netherlands.
The tool used in the Netherlands is software called PC-Ring which has been developed to
allow system based calculations on the risk of flood defence failure. This first application of
PC-Ring in the UK supports an evaluation of the appropriateness of this reliability method for
flood defences as part of the detailed level methodology in RASP.
Sea dikes are amongst the most important coastal structures along German coastlines.
Reliability and risk based design concepts have been increasingly proposed during the last
years in Germany (see Oumeraci and Kortenhaus, 2002). The probabilistic methods on which
these concepts are based allow accounting for the uncertainties in the input parameters and
the models describing possible failure modes of various types of coastal structures. However,
these methods are very often limited to simple cases or to just one or a couple of failure
modes.
2.3.
An introduction to PC-Ring
Technological developments of computers in the nineties have enabled the calculation of

probabilities of failure of flood defence systems. The limit state functions applied in this
software are based on former non-probabilistic reliability methods employed in the
Netherlands.
The probabilistic calculations done with PC-Ring correspond with the detailed level
methodology in RASP and take into account a large number of flood defence sections and
multiple limit state functions. The main outputs from these calculations are:
Probabilities of failure for each flood defence section included in the calculations and
therefore an overview of the weak areas in the flood defence system;
Insight into the key failure mode of a system of flood defences;
Insight into the uncertainties associated with the parameters in the limit state functions
and their contributions to the total probability of failure of the flood defence sections.
The local probabilities of failure can be used in determining the spatial distribution of risk.
Defence improvements can be targeted to flood defence sections contributing most to the risk
in the floodplain. The insight in which model parameter contributes most to the probability of
failure of the flood defence section in combination with the limit state function provides
advice on what kind of improvement activities are expected to be most effective. The
effectiveness of different improvement options can be compared by analysing the reduction of
risk in the floodplain associated with each option (see Buijs et al. (2003)i).
The reliability models applied in the limit state functions in PC-Ring are similar to those
applied in the UK within RASP. The limit state functions of the failure modes implemented in
PC-Ring are given as an example of how to fit current practice models for failure modes into
limit state functions. Specific details can be found in Buijs (2003)ii and translated from
Vrouwenvelder et al. (2001) and in Lassing (2003)iii. A very comprehensive discussion of
limit state functions in connection to embankments can also be found in Kortenhaus &
Oumeraci (2002)iv.
2.3.1. An introduction to the failure modes used in PC-Ring
PC-Ring only includes failure modes concerned with structural failure. The following failure
modes of embankments are included in PC-Ring:
Overtopping/overflow.
Instability of the inside slope.
Piping.
Damage of the revetment on the outside slope and consequently erosion of the
embankment body.
The fault tree of these failure modes related to an embankment is given in Figure1.
To calculate the likelihood of failure via each of these different failure modes, limit state
equations have been developed and are applied in conjunction with a measure of loading. This
approach allows the analysis of an entire flood defence system and permits extraction of the
most probable cause and location of failure. A more detailed explanation of this approach can
be found in Appendix A, including details of the limit state conditions.
2.3.2. Main steps taken in PC-Ring calculations

The following steps are taken in the calculation of the flood defence systems probability of
flooding:
1. Calculation of the probability of failure of one flood defence cross section for one tide,
one partial failure mode (for instance failure mode overtopping, partial failure mode
saturation), given the wind direction.
2. Combination of the partial failure modes resulting in the probability of failure of one total
failure mode.
3. Taking the probability of the wind directions into account.
4. Determining the probability of failure due to one failure mode for the total flood defence
stretch for which the under step 1 mentioned flood defence cross section is representative.
5. Combining the probabilities of failure of all the wind directions.
6. Determining the probability of failure for the total regarded period.
7. Combining the probabilities of the different failure modes.
8. Combining all the flood defence stretches to find a total flood defence systems
probability of flooding.
The process of cross section selection and data gathering is as follows:
1. Division of the water defence system in defence types.
2. The next step is to divide the water defence system in embankment stretches. To this end
rough information and insights are used. The division is based on the external physical
characteristics and not yet on the characteristics directly connected to the failure modes,
although implicitly the connections are there. The following characteristics are important
for this selectionv:
Orientation to the wind directions: embankment stretches that are orientated

differently will be loaded by different wave regimes and therefore must be discerned
as different embankment stretches.
High water regimes, differences in extreme water levels: lengths of the water defence
system for which different high water regimes are relevant must be discerned as
separate embankment stretches.
Geometrical characteristics foreshore: Embankment stretches with significant
different sizes of the foreshore in terms of height and width.
External geometry of the water defence: lengths of the water defence system with
significant differences in height and (external) construction are discerned as different
embankment stretches. Differences in geometry will lead to differences in loading
conditions due to the same hydraulic boundary conditions.
3. The water defence system has now been divided into rough stretches with the same type
of characteristics. However, cross sections have to be determined which can be regarded
as representative of the total embankment stretch. If still significant differences between
cross sections in an embankment stretch are present, then the stretches need to be divided
into further parts: the flood defence sections. A first insight with regard to weak spots in
the water defence system can be given by managing authorities. These authorities can
also help to determine the relevant failure modes for certain embankment sections. The
following failure mode related considerations can form a basis for a division in
embankment sections:
Different types of outside slope revetment (types and construction), this will lead to a
further division for the failure mode: damage of the revetment on the outside slope
and erosion of the embankment body.
Differences in geometry on a detailed level have consequences for each of the failure
modes.
Differences in the foundation soil can have a considerable effect on the contributions
to the probability of failure of geotechnical failure modes. For these failure modes a
further division has to be made.
Differences in the inside slope revetment of embankments (quality of the grass,
thickness and qualification of the clay cover layer on the inside slope, the angle of the
inside slope, etc.), this kind of information is especially useful for the division in
embankment sections for the failure modes overtopping and consequently erosion of
the inside slope or instability of the inside slope.
Information about the construction of the embankment (clay embankment, sand
embankment with a clay core, etc) and information about the soil layers underneath
and directly next to the embankment (in front of and behind the embankment), this
information is relevant to the failure modes heave and piping, instability of the inside
slope and damage to the revetment and erosion of the embankment body.
4. After step 3 the water defence system has been divided in embankment sections. The
following step is to select the relevant sections for the reliability analysis. The procedure
to come to this selection of sections is given below:
Regard a failure mode for which it is desirable to reduce the number of embankment
sections. The first logical step is to eliminate all the embankment sections for which
the mode is not relevant, or in other words: the contribution of the section to the
probability of failure due to a certain mode is negligible in advance. Well known
weak spots can provide valuable first insight in which sections contribute
significantly and which ones do not.
For the remaining sections, indicators are used to rank them. These indicators are
related to the failure modes. The number of selected sections can be limited based on
this ranking.
Apart from the selected weak sections based on the indicators, sections from the
middle and strong categories have to be chosen. This is done because it is practical to
be able to make an estimate of the probability of flooding after eliminating the weak
spots in the probability of failure calculations.
The former three steps have to be performed for all failure modes, which can result in
a different selection of embankment sections for each mode.
Check the spreading of the sections along the water defence system with respect to
the magnitude of the expected consequences. The sections with substantial
consequences that fall out off the analysis should be added or shift a bit with the
choice in the middle and strong sections. With the total risk analysis in mind, a strong
section with extensive consequences can contribute just as much or even more to the
total risk as a weak section with hardly any consequences.
5. The first selection of embankment sections has been finished. For each section it is clear
which failure modes are regarded. The next step is to gather data for the regarded failure
modes and embankment sections.
6. After the first calculations of the probability of failure with PC-Ring a check is made if
sections have to be added or adjusted:
First the contribution of the failure modes to the total probability of failure is
considered.
For the mode with the largest contribution a check has to be made if the last selected
sections still have a significant contribution to the probability of failure. If they do an
additional selection of sections for that mechanism has to be made. This check needs
to be made for all the failure modes with an emphasis on the ones with the largest
contribution.
This process has to be repeated until no more sections need to be included in the
analysis. The number of cycles depends on the number of embankment sections
which are chosen initially and after expansion.
These steps are shown schematically in Figure 2 below.
INPUT
ACTION
OUTPUT
Maps / information
about relief
Definition of boundaries
of system defences
Floodplain boundaries /
definition of protected
areas
Site visit / drawings of

defences / available
design reports
Definition of the defence

types in the system
Overview of the relevant

defence types / their
location
Knowledge about past

failure events /
literature / local expert
knowledge
Analysis of the failure

modes for the defence
types
Fault tree / limit state

functions / physical
process-based models /
statistical distribution
functions of random
variables
Maps / geometry /
rough external
characteristics
Divide system up into

stretches with similar
characteristics
Stretches with eg. Similar

orientation, crest levels,
revetment, etc
Geometry detailed
characteristics
Division into smaller

sections for which one
fragility curve is taken to
be representative
System sections suitable

for use in calculations
Existing databases /
design reports / site
visit / measurements /
local expert knowledge
Data collection to
populate the model
Model of physical system

expressed in terms of data
Data
Calculation of the fragility

curves
Fragility curves for the

sections
Figure 2 Steps in a system analysis of coastal defences to come to fragility, after Buijs et al,
2003
2.4.
An introduction to the RASP tiered methodology and fragility

curves
2.4.1 RASP
Interest in risk-based design and maintenance of flood defences has grown significantly in the
UK in recent years. The main advantages of a risk-based safety approach are:
It is based on the concept of risk and therefore considers all the aspects related to failure
of a flood defence system: the strength and the loading conditions of the flood defence
system as part of the probability of inundation as well as the consequences of inundation
in case of failure of the flood defence system.
It supports the process of decision-making with respect to maintenance of a flood defence
system as a risk-based analysis of flood defence systems points out the systems weak
links and which parameters contribute most to the probability of failure (i.e. potential
breach location). This knowledge enables the decision-maker to target maintenance
activities.
In case of large scale flood defence improvements the decision-maker can compare
different design options in terms of the actual risk reduction and the costs which are
associated with the improvement option.
To support a wide application of risk methodologies in flood defence an overarching riskbased framework (RASP) is being developed that integrates decisions on different levels (e.g.
national, large-scale, strategy, scheme, etc) and across differing functions (local authorities,
flood warning, operation and maintenance, etc.).
RASP stands for Risk Assessment of flood and coastal defence systems for Strategic
Planning. It provides a tiered risk assessment methodology for systems of flood and coastal
defences underpinning different levels of decision-making. RASP consists of a High Level
Methodology informing national level decision making, an Intermediate Level informing
regional decision making and a Detailed Level methodology informing decision making on
the level of a flood defence system. Each level involves different types of decisions and has
different data sources at its disposal. The tiered methodologies are being developed taking
these different circumstances into account. An overview of the issues is given in the table
below.
Table 1. Tiered risk assessment approach in RASP
Level
High
Decisions to inform
National assessment of
economic risk, risk to life or
environmental risk
Prioritisation of expenditure
Data sources
Defence type
Condition grades
Standard of Service
Indicative flood plain maps
Socio-economic data
Land use mapping
Intermediate
Above plus:
Flood defence strategy
planning
Above plus:
Defence crest level and other
dimensions where available
Regulation of development
Joint probability load

distributions
Prioritisation of maintenance
Planning of flood warning
Detailed
Above plus:
Scheme appraisal and
optimisation
Flood plain topography

Detailed socio-economic data
Above plus:
All parameters required
describing defence strength
Synthetic time series of loading
conditions
Methodologies
Generic probabilities of
defence failure based on
condition assessment and crest
freeboard
Assumed dependency between
defence sections
Empirical methods to
determine likely flood extent
Probabilities of defence failure
from reliability analysis
Systems reliability analysis
using joint loading conditions
Modelling of limited number of
inundation scenarios
Simulation based reliability
analysis of system
Simulation modelling of
inundation
2.4.2 RASP and fragility curves

To develop an approach that considers the full potential risk distribution, rather than just limit
state conditions, requires a relationship between defence performance and loading throughout
the full range of loading conditions. This may be provided through the use of fragility
curves. The following issues surrounding the concept of fragility are addressed:
The definition of the concept of fragility
The role of fragility curve in flood risk assessments
Appearances of fragility curves in tiered risk
assessments
Definitions
In RASP High Level Methodologyvi, the concept of fragility

was first introduced as a tool in a system of tiered risk
assessments.
The fragility of a structure was defined as the probability of
failure conditional on a specific loading.
Role of the fragility curve in risk assessment in general
In a risk assessment the aim is to get an impression of the

distribution of flood risk across a floodplain. Based on this
distribution of risk, comparisons can be made where to
target investments and which improvement options are most
efficient in reducing the risk given an equal investment.
Figure 3: Example of a fragility curve
Risk is a function of the likelihood of an undesired event and the magnitude of the
consequences given this undesired event. Purely considering flooding events, the likelihood is
represented by the probability of failure of a flood defence given a certain set of loading
conditions. The consequences are expressed by the damage caused by the flooding scenario
that occurs under that set of loading conditions in the event of failure of the flood defence.
{Flood risk | flooding scenario} = P(failure | loading conditions) x {damage | flooding scenario}
The fragility curve representing the probability of failure given a set of loading conditions is
therefore a format that connects well with the approach to establish flood risk.
Appearances of fragility curves in a tiered risk assessment
The use of a fragility curve to represent flood defence performance may be applied at each of
the three levels of RASP assessment. However, as the level of risk assessment connected to
flooding gets more detailed, the analysis of the shape of the fragility curve and the flooding
scenarios needs to be increasingly detailed and hence also the required information. Below an
impression is given of how the difference in level of risk assessment works out for the
fragility curves by contrasting the highest level and lowest level.
The highest level of risk assessment is relatively simple, easily applicable but still roughly
representative of the distribution of flood risk. The main source of information (in the UK) is
the NFCDD, a national database containing rough information about the flood defences. The
fragility curves are taken to be generic for a limited number of types of flood and coastal
defences. This background results in a fragility curve in which the loading conditions are
expressed in one parameter on the horizontal axis.
In contrast, the detailed level of risk assessment is most complex, takes into account all failure
modes irrespective of whether they are expected to contribute significantly or not and is based
on comprehensive data. The fragility curves are determined for each flood defence section
based on the local information. Instead of expressing loading in one parameter, the loading
10
conditions are approached in a more differentiated way. This results in conditional

probabilities of failure given a certain water level, significant wave height, wave period, etc.
This approach is graphically not very attractive but allows much more differentiation in
flooding scenarios and accompanying damage levels.
Figure 4 below shows how the fragility curve sits within an overall risk based approach
linking the source of flooding, through the pathway (in this case embankment) to the
receptor.
Asset with pathway (or barrier) to flooding

(e.g. embankment or waterfront wall) Receptor
(e.g. people in the floodplain)
Source
(River or sea)
Figure 4
Source Pathway Receptor approach
11
3. Local factors affecting embankment performance

A logical assessment, based on cause/consequence relationships, will show that whatever the
type of failure mode, the location of the failure is normally influenced by a combination of
several causes or factors, although one of these may be dominant. The following sections
consider different factors that may affect breach formation. Figure 5 below shows an example
of how different features may affect embankment performance.
Figure 5 An example of prioritisation of components contributing most to defence

failure, from Defra / Environment Agency (2004)
3.1.
An interactive problem
The following provides an example of factors leading to failure of an embankment. These

have been ordered chronologically another way of viewing interaction between factors on,
say, a cause consequence diagram. The factors are also categorised according to possible
type.
Ramp access
Loads on the
crest.
Visual indicator
External indicator
Compaction
Crest level
Internal indicator Visual indicator
Settlement
Visual indicator
Overtopping
Breaching
Pathway
FAILURE
Chronological factors
Although these indicators are sorted according to the time, the first one is not the most import
one, since all play a vital role leading to embankment failure and hence all factors need to be
considered in the future analysis.
The factors may be ranked within the following classes:
Internal factors: these factors need a complete knowledge of the inner part of the
embankment otherwise the embankment owner should extract a material sample
in order to have an idea of the soil structure and composition.
12
External factors: these factors could be detected by a visual survey; they are
located on the surface of embankments.
Environmental factors: these factors correspond to the physical elements

surrounding embankments and affecting their overall performance.
Human factors: these factors involve human actions and events; it can be as well
physical actions toward embankments as lack of maintenance (legislation).
The following summaries have been drawn from reviews undertaken in Hungary as part of
research into factors affecting breach formation under WP6. It was found that the data
collected was insufficient (at this time) to allow a reliable statistical analysis of the role that
the factors play. However, the work does provide an initial check list.
13
3.1.2. Internal factors

Potential internal factors include:
INTERNAL FACTORS
Factors affecting
embankment
performance
Example of risk generated by these factors
Moisture content
Lead to shallow instability due to variation of pore pressure
Friction angle
A high friction angle will allow a higher resistance to failure and

vice versa
Grading
A bad gradation can make the embankment more permeable

and leads to seepage and piping
Dry unit weight
A material with a high dry unit weight could be less erodible

than a low one and vice versa
Plasticity index
A material with a poor plasticity index leads easily to piping

failure
Cohesion
Fine particle soils with low cohesion can be dislocated and

washed away at lower speed of water than hightly cohesive
soils and then lead to a faster erosion of the body
Permeable layers
The presence of hightly permeable layer strata within

embankment either leading to excessive seepage.
Foundation inerface
properties
The foundation interface between two different materials is a

sensitive area for piping, a weak interface material with a high
lateral load due to inexpected rising of water level can lead to a
translational sliding
Compaction
Compaction is directly linked with permeability property of the

embankment, in other word the piping phenomena is
significantly governed by this factor
High groundwater
pressure
High groundwater pressure can trigger a deep rotational failure

by acting in a permeable layer beneath the embankment
Inner temperature
Temperature variations trigger cracks propagation by acting on

natural dilatation and compression of the material
..
..
14
3.1.3. External factors

Potential external factors include:
Reduction of crest
level
The reduction of crest level increases considerably the risk of

overtopping during flooding
Settlement of the
crest
Leads to a dicrease of the crest level therefore to an increase

of the overtopping risk
Localised dipping of
crest
Corresponds with a geometrical default of the crest which can

be considered as a sensitive area for the breaching process
Cracking, bulging,
slumping of the
surface protection
Corresponds with localized settlements on the surface

protection, they lead to a global settlement of the embankment
EXTERNAL FACTORS
Sink holes on outward

Visual factor which indicates an high risk of piping
face
The root mesh of this vegetation provides a network of
Vegetation properties
reinforcement to the upper layer of the soil which improves
and changes
resistance to erosion and to slope instability
Longitudinal cracking
It is synonym of initiation of a deep rotational failure
along the crest
Bulging at the toe
The longitudinal cracking along the crest is generally combined

with the bulging of the outward toe
A high embankment crest level with a very steep slope can't

Steep slope and high
withstand efficiently the shear stress induced by the load of the
crest level
water
Raising of
embankment
This raising will load the crest of the old embankment and
could lead to loose the global stability of the strcuture then it
can trigger a rotational failure
Bare patches along

embankment
This visual factor corresponds with a fragile area where

erosion will have a higher development than in other
embankment parts
Channelling across
crest and other
outward face
These channels could be compared to small breach initiations

therefore channelling process represents a high risk of breach
formation during a flooding
..
..
15
3.1.4. Environmental factors

Potential environmental factors include:
ENVIRONNMENTAL FACTORS
Corresponds with a previous overtopping, if an other

overtopping occurs this part of the dam would be quickly
Gullies and headcuts
eroded. Moreover, these factors will increase the global
weakness of the rear face of the embankment
Leakage with
changes of water
colour
A high risk of piping must be considered
Animals (Rabbits,
rats, moles etc.)
The burrow digs by these animals could quickly lead to a piping

initiation
Flow velocity
The sediment transport increases considerably with the flow

velocity and the turbulences then the erosion peaks
Water volume
it influences directly the mechanical equilibrium of the

embankment then for example the lateral load of the water can
trigger translational sliding failure
Areas of standing and These areas are exposed to constant seepage and high
flooding water
moisture content
Waves properties
Wave height and velocity can as well erode as totally destroy

embankments
Flow content
A powerful flow can carry large and heavy objects as branches

or rocks, these objects can greatly damage the structure
integrity of embankments
River morphology
River singularities generate turbulent sources which increase

substantially the erosion rate
Climatic conditions
Hailstones falls and heavy rain frequency affect embankment

surfaces and lead to slope instabilities
Overtopping
Acting on crest erosion and then trigger breach formation
Trees growing throw

embankments
The overall structure becomes non-homogeneous, every kind

of sliding failure can occur within the embankment/tree
interface, trees can also amplify wind effect
..
..
16
3.1.5. Human factors

Potential human factors include:
Outfall structures
Outfall and culvert structures built through and into

embankments induce weak points leading to failure if they
were not well designed
Embankment age
An old embankment has undergone a large amount of

seasonal loads during his life which create natural cracks due
to material dilatation and moisture evaporation
Human crest loads
Cars and engines used by human on embankment cause

longitudinal cracks and geometrical defaults and then rotational
failure
Ramp access
These ramps represent areas of frequent human loads
HUMAN FACTORS
Engine vibrations
Harmful factor for dry and stiff materials, formation of random
(Tractors, trains etc.) cracks
Wash from boats
Equivalent to waves
An overall factor could be estimated according to the distance

Distance from human from the nearest habitations. Habitations are in general
habitation
harmful for embankments, they are sources of frequent people
and vehicule movements, building operations etc.
Agriculture
An embankment located next to agriculture fields can be

affected by a constant maintenance of the field ( fencing,
watering ) but also by farm animals living on. They can cause a
severe embankment surface erosion due to a confined grazing
during wet conditions
Wood poles
Wood poles throw embankment create structure discontinuity

due to their height, they include the transmission of dynamics
effects of heavy wind onto embankment, leading to movement
then to failure
Legislation
A poor legislation can lead to a lack of maintenance, cracks

and defaults expand without any survey
..
..
17
4. Methodology for identifying potential breach location

4.1
Concluding review
The problem of identifying breach location may be divided into two approaches:
Assessing the relative risk of breach occurring based upon an assessment of the flood
defence system
Assessing the risk of breach formation at a specific location based upon local factors
4.1.1 Systems approach
A systems based approach has been developed in the Netherlands which uses limit state
equations to define a number of possible embankment failure mechanisms. However, the
current state of art concerning factors used in the limit state functions is quite limited. Indeed,
the factors concerned are only factors which can easily and directly be measured with sensors
or others measurement devices [e.g. water level, discharge, etc.]. Other factors exist that need
to be integrated in these limit state functions [e.g. wind, volume, flow velocity, temperature
variations etc.]. A detailed analysis of failure modes needs to be performed and afterward
used to derive a complete set of limit state equations for the description of failure scenarios if
the reliability of this approach is to be improved.
It has also been observed that certain factors are perceived to be very difficult to represent
simply (e.g. animal burrowing, vegetation patches etc.). Nevertheless, this does not mean that
they cannot be estimated through the use of a semi-quantitative approach.
The UK approach (RASP) adopts the concept of fragility curves to represent the performance
of flood defences. The example in Figure 6 show possible curves for 5 different embankment
condition grades (CG) and potential uncertainty around one condition grade curve. This
uncertainty might be dependent upon a number of factors such as type of vegetation,
embankment compaction, core material etc.
4.2
Conclusions
Since fragility curves build upon limit state equations, and we have seen that current
knowledge regarding limit state equations is relatively low, we have a similar problem
relating to the accuracy of fragility curves. In addition, the methods and assumptions
underpinning the overall framework need to be recognised to avoid any misconceptions
regarding overall accuracy. The accuracy of four components may be identified as key issues.
These are:
The quality of the process-based model and the way the model is represented in
the limit state functions
The representation of the uncertainties in the model and data
The accuracy of the calculations
The quality of the available data
4.1.1 Local approach

Efforts within IMPACT WP6 to correlate historic breach data (in Hungary) against different
failure mechanisms / factors have not provided conclusive evidence of key and priority
factors. However, correlation between location in a river catchment and typical size of breach
has been established. It is anticipated that a more targeted analysis of a smaller set of breach
events may still allow correlation of failure with various factors such as material type,
condition etc.
Equally, an alternative approach by Partner 2 within WP2 of looking specifically at detailed
embankment crest level against predicted flood water level, and relating embankment failure
18
to just depth of flow over the embankment, had a very successful outcome. This approach
simply assumes that the dominant factor in the majority of failures is overflowing water, and
hence analysis of this will predict the majority of failures.
1.0
0.9
CG1
P(breaching|overtopping rate)
0.8
0.7
CG2
0.6
CG3
0.5
0.4
CG4
0.3
CG5
0.2
0.1
0.0
0.0
0.5
1.0
1.5
2.0
2.5
2 .0
2 .5
Overtopping rate (m /s/m)

1 .0
0 .9
Upper band
P(breaching|overtopping rate)
0 .8
Lower band
0 .7
CG1
0 .6
0 .5
0 .4
0 .3
0 .2
0 .1
0 .0
0. 0
0. 5
1. 0
1 .5
Overtopping rate (m3/s/m)
Figure 6 Example of fragility curves for broad scale risk assessments. Above fragility curves of 5
different condition grades (1=excellent, 5=very poor) for a narrow coastal impermeable
embankment, turf front face and crest protection.
4.3
Conclusions
The following points may be concluded:

1
A framework for assessing the relative risk of breach occurring within a system of
flood defences is provided within the RASP methodology being developed in the UK.
This builds upon the earlier methodology of PC RING, currently in use in the
Netherlands.
Whilst the RASP and PC RING approaches offer a framework for analysis, the
reliability of the systems remains very dependent upon the limit state equations or
fragility curves used and the assumptions underpinning the overall framework to
represent embankment performance. These equations, curves and frameworks require
validation and extension in order to refine overall model performance.
19
Data collected within IMPACT WP6 in Hungary may provide a useful base of
information against which further refinement of fragility curves may be made.
Analysis of the data to date has demonstrated a wide range of factors that affect
embankment performance, leading to failure.
Focussing on one or two factors (e.g. overflowing water depth) may be sufficient to
identify a majority of high risk locations, without the need to analyse large numbers
of factors in detail. This approach requires further validation.
20
5. References
F. A. Buijs, P.H.A.J.M. van Gelder, J.K. Vrijling, A.C.W.M. Vrouwenvelder, J.W. Hall, P.B. Sayers,
M.J. Wehrung, Application of Dutch reliability-based flood defence design in the UK, proc. Conf.
ESREL 2003 (1): 311-319, Maastricht, The Netherlands, June 15-18 2003
Buijs, F.A., Reliability analysis of the Caldicot Levels flood defence system by using Dutch reliability
methods for flood defences, Msc. thesis, Delft University of Technology 2003
B.L. Lassing, A.C.W.M. Vrouwenvelder, P.H. Waarts, Reliability analysis of flood defence systems in
the Netherlands, proc. Conf. ESREL 2003 (2): 1005-1013, Maastricht, The Netherlands, June 15-18
2003
Kortenhaus, A., Oumeraci, H, ProDeich: Probabilistische Bemessungsmethoden fr Seedeiche
(Probabilistic design methods for sea dikes (in German)), Leichtweiss Institut fr Wasserbau 2002
Calle, E., Jonkman, B., Lassing, B., Most, van der, H., Data gathering and flood defence modelling to
support the calculation of probabilities of flooding of ring dike systems (in Dutch), Manual (version
3.2), Delft 2001
HR Wallingford, Risk assessment for Flood and Coastal Defence for Strategic Planning, High Level
Methodology, A review, Report SR603, 2002
Buijs, F.A., Reliability analysis of the Caldicot Levels flood defence system by using Dutch reliability
methods for flood defences, Msc. thesis, Delft University of Technology 2003
B.L. Lassing, A.C.W.M. Vrouwenvelder, P.H. Waarts, Reliability analysis of flood defence systems in
the Netherlands, proc. Conf. ESREL 2003 (2): 1005-1013, Maastricht, The Netherlands, June 15-18
2003
Vrouwenvelder, A.C.W.M. , Steenbergen, H.M.G.M., Slijkhuis, K.A.H., Theoretical manual of PCRing, Part A: descriptions of failure modes (in Dutch), Nr. 98-CON-R1430, Delft 2001
Tol, van A.F., Oostveen, J.P., CUR 162, Constructing with ground. Structures made of ground on and
in soil with little bearing capacity and strong compressible subsoil (in Dutch), Delft 1999
Technisch rapport Asfalt voor Waterkeren (Technical report Asphalt for Water Retaining (in Dutch)),
Concept revision 6.6, 31-08-2000
Pilarczyk, K.W. (ed), Dikes and Revetments. Design, maintenance and safety assessment, Balkema,
Rotterdam 1998
TAW, The use of asphalt in hydraulic engineering, Technical Advisory Committee on Water defences,
Rijkswaterstaat communications, The Hague 1985
Cooke, R.M., Noortwijk, van, J., Bedford, T.J., Uncertainty analysis of inundation probabilities,
TUDelft & HKV, 1998
Elst, van, N.P., Betrouwbaarheid van het sluitproces van beweegbare waterkeringen (Reliability of the
closure process of water retaining gates (in Dutch)), TUDelft: Delft University Press 1997
21
Vellinga, P., Beach and dune erosion during storm surges. Thesis Delft University of Technology,
also: Delft Hydraulics, Communications No.372, the Netherlands
Vrouwenvelder, A.C.W.M. , Steenbergen, H.M.G.M., Slijkhuis, K.A.H., Theoretical manual of PCRing, Part B: Statistical models (in Dutch), Nr. 98-CON-R1431, Delft 2001
Vrouwenvelder, A.C.W.M., Theoretical manual of PC-Ring, Part C: Calculation methods (in Dutch),
98-CON-R1204, Delft 1999
M. Hohenbichler & R. Rackwitz, First-order Concepts in System Reliability, Structural Safety, 1, 1983,
pages 177-188
3.2), Delft 2001
Defra/Environment Agency, Performance-based Asset Management System (PAMS), Phase 1 Scoping
Study, HR Wallingford, 2004
22
Appendices
23
Appendix A
PC-Ring
An introduction to PC-Ring
Technological developments of computers in the nineties have enabled the calculation of
probabilities of failure of flood defence systems. The limit state functions applied in this
software are based on former non-probabilistic reliability methods employed in the
Netherlands.
The probabilistic calculations done with PC-Ring correspond with the detailed level
methodology in RASP and take into account a large number of flood defence sections and
multiple limit state functions. The main output from these calculations is:
Probabilities of failure for each flood defence section included in the calculations and
therefore an overview of the weak areas in the flood defence system.
Insight in the key failure mode of a system of flood defences.
Insight in the uncertainties associated with the parameters in the limit state functions and
their contributions to the total probability of failure of the flood defence sections.
The local probabilities of failure can be used in determining the spatial distribution of risk.
Defence improvements can be targeted to flood defence sections contributing most to the risk
in the floodplain. The insight in which model parameter contributes most to the probability of
failure of the flood defence section in combination with the limit state function provides
advice on what kind of improvement activities are expected to be most effective. The
effectiveness of different improvement options can be compared by analysing the reduction of
risk in the floodplain associated with each option (see Buijs et al. (2003)vii).
The reliability models applied in the limit state functions in PC-Ring are similar to those
applied in the UK. The limit state functions of the failure modes implemented in PC-Ring are
given as an example of how to fit current practice models for failure modes into limit state
functions. Specific details can be found in Buijs (2003)viii and translated from Vrouwenvelder
et al. (2001) and in Lassing (2003)ix. A very comprehensive discussion of limit state functions
in connection to embankments can also be found in Kortenhaus & Oumeraci (2002)x.
24
Introduction to the failure modes used in PC-Ring

PC-Ring only includes failure modes concerned with structural failure. The following failure
modes of embankments are included in PC-Ring:
Overtopping/overflow.
Instability of the inside slope.
Piping.
Damage of the revetment on the outside slope and consequently erosion of the
embankment body.
The fault tree of these failure modes related to an embankment is given in fig. 4.1.
Non-structural
failure not included
in PC-Ring
Failure of
embankment
Structural
failure
Overtopping/fl
owing over
Overtopping
Instability of
inside slope
Non-structural
failure
Damage of revetment and

erosion of the embankment
Heave/piping
Erosion of the
embankment
Piping
Overflow
Uplifting
Erosion
inside slope
Erosion
inside slope
Saturation
Instability of the
inside slope
Saturation with
water of pores in
clay of inside
slope
Saturation
Instability of the
inside slope
Saturation with
water of pores in
clay of inside
slope
Damage of
revetment on
outside slope
= OR gate
= AND gate
= INHIBIT gate. The event
at the right hand side of the
gate can only occur if the
basic event below the gate
has taken place
Figure 4.1. Failure modes of the embankment as applied in PC-Ring
25
Overtopping/overflow
Water discharges passing the crest of the embankment either due to overtopping overflow are
the cause of loading of the inside slope. Water discharges due to overflow are in PC-Ring
only assumed to be relevant in case of off-shore wind or wave heights smaller than 1 mm. In
the other situations the water discharges are assumed to occur due to wave overtoppingxi.
Failure of the inside slope due to the loading by the overtopping/overflow discharges can
occur in two ways:
Erosion of the inside slope.
Saturation of the pores in the clay and consequently instability of the inside slope.
These failure modes are discussed below.
Erosion of inside slope
Water discharges due to overtopping or overflow respectively hit or scour the inside slope of
the embankment. Due to this loading of the inside slope the grass gets damaged. After the
grass has been damaged, the embankment body is exposed to the overtopping/overflow
water. In the end, if this erosion process continues long enough, the embankment breaches.
The duration of this erosion process depends on the duration of the storm.
In case of discharges due to overtopping the limit state function is:
Z = mqc qc - mqo qo / Pt
In which qc is the critical discharge expressing the limit discharge for which almost
damage of the grass occurs, qo is the actual occurring overtopping discharge due to the
hydraulic boundary conditions in combination with the geometry of the embankment,
mqc is the model uncertainty with respect to the critical discharge qc, mqo is the model
uncertainty with respect to the actual discharge and Pt is the percentage of time that
overtopping occurs, this variable is applied to take the pulsating character of overtopping
in account.
The critical discharge qc can be determined in two ways: either a model based on the
strength of the grass or the desired limit discharge can be entered manually.
The actual overtopping discharge qo is calculated with the overtopping equations
according to Van der Meer, revised version1.
In case of discharges due to overflow the limit state function is:
Z = hd + hc h
In which hd is the crest level of the embankment, hc expresses the critical height for
which almost damage of the grass occurs and h is the actual occurring water level.
The critical height hc is derived from the critical overtopping discharge qc, see
Appendix 4-A. The latter is represented by the model based on the grass strength as is
applied in case of failure due to overtopping.
The actual occurring water level h is available from the hydraulic boundary conditions.
26
Saturation
Water from the overtopping or overflow discharges infiltrates the pores of the clay soil of the
crest and inside slope of the embankment. Increasing water pressures in the pores of the clay
cause decreasing effective stresses and therefore, a decreasing shear strength. If the pores of
the clay are completely saturated with water from the overtopping or overflow discharges the
shear strength is at its lowest and the inside slope is most susceptible to instability. This
description points out that failure consists of two events: the process of saturation of the
pores in the clay and instability of the inside slope due to low shear strength.
The limit state function describing the process of saturation of the pores in the upper clay
layer is:
Z I = qcv mqo qo
In which qcv is the critical discharge for which within a few hours during a storm complete
saturation of the upper layer of the inside slope occurs. The value of this qcv depends on
whether the water discharge is caused by overflow or wave overtopping. A water discharge
due to overflow infiltrates the upper layer more progressively than due to wave overtopping.
The extent of infiltration of the latter depends on the wave height. qo is the actual
overtopping discharge according to Van der Meer revised. mqo is the model uncertainty with
respect to the actual discharge.
The limit state function describing the process of instability of the inside slope due to the low
shear strength caused by the high water pressures is:
Z II = tan( c ) tan( i )
In which tan (c) expresses the strength of the with water saturated clay layer at the inside
slope, if this value is lower than the actual slope then instability of the inside slope occurs.
Instability of the inside slope
First, below a general description is given of how the stability of an embankment slope can be
modelled. Second, the failure mode instability of the inside slope is presented.
Background information: stability according to Bishop
Instability of an embankment
slope occurs if part of the
embankment slides away along a
slip plane. According to Bishops
approach this slip plane is
circular and the stability is
expressed in the form of a
stability factor. To determine this
stability factor the embankment is
divided into vertical slices. The
stability factor consists of a ratio
between two moments that are
taken with respect to the centre of
this slip circle:
The first moment is
formed by the weight of
the slices and the arm of
M = centre of slip circle
Embankment
Slip circle
Figure 4.2. Slip circle model according to Bishop (From

CUR162, 1999)
27
this weight with respect to the centre of the slip circle. This moment represents the
loading side of the ratio.
The second moment is formed by the shear force along the slip plane of each slice
and the arm of this shear force with respect to the centre of the circle. This moment
represents the resisting part of the ratio.
A lower stability factor implies a lower stability. The embankment slope is considered to be
instable if the stability factor reaches a value smaller than 1.
The slip circle approach according to Bishop is shown in fig. 4.2xii.
Failure mode: instability of the inside slope
If the water level outside the

embankment increases, the
water
heads
in
the
embankment body increase as
well. These increasing water
heads in the embankment
body influence the ratio
between the shear strength,
the water pressures and the
weight of the embankment. Figure 4.3. The Bishop method in the three dimensional
Eventually, the ratios are plane
influenced to such an extent that part of the embankment becomes instable and slides away.
According to Bishops model this is defined as the situation in which the stability factor
drops below a value of 1.
Software called MPROSTAB is available to calculate the probability of failure due to
instability of the inside slope given a certain outside water level. The following limit state
function is applied:
Z=-q
In which is the stability factor according to Bishop and q is the threshold value of the
stability factor for which instability occurs. Theoretically speaking, this threshold value q is
equal to 1.
MPROSTAB takes the spatial correlations between soil properties into account and becomes
a three dimensional approach instead of a two-dimensional approach, see fig. 4.3.
MPROSTAB is used to calculate the probability of failure due to instability given a water
level in three different situations: for instance an average water level, an extreme water level
with a return period of 1 in 1000 years and the latter extreme water level minus one meter. In
PC-Ring the output of MPROSTAB is used to calculate the total probability of failure due to
instability of the inside slope. To this end, the reliability indices and the alfa values are used
in the following limit state function in PC-Ring:
Z = ( h) +
nMPROSTAB
( h) u
i =1
In which (h) is the reliability index given the water level resulting from the MPROSTAB
calculations, i(h) are the influence coefficients given this water level and ui are variables
with a standard normal distribution.
28
Uplifting and Piping
First uplifting causes openings in the impervious clay layer covering the sand layer. Second,
a flow of water through these openings initialises an erosion process. This process can
progress from the point of the openings caused by the previous uplifting behind the
embankment towards the water outside. The erosion process takes the form of pipes
undermining the foundation of the embankment. These pipes can eventually cause failure.
Uplifting
Uplifting occurs if the difference between the local water level h, and the water level
inside, hb is larger than the critical water level hc, see fig. 4.4. This is expressed in the limit
state function as:
Z = mo hc m h ( h hb )
In which mo takes the model uncertainty of the model which determines hc in account and mh
the level of damping. The critical water level expresses the limit water level for which almost
uplifting occurs. This water level is based on the properties of the impervious layer
Piping
The embankment fails as a consequence of piping if the difference between the local water
level h and the inside water level hb, reduced with a part of the vertical seepage length d,
exceeds the critical water level hp.
Z = m p hp (h 0.3d hb )
In which mp is the model uncertainty of the model with which hp is described. The critical
water level hp is described by Sellmeijers model of piping.
Damage of revetment on the outside slope and erosion of the embankment
body
The following types of revetments are discussed below:

Grass.
Placed stone revetment (directly on clay and placed on a granular filter).
Asphalt revetments.
Grass
The waves load the outside slope of the

embankment. If the grass gets damaged
the body of the embankment is fully
exposed to the loading by the waves and
starts to erode. The body of the
embankment consists of two parts: the
clay cover layer and the embankment
core. If both components are eroded, the
embankment breaches. This failure
mode is represented by the following
limit state function:
hb
Clay
Klei
Sand
Zand
d
D
Klei
Figure 4.4. Parameters for uplifting/piping (from

Vrouwenvelder et al., 2001)
29
Z = t RT + t RK + t RB t s
In which tRT is the time that a storm takes to damage the grass, tRK is the time that a storm
takes to erode the clay cover layer and tRB is the time that a storm takes to erode the rest of
the embankment body. ts is the duration of the storm.
Placed stone revetment
Two types of placed stone revetment are discussed below: placed directly on clay and placed
on a granular filter. The chain of events is similar for both types of placed stone revetment.
The waves load the revetment on the outside slope of the embankment. If the placed stones
are damaged the body of the embankment is fully exposed to the loading by the waves and
starts to erode. If the body of the embankment is eroded, breach occurs. The difference
between stone revetment placed directly on clay and on granular filter is the description of
damage of the revetment in terms of limit state functions.
Stone revetment placed directly on clay
The failure mode damage of the stone revetment placed directly on clay is represented by the
limit state function:
Z = ck D - r Hs
In which ck is a coefficient for the strength of the placed stones, the relative density and D
the thickness of the placed stones. Apart from this, the reduction factor r and the significant
wave height Hs are part of the limit state function.
Stone revetment placed on granular filter
Failure of the stone revetment placed on granular filter is described by two limit state
functions, represented by Zb1 < 0 OR Zb2 < 0.
Z b1 =
c f D 1.67 1.67
( tan u )
0.67
rHs
(r S )
0.33
op
In which cf is a coefficient for the strength of the stone revetment, is the relative density, D
is the thickness of the revetment, is a factor of influence of the friction between stones,
inertia, etc.., is the leakage length, u is the angle of the slope, Sop is the wave steepness, Hs
is the significant wave height and r is a reduction factor taking the obliqueness of the waves
into account.
Z b2
tan
u
= c gf
S
op
2 / 3
Hs
D
In which cgf is a coefficient for the strength of the revetment and the other parameters are
discussed with the first limit state function.
Erosion of the embankment body leading to breach
Erosion of the embankment is represented by the following limit state function:

Z = tRK + tRB - ts
In which tRK is the time that a storm takes to erode the clay cover layer and tRB is the time that
a storm takes to erode the rest of the embankment body. ts is the duration of the storm. The
models that are used to determine these values are equal to those applied in the failure mode
of revetment type grass.
30
Asphalt revetments
Asphalt revetments fail either due to uplifting by water

overpressures or due to wave impacts, see fig. 4.5. After
failure of the revetment the embankment body is fully
exposed to loading by the waves. The embankment
breaches after the body of the embankment has completely
eroded.
Failure asphalt
due to water
overpressures
Failure asphalt
due to wave
impacts
Figure 4.5. Failure mode damage
There are three main types of asphalt revetment: open stone asphalt and erosion core of
asphalt, fully penetrated and saturated riprap revetment, embankment in PC-Ring
partially penetrated riprap revetment. For these types the
limit state function of failure due to uplifting is equal but that of failure due to wave impacts
differs.
Failure of asphalt revetment due to uplifting
Failure of asphalt revetment occurs when the pressure difference over the revetment at the
level of the water line exceeds the weight of the asphalt. This leads to the following limit
state function:
Z = D - 0,21 Qn (a + v) Rw
(from Technisch rapport Asfalt voor Waterkeren (2000)xiii)
In which is the relative density, D is the thickness of the asphalt, Qn is a factor depending
on the angle of the outside slope u, a is the vertically measured distance between the toe of
the impermeable revetment and the outside water level, v the vertically measured distance
between the outside water level and the groundwater level and Rw a reduction factor in
connection to the position of the outside water level. For background information, see also
chapter 9 in Pilarczyk (1998)xiv.
Failure due to impact of waves: open stone asphalt
Failure of open asphalt revetment due to the impact of waves can be represented by the
following limit state function:
Z = D Drequired
In which D is the thickness of the open stone asphalt and Drequired can be determined
according to a diagram which plots the required asphalt thickness as a function of the
significant wave height for different slopes and clay or sand soil (see TAW (1985)xv).
Failure due to impact of waves: fully penetrated and saturated riprap revetment
Failure due to wave impact of fully penetrated and saturated riprap revetment is considered
to be an irrelevant failure mode.
Failure due to impact of waves: partially penetrated riprap revetment
The limit state function for failure of partially penetrated riprap revetment due to impact of
waves is given by:
Z = Dn50 -
H s pb
m u sw cos( )
In which Dn50 is the nominal diameter for which 50% of the weight of the grains is larger or
smaller than this value, p is the breaker parameter, m is the relative density, u is a
parameter for penetration of the asphalt, sw is the stability factor and is the angle of the
outside slope.
31
Erosion of the embankment body leading to breach
The limit state function of the erosion of the embankment body after being fully exposed to
the wave loading is:
Z = tRB - ts
In which tRB is the time needed to erode the core of the embankment and ts is the duration of the
storm.
Structures
In PC-Ring the failure modes considered for structures are:

Piping underneath structures
Failure of closure of the water retaining gate (moving structure)
Piping underneath structures
The limit state function applied for piping underneath structures is based on the classical
approach according to Lane (more sophisticated methods are under development):
Z = mL L - cL mc (h - hb)
L = Lv + Lh/3
In which cL is the coefficient according to Lane, h is the outside water level, hb is the inside
water level and mL and mc are parameters that take the model uncertainty into account. Lv
and Lh are respectively the vertical and horizontal seepage lengths. For structures founded on
piles Lh = 0.
Failure of closure of the water retaining gate
The fault tree for this failure mode is given in figure 4.6. The main thought behind this fault
tree is that if the gate fails to close, problems start occurring when the volume of water
flowing inland exceeds the available volume of storage.
Water retaining
gate fails
Insufficient inland
storage volume to
accommodate volume
of inflow
Failure of closing
process
Technical /
human failure
closing process
Failure of
warning phase
Failure of
mobilisation
phase
Failure due to
lack of time
Failure of closure
phase
Figure 4.6 Fault tree of failure of closure of a water retaining gate

Insufficient inland storage volume
32
The limit state function representing insufficient inland storage volume to accommodate the
volume of water flowing in due to failure of the water retaining gate is as follows:
Z = mstor Astor hpv - min ts Qin
In which mstor Astor hpv represents the inland storage volume, consisting of Astor which is the
area of the available storage, hpv which is the allowed increase in water level in the storage
area and mstor is a factor taking the model uncertainty into account. min ts Qin represents the
volume of water flowing in because of the failing water retaining gate, consisting of Qin
which is the discharge of the water flowing in, ts which is the duration of the storm and min
which is a factor taking the model uncertainty into account.
Failure due to lack of time
Failure due to lack of time occurs when the time required to close the gate exceeds the
maximum available time. The limit state function is:
Z = MAT Tcp
In which MAT is the Maximum Available Time and Tcp is the time required to close the gate.
Tcp is the sum of the required time for the warning, mobilisation and closure phase. The
maximum available time is determined partly by the time between the warning for the storm
and the actual start of the storm. The other part of the maximum available time is formed by
the time required to fill the available inland storage volume (see previous limit state
function).
Technical / human failure
Probabilities of failure due to technical / human failure can be established according to for
instance Cooke et al. (1998)xvi and Van Elst (1997)xvii. The probability of technical / human
failure is a combination between failure in the warning, mobilisation and closure phase, see
below. The accompanying reliability index can be determined according to the second
equation.
Fnc = FW FM FCF
nc = - -1(P(Fns))
The limit state function for technical / human failure is given by:
Z = nc - vnc
For nc see equations mentioned above and vnc is a variable with mean 0 and standard
deviation 1 which represents the intrinsical uncertainty.
2.3.2.1.
Dune
During a storm the front face of the dune erodes and the eroded material is deposited on the
foreshore of the dune. Breach occurs when the remaining profile is insufficient to withstand
storm conditions. The profile of the dune as a function of the loading conditions during storm
is predicted with the model according to Vellinga (1986)xviii, see figure 4.7.
In PC-Ring failure of dunes is approached by comparing the initial profile of the dune and a
minimum allowed profile as a result of the storm, see figure 4.7. The minimum allowed
profile under a storm is represented by the line BCDEF, for which the stretch between D and
E is determined according to Vellinga (1986), the formula is given in the figure. The limit
state function establishes whether the initial profile is sufficient to provide the minimum
allowed profile:
33
Z = mD V1 + V2 - V3
In which V1, V2 and V3 are defined according to figure 4.7 and mD is a factor taking the
model uncertainty into account.
Initial dune profile
0.12 Tp Hs 2,5 m
Minimum allowed dune
profile after storm
Figure 4.7 Comparison of the initial profile of the dune and the minimum allowed profile as a
result of the storm (from Vrouwenvelder et al. (2001))
34
Statistical models
The statistical models that are applied for the random variables in PC-Ring are described
below. First the statistical models of random variables in PC-Ring in general are discussed.
Second the statistical models of the hydraulic boundary conditions are presented separately.
Statistical models of random variables in PC-Ring in general
The statistical models consist of the following components:

Statistical distribution functions.
Spatial correlation function.
Model representing the correlation in time.
These components are discussed below.
Statistical distribution functions
For each variable in the above mentioned limit state

functions a choice has to be made whether the
variable is of a deterministic or random nature. In
the latter case the distribution functions have
already been established in the computer code and
cannot be altered by means of input. However, the
parameters accompanying the distribution function
in the form of mean values and standard deviations
have to be defined. Instead of the standard
deviation regularly the expression of the variation
coefficient, V = /, is used. Apart from the
random variables related to the hydraulic boundary
conditions, most random variables in PC-Ring are
normal or lognormal distributed.
Figure 4.8. Shape of the correlation

function (from Vrouwenvelder et al.,
2001)
Spatial correlation function
The in PC-Ring applied spatial correlation function isxix:
x 2
2
dx
(x) = x + (1 x ) exp
In which x is a constant correlation and dx is the correlation

distance. In fig. 4.7. an impression is given of the shape of the
function.
Model representing correlation in time
In PC-Ring the Borges Castanheta model is applied to

represent the correlation in time. According to this model the
time is divided into intervals t in which complete correlation
is assumed. Between the time intervals a constant correlation dt
is taken. An impression of this model is given in fig.4.9.
Figure 4.9. Representation of

the Borges Castanheta model
(from Vrouwenvelder et al.,
2001)
Statistical models of hydraulic boundary conditions
In PC-Ring a number of models for different situations of hydraulic boundary conditions are
incorporated. As an example below the model for a tidal river is presented. In fig. 4.10. and
fig. 4.10. the model that is applied to determine the local hydraulic boundary conditions and
35
hsea
Basic random variables for the
hydraulic boundary conditions
(hsea, Q, U, statistics)
F and
Q
Model:
Mike11
U
F
Local water
levels (h)
Model:
Bretschneider
Local wave
conditions (Hs, Ts)
d
h
Hs
Ts
Z-function
= water level at the

mouth of the
Severn Estuary
(m).
= river discharge
upstream at a
point where the
local water levels
are independent
of the tidal
variations (m3/s).
= wind speed (m/s).
= fetch of the wind
(m).
= depth along the
fetch (m).
= local water level
(m).
= significant wave
height (m).
= significant wave
period (s).
Figure 4.10. Model that is applied to determine the local hydraulic boundary conditions in the Zfunctions
Data requirements at the
mouth of the river
1.
Water levels, hsea
2.
Wind speeds, U
3.
Statistics of water
levels given the
wind direction
F(hsea<hsea | )
4.
Statistics of wind
speeds given the
wind direction
F(U<U | )
5.
Probability of the
wind directions
P()
Correlation
Data requirements
upstream of the river
1.
Discharges Q at a
location upstream
independent of tidal
influences.
2.
Statistics of Q
3.
The magnitude of
t according to the
Borges Castanheta
model.
A
B
C
Flow
direction
Figure 4.11. The data requirements of the basic random variables and the statistics that are used to determine
the local hydraulic boundary conditions at for instance locations A, B, C and D
the data requirements for this model are presented. Below the following aspects of this model
are further explained:
The way in which the local water levels are determined in PC-Ring.
The statistics that are mentioned in fig. 4.11.
Local water levels
To explain the model for the tidal river as applied in PC-Ring fig. 4.11. is used as an
example. The basic random variables hsea, Q and U can occur in various different
combinations. Each different combination results in a different local water level. The local
water levels at for instance locations A, B, C and D are predicted as a function of different
combinations of the basic random variables using Mike11, sobek, etc.. The results of these
calculations are laid down in one table for each location A, B, C and D. To determine the
36
local water level for flood defences situated for example between A and B, PC-Ring linearly
interpolates between the water level at A and the water level at B. This linear interpolation
takes place according to the distance of the location of the flood defence with respect to A
and with respect to B.
The combinations of the basic random variables are formed by:
Nine different discharges. The discharge values are chosen such that the range of
occurring discharges is sufficiently represented. The extreme values are emphasised
in this choice.
Five different wind speeds. The wind speed values are chosen such that the range of
occurring wind speeds is sufficiently represented.
A number of wind directions: those wind directions are chosen that are relevant to the
Six different water levels at sea. The water level values are chosen such that the range
of occurring water levels is sufficiently represented. The extreme values are
emphasised in this choice.
Statistics
The following statistics are applied in PC-Ring with respect to the hydraulic boundary
conditions:
Water levels at sea given the wind direction:
For h sea > m d :
Fweibull (h
sea
) = P(h sea
< h ) = 1 pc exp sea

sea

m
+ d

In which hsea is the water level at the sea, is the wind direction and pc, md, , are
variables that determine the shape of the distribution function.
Wind speeds given the water level and the wind direction:
K (u ) + w (hsea Ah ) / Bh
F (u hsea , ) = P (u < u hsea , ) = exp exp
mw
K(u)=awu2+bwu+cw
In which u is the wind speed, hsea is the water level, is the wind direction, w is the
correlation between the wind speed and the water level given a wind direction, Ah, Bh
and mw are fitting parameters. This model for the correlation between the wind speed and
water level originates from the model developed by Volker.
The probability of the wind directions:
The wind direction is a discrete random variable. The statistics consist of a probability of
each of the 16 wind directions.
The discharge Q:
the statistics of the discharge Q are represented by Q as a function of the return period.
This function is in the form of:
Q = a*ln(R) + b
In which Q is the discharge and R is the return period of Q. a and b are fitting parameters.
The statistics of Q can consist of more than one connecting functions of the same form as
presented above. The statistics of Q cannot be entered as variables in PC-Ring but are fixed
in the computer code.
37
Available calculation methods in PC-Ring

First an overview is given of the main steps that PC-Ring takes to come to an annual
probability of flooding of a flood defence system. Second the main calculation methods are
mentioned that are applied. The information below is taken from Vrouwenvelder (1999)xx.
Main steps taken in PC-Ring calculations
The following steps are taken in the calculation of the flood defence systems probability of
flooding:
9. Calculation of the probability of failure of one flood defence cross section for one tide,
one partial failure mode (for instance failure mode overtopping, partial failure mode
saturation), given the wind direction.
10. Combination of the partial failure modes resulting in the probability of failure of one total
failure mode.
11. Taking the probability of the wind directions into account.
12. Determining the probability of failure due to one failure mode for the total flood defence
stretch for which the under step 1 mentioned flood defence cross section is representative.
13. Combining the probabilities of failure of all the wind directions.
14. Determining the probability of failure for the total regarded period.
15. Combining the probabilities of the different failure modes.
16. Combining all the flood defence stretches to find a total flood defence systems
Calculation methods as applied in PC-Ring
When regarding the above mentioned eight steps to calculate the systems probability of
flooding, two main calculation methods occur:
The calculation of the probability of failure represented by one limit state function, as
in the above mentioned step 1.
The combination of different limit state functions taking mutual correlations into
account, as in the above mentioned steps 2 to 8.
Probability of failure of one limit state function
In PC-Ring the below mentioned main methods are available to calculate the probability
of failure of one limit state function:
FORM (First Order Reliability Method)
SORM (Second Order Reliability Method)
MC (Crude Monte Carlo)
DS (Directional Sampling)
A number of combinations of the above mentioned methods: for instance an option
that PC-Ring automatically switches to DS if convergence does not occur in a
calculation with FORM or SORM. Other options involve the combination of DS and
FORM, the latter method is then used to find the design point.
Combination calculations
Consider a system consisting of n elements. An element can for instance be: a cross
section, a tide, a wind direction, a stretch, a failure mode. Each element is represented by
one Z-function. Two elements of the system are picked and are combined to form one
equivalent representative element. In other words two Z-functions are combined to one.
The total amount of elements in the system is reduced from n to n-1. Repeating this
procedure over and over again will eventually reduce the amount of elements in the
system to one. In other words, the system is wrapped up.
The procedure to find one equivalent representative Z-function is according to the
method of Hohenbichlerxxi. This procedure calculates P(Z1<0 AND Z2<0) taking the
38
mutual correlation into account. If this probability is known, then P(Z1<0 OR Z2<0) can
be determined.
Limiting the number of flood defence sections in calculations
The process of flood defence modelling and data gathering presents time-consuming
activities in practice. The main thought behind solving this practical problem is considering
the flood defence system as a serial system. This main thought results in a practical approach
to select the appropriate cross sections for the calculations with PC-Ring.
Practical problem: laborious flood defence modelling and data gathering
In order to make the calculations with PC-Ring, the flood defence system must be translated
into a model. This model can be expressed in data, and these data are used in the
calculations. Ideally, the complete flood defence system is thus expressed in data and taken
into account in the probability calculations. However, in practice this takes a lot of time in
terms of flood defence modelling and data gathering. This time is usually not available.
Serial system and weakest link
A way to deal with this problem is to regard the flood defence system as a serial system. The
weakest link in a serial system dominates the total systems probability of failure. Therefore,
only the cross sections are taken into account that are expected to contribute most to the total
systems probability of failure.
Practical approach of flood defence modelling and data gathering
The process of cross section selection and data gathering is as follows:

1. Division of the water defence system in defence types.
2. The next step is to divide the water defence system in embankment stretches. To this end
rough information and insights are used. The division is based on the external physical
characteristics and not yet on the characteristics directly connected to the failure modes,
although implicitly the connections are there. The following characteristics are important
for this selectionxxii:
Orientation to the wind directions: embankment stretches that are orientated
differently will be loaded by different wave regimes and therefore must be discerned
as different embankment stretches.
High water regimes, differences in extreme water levels: lengths of the water defence
system for which different high water regimes are relevant must be discerned as
separate embankment stretches.
Geometrical characteristics foreshore: Embankment stretches with significant
different sizes of the foreshore in terms of height and width.
External geometry of the water defence: lengths of the water defence system with
significant differences in height and (external) construction are discerned as different
embankment stretches. Differences in geometry will lead to differences in loading
conditions due to the same hydraulic boundary conditions.
3. The water defence system has now been divided into rough stretches with the same type
of characteristics. However, cross sections have to be determined which can be regarded
as representative of the total embankment stretch. If still significant differences between
cross sections in an embankment stretch are present, then the stretches need to be divided
into further parts: the flood defence sections. A first insight with regard to weak spots in
the water defence system can be given by managing authorities. These authorities can
also help to determine the relevant failure modes for certain embankment sections. The
following failure mode related considerations can form a basis for a division in
embankment sections:
Different types of outside slope revetment (types and construction), this will lead to a
further division for the failure mode: damage of the revetment on the outside slope
and erosion of the embankment body.
39
Differences in geometry on a detailed level has consequences for each of the failure
modes.
Differences in the foundation soil can have a considerable effect on the contributions
to the probability of failure of geotechnical failure modes. For these failure modes a
further division has to be made.
Differences in the inside slope revetment of embankments (quality of the grass,
thickness and qualification of the clay cover layer on the inside slope, the angle of the
inside slope, etc.), this kind of information is especially useful for the division in
embankment sections for the failure modes overtopping and consequently erosion of
the inside slope or instability of the inside slope.
Information about the construction of the embankment (clay embankment, sand
embankment with a clay core, etc) and information about the soil layers underneath
and directly next to the embankment (in front of and behind the embankment), this
information is relevant to the failure modes heave and piping, instability of the inside
slope and damage to the revetment and erosion of the embankment body.
4. After step 3 the water defence system has been divided in embankment sections. The
following step is to select the relevant sections for the reliability analysis. The procedure
to come to this selection of sections is given below:
Regard a failure mode for which it is desirable to reduce the number of embankment
sections. The first logical step is to eliminate all the embankment sections for which
the mode is not relevant, or in other words: the contribution of the section to the
probability of failure due to a certain mode is negligible in advance. Well known
weak spots can provide valuable first insight in which sections contribute
significantly and which ones do not.
For the remaining sections, indicators are used to rank them. These indicators are
related to the failure modes. The number of selected sections can be limited based
on this ranking.
Apart from the selected weak sections based on the indicators, sections from the
middle and strong categories have to be chosen. This is done because it is practical
to be able to make an estimate of the probability of flooding after eliminating the
weak spots in the probability of failure calculations.
The former three steps have to be performed for all failure modes, which can result
in a different selection of embankment sections for each mode.
Check the spreading of the sections along the water defence system with respect to
the magnitude of the expected consequences. The sections with substantial
consequences that fall out off the analysis should be added or shift a bit with the
choice in the middle and strong sections. With the total risk analysis in mind, a
strong section with extensive consequences can contribute just as much or even
more to the total risk as a weak section with hardly any consequences.
5. The first selection of embankment sections has been finished. For each section it is clear
which failure modes are regarded. The next step is to gather data for the regarded failure
modes and embankment sections.
6. After the first calculations of the probability of failure with PC-Ring a check is made if
sections have to be added or adjusted:
First the contribution of the failure modes to the total probability of failure is
regarded.
For the mode with the largest contribution a check has to be made if the last selected
sections still have a significant contribution to the probability of failure. If they do an
additional selection of sections for that mechanism has to be made. This check needs
to be made for all the failure modes with an emphasis on the ones with the largest
contribution.
This process has to be repeated until no more sections need to be included in the analysis. The
number of cycles depends on the number of embankment sections which are chosen initially
and after expansion.
40
ii
Buijs, F.A., Reliability analysis of the Caldicot Levels flood defence system by using Dutch
reliability methods for flood defences, Msc. thesis, Delft University of Technology 2003
iii
B.L. Lassing, A.C.W.M. Vrouwenvelder, P.H. Waarts, Reliability analysis of flood defence systems
in the Netherlands, proc. Conf. ESREL 2003 (2): 1005-1013, Maastricht, The Netherlands, June 15-18
2003
iv
v
3.2), Delft 2001
vi
HRWallingford, Risk assessment for Flood and Coastal Defence for Strategic Planning, High Level
Methodology, A review, Report SR603, 2002
vii
viii
Buijs, F.A., Reliability analysis of the Caldicot Levels flood defence system by using Dutch
reliability methods for flood defences, Msc. thesis, Delft University of Technology 2003
ix
B.L. Lassing, A.C.W.M. Vrouwenvelder, P.H. Waarts, Reliability analysis of flood defence systems
in the Netherlands, proc. Conf. ESREL 2003 (2): 1005-1013, Maastricht, The Netherlands, June 15-18
2003
x
xi
Vrouwenvelder, A.C.W.M. , Steenbergen, H.M.G.M., Slijkhuis, K.A.H., Theoretical manual of PCRing, Part A: descriptions of failure modes (in Dutch), Nr. 98-CON-R1430, Delft 2001
xii
Tol, van A.F., Oostveen, J.P., CUR 162, Constructing with ground. Structures made of ground on
and in soil with little bearing capacity and strong compressible subsoil (in Dutch), Delft 1999
xiii
Technisch rapport Asfalt voor Waterkeren (Technical report Asphalt for Water Retaining (in
Dutch)), Concept revision 6.6, 31-08-2000
xiv
Pilarczyk, K.W. (ed), Dikes and Revetments. Design, maintenance and safety assessment, Balkema,
Rotterdam 1998
xv
TAW, The use of asphalt in hydraulic engineering, Technical Advisory Committee on Water
defences, Rijkswaterstaat communications, The Hague 1985
xvi
Cooke, R.M., Noortwijk, van, J., Bedford, T.J., Uncertainty analysis of inundation probabilities,
TUDelft & HKV, 1998
xvii
Elst, van, N.P., Betrouwbaarheid van het sluitproces van beweegbare waterkeringen (Reliability of
the closure process of water retaining gates (in Dutch)), TUDelft: Delft University Press 1997
xviii
Vellinga, P., Beach and dune erosion during storm surges. Thesis Delft University of Technology,
also: Delft Hydraulics, Communications No.372, the Netherlands
xix
Vrouwenvelder, A.C.W.M. , Steenbergen, H.M.G.M., Slijkhuis, K.A.H., Theoretical manual of PCRing, Part B: Statistical models (in Dutch), Nr. 98-CON-R1431, Delft 2001
xx
Vrouwenvelder, A.C.W.M., Theoretical manual of PC-Ring, Part C: Calculation methods (in
Dutch), 98-CON-R1204, Delft 1999
xxi
M. Hohenbichler & R. Rackwitz, First-order Concepts in System Reliability, Structural Safety, 1,
1983, pages 177-188
xxii
Calle, E., Jonkman, B., Lassing, B., Most, van der, H., Data gathering and flood defence modelling
to support the calculation of probabilities of flooding of ring dike systems (in Dutch), Manual (version
3.2), Delft 2001
Defra/Environment Agency, Performance-based Asset Management System (PAMS), Phase 1 Scoping
Study, HR Wallingford, 2004
41

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Investigation of Extreme Flood

Processes & Uncertainty (IMPACT)

Identifying Potential Breach Location

WP2: Deliverable D2.4.1

EXISTING METHODOLOGIES AND POTENTIAL APPROACHES...................................4

LOCAL FACTORS AFFECTING EMBANKMENT PERFORMANCE ..............................12

METHODOLOGY FOR IDENTIFYING POTENTIAL BREACH LOCATION.................18

2. Existing methodologies and potential approaches

What local factors are affecting embankment performance

UK, Dutch and German approaches

Technological developments of computers in the nineties have enabled the calculation of

2.3.2. Main steps taken in PC-Ring calculations

Orientation to the wind directions: embankment stretches that are orientated

Site visit / drawings of

Definition of the defence

Overview of the relevant

Knowledge about past

Analysis of the failure

Fault tree / limit state

Divide system up into

Stretches with eg. Similar

Division into smaller

System sections suitable

Model of physical system

Calculation of the fragility

Fragility curves for the

An introduction to the RASP tiered methodology and fragility

Joint probability load

Flood plain topography

2.4.2 RASP and fragility curves

In RASP High Level Methodologyvi, the concept of fragility

In a risk assessment the aim is to get an impression of the

Figure 3: Example of a fragility curve

conditions are approached in a more differentiated way. This results in conditional

Asset with pathway (or barrier) to flooding

Source Pathway Receptor approach

3. Local factors affecting embankment performance

Figure 5 An example of prioritisation of components contributing most to defence

The following provides an example of factors leading to failure of an embankment. These

Internal indicator Visual indicator

Environmental factors: these factors correspond to the physical elements

3.1.2. Internal factors

Example of risk generated by these factors

Lead to shallow instability due to variation of pore pressure

A high friction angle will allow a higher resistance to failure and

A bad gradation can make the embankment more permeable

Dry unit weight

A material with a high dry unit weight could be less erodible

A material with a poor plasticity index leads easily to piping

Fine particle soils with low cohesion can be dislocated and

The presence of hightly permeable layer strata within

The foundation interface between two different materials is a

Compaction is directly linked with permeability property of the

High groundwater pressure can trigger a deep rotational failure

Temperature variations trigger cracks propagation by acting on

3.1.3. External factors

The reduction of crest level increases considerably the risk of

Leads to a dicrease of the crest level therefore to an increase