“A probabilistic flood risk assessment and the impact of compartmentation ”

Graduation committee:

Prof. drs. ir. J.K. Vrijling (DUT, chairman) Dr.ir M. Kok (DUT, HKV) Prof.ir. A.W.C.M. Vrouwenvelder (DUT) Drs. A. Roos (RWS)

Information student:

Student: R.P.G.J. Theunissen Address: Voorstraat 95-II 2611 JM, Delft Phone: 0641436940 Email: [email protected] Student no: 1005820

This work has been supported by:

Directorate-General Public Works Delft University of Technology and Water Management Faculty of Civil Engineering and Road and Hydraulic engineering Province of South Holland Geosciences Institute

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Preface

This thesis entitled ‘a probabilistic flood risk assessment and the impact of compartmentation’ marks the end of my study at the Faculty of Civil Engineering and Geosciences at Delft University of Technology and has been executed at the ‘Road and Hydraulic Engineering division of the Directorate General of Public Works and Water Management’. The study was supported by the Province of South Holland. I would like to thank the members of my committee for their interest and constructive criticisms during the process.

R.P.G.J. Theunissen January 2006

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Summary

The current safety philosophy against flooding in the Netherlands as recorded in the Flood Defence Act was introduced in 1960. At the time a policy was chosen based on pragmatic considerations that focused on strengthening and maintaining the primary defences. By defining safety standards, periodical adjustments of hydraulic loads and a five yearly assessment of the quality of the primary defences it was ensured the protection against flooding grows along with physical developments. However besides physical developments like sea level rise and increasing river discharges since 1960 economical and social developments have occurred. The population density and the protected value have increased significantly and furthermore society seems to accept less risk of flooding, as flood disasters are not seen as acceptable natural phenomena’s anymore. In terms of modern risk analyses the probability of many casualties is larger than all other external safety risks together. The current safety philosophy hardly takes economical and social developments into account. Recently the National Institute of Public Health and Environment (RIVM) concluded the current safety philosophy does not lead to a safe and livable Netherlands as was intended.

Contrary to the current safety philosophy the flood risk approach takes economical and social developments into account by including the consequences in the analysis. The consequences consist of the expected economical damage and the expected number of casualties. The first objective in this thesis is to apply the flood risk approach at dike ring area IJsselmonde. Therefore flood scenario probabilities have been determined and their corresponding flood simulations have been carried out, multiplying them results in the flood risk. The second objective was to investigate the impact of compartmentation on the flood risk. This summary first describes the determination of the flood risk at IJsselmonde and continues with a description of the impact of compartmentation.

Flood risk assessment IJsselmonde IJsselmonde is a relatively small dike ring area surrounded by primary defences that were designed on a safety standard with an exceedance frequency of 1/10000 per year. These primary defences were designed before the implementation of the Maeslantkering and the Hartelkering in the tidal river area. These storm surge barriers significantly reduced the hydraulic loads and therefore the probability of flooding in the tidal river area. After the construction of the storm surge barriers it was decided to reduce the safety standard at IJsselmonde to an exceedance frequency of 1/4000 per year.

In this thesis the failure mechanisms overtopping, wave overtopping and damage to the revetment and erosion of the dike body are included in the dike section failure probability analysis. The failure mechanism instability of the inside slope and all mechanisms concerning civil engineering structures have not been analysed for reasons of time and lack of data, furthermore the results of the failure mechanism piping were judged unreliable and are not included in the end results.

The primary defences at IJsselmonde consist of 73 dike sections. As the different states of the storm surge barriers have to be included in the failure probability analysis a dike section failure probability at IJsselmonde can be written as follows:

PF = P (Failure ∩ hQ ≥ Closure Condition ∩ Correctly Closed) + P (Failure ∩ hQ ≥ Closure Condition ∩ Incorrectly Open) + P (Failure ∩ hQ < Closure Condition ∩ Incorrectly Closed) + P (Failure ∩ hQ < Closure Condition ∩ Correctly Open)

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Dike section failure probabilities are insufficient for the calculation of the flood risk and need to be processed to flood scenario probabilities, which are coupled to a partial dike ring part. A partial dike ring part is defined as a part of the dike ring in which the consequences of a flood vary little if the position of the breach is changed. This definition ensures one flood simulation per partial dike ring part is sufficient. The division in partial dike ring parts as used in this thesis is presented in Figure A and is based on the division in compartments by the secondary defences which also are indicated in Figure A. Furthermore the breach locations that are applied in the flood simulations are indicated this figure, these breaches are situated at the dike sections with the greatest failure probability in the partial dike ring part.

1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 1.0E-06 1.0E-07 1.0E-08 1.0E-09

Probability of exceedance 1-FN(x) 100 1000 10000 100000 Number of casualties (N) FN-curve dike ring IJsselmonde Figure A: Schematization IJsselmonde Figure B: FN-curve

The flood risk is approximated by the dominant flood scenarios that contribute for more than 99% to the dike ring failure probability (approximately 1 / 334000 per year). The list of these dominant flood scenarios is presented in Figure C. In this thesis a flood scenario refers to one breach location and one state of the storm surge barriers. As can be seen the correctly closed state and the incorrectly open state are dominant in the failure probability analysis.

Flood Breach Failing partial State Scenario Economical dama- Number of Economical Risk of Scenario Location dike ring areas Barriers Probability ge (Billion euro) Casualties Risk (Euro) Casualties 1 A 6 incorrect open 1.18E-06 4.1 600 4854 0.000710 2 A 6 correctly closed 3.10E-07 4 504 1241 0.000156 3 B 7 correctly closed 2.90E-07 2.9 364 840 0.000105 4 A and C 5 and 6 incorrect open 2.58E-07 4.1 600 1057 0.000155 5 A and B 6 and 7 incorrect open 2.20E-07 6.6 1045 1453 0.000230 6 A, B and C 5, 6 and 7 incorrect open 1.30E-07 6.6 1045 858 0.000136 7 A and B 6 and 7 correctly closed 6.18E-08 6.9 868 426 0.000054 8 A, B, C and D 4, 5, 6 and 7 incorrect open 4.87E-08 7.6 1194 370 0.000058 9 E 8 correctly closed 3.96E-08 4.4 789 174 0.000031 10 B and E 7 and 8 correctly closed 2.33E-08 7.3 1153 170 0.000027 11 A and E 6 and 8 correctly closed 1.95E-08 8.4 1293 163 0.000025 12 C 5 incorrect open 1.75E-08 0.005 0 0 0.000000 13 F 1 correctly closed 1.67E-08 0.4 46 7 0.000001 14 B and F 1 and 7 correctly closed 9.58E-09 3.3 410 32 0.000004 15 F 7 incorrect open 8.25E-09 2.5 445 21 0.000004 16 A and F 1 and 6 correctly closed 7.43E-09 4.4 550 33 0.000004 17 A, C and D 4, 5 and 6 incorrect open 7.39E-09 5.1 749 38 0.000006 18 E and F 1 and 8 correctly closed 7.24E-09 4.8 835 35 0.000006 19 6 and 8 incorrect open 5.22E-09 6.3 1124 33 0.000006 20 A, C and E 5, 6 and 8 incorrect open 4.93E-09 6.3 1124 31 0.000006 Total Risk: 11836 0.001723 Figure C: List of dominant flood scenarios

Based on the design points of the dominant flood scenarios flood simulations have been made. The hydraulic development of these simulations is described in the main report. The hydraulic consequences of a flood scenario have been translated to an expected economical damage and an expected number of casualties, which is indicated in Figure C. Multiplication of flood scenario probabilities with their consequences results in the risk of a flood scenario. In Figure B the risk is presented as a FN-curve, which indicates the probability of exceedance of a certain number of casualties. The presence of the Maeslantkering and the Hartelkering results in extremely low flood scenario probabilities. IJsselmonde therefore is a

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very special dike ring and is not representative for other dike ring areas, where the flood scenario probabilities are expected to be significantly higher. Due to the great population density and the enormous protected value at IJsselmonde the consequences immediately are very extreme if a breach occurs. However at IJsselmonde even the extreme consequences are dominated by the flood scenario probabilities resulting in an extremely low flood risk.

Impact of compartmentation Compartmentation can be defined as the division of the overall system in compartments by secondary defences (see Figure B) resulting in isolation per compartment and therefore providing protection to the overall system by reducing the consequences of initial failure. In many areas in the Netherlands secondary defences are present in the landscape and will influence the flood progress. Also natural differences in terrain level and artificial earth embankments (railroads) will affect the development of a flood. The flood progress determines the expected economical damage and the expected number of casualties.

To describe the impact of compartmentation the following characteristics are identified: 1. The distribution of flood scenario probabilities over the primary defences. 2. The hydraulic loads on a functioning secondary defence. 3. The reliability of the secondary defences. 4. The spatial distribution of value over the compartments.

The quantity of these characteristics together with their variety in nature implies the impact of compartmentation is highly dependent on local characteristics. In this thesis flood simulations with the presence of a functioning secondary defence and without the secondary defence have been executed to describe various possible impacts. Based on these simulations it can be concluded secondary defences can have a significant impact on the flooded area, the water depths, the flooding velocities, the expected economical damage and the expected number of casualties of a flood scenario. The simulations show a reduction of both the expected economical damage and the expected number of casualties due to the presence of a secondary defence in a flood scenario is possible. In this case the additional economical damage and casualties in the flooded compartment are outweighed by the prevention of greater economical damage and more casualties in neighbouring compartments. Furthermore the simulations show it is also possible the presence of a secondary defence results in a reduction of the expected economical damage while simultaneously resulting in an increase of the expected number of casualties. In this case the higher flooding velocities and greater water depths in the flooded compartment result in an increase of the expected number of casualties in the flooded compartment, which outweighs the prevention of casualties in neighbouring compartments. It can be concluded that a positive impact of compartmentation on expected economical damage does not have to result in a similar positive impact on the expected number of casualties. To determine the overall impact of a secondary defence this analysis has to be broadened from one flood scenario to all flood scenarios that are affected by the secondary defence. In this thesis it is shown that also averaged over multiple flood scenarios compartmentation can have a positive impact on the economical flood risk.

In the last part of this thesis is focused on the question whether investing in secondary defences is a cost-effective measure. A method is introduced that describes how compartmentation measures or in general all measures that reduce the consequences of a flood can be included in an economical risk optimisation. By defining several sorts of risk reducing measures (for example strengthening the primary defences which reduces the flood scenario probabilities or compartmentation which reduces the consequences) a choice is introduced in which way risk reduction can be achieved. The most effective measure should be applied in an improvement round. In Figure D an example of such a choice is presented. IX

The measure with the steepest downward inclination is most effective and should be applied. This procedure should be repeated till the optimal situation at an inclination of –1 is reached. The succession of measures with the steepest downward inclination would be the optimal risk reduction strategy.

300 300 250 250 200 200

150 150

100 100 Risk (millions) Risk (millions) 50 50

0 0 0 204060 0204060 Investments (millions) Investments (millions)

Strengthening primary dike section 2 Strengthening primary dike section 3 Introduction new secondary defence Introduction new secondary defence

Figure D: Effect investments in primary ring versus investments in secondary defences

Compartmentation would be cost-effective if it is a part of the optimal risk reduction strategy. However compartmentation probably is not the most effective measure as conditions for an effective risk reduction due to investments in secondary defences seem to be less favorable compared to risk reduction by investments in the primary ring. By strengthening primary dike sections a flood scenario probability relatively fast is reduced by an order while reducing the consequences of a flood with an order by investing the same amount in secondary defences in general is harder to accomplish. It is recommended to do further research into system configurations in which compartmentation would be cost-effective.

Finally in this thesis a concept is proposed in which by separating the investments (I) in investments in the primary ring (IP) and investments in secondary defences (Is) it becomes possible to define an economical flood risk optimisation as a function of two variables. By investing in the primary ring the flood scenario probabilities are reduced and by investing in the secondary defences the expected economical consequences can be reduced. This distinction adds an extra dimension to the optimisation. This is illustrated in Figure E which is based on the original economical optimisation of the Delta Committee. Figure E presents the total costs as a function of Ip and Is.

Total costs as function of Ip and Is

4.5E+08 4.0E+08 4E+08-4.5E+08 3.5E+08 3.5E+08-4E+08 3.0E+08 3E+08-3.5E+08 2.5E+08 Ctot 2.5E+08-3E+08 2.0E+08 2E+08-2.5E+08 1.5E+08 1.0E+08 1.5E+08-2E+08 7.5E+7 5.0E+07 5.0E+7 1E+08-1.5E+08 0.0E+00 2.5E+7 5E+07-1E+08 0 0-5E+07 Is 1.8E+08 2.0E+08 2.1E+08 2.3E+08 2.4E+08 Ip 2.6E+08

Figure E: Total costs as function of Ip and Is

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Table of contents

PREFACE V

SUMMARY VII

TABLE OF CONTENTS XI

LIST OF FIGURES XIV

LIST OF SYMBOLS XVII

1 INTRODUCTION 1

1.1 THE DUTCH SAFETY PHILOSOPHY AGAINST FLOODING 1 1.1.1 Origin of the safety philosophy against flooding 1 1.1.2 Properties of the current safety philosophy 3 1.1.3 Recent developments in the Netherlands 3 1.2 PROBLEM ANALYSIS 5 1.3 THE FLOOD RISK APPROACH 6 1.4 OBJECTIVE OF THE RESEARCH 8 1.5 OUTLINE OF THE RESEARCH 9

2 SYSTEM DESCRIPTION IJSSELMONDE 11

2.1 CHARACTERISTICS 11 2.2 PARTIAL DIKE RING PARTS AND COMPARTMENTS 13

3 FAILURE PROBABILITY ANALYSIS 15

3.1 PC-RING THEORY 15 3.1.1 General description of the failure probability of a dike section 15 3.1.2 Failure mechanisms 17 3.1.3 Uncertainty 19 3.1.4 Combination procedures 19 3.2 IJSSELMONDE MODEL 20 3.2.1 Hydraulic loading 20 3.2.2 Characteristics of the water defences 22 3.3 RESULTS 22 3.3.1 Reference level control 22 3.3.2 Overtopping 23 3.3.3 Wave overtopping 24 3.3.4 Damage to the revetment and erosion of the dike body 27 3.3.5 Uplifting and Piping 28 3.3.6 Dike Ring results 29 3.4 FLOOD SCENARIOS 30 3.4.1 Failure probability of a partial dike ring part 30 3.4.2 Probability of a flood scenario 30 XI

3.4.3 Results 34 3.4.4 Flood simulations 36

4 CONSEQUENCES OF A FLOOD 39

4.1 MODELING OF THE FLOOD SIMULATIONS 39 4.1.1 Spatial information 39 4.1.2 Water level development at the river 42 4.1.3 Modeling of the breach 46 4.1.4 Economical damage 47 4.1.5 Casualties 49 4.2 RESULTS OF THE FLOOD SIMULATIONS 50 4.2.1 Breach location A at partial dike ring part 6 51 4.2.2 Breach location B at partial dike ring part 7 56 4.2.3 Breach location C at partial dike ring part 5 58 4.2.4 Breach location D at partial dike ring part 4 59 4.2.5 Breach location E at partial dike ring part 8 60 4.2.6 Breach location F at partial dike ring part 1 60 4.3 OVERVIEW CONSEQUENCES OF FLOOD SCENARIOS 61

5 DETERMINATION OF THE FLOOD RISK 63

5.1 FLOOD RISK CONCERNING CASUALTIES 63 5.1.1 Group risk presented as FN-curve 64 5.1.2 Comparison with the external safety domain 65 5.1.3 Comparison with the VROM standard 66 5.2 FLOOD RISK CONCERNING ECONOMICAL DAMAGE 67 5.3 METHODS TO REDUCE THE FLOOD RISK 68 5.3.1 Effect of the Maeslantkering and the Hartelkering 69 5.3.2 Compartmentation 70

6 IMPACT OF COMPARTMENTATION ON FLOOD RISK 71

6.1 AN INTRODUCTION TO COMPARTMENTATION 71 6.2 COMPARISON OF COMPARTMENTATION IN DIFFERENT ENGINEERING FIELDS 73 6.3 COMPARTMENTATION IN DIKE RING AREAS 74 6.3.1 Distribution of flood scenario probabilities 75 6.3.2 Hydraulic loading on a functioning secondary flood defence 75 6.3.3 Reliability of secondary defences 76 6.3.4 Spatial distribution of value over compartments 78 6.4 CASE STUDY IMPACT SECONDARY DEFENCES 80 6.4.1 Impact secondary defences on flood scenarios 80 6.4.2 Averaged impact of a secondary defence on flood scenarios 82 6.5 ECONOMICAL OPTIMISATION 84 6.5.1 Example economical risk optimisation by strengthening primary ring 84 6.5.2 Inclusion of compartmentation measures in a economical optimisation 87 6.5.3 Economical risk optimisation case IJsselmonde 90 6.5.4 Example economical optimisation as a function of two variables 91 6.5.5 Qualitative analysis 98

7 CONCLUSIONS AND RECOMMENDATIONS 100 XII

7.1 CONCLUSIONS 100 7.2 RECOMMENDATIONS 102

REFERENCES 105

APPENDICES 108

A. DIKE RING AREAS IN THE NETHERLANDS 109 B. SCHEMATIZATION OF DIKE SECTIONS 110 C. PC-RING CALCULATION LAY-OUT 120 D. FAILURE MECHANISMS 124 E. PC-RING OUTPUT AND DESIGN POINT ANALYSIS 129 F. WATER LEVEL DEVELOPMENTS AT BREACH LOCATIONS 142 G. OUTPUT HIS-SSM 143 H. FLOOD RISK CALCULATION SCHEME 144 I. IMPACT FUNCTIONING SECONDARY DEFENCES ON FLOOD SCENARIOS 145 J. RISK OPTIMISATION IJSSELMONDE 150

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List of Figures

Figure 1-1: Flooded area in 1953 ...... 1 Figure 1-2: Breach...... 1 Figure 1-3: Possible evaluation of economical and social developments ...... 5 Figure 1-4: Current philosophy (probability of exceedance per dike section)...... 6 Figure 1-5: Flood risk approach...... 6 Figure 1-6: Conceptual FN-curve ...... 8 Figure 1-7: Outline of the research...... 9 Figure 2-1: Dike ring area 17 IJsselmonde...... 11 Figure 2-2: Maeslantkering / Hartelkering ...... 12 Figure 2-3: Reduced influence sea...... 12 Figure 2-4: Surface levels relative to NAP...... 12 Figure 2-5: Division in partial dike ring parts ...... 13 Figure 2-6: Division in compartments...... 14 Figure 3-1: Visual interpretation of equation 3.4...... 16 Figure 3-2: Failure Mechanisms...... 18 Figure 3-3: MHW-control ...... 22 Figure 3-4: Results failure mechanism overtopping ...... 23 Figure 3-5: Graph Reliability Index Overtopping ...... 23 Figure 3-6: Table results failure mechanism wave overtopping ...... 24 Figure 3-7: Graph Reliability Index Wave Overtopping ...... 24 Figure 3-8: Comparison between failure mechanism overtopping and wave overtopping.....25 Figure 3-9: Failure probabilities overtopping and wave overtopping...... 25 Figure 3-10: Results failure mechanism damage to revetment and erosion of dike body...... 27 Figure 3-11: Graph Reliability index damage to Revetment and erosion of dike body...... 27 Figure 3-12: Results failure mechanism uplifting and piping...... 29 Figure 3-13: Flood dominated by river and by storm at sea...... 31 Figure 3-14: Graphical interpretation of the four states of the barrier...... 32 Figure 3-15: Rotterdam with / without breach in case 1/10000 water level development ...... 33 Figure 3-16: Breach locations of the necessary flood simulations ...... 37 Figure 4-1: Overview of IJsselmonde (yellow) with urban areas (pink), primary and secondary water defences (red), additional earth embankments (orange) and waterways (blue). ..40 Figure 4-2: Classification of land use ...... 40 Figure 4-3: Modelled passages in earth embankments (culverts green, structures blue) ...... 41 Figure 4-4: Design Point PC-Ring versus physical maximum ...... 43 Figure 4-5: Water level development in case of incorrect open barriers ...... 44 Figure 4-6: Water level development in case of correctly closed barriers...... 45 Figure 4-7: Breach growth formula Verheij – Van der Knaap...... 46 Figure 4-8: Breach locations per partial dike ring part and compartment...... 50 Figure 4-9: Legend ...... 50 Figure 4-10: Breach location at Maashaven...... 51 Figure 4-11: Flood after 1, 2, 6,12, 24, 48, 96 and 120 hours with incorrect open barriers....51 Figure 4-12: Development of discharge through breach...... 52 Figure 4-13: Water level variation near Breach (left) and further from breach (right)...... 52 Figure 4-14: Flood progress after 120 hours for three breach locations ...... 53 Figure 4-15: Flood after 1, 2, 6, 12, 24, 48, 96 and 120 hours with correctly closed barriers 53 Figure 4-16: Development of discharge through breach ...... 54 Figure 4-17: Water level variation near Breach (left) and further from breach (right)...... 54 Figure 4-18: Breach location B at Bolnes...... 56 Figure 4-19: Flood after 1, 2, 6, 12, 24, 48, 96 and 120 hours with incorrect open barriers...56 Figure 4-20: Discharges through breach incorrect open (l) correctly closed barriers (r) ...... 57

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Figure 4-21: Breach location at IJsselmonde ...... 57 Figure 4-22: Flood after 1, 2, 6, 12, 24, 48, 96 and 120 hours with incorrect open barriers...58 Figure 4-23: Flood after 1, 2, 6 and 12 hours in case of incorrect open barriers...... 58 Figure 4-24: Breach location D at Hoogvliet...... 59 Figure 4-25: Flood after 1, 2, 4, 6, 12 and 24 hours in case of incorrect open barriers...... 59 Figure 4-26: Flood after 1, 2, 6, 12, 24, 48, 72 and 120 hours with incorrect open barriers...60 Figure 4-27: Overview consequences per flood scenario ...... 61 Figure 5-1: Probability density function number of casualties ...... 64 Figure 5-2: Cartoon “IJsselmonde”...... 64 Figure 5-3: Probability of exceedance of the number of casualties...... 65 Figure 5-4: Comparison with external safety domain ...... 65 Figure 5-5: Comparison with VROM standard...... 66 Figure 5-6: Probability density function of the economical damage ...... 67 Figure 5-7: Probability of exceedance of economical damage...... 68 Figure 5-8: Reduction of consequences left and failure probability right [20]...... 68 Figure 5-9: Effect of measures presented in the form of a FN-curve [20] ...... 69 Figure 5-10: Impact storm surge barriers presented in FN-curve...... 69 Figure 5-11: Possible Impact of compartmentation (negative in flooded compartment, positive in other compartments ...... 70 Figure 6-1: Ship compartmentation ...... 71 Figure 6-2: Ballasted tunnel element without / with compartmentation ...... 72 Figure 6-3: Conceptual model of the development of damage due to flooding...... 74 Figure 6-4: Graphical interpretation of the indicator Isd...... 76 Figure 6-5: Event tree for failure of section I of the fictitious dike ring [25]...... 76 Figure 6-6: Number of distinct flooding scenarios for a simple dike ring [25]...... 76 Figure 6-7: Three states of secondary water defences ...... 77 Figure 6-8: Impact spatial distribution of value over compartments ...... 78 Figure 6-9: Locations investigated secondary defences ...... 80 Figure 6-10: Reduction economical damage because of presence secondary defence...... 81 Figure 6-11: Flood progress compartment 3 with and without secondary defence ...... 81 Figure 6-12: Change in number of casualties due to presence secondary defence ...... 82 Figure 6-13: Economical damage with and without functioning secondary defence...... 83 Figure 6-14: Flood risk with and without functioning secondary defence...... 83 Figure 6-15: Lay out conceptual dike ring ...... 84 Figure 6-16: Initial situation dike ring area...... 84 Figure 6-17: Development of flood scenario probabilities (beta) per improvement round...... 85 Figure 6-18: Development of net present flood scenario risks in million euro per improvement round ...... 85 Figure 6-19: Improvement costs per dike section in million euros...... 85 Figure 6-20: Improvement rounds at risk optimisation ...... 85 Figure 6-21: Risk as a function of investments in a risk optimisation...... 86 Figure 6-22: Conceptual dike ring with secondary defences...... 87 Figure 6-23: Strengthening primary dike section versus new secondary defence ...... 88 Figure 6-24: Strengthening primary dike section versus upgrading secondary defence...... 89 Figure 6-25: Investment strategies...... 89 Figure 6-26: Economical flood risk as function of investments in measures in improvement rounds ...... 90 Figure 6-27: Two methods to reduce flood risk ...... 91 Figure 6-28: Partial derivatives to Ip and Is ...... 92 Figure 6-29: Total costs as a function of Is and Ip for c = 100...... 95 Figure 6-30: Risk as a function of Is and Ip for c = 100...... 95 Figure 6-31: Total costs as a function of Is and Ip for c=250 ...... 96 Figure 6-32: Risk as a function of Is and Ip for c = 250...... 96 Figure 6-33: Different paths to unsure minimum value...... 97 XV

Figure 6-34: Integral strengthening primary ring ...... 98 Figure 6-35: Secondary defence system in form of ring versus cross...... 99 Figure 6-36: Event tree for state of secondary defence ...... 99

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List of symbols

Variable Description Unit a Wall friction coefficient m-1 B0 Initial width of breach m B Width of breach m C Chezy coefficient m1/2/s 3 Ccomp Capacity of compartment m Ctot Total costs Euro d Depth below plane of reference m +NAP d Thickness of the top layer m D Economical Damage Euro dx Correlation distance m E(S) Expected total Damage Euro or N f1 Breach growth factor - f2 Breach growth factor - FNdij Probability distribution function for the number of casualties in a - year as result of activity I at location j Fpip Safety against piping - fRS Joint probability density function for strength R and load S - FR Probability distribution function for strength R - FS Probability density function for load S - Fupl Safety against uplifting - g Gravity acceleration m/s2 h Total water depth:ζ+d (m) in flood simulations m +NAP H Normative water level m +NAP hb Water level inside dike ring m +NAP hd Crest level of the dike m +NAP hdown Downstream water level m +NAP hw Local water level m +NAP hHvH;predicted Predicted water level at Hook of Holland m +NAP hHvH;real Real water level at Hook of Holland m +NAP hkd Critical crest level of dike m + NAP hQ Combination of water level (h) and discharge (Q) that is - compared with closure criterion hup Upstream water level m +NAP I Moment of inertia m4 4 Ie Moment of inertia due to surface crossed by water m 4 Ii Moment of inertia of ballast water with respect to median of m compartment Isd Indicator for impact of functioning secondary defence - k Roughness factor according to Strickler m Lavailable Available leakage length m Lnecessary Necessary leakage length m MA Driving moment in slip circle kNm mqc Model factor for qc - mq0 Model factor for q0 - MR Resisting moment in slip circle kNm N Number of casualties - N Number of scenarios - Ndij Number of casualties of activity i on location j - PF Failure probability dike ring area -

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PF Flood scenario probability - PF Dike section failure probability - Pt Percentage of time that wave overtopping takes place Q Discharge m3/s 2 qc Critical discharge m /s 2 q0 Occuring overtopping discharge m /s R Risk Euro/year R Risk N/year R Strength parameter - S Total Damage that results from flood Euro or N S Load parameter - t Time hours tstart Point in time at which breach starts to develop hour te Time after which failure of grass revetment occurs in case of critical velocity υc t0 Point in time when maximum breach depth is reached hour T0 Time span in which maximum breach depth is reached hours u Velocity in x-direction m/s uc Critical flow velocity sediment / soil (breach) m/s V Velocity m/s v Velocity in y-direction m/s 3 Vflood Volume of incoming water m x Vector with all relevant parameters (all treated as stochastic - functions and inclusively the to be applied discount rate) Z Limit state function - z Elevation of dike breach m +NAP zcrest-level Initial crest level at start breach m +NAP zmin Min elevation dike breach m +NAP 3 γw Volumetric weight of water KN/m 3 γwet Volumetric weight of the wet top layer KN/m α Damage factor -

αi Angle of the inner slope ° αi Influence factor of random variable i - β Reliability index - Δ Prediction error in water level at Hook of Holland m Δx Correlation distance for spatial spreading m ζ Water level above NAP in flood simulation m +NAP μ Mean value σ Standard deviation -

ρx Constant correlation - υc Critical flow velocity (overtopping) m/s

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1 Introduction

1 Introduction

This chapter describes the background of the flooding problem, which is described in this thesis. Paragraph 1.1 presents the current Dutch safety philosophy against flooding. Paragraph 1.2 continues with the problem description and it explains why the current philosophy doesn’t satisfy the demands anymore. Subsequently paragraph 1.3 globally describes an improved safety philosophy: the flood risk approach. In paragraph 1.4 the objective of the research is given and finally in paragraph 1.5 the approach of the report is presented.

1.1 The Dutch safety philosophy against flooding

In this paragraph the backgrounds of the Dutch safety philosophy against flooding are described in three sections. First the origin is treated, then its properties are described and finally the developments in the Netherlands with which it has to cope are described.

1.1.1 Origin of the safety philosophy against flooding

The origin of the current safety philosophy against flooding goes back to 1940. Based on analyses of the possible simultaneous occurrence of circumstances, which lead to storm floods the committee of storm floods concluded that it would be wise to use design flood levels higher then the flood levels that had occurred so far. The committee of storm floods advised to use design conditions based on a water level of 4m above NAP (the Normal Amsterdam Water Level) at Hook of Holland. This level was higher than the highest measured water level (3,28m above NAP) that had occurred so far. As a result of this advise it was decided that the coastal defense would be strengthened and a modest start was made. Thirteen years later in the night of 31 January to 1 February 1953 a great storm flood threatened the Netherlands. That night the water level was 3,85m above NAP at Hook of Holland. This extreme water level resulted in dike breaches and in flooding of a large part of the southern part of the Netherlands. Approximately 1850 people were killed in the flood. The disaster initiated the development of the current Dutch safety philosophy against flooding.

Figure 1-1: Flooded area in 1953 Figure 1-2: Breach

Three weeks after the flood disaster the Delta Committee was installed. The Delta Committee was of the opinion that the safety philosophy against flooding had to deal with future possible flood levels. In this way it could be ensured every area would be protected in an economical and social reliable way. The Delta committee used three analyses:

1

1 Introduction

1. An analysis of the highest possible water level, which could have occurred in the night of the disaster:

Conclusion analysis 1: The highest measured water level at Hook of Holland at February one 1953 was 3,85m above NAP. This level existed of an astronomical high water of 0,81m above NAP combined with a storm surge of 3,04m. In the same winter season the tide-tables showed a maximum astronomical high water of 1,25m above NAP, besides that the storm surge several hours before the peak was 0,21m higher than on the peak itself. The storm surge could even have been higher as the depression had followed another track. All these factors led to the conclusion that the most unfavorable combination of tide, storm surge etc (the combined storm effect) could add up to 5m above NAP. The Delta committee took this value as a preliminary starting point for further investigation.

2. An analysis of the frequency of occurrence of this storm flood:

Conclusion analysis 2: Based on measured water levels probabilities of exceedance of water levels were formulated. To assess the probability of exceedance of the preliminary starting point an extrapolation was required. A research of the mathematical center showed that a water level of 5m above NAP had an exceedance frequency of 1/10000 year.

3. A comparison between the costs of dike strengthening versus the economic value (including loss of lives and immaterial values) of dike ring area Central Holland:

Conclusion analysis 3: The protection of a dike ring area against flooding costs more if a high protection level is chosen. This higher protection level leads to a reduction of the risk of damage (probability multiplied with consequence) because the probability of flooding decreases. Thus an increase in costs of protection comes along with a decrease in the risk of damage. As long as with an increase in protection, the costs of this protection increase less than the risk of damage decreases, the investments in protection are justified from an economical point of view. By further investments in protection there will be a level where the risk of damage no longer decreases more than the costs of protection increase: the sum of the risk of damage and the costs of protection have reached a minimum, the economical optimum. The Delta Committee concluded that the optimal economic protection of Central Holland had a frequency of flooding of 1/125.000 per year.

The Delta committee related the probability of exceedance of 1/10.000 per year to the optimal economic protection with a probability of flooding of 1/125.000 per year. The difference in frequency between the economical optimal probability of flooding and the probability of exceedance can be explained with the idea that a dike does not fail immediately when the design level is exceeded: a probability of exceedance of 1/10.000 years would correspond to a lower probability of flooding. Furthermore it was assumed in the analysis of the economic optimum that maximum damage would occur, which is considered as an overestimation. Therefore according to the Delta committee a more realistic protection level than this worst-case scenario should be lower than the economic optimum of 1/125.000 per year. Above-mentioned water level, corresponding to a frequency of 1/10.000 per year, is called the Normative High Water Level. The height of the Normative High Water Level fluctuates along the coast. The design water levels are based on the Normative High Water Level. The design water levels often have been chosen lower than the Normative High Water Level on the basis of economic values of the to be protected areas lower than the value of Central Holland. At Central Holland the Normative High Water Level and the design water level are similar. The reduction from Normative High Water Level to design water based on 2

1 Introduction

economic grounds was called the economic reduction factor. In each area an exceedance probability of the design water level was introduced, related to the choice of the economic reduction factor. Intrinsic to the choice of an economic reduction factor different probabilities of exceedance of the design water level for an area were introduced [26].

The flood disaster also increased the doubt about the strength of the river dikes. In 1956 the design discharge for the Rhine was determined at 18.000 m3/s, with a probability of exceedance of 1/3000 per year. The strengthening of dikes due to this normative discharge caused a lot of resistance from society. A River Dikes committee (Becht Committee) was installed to evaluate this design discharge. The focus of the Becht Committee was to preserve landscapes, cultural-historic and social-economic values by sophisticated design. The Becht committee advised a probability of exceedance of 1/1250 per year, corresponding to a normative discharge of 16.500 m3/s. The resistance from society against the still required dike strengthening persisted and therefore the Boertien committee was installed. In 1993 the Boertien committee stated it was not wise to lower the probability of exceedance and simultaneously concluded after several statistical analyses that the normative discharge could be reduced to 15.000m3/s. The flood waves of 1993 and 1995 influenced the statistical distributions and on these grounds the normative discharge was re-adjusted to 16.000 m3/s [26].

1.1.2 Properties of the current safety philosophy The foundation for the realization of protection against flooding is situated in article 21 of the constitution. This article guarantees the citizens a country where they can live with no problem. Therefore it is the duty of the Dutch government to formulate a policy on water safety. This policy was constitutionalized in 1996 in the Flood Defence Act.

The Flood Defence Act divides the Netherlands in 53 dike ring areas. A dike ring area is an area protected against flooding by a series of water defences (dikes, dunes or hydraulic structures) and / or high grounds. Appendix A presents a map with the classification of the dike ring areas. The water defences in each dike ring are adjusted to their own safety standard. For dike ring areas along the coast or estuaries the advise of the Delta Committee (probability of exceedance of 1/10.000 per year or 1/4000 per year) was adopted in the Flood Defence Act. For dike ring areas along rivers a value of 1/1250 per year was constitutionalized and for transitional dike ring areas a value of 1/2000 per year was adopted.

In the Flood Defence Act (article 9) a periodical evaluation is introduced with a period of five years. Every five years the water boards have to give an account of the quality of the water defences. Based on this report actions are undertaken to maintain the quality of the water defences on the safety standard [26].

1.1.3 Recent developments in the Netherlands Part of the periodical check is an update of the hydraulic loads. This update ensures that water safety grows along with physical developments. The water defences in the Netherlands have been designed to withstand water levels and waves, which can occur under extreme circumstances. It seems likely that these circumstances become more extreme: - Along the coast already waves have been measured which were more extreme than the design waves. - Water levels along the coast have increased by 10-20 cm in the last century, but the Normative High Water Levels were reduced. The reduction of the Normative High Water Levels is based on calculations with average values of the storm flood levels. The uncertainty in these calculations however turns out to be larger. From this perspective the reduction of the Normative High Water Level is not based on scientific procedures. It may result in an increase of the probability of flooding above the standard.

3

1 Introduction

- Another physical development concerns the Dutch rivers. It is probable that the rivers Rhine and Meuse have to process higher discharges due to climate change. Because of the fact that a tendency for higher discharges first has to appear before design water levels and design discharges will be adapted, the probability of flooding may be larger than intended. - The periodical update of hydraulic loads ensures safety adjusts to among others above- mentioned developments. Although not completely perfect, it is still a reactive system instead of a pro-active system; the periodical update of natural loads ensures that safety is adapted in line with physical developments.

However physical developments do not present the full picture of future developments. Economical and social developments in the dike ring areas cannot be neglected. Since 1960 the economic value of the Netherlands has increased with a factor 6 (locally even more), while the costs for dike strengthening have increased relatively less. Compared to 1960 safety may be relatively cheap. The cost of the realization of the safety standard for Central Holland at the time was 0,5% of the protected value (total damage). If the same cost function as used by the Delta Committee is used for investment rich Central Holland in the year 2004 the dike strengthening, focused on the realization of the legislative safety standard, at the present economical value of Central Holland would cost at the most 0,1% of the damage. The costs for extra safety as percentage of the flood damage have decreased with 40 to 90% in the period from 1960 to 2000. This means that if the mathematical derivation for the optimal dike levels in 1960 was correct, with help from the same formulas in the year 2000 a higher optimal dike level and thus a higher safety level would result from the calculations. Stated otherwise: if the 1960 Central Holland safety level was optimal, the current protection of Central Holland, and thus the rest of the low-lying parts of the Netherlands is insufficient [26].

Finally a change in public perception can be noticed. Society does seem not to accept a high risk of flooding. The safety given by the flood defences and the management of the water boards and the Ministry of Transport, Public Works and Water Management gives society the feeling that prevention of flooding is arranged quite well. In public perception the danger of flooding has shifted from a natural disaster to an external safety risk (like an accident at an industrial installation). So it has shifted from something that may happen once in a while because of extreme natural circumstances to something that is not allowed to happen. External risk domains know very strict standards in comparison to risks of flooding, especially for the socially acceptable risk (group risk). The group risk of flooding is much higher than the summation of the group risk of all other external risk domains. The probability of many casualties because of the danger of flooding is considerably higher than all other dangers together [26].

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1 Introduction

1.2 Problem analysis

The current safety philosophy focuses by means of the five yearly evaluations on actualized hydraulic loads and on the strength of the defences. This approach is limited to developments in physical conditions. It doesn’t take the consequences of the economical growth on the expected level of damage into account. The classification in dike ring areas with different safety standards was largely based on economical arguments. For the present situation it can be shown to what extent the height of the standard has a relation with the financial-economical value of the protected area. Such a relation would imply that a relatively strict standard would be accompanied with a relatively high financial value of the hinterland per km. It can be shown for the present situation that by now the current distinction in four standards for safety lacks a relation with the spatial differentiation of the maximal financial- economical damage in the Dutch dike ring areas [26].

In their evaluation of the safety policy the RIVM (National Institute of Public Health and Environment) concluded that the current safety philosophy doesn’t lead to a safe and livable Netherlands as intended with introduction of the safety standards in 1960. At the time of the introduction of the safety standards the attention concentrated on both probabilities and consequences. Based on pragmatical considerations a policy was chosen based on strengthening and maintaining the primary water defences. This policy mainly has achieved a reduction of the individual risk [26].

Since then developments have occurred which had a large influence on safety against flooding: changes in physical circumstances like sea level rise, river discharges and economical circumstances like spatial planning, invested capital and increase of population density. The current safety philosophy focuses on adjustments of technical boundary conditions but hardly takes economical and social developments into account (Figure 1-3). Because of the increase in protected values the economical risk has grown: the safety standards no longer are attuned cost-effective on the spatial differentiation of economic values. Furthermore society seems to accept less risk of flooding: flood disasters are not seen anymore as acceptable natural phenomena’s. In terms of modern risk analyses the probability many casualties (group risk) is larger than all other external safety risks together. It can be concluded that economical values and human lives are protected less than intended in 1960 [26].

Therefore the problem definition becomes:

The current safety philosophy based on probabilities of exceedance has achieved a reduction of the individual risk, but simultaneously has realized an increase in group risk and economical risk and therefore does not seem to lead to safety.

Figure 1-3: Possible evaluation of economical and social developments 5

1 Introduction

1.3 The flood risk approach

The overloading approach per dike section is the usual approach and is also recorded in the Flood Defence Act. This approach has some disadvantages. A more risk-oriented approach to water safety is desired. The first step to implement this concept was made by the Technical Advisory Committee on Water Defences (TAW) in 1992 with the implementation of the Marsroute, a research program directed at “an elaboration of the quantitative flood risk approach based on scientific insights”. Currently in the review of the Flood Defence Act a risk-oriented approach is prepared. Meanwhile the gaps in knowledge that obliged to choose for the overloading approach per dike section have been filled up, a risk-oriented approach of flooding is possible.

Figure 1-4: Current philosophy (probability of Figure 1-5: Flood risk approach exceedance per dike section)

Risk is defined as probability multiplied with consequence. The consequences consist of two dimensions, economical damage and casualties. The simplest definition for the risk of flooding is as follows:

R ==⋅ES() PF S [Equation 1-1]

In which: R = Risk per year (in Euro per year or number of casualties per year)

PF = Failure probability of a dike ring area per year S = Damage that follows in case of failure (in Euro or number of casualties)

This expression does not include an important aspect: the damage depends on the location of failure of the water defence, the breach location. This is also true in case of multiple breaches. Furthermore the failure probability is also dependent on the effect of relaxation of the hydraulic load on downstream dike sections due to the first breach. A second aspect that is not included in this expression is time. The risk is not only defined by the failure probability in one year, but also by the failure probability in the years to come. Because of correlation in time (the strength of a dike ring in a certain year is strongly dependent on the strength in the previous year) the failure probability is not constant in time. A better definition of the risk becomes [14]:

R ==ES()∫ Sx () f () xdx [Equation 1-2]

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1 Introduction

In which: R = Risk per year (in Euro per year or number of casualties per year) x = Vector with all relevant parameters (all treated as stochastic functions and inclusively the discount rate) S = Damage that follows in case of failure (in Euro or number of casualties now the Damage is dependent on the breach location and time)

Formally this means all combinations of all possible realisations of all stochastic functions x have to be considered, furthermore for each of these combinations the damage S has to be calculated and this damage S has to be summed pro rata with the failure probability of the realisation. This method implies very many calculations have to be done and in practice this theoretical approach is impossible.

Therefore it is necessary to introduce some simplifications. The most important simplification is that the calculation is done with only a limited number of flood scenarios. This can be done because the damage caused by a flood scenario stretches over a large area. In case the breach is moved a few meters the global damage will show no large variation. This statement however is only valid in case no discontinuities are present in the surroundings of the dike. In case the breach is on the other side of such a discontinuity the damage does vary significantly. An example of such a discontinuity is the connection with a secondary defence. To determine the number of flood scenarios it is necessary to find all discontinuities present in the dike ring. Based on these discontinuities partial dike ring parts can be defined in which the consequences of a flood do not vary significantly. The introduction of partial dike ring parts reduces the number of necessary flood scenarios significantly. However it is important to ensure enough partial dike ring parts are calculated to give a good approximation of the risk [see paragraph 2.2].

In the second simplification it is assumed the damage will show little variation due to the variation of the remaining stochastic functions, of which the breach discharge is the most important. This simplification says that given a breach at a certain location there is no uncertainty concerning the damage. This simplification implies “only” the probability of each scenario has to be determined (and the damage connected to this scenario is considered to be deterministic). With these simplifications the risk of flooding can be defined as [14]:

N R ==⋅ES() S p [Equation 1-3] ∑ iFi i=1 In which:

PF = Probability of a flood scenario S = Deterministic value of the damage corresponding to scenario i. i = Index number N = Number of Scenarios

The damage S can be calculated with average values (best possible estimations of geometry, the value of goods and the average number of people) with one exception: the local water level at the breach location. The necessary local water level follows from the failure probability analysis.

The definition in equation 1-3 makes it is also possible to present the risk in the form of a FN- curve, which indicates the probability of exceedance of a certain number of casualties or a certain value of the economical damage. Figure 1-6 presents a conceptual FN-curve, with on the horizontal axis the number of casualties on a logarithmic scale and on the vertical axis the probability of exceedance on a logarithmic scale.

7

1 Introduction

Figure 1-6: Conceptual FN-curve

1.4 Objective of the research

The objective of this research is to assess the flood risk using flood scenario probabilities and flood simulations of these scenarios in a case study. The study area is dike ding area 17 IJsselmonde. Furthermore the impact of compartmentation as a measure to reduce flood risk is investigated.

To satisfy the objective the following sub objectives are fulfilled:

1. Flood scenario probabilities; The probabilities of flood scenarios are determined. The set of flood scenarios that contributes for more than 99% to the dike ring failure probability (the dominant flood scenarios) gives a good approximation of the flood risk.

2. Flood simulations for the estimation of the consequences For the dominant flood scenarios flood simulations are made. The hydraulic consequences are used to assess the economical damage and the number of casualties for the dominant flood scenarios.

3. Flood risk The probabilities of the dominant flood scenarios and the consequences of these flood scenarios have to be multiplied. This results in the flood risk of the dike ring.

4. Impact of Compartmentation Compartmentation can be defined as the dividing of the overall system in compartments resulting in isolation per compartment and therefore providing protection to the overall system by reducing the consequences of initial failure. Characteristics that determine the impact of compartmentation will be identified and the impact of compartmentation as a measure to reduce flood risk will be investigated.

Paragraph 1.5 describes the outline of the research.

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1 Introduction

1.5 Outline of the research

Figure 1-7 presents the outline of the research. The dotted boxes indicate the contents of a chapter. The numbered boxes contain the calculation steps necessary for the determination of the flood risk. The schematizations and models described by box A, B and C are supplied by the province of South Holland.

Figure 1-7: Outline of the research

9

2 System description IJsselmonde

10

2 System description IJsselmonde

2 System description IJsselmonde

In this chapter the characteristics of dike ring area 17 IJsselmonde are described (paragraph 2.1) and the division of the dike ring in partial dike ring parts is described (paragraph 2.2).

2.1 Characteristics

Dike ring area 17 consists of the island of IJsselmonde, which is situated in the province of South-Holland. Dike ring area IJsselmonde is surrounded by the Oude Maas in the south and west, by the Noord in the east and by the Nieuwe Maas in the north. IJsselmonde is situated in a tidal river area and can be threatened by high water levels due to high river discharges and storm surges at sea. The primary water defences consist of approximately 62 km of dikes. These dikes are divided in 73 dike sections (See appendix B). Figure 2-1 presents a map of dike ring area 17. In this figure the primary defences (located at the exterior of the island) and the secondary defences (located at the interior) are indicated with a red line.

Figure 2-1: Dike ring area 17 IJsselmonde

The primary defences of the dike ring protect an area of approximately 13.000 hectares. 400.000 inhabitants live in the area. In the dike ring the municipalities Rotterdam (Zuid), Albrandswaard, Barendrecht, Ridderkerk, Heerjansdam, Zwijndrecht en Hendrik-Ido- Ambacht are situated. Especially the urban agglomeration of the southern part of Rotterdam represents a large economical value. The major land use in the dike ring is reserved for agriculture (48%) followed by urban areas (38%). The remaining surface consists of 5% surface water, 3% industry, 3% recreation and 3% of roads (see Figure 4-2). Main roads like the A15 and A16 pass through this dike ring area and fulfil a major role in the accessibility of the Randstad. In Figure 2-1 they are indicated with yellow lines. These main roads cross the primary defences by means of

11

2 System description IJsselmonde

tunnels. Next to the road infrastructure the dike ring area is also an important link in the rail infrastructure network. The reason is the accessibility of the Randstad, but also the presence of the Kijfhoek is important, which is the shunting yard where freight trains from the port of Rotterdam are gathered to start their trips to Germany. The rail infrastructure is absent in Figure 2-1 but is indicated with a black line in Figure 4-2.

After the flood disaster of 1953 the strengthening of the primary water defences started. The dikes of IJsselmonde were strengthened in such a way they could withstand a probability of exceedance of 1/10.000 per year. The construction of the Maeslantkering and the Hartelkering (Figure 2-2) reduced the influence of storm surges from the sea in the western part of the Netherlands (Figure 2-3). Furthermore it was decided after the construction of the storm surge barriers to reduce the safety standard of IJsselmonde to a probability of exceedance 1/4000 per year [12]. The design loads at IJsselmonde were reduced, while the dikes of IJsselmonde remain strong.

Figure 2-2: Maeslantkering / Hartelkering Figure 2-3: Reduced influence sea

The area outside the dikes in the North West corner of the dike ring forms the most inland section of the port of Rotterdam. In the past these areas have been raised to a level of approximately 3.5 m above NAP. The major part of the surface inside the dikes is below NAP as can be seen in Figure 2-4.

Figure 2-4: Surface levels relative to NAP

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2 System description IJsselmonde

2.2 Partial dike ring parts and compartments

The consequences of a flood are dependent on the location of the breach. It is not sufficient to determine the failure probability of the dike ring. Flood scenarios have to be determined. Theoretically the dike ring can breach at every location, in combination with every other location and every breach or combination of breaches may result in different consequences. In practice however the risk of flooding can only be determined by separating the dike ring in a number of partial dike ring parts of which it is assumed the consequences of a breach in a partial dike ring part are not dependent on the exact location of the breach.

A choice has to be made to divide the dike ring in a number of partial dike ring parts. On the one hand the number of partial dike ring parts should be small to limit the number of necessary flood simulations. On the other hand when the number of flood simulations is too low the accuracy of the calculated risk is insufficient, because too many scenarios are not included in the flood simulations.

The division of the dike ring area in partial dike ring parts is based on the topography. Based on the topography an evaluation of the impact of “discontinuities” in the landscape on the flood progress can be made. Possible discontinuities are: - The connection with a secondary defence. - The connection with an earth embankment that is not designed as a dike, but probably will function as one (for example the soil body of a railway or a main road) - The transition from one threat to another (for example a transition from river to sea) - The bifurcation of a river - A transition in function behind the dike (for example a transition from a rural to a urban function) - In case of a sloping dike ring area the distance over which the breach is moved plays a role because the water flows to the lowest point of the dike ring. Depending of the distance between the lowest point and the location of the breach a large variation in damage is possible.

Figure 2-5: Division in partial dike ring parts

IJsselmonde is a relatively small dike ring surrounded by primary defences that were designed on a 1/10000 frequency [12]. Extreme hydraulic conditions will be necessary for 13

2 System description IJsselmonde

failure of a dike section, which also implies that if failure occurs a great volume of water enters the area. Because of this the division in partial dike ring parts has been based only on the connection of secondary defences to the primary defences and has not been based on the connection with railways or highways because of the lower levels of these embankments and because of the possible presence of (bicycle) tunnels and culverts in them. In this way the number of partial dike ring parts has been kept low. This choice intrinsically means the partial dike ring parts are similar to the exterior part of the compartments. Figure 2-5 (previous page) and Table 2-1 present the division in partial dike ring parts used in this thesis.

Partial dike ring part Name Dike sections present 1 Nespolders 1 to 6 2 Zuidpolder 7 to 10 3 Zegen-Molen- and Portlandpolder 11 to 19 4 Hoogvliet 21 to 28 5 Abrandswaard and Rhoonse polder 20, 31 to 34 6 Rotterdam-Zuid 35 to 46 7 Reijerwaardse polders 47 to 63 8 Zwijndrechtse waard 64 to 73 Table 2-1: Division in partial dike ring parts

Appendix B presents a map with the division of IJsselmonde in primary dike sections. In Figure 2-6 the division in compartments is presented. The compartments are divided by secondary defences. As stated the primary defences at the exterior of the compartments form the partial dike ring parts.

Figure 2-6: Division in compartments

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3 Failure probability analysis

3 Failure probability analysis

In this chapter the results of the failure probability analysis of dike ring area 17 are presented. The failure probability of a dike ding area can be determined with the computer program PC- Ring. Paragraph 3.1 gives a short description of the underlying theory of PC-Ring. Paragraph 3.2 continues with a description of the hydraulic conditions (the load model) and with a schematization of the dikes (the strength model) at IJsselmonde as implemented in the computer model. Paragraph 3.3 presents the failure probabilities per dike section and in paragraph 3.4 these results are translated to flood scenario probabilities.

3.1 PC-Ring Theory

This paragraph first focuses on a general description of the failure probability of a dike section. Then a description is given of the failure mechanisms used in PC-Ring, after which some remarks are given about how to cope with uncertainties in the calculation of a dike section failure probability. Then it is discussed how dike section failure probabilities are combined to calculate the failure probability of the dike ring.

3.1.1 General description of the failure probability of a dike section The failure probability of a dike ring is calculated by combining the failure probabilities of the dike sections in the ring. Therefore the failure probability of a dike section is the basis for the PC-Ring calculation. A simple definition of the failure probability of a dike section is as follows [13]:

PPZ=≤=≤=(0)() PRS frsdrds (,) (Equation 3-1) fRS∫∫ Z ≤0 In which:

PF = Failure probability dike section per year Z = Limit state function R = Strength parameter S = Load parameter fRS = Joint probability density function of R and S

Assuming R and S to be independent the failure probability can be described by the following integral, where s is a certain value of the load S.

ss=∞ s =∞ s P=⋅=⋅ fsfrdrdsfsfrdrds (Equation 3-2) fSRSR∫∫() () ∫ () ∫ () sr=−∞ =−∞ s =−∞ R =−∞

Which can be written as:

∞ PfSFsds=⋅ (Equation 3-3) fSR∫ () () −∞

Where: fS ()S = Probability density function for random variables of load S

FSR () = Probability distribution function which returns the failure probability given the value s of a certain load S. 15

3 Failure probability analysis

Intermezzo Assume the water level hw is the only load parameter in equation 3.3, then it can be written as:

PfhFhdh=⋅ (Equation 3-4) f ∫ hw() w R () w w

Figure 3-1 illustrates the contents of equation 3.4. The first graph presents a probability density function of the water level hw. The black line in the second graph shows a cumulative probability distribution function for the strength of a dike, which in this case is the crest level. The red line represents a deterministic value of the crest level. Failure occurs when the water level exceeds the crest level. The third graph combines the load and strength parameters and presents the probability density function of the failure of a dike. The area under this graph denotes the failure probability of the dike section.

Figure 3-1: Visual interpretation of equation 3.4

In the simple case in the intermezzo the crest level of the dike forms the strength and the water level forms the load. In a realistic reliability analysis of a dike more variables and failure mechanisms are involved. This results in several Limit State Functions that are more complex compared to the Limit State Function in the intermezzo. Paragraph 3.1.2 gives a description of the failure mechanisms of a dike and in appendix D the corresponding Limit State Functions are presented.

In each of the Limit State functions variables occur that are uncertain: the stochastic functions. The uncertainty in stochastic functions is described with probability density functions or cumulative distribution functions. Examples of these distributions are the normal distribution, the exponential, the lognormal, the uniform etc. The type of distribution does not determine the characteristics of the probability density function of a stochastic function completely. The average of the stochastic function is necessary to fix the position of the probability density function and the standard deviation (or the variation coefficient) is needed as a measure for the spreading of a variable. PC-Ring requires values for the average and

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3 Failure probability analysis

the standard deviation (or the variation coefficient) for each stochastic function in a Limit State Function.

Furthermore the analysis in the intermezzo is insufficient for a realistic dike reliability analysis as it only describes a comparison of R and S in one cross-section of a dike. Many of the stochastic functions playing a role in a realistic dike reliability analysis show a fluctuation in the time domain or a fluctuation in the space domain or in both. The knowledge that a stochastic function has a certain realisation at a certain location x and a certain point in time t does not have to result in a removal of the uncertainty at another location or at another point in time. Usually the uncertainty at a nearby location x only will be reduced. The same is true for the uncertainty at the same location after a certain time span. In PC-Ring the extent too which this happens is modelled with help of correlation functions. A correlation function gives a correlation coefficient as a function of the distance or the time span between two points. As a general form of (one-dimensional) spatial correlation PC-Ring uses the following function (notice that it consists of a constant part and a damping part):

2 ⎧⎫Δ x ρρρ()Δ=x xx +− (1)exp⎨⎬ −2 (Equation 3-5) ⎩⎭dx In which:

ρx = Constant correlation

Δ x = Correlation distance for spatial spreading dx = Correlation distance

The processes in the time domain are discretisized as a Borges Castanheta model. For more information about the modelling of correlation in the space domain or the time domain is referred to [6]. In appendix C the PC-Ring calculation scheme is described more elaborately.

3.1.2 Failure mechanisms As stated a dike can fail in several ways. PC-Ring is capable of calculating the following failure mechanisms (see Figure 3-2):

1. Overtopping / wave overtopping 2. Uplifting and piping 3. Damage to the revetment and erosion of the dike 4. Instability of the inside slope

The failure of a dike due to a certain failure mechanism is dependent on the strength of the dike as well as the load on the dike. The condition of the dike (whether it fails, is still functioning or if it is only a brink from failing) is described in the Limit State Function (Z- function). As already stated in paragraph 3.1.1 the general form of the Limit State Function is ‘Z = R – S’. In which R is the strength or ‘Resistance’ of the dike and S is the load or ‘Solicitation’ on the dike. When the load is larger then the strength (Z < 0) failure occurs and vice versa. In PC-Ring for every failure mechanism a Limit State Function is defined. This means that for every failure mechanism a strength model and a load model have been defined. In the text below a short description of the failure mechanism and its strength and load model is given.

1. In the failure mechanism overtopping / wave overtopping the dike fails due to great quantities of water running over the dike crest as a result of which the inner slope erodes. Overtopping occurs when offshore wind is present or no wind at all. In case of overtopping the local water level hw exceeds the crest level of the dike hd. In this case the water level is the only load parameter and the crest level is the only strength parameter. Overtopping can 17

3 Failure probability analysis

be described mathematically as done in the intermezzo in paragraph 3.1.1. In case of onshore wind also waves are included in the model. In case of onshore wind the combination of water level and waves are responsible for water running over the crest and thus erosion of the inner slope. This is called wave overtopping. The load model has been extended with wind, water depth and fetch parameters so that with the Bretschneider equation waves can be determined. For the strength models this implies more information like for example orientation and geometry of the dike is required and is implemented in PC-Ring (See appendix D).

Figure 3-2: Failure Mechanisms

2. In the failure mechanism uplifting and piping the dike fails due to washing away of sand from under the dike. If this mechanism occurs the pressure of the water firstly lifts up the if present impermeable top layer, after which pipes start to develop which transport the sand from under the dike. In the Limit State Function the loading part is formed by the water level difference over the dike reduced with a measure for the vertical seepage length. The strength model is formed by a measure for the critical value of the loading model (See appendix D).

3. In the failure mechanism damage to the revetment and consequent erosion of the dike body wave attack damages the revetment after which the cross-section of the dike is reduced due to erosion. The dike fails when a part of the dike becomes instable. The loading part of the Limit State Function is formed by the storm duration. This storm duration is compared with a strength model that describes the time needed to damage the revetment. If the storm duration is longer then the time needed to damage the revetment and the time needed to erode the dike body failure occurs (See appendix D).

4. In the failure mechanism instability of the inside slope the dike fails because a part of the dike becomes unstable. In principle this phenomenon can occur on the outside as well as on the inside of the dike. In general only the instability on the inside is reckoned with. Stability of a dike can be modelled with the Bishop Method. In the Limit State Function the loading model consists of the driving moment MA that urges the dike body to move along a normative

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3 Failure probability analysis

slip circle. The strength model is formed by the resisting moment MR, which due to shear stresses along the slip circle opposes the dike body to move.

Certain failure mechanisms consist of several other failure mechanisms. This is the case for instance at the mechanism of uplifting and piping. Pipes can only develop after the top layer has been uplifted. This is an example of a so-called ‘AND-statement’, which implies the dike only fails if both partial failure mechanisms occur. There also exist partial failure mechanisms that are coupled with an ‘IF-statement’. In case of an ‘IF-statement’ the dike fails if only one of the partial failure mechanisms occurs as is the case with overtopping / wave overtopping [4].

The failure probability of a dike section (the probability that Z is smaller than zero: Pf (Z<0)) can be determined with the help of several probabilistic calculation techniques. PC-Ring contains several of these techniques like FORM, Directional Sampling etc. Each of these techniques has distinct advantages and disadvantages, which are described in appendix C.

3.1.3 Uncertainty As stated the strength of a dike and the load on a dike is not explicitly known. The input contains uncertainty and the uncertainty is described with stochastic functions. Uncertainty can be classified in several sources of uncertainty. The load models in the Limit State Functions are natural processes that fluctuate continuously in time. These processes are described with probability density functions to cope with this natural variability. These probability density functions however are based on observations that are rather limited, a hundred years of data is maximum while probabilities are calculated which are several orders lower. This introduces statistical uncertainty. Furthermore the use of models implicitly introduces model uncertainties, while models merely are a schematisation and never reproduce full reality. PC-Ring copes with natural, statistical and even model uncertainties by interpreting load, strength and model parameters as stochastic functions [6].

3.1.4 Combination procedures The procedure for the determination of the failure probability of the dike ring starts with the failure probability of a dike section. The first step is to determine the failure probability of one failure mechanism for one dike section, one wind direction and one tide. To arrive at the failure probability of a dike section for a certain failure mechanism all the calculations have to be combined taking into account the wind direction. This is done with the Hohenbichler and Rackwitz method. The next step is to transform the calculation for one tide so that the regarded time period is taken into account. Therefore the Borges Castanheta method is used. Now the failure probability for one failure mechanism for one dike section is known. Again the Hohenbichler and Rackwitz method is used to combine all failure mechanisms for one dike section. Then the Hohenbichler and Rackwitz method is used for the last time by combining the failure probabilities for each dike section into the failure probability of the dike ring. The procedure of the PC-Ring calculation is described more elaborately in appendix C. For more information about the Hohenbichler and Rackwitz method and the Borges Castanheta method is referred to [7].

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3 Failure probability analysis

3.2 IJsselmonde model

The previous paragraph briefly discussed the procedure for a PC-Ring calculation and summarized in a global way the input PC-Ring uses for a calculation. This paragraph shows which input is used for the calculation of dike ring 17. The paragraph is divided in a section on hydraulic loading and a section on the characteristics of the primary water defences.

3.2.1 Hydraulic loading The PC-Ring model for the hydraulic load in the tidal river area is based on the following stochastic functions: the discharge of the Rhine at Lobith, the discharge of the Meus at Lith, the wind direction at Schiphol and Deelen, and also the wind speed at Schiphol and Deelen, the sea water level at the Maasmond and the prediction error at Hook of Holland due to closure of the Maeslantkering and the Hartelkering. Between these stochastic functions certain correlations have been introduced in the PC-Ring model. In the following the stochastic functions will be discussed briefly and if necessary also the dependence between certain stochastic functions will be treated.

Tidal river area IJsselmonde is surrounded by rivers, by the Oude Maas in the south and west, by the Noord in the east and by the Nieuwe Maas in the North. In general in downstream direction of a river an increasing influence of seawater levels can be noticed. The part of the rivers that is determined by both river discharges and sea water levels is called the tidal river area. In the Netherlands the transition between the tidal river system and the upper river system is approximately situated at Gorinchem, which implies that IJsselmonde belongs to the tidal river area. In the PC-Ring model the local water levels in the tidal river area are determined using Q-h relations. Q-h relations describe the physical relation between the local water level on the one side and the sea water level at the Maasmond and the river discharges at Lobith and Lith on the other side. Therefore the local water levels in the tidal river area are determined by the discharge of the Rhine as well as the discharge of the Meus. The correlation between both discharges is included in the calculations, while this correlation presents the probability of a situation in which both discharges are extremely high. The correlation between Rhine and Meus in PC-Ring is modelled by means of writing the discharge of the Meus as a function of the discharge of the Rhine. The function description has been built up from a totally dependent part and a totally independent part. Furthermore it should be noted that the term Q-h relation actually is too limited, while the wind and the state of the storm surge barriers also have an influence on the local water level hw. Especially the closure of the storm surge barriers has a large influence on the local water levels in the tidal river area. Therefore different Q-h relations are used in the model for a situation with a closed barrier and for a situation with an open barrier.

Storm surge barriers In the tidal river area two storm surge barriers are located, the Maeslantkering and the Hartelkering. During high storm surges these barriers are closed. The command to close the barriers is based on water level predictions of the sea water level at Hook of Holland. Because the closure takes several hours it is not possible to base the choice of closure or no closure on actual water levels. The water level predictions are given by the Storm Surge Signal Service (Stormvloedseindienst SVSD). This service gives its predictions for the sea water level at Hook of Holland six hours before the moment of high water. This period is long enough to close both barriers. The closure command for both barriers is given when the water levels in Rotterdam and Dordrecht threaten to exceed the so-called closure criteria. The closure criterion for Rotterdam is determined on 3m above NAP and for Dordrecht it is determined on 2.9m above NAP. The SVSD gives its prediction of the sea water level at Hook of Holland six hours before high water. Implicitly a prediction error comes with a 20

3 Failure probability analysis

prediction. According to Geerse [2000] the prediction error is a stochastic function with a normal distribution, a mean value μ and a standard deviation σ. The prediction error Δ is defined as the predicted water level in Hook of Holland during high water minus the real sea water level in Hook of Holland during high water. In formula:

hhHvH;; predicted=+Δ HvH real (Equation 3-6)

The position and the spreading of the stochastic function Δ is chosen as μ = -0.09m and σ = 0.18m [6]. The prediction error Δ is incorporated in PC-Ring and makes it possible to determine the reliability and the design point for the closure regime. The closure strategy for the Maeslantkering and the Hartelkering is such that both barriers are closed simultaneously.

For the determination of the dike section failure probabilities at IJsselmonde the probability that closure of one of the barriers fails has to be taken into account. The modelling of the failure of the barriers is based on the concept of dependent failure, which implies if one barrier fails the other also fails [6]. The assumption of dependent failure leads to slightly higher frequencies of exceedance of water levels in the area than independent failure of the barriers would have done and is therefore a safe approach. Furthermore this assumption limits the number of calculations. The barriers are modelled as if only one exists.

For the determination of the dike section failure probabilities at IJsselmonde four different closure configurations are necessary: - Two configurations with different combinations of water levels and discharges. - hQ ≥ Closure criterion (barrier should be closed) - hQ < Closure criterion (barrier should be open) - Two configurations that relate to the state of the barrier. - Correctly open or closed - Incorrectly open or closed

The failure probability of a dike section can now be described as follows:

PF = P (Failure ∩ hQ ≥ Closure Condition ∩ Correctly Closed) + P (Failure ∩ hQ ≥ Closure Condition ∩ Incorrectly Open) + P (Failure ∩ hQ < Closure Condition ∩ Incorrectly Closed) + P (Failure ∩ hQ < Closure Condition ∩ Correctly Open)

In which: PF = Failure probability dike section per year hQ = Combination of water level (h) and discharge (Q) which is compared with Closure criterion (Figure 3-14).

The definition of failing amounts to the situation that barriers do not close while they should and to the situation that the closed barriers fail. The failure probability of the barriers is 0.001 per closure.

Wind The model uses two stochastic functions for the wind, the wind speed and the wind direction. For the tidal river area the wind at Hook of Holland is used in the model. The wind at Hook of Holland is represented by the wind statistics at Schiphol. The wind speed is dependent on the wind direction. The model uses 16 wind directions, which implicates direction sectors of 22.5° are used. Furthermore in the tidal river area wind and sea water levels are correlated for the western winds. Seven of these correlated western winds have been defined: SW, WSW, W, WNW, NW, NNW and N. The eastern winds are supposed to be uncorrelated. 21

3 Failure probability analysis

3.2.2 Characteristics of the water defences According to the Flood Defence Act dike ring area IJsselmonde currently has a safety standard of 1/4000 per year. This safety level has been assigned to IJsselmonde after the construction of the Maeslantkering. Before the completion of the Maeslantkering a probability of exceedance of 1/10000 per year was connected to IJsselmonde. The water defences of IJsselmonde are of category A. The length of the primary defences is approximately 62 km and consists of dikes and some civil engineering structures. The dikes are administered by the water board of Hollandsche Delta. The water board commissioned an inventory of the dike profiles of IJsselmonde. This inventory [12] is the source of data used in the strength model of the failure probability analysis. Appendix B presents data on all dike sections in IJsselmonde.

3.3 Results This paragraph presents the results of the probabilistic calculation for the failure mechanisms overtopping, wave overtopping, damage to the revetment and erosion of the dike body and piping. No calculations have been made for the failure mechanisms instability of the inside slope and all mechanisms concerning civil engineering structures for reasons of time and lack of data. The development from the schematisation as received from the province to the here presented calculation will not be treated. Only the results of the calculation will be presented. The calculation scheme is described in appendix C. Furthermore the results are compared with the results from the national dike safety assessment and the judgement of the water board.

3.3.1 Reference level control As a first check of the hydraulic loading in the model a reference level control has been done. A reference level control uses the failure mechanism overtopping (without waves). In the reference level control the design water levels are calculated. The design water levels (1/4000 at IJsselmonde) calculated with PC-Ring have to approximate the reference levels from the hydraulic load book [10] with an accuracy of a few centimetres [3]. If PC-ring calculates a deviation larger than 10 cm from the reference levels a correction has to be performed. This correction is done with a local set-up, which shifts the entire frequency distribution. Figure 3-3 presents the results from the reference level control. As can be seen the differences fall within the range.

Dike Reference PC-Ring Reference Levels MHW-Control Normative level PC-Ring Section level result 3 2.9 3.007 3.4 8 2.9 2.96 3.3 17 2.9 2.926 3.2 23 3 2.981 3.1 29 3.2 3.194

above NAP 3 Water Level Water Level 30 3.2 3.223 2.9 33 3.3 3.28 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 42 3.4 3.368 Dik e s e ction 48 3.2 3.188 58 3.2 3.223 Figure 3-3: MHW-control

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3 Failure probability analysis

3.3.2 Overtopping An overtopping calculation is a modified wave overtopping calculation. In the overtopping calculation the wind loads and thus the waves have been turned off. In appendix D the overtopping model is described. Figure 3-4 presents the reliability indexes and the failure probabilities resulting from the calculations. Figure 3-5 gives a graphical interpretation of the reliability indexes. Not all dike sections have been calculated. The omitted dike sections are characterised by extreme heights and forelands and will not contribute to the failure probability of the dike ring. Appendix E gives an example and an explanation of the PC-Ring output for a few characteristic dike sections at IJsselmonde.

Dike Reliability Failure Dike Reliability Failure Dike Reliability Failure Sect. index probability Sect. index probability Sect. index probability 1 5.6809 6.72E-09 26 5.9507 1.34E-09 51 5.5119 1.78E-08 2 --27 --52 5.6792 6.79E-09 3 5.8386 2.64E-09 28 6.5178 3.58E-11 53 5.7027 5.91E-09 4 6.0826 5.93E-10 29 --54 4.8712 5.55E-07 5 5.9847 1.09E-09 30 5.3784 3.76E-08 55 5.6813 6.70E-09 6 5.1992 1.00E-07 31 5.1153 1.57E-07 56 -- 7 5.9155 1.66E-09 32 5.1338 1.42E-07 57 -- 8 --33 --58 -- 9 --34 5.0139 2.67E-07 59 5.694 6.22E-09 10 5.9356 1.47E-09 35 5.0643 2.05E-07 60 5.9536 1.32E-09 11 5.6559 7.77E-09 36 5.1457 1.33E-07 61 6.0688 6.47E-10 12 5.6796 6.77E-09 37 5.508 1.82E-08 62 5.2431 7.91E-08 13 --38 4.62 1.95E-06 63 -- 14 5.0397 2.34E-07 39 5.39 3.53E-08 64 6.4084 7.39E-11 15 5.5156 1.74E-08 40 5.1282 1.47E-07 65 5.7241 5.21E-09 16 5.612 1.00E-08 41 5.2852 6.29E-08 66 5.7106 5.64E-09 17 --42 5.2338 8.32E-08 67 5.6536 7.88E-09 18 --43 5.1802 1.11E-07 68 5.1598 1.24E-07 19 --44 5.3147 5.35E-08 69 -- 20 5.3572 4.24E-08 45 5.359 4.19E-08 70 5.1923 1.04E-07 21 5.4441 2.61E-08 46 5.6803 6.74E-09 71 5.5572 1.37E-08 22 5.8158 3.03E-09 47 5.5573 1.37E-08 72 5.6424 8.41E-09 23 6.0245 8.51E-10 48 5.379 3.75E-08 73 5.7474 4.54E-09 24 6.3263 1.26E-10 49 5.2896 6.14E-08 25 6.0086 9.39E-10 50 5.3276 4.99E-08 Figure 3-4: Results failure mechanism overtopping

Reliability Index Overtopping

7

6

5

4

3 1 3 4 5 6 7 10 11 12 14 15 16 20 21 22 23 24 25 26 28 30 31 32 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 59 60 61 62 64 65 66 67 68 70 71 72 73 Dik e Se ction

Figure 3-5: Graph Reliability Index Overtopping

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3 Failure probability analysis

3.3.3 Wave overtopping This paragraph presents the results of the failure mechanism wave overtopping. In the failure mechanism wave overtopping the dike fails due to water running over the dike crest. In Appendix D the wave overtopping model is described. Figure 3-6 presents the reliability indexes and the failure probabilities resulting from the calculations. Figure 3-7 gives a graphical interpretation of the reliability indexes. Not all dike sections have been calculated. The omitted dike sections are characterised by either extreme heights and forelands or unreliable results in the calculation and will therefore either not contribute to the failure probability of the dike ring or not give a robust result. Appendix E gives an example and an explanation of the PC-Ring output for a few characteristic dike sections at IJsselmonde.

Dike Reliability Failure Dike Reliability Failure Dike Reliability Failure Sect. index probability Sect. index probability Sect. index probability 1 5.6809 6.72E-09 26 5.5508 1.43E-08 51 5.4174 3.03E-08 2 --27 --52 5.4331 2.78E-08 3 5.5135 1.76E-08 28 6.5176 3.59E-11 53 5.4635 2.34E-08 4 5.9326 1.50E-09 29 --54 4.87 5.56E-07 5 5.8056 3.22E-09 30 5.3011 5.77E-08 55 5.6552 7.80E-09 6 5.1598 1.24E-07 31 5.1153 1.57E-07 56 -- 7 5.9155 1.66E-09 32 5.1338 1.42E-07 57 -- 8 --33 --58 -- 9 --34 4.9827 3.14E-07 59 5.6921 6.29E-09 10 5.9356 1.47E-09 35 5.0316 2.44E-07 60 5.95 1.32E-09 11 5.6559 7.77E-09 36 4.9122 4.51E-07 61 6.0627 6.72E-10 12 5.6796 6.77E-09 37 5.335 4.78E-08 62 5.2385 8.11E-08 13 --38 4.616 1.95E-06 63 -- 14 5.0403 2.33E-07 39 5.39 3.53E-08 64 6.4084 7.39E-11 15 5.4626 2.35E-08 40 4.9487 3.74E-07 65 5.7235 5.23E-09 16 5.6 1.07E-08 41 5.064 2.06E-06 66 5.7106 5.64E-09 17 --42 5.23 8.63E-08 67 5.6536 7.88E-09 18 --43 5.1802 1.11E-07 68 5.1598 1.24E-07 19 --44 5.288 6.19E-08 69 -- 20 5.3572 4.24E-08 45 5.36 4.22E-08 70 5.1923 1.04E-07 21 5.4441 2.61E-08 46 5.5139 1.76E-08 71 5.528 1.62E-08 22 5.7754 3.85E-09 47 5.321 5.17E-08 72 5.5512 1.42E-08 23 5.9648 1.23E-09 48 5.3 5.82E-07 73 5.5833 1.18E-08 24 6.288 1.61E-10 49 5.12 1.53E-06 25 5.8414 2.60E-09 50 5.156 1.26E-06 Figure 3-6: Table results failure mechanism wave overtopping

Reliability Index Wave Overtopping

7

6

5

4

3 1 3 4 5 6 7 10 11 12 14 15 16 20 21 22 23 24 25 26 28 30 31 32 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 59 60 61 62 64 65 66 67 68 70 71 72 73 Dik e Se ction

Figure 3-7: Graph Reliability Index Wave Overtopping

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3 Failure probability analysis

In Figure 3-8 a comparison between overtopping and wave overtopping is presented. The vertical axis denotes the inverse of the failure probabilities. On the horizontal axis the dike sections that not have been calculated have been omitted. For the majority of the dike sections probabilities of overtopping and wave overtopping are equal, which indicates wind is not normative for these sections. A minor part however shows a greater probability for wave overtopping. This difference can be explained by looking at the orientation of these dikes (See appendix B). The analogy between these sections is that they all more or less have a North West orientation, which is the normative wind direction.

Comparison Overtopping/ Wave Overtopping

1,0E+11 1,0E+10 1,0E+09 1,0E+08 1,0E+07 1,0E+06 1,0E+05 1 / Probability of w ave overtopping 1,0E+04 1 / Probability of overtopping 1,0E+03 1 3 4 5 6 7 10 11 12 14 15 16 20 21 22 23 24 25 26 28 30 31 32 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 59 60 61 62 64 65 66 67 68 70 71 72 73 Dik e Se ction

Figure 3-8: Comparison between failure mechanism overtopping and wave overtopping

Figure 3-9 presents the results in such a way that a good view of the weak links in the dike ring is given.

Failure Probability

2,5E-06 Failure Probability Wave Overtopping 2,0E-06 Failure Probability Overtopping

1,5E-06 1,0E-06

5,0E-07

0,0E+00 1 3 4 5 6 7 10 11 12 14 15 16 20 21 22 23 24 25 26 28 30 31 32 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 59 60 61 62 64 65 66 67 68 70 71 72 73 Dik e Se ction

Figure 3-9: Failure probabilities overtopping and wave overtopping

PC-Ring recognises sections 38 and 54 to a lesser extent as weak links for overtopping. Sections 38, 41, 48, 49 and 50 are recognised as weak links for wave overtopping. The relative high probability of section 38 and 54 for overtopping can be explained by the fact that these sections have the lowest crest levels of the dike ring. The surrounding sections of section 38 are approximately 1m higher and the neighbouring sections of 54 are approximately 0.7m higher. The sections that have a relatively high failure probability for wave overtopping and a small failure probability for overtopping (41, 48, 49, 50) are sections with a North West orientation in combination with long fetch lengths. For example section 41 is situated at the banks of the Maashaven, which has a width of approximately 2km. Section 48, 49 and 50 are situated at Oud-IJsselmonde at the south side of a northward bend in the Nieuwe Maas. Therefore a longer fetch length is available at these sections. 25

3 Failure probability analysis

In case of dike ring 17 the use of the term “weak link” for the highest failure probabilities for overtopping / wave overtopping doesn’t give a good a view of the situation as the values of the failure probabilities (including the “weak” links) are extremely low.

To evaluate the results for overtopping and wave overtopping a comparison will be made with the results of the national dike safety assessment and the judgement of the water board:

National dike safety assessment Based on the reference levels from the hydraulic load book the Province of South-Holland has calculated the dike table heights. The basic assumption for these calculations was a wave overtopping discharge of 0,1 litre/metre/second. It was concluded that with an average setting of 0,05m during the check period all dike sections could be judged with the classification ‘Good’, which confirms the results from PC-Ring [11].

Judgement of water board Hollandsche Delta Water board IJsselmonde indicates the dike sections 38, 45 and 48 as weak. Dike section 38 contains the entrance to the tunnel under the Nieuwe Maas, and with an over height of 0,23m deserves the classification ‘weak’. Section 45 contains the coupure for the railway Rotterdam-Dordrecht that is classified as ‘weak’. However objects are not part of the available schematisation and therefore not taken into account in this research. Dike section 48 has an over height of less than 0,50m and therefore also is classified as weak [12].

The resemblance with the results from PC-Ring is quite good. Both PC-Ring and the water board confirm section 38 and 48 as weak links in this dike ring, however both sections still satisfy the norm amply. The failure probabilities for overtopping and wave overtopping of all dike sections in dike ring area 17 can be characterised as extremely small. This was expected as these dikes have been designed to withstand circumstances that would occur without the presence of the Maeslantkering and the Hartelkering. Also without these barriers and a probability of exceedance of 1/10000 per year all dike sections satisfy the requirements for the failure mechanisms overtopping and wave overtopping.

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3 Failure probability analysis

3.3.4 Damage to the revetment and erosion of the dike body In the failure mechanism damage to the revetment and erosion of the dike body wave attack damages the revetment after which the cross-section of the dike is reduced due to erosion. This mechanism therefore consists of two sub mechanisms: one for damage to the revetment and one for the erosion of the dike body. Failure is described with two limit state functions. The revetments at the dikes in dike ring area 17 consist of grass, stone or a combination of both. PC-Ring is not capable of calculating a dike profile covered with two or more different kinds of revetments. In such a case the normative revetment is determined and included in the results presented in Figure 3-10 and Figure 3-11. Appendix C treats the applied models used in the calculation. The results include a limited number of dike sections mainly due to lack of data in the schematisation.

Dike Reliability Failure Dike Reliability Failure Sect. index probability Sect. index probability 12 10.1603 1.52E-24 50 7.9888 6.88E-16 15 6.9131 2.39E-12 52 7.534 2.48E-14 20 7.1598 4.07E-13 53 7.5397 2.38E-14 23 6.3936 8.14E-11 55 6.746 7.64E-12 25 6.0108 9.27E-10 59 7.5059 3.08E-14 26 6.6625 1.35E-11 62 9.0563 6.85E-20 30 7.8696 1.80E-15 65 9.2909 7.78E-21 33 6.2892 1.60E-10 71 6.6526 1.45E-11 44 8.0876 3.08E-16 72 7.1433 4.59E-13 47 6.7899 5.64E-12 73 7.0962 6.46E-13 49 7.5165 2.84E-14 Figure 3-10: Results failure mechanism damage to revetment and erosion of dike body

Reliability Index Damage to Revetment and erosion of dike body

12 Reliability Index Stone Revetment 11 Reliability Index Grass Revetment 10 9 8 7 6 5 12 15 20 23 25 26 30 33 44 47 49 50 52 53 55 59 62 65 71 72 73 Dik e s e ction

Figure 3-11: Graph Reliability index damage to Revetment and erosion of dike body

In the national dike safety assessment the majority of the grass revetments of IJsselmonde were classified as good. However dike section 32 to 41 were classified as doubtful because the grass revetment contained some bare spots [11]. The results from the national dike safety assessment agree with the PC-Ring results. One section with the classification doubtful (section 33) has been calculated. As can be seen in figure 3.11 this section has a relatively small reliability index compared to the other sections. All in all it can be concluded failure probabilities for the mechanism damage to the revetment and erosion of the dike body are extremely small, which also can be explained by the construction of the Maeslantkering and the Hartelkering.

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3 Failure probability analysis

3.3.5 Uplifting and Piping In the failure mechanism uplifting and piping the dike fails due to erosion of sand from under the dike. If this mechanism occurs the pressure of the water firstly lifts up the if present impermeable top layer at the inland toe, after which pipes start to develop which transport the sand from under the dike. In appendix D the piping model is described. After the Second World War on a large scale forelands have been raised to cope with the problem of sedimentation in the tidal river area. Materials used to construct these elevated terrains (in dutch: “loswallen”) often came from dredge operations. 36% of the surface of the forelands of the Oude Maas consists of these elevated terrains. Often these terrains have been raised to the level of the dikes and are very wide [21]. At these locations the danger of piping is negligible and therefore these dike sections have been omitted from the calculations.

For the remaining dike sections a selection has been made based on the value of the indicator Ip [22]. With these criteria a rough distinction can be made between weak, middle and strong dike sections.

The indicator Ip is defined as: γ −γ d With: F wet w IFpuplpip=−+−3( 1) ( F 1) upl = γ wb0.8()Hh−

LLavailable available And with: Fpip == LHhdnecessary18(−− b 0.3 ) In which: Fupl = Safety against uplifting Fpip = Safety against piping Lavailable = Available leakage length Lnecessary = Necessary leakage length γwet = The volumetric weight of the wet top layer γw = The volumetric weight of water d = Thickness of the top layer H = Normative outside water level hb = The inside water level

In case Fupl < 1, then it is adapted to Fupl = 1. In case Fpip < 1, then it is adapted to Fpip = 1.

The distinction in classes is done as follows:

Iupl/pip < 1.1 Weak 1.1 < Iupl/pip < 3.5 Middle Iupl/pip > 3.5 Strong

The values of Ip have been determined. Sections with the classification “weak” were not present. Only sections indicated as middle and a few sections with the classification strong have been included in the calculations. In the data assembly [12] values of the average permeability were missing. Instead a conservative value was used in the calculations. The results for the failure mechanism piping are presented in Figure 3-12.

28

3 Failure probability analysis

Dike Ip Reliability Failure Section index probability 4 5.03 4.3256 7.61E-06 5 2.35 2.8514 2.18E-03 Reliability index uplifting and piping 6 3.01 4.0564 2.49E-05 5 22 3.72 3.6288 1.42E-04 25 3.67 1.9038 2.85E-02 4 26 3.1 1.2891 9.87E-02 3 47 5 2.593 4.76E-03 48 22.42 2.3335 9.81E-03 2

49 6.62 2.9025 1.85E-03 1

50 2.65 3.8566 5.75E-05 4 5 6 22 25 26 47 48 49 50 61 72 61 2.6 2.9834 1.43E-03 Dike Section 72 2.43 2.5575 5.27E-03 Figure 3-12: Results failure mechanism uplifting and piping

The results show a large spreading and great probabilities, while piping is not recognized as a problem in the national dike assessment. The results are based on a conservative choice of the permeability, as no data was available. Furthermore the used model (See Appendix D) is rather basic. Only one water-transporting sand layer can be defined. In reality the presence of multiple layers is important in the question whether piping occurs or not. With the implementation of multiple layers failure probabilities are reduced significantly. Both because of the lack of data and the absence of multiple layers in the model there is no confidence in these results. This results in an overestimation of the failure probabilities. Such a situation has been covered in the global idea behind the flood risk approach. In such a situation the usual approach would be to conduct further research to get more accurate data or to do extra research so ultimately a better model can be implemented to get a better approximation of the true failure probability for piping. This does not fall within the goal of this research. Therefore it is decided not to base the calculation of the flood risk on the results of piping. This however does not mean piping has no contribution in the failure probability. Further research is necessary.

3.3.6 Dike Ring results

The combination of the failure probabilities per dike section results in the following dike ring failure probabilities. The ring failure probability for wave overtopping is: 2.99 E-06 per year (approximately 1 / 334000 per year) with a reliability index 4.53. The ring failure probability for overtopping is: 2.68 E-06 per year (approximately 1 / 373000 per year) with a reliability index 4.55. The ring failure probability for damage to the revetment and erosion of the dike body is: 9.67 E-10 per year (approximately 1 / 1000000000 per year) with a reliability index 6.00. In appendix C a description of the combination procedure is given.

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3 Failure probability analysis

3.4 Flood scenarios

In the previous paragraphs the failure probability for each dike section and the failure probability for the entire dike ring have been presented. However these probabilities are not useful in the flood risk calculation. In the flood risk approach it is necessary to know the probability of a flood scenario.

3.4.1 Failure probability of a partial dike ring part The dike section failure probabilities have to be transformed to flood scenario probabilities. A flood scenario is coupled to a partial dike ring part. A partial dike ring part is defined as a part of the dike ring in which the consequences of a flood vary little if the position of the breach is changed (See chapter 2). The definition of partial dike ring parts ensures only one flood simulation per partial dike ring part is necessary for the determination of the consequences. Because of the use of one flood simulation per partial dike ring part it is necessary to calculate the failure probabilities of the partial dike ring parts. The computer program “Scenariotool” has been used for this purpose. Table 3-1 shows the reliability indexes of the partial dike ring parts in the simple case the Maeslantkering and the Hartelkering would be absent. Because of the presence of the storm surge barriers one flood simulation per partial dike ring part is insufficient, a flood simulation per partial dike ring part per state of the barriers is necessary. This will be explained in paragraph 3.4.2.

Partial dike Reliability index ring part No barrier present 1. Nespolders 4.2100 2. Zuidpolder 4.6828 3. Zegen-Molen-en Portlandpolders 4.1485 4. Hoogvliet 3.8296 5. Abrandswaard en Rhoonse Polders 3.3790 6. Rotterdam-Zuid 2.9308 7. Rijerwaardse polders 3.4823 8. Zwijndrechtse Waard 4.4060 Table 3-1: Reliability index per partial dike ring part in case no barriers are present

3.4.2 Probability of a flood scenario Suppose that a dike ring consists of two partial dike ring parts, than the following is known:

P (Partial dike ring part 1 fails) = P (Z1<0) P (Partial dike ring part 2 fails) = P (Z2<0) P (Dike ring fails) = P (Z1<0) + P (Z2<0) – P (Z1<0 and Z2<0)

However for the flood risk calculation the probability of a flood scenario is necessary. Flood scenarios probabilities are defined as:

P (Scenario 1) = P (Partial dike ring part 1 fails and Partial dike ring part 2 does not fail) P (Scenario 2) = P (Partial dike ring part 2 fails and Partial dike ring part 1 does not fail) P (Scenario 3) = P (Partial dike ring part 1 and 2 fail both)

Because of the presence of the storm surge barriers it is desirable to calculate flood scenario probabilities per state of the barrier. This is explained here after.

30

3 Failure probability analysis

Storm surge Barriers The water levels on the Nieuwe Maas and the Oude Maas are influenced by the sea water level as well as the discharges of the Meus and the Rhine. In general the water levels on the river follow the tidal variation of the sea. In case of high water levels at sea the Maeslantkering and the Hartelkering are closed to protect the hinterland. When the storm surge barriers are closed the water levels at the Nieuwe Maas and the Oude Maas are completely determined by the river discharges. In case the storm surge barriers are closed the river water levels will rise, because the river water can’t pass the storm surge barriers. The larger the river discharge, the faster the river water levels will rise. As soon as the river water levels are higher than the sea water levels the storm surge barriers are opened again.

There are two possibilities to get extremely high river water levels at IJsselmonde: 1. High sea water levels and failure of the storm surge barriers (incorrect open). 2. High sea water levels, closure of the storm surge barriers and high discharges at the rivers (correctly closed).

In both situations high sea water levels are necessary. Besides the high sea water levels either the storm surge barriers have to fail (failure probability 10-4) or the discharges of the Rhine and the Meus have to be very high. With consideration to the flood simulations it deserves preference to distinguish separate flood scenario probabilities for an open and closed state of the storm surge barriers.

This distinction is desirable because the consequences of a flood due to these situations are expected to be different. In case of high river discharges in combination with high sea water levels more water is expected to be available to flow through the breach compared to the situation in which the storm surge barriers are incorrectly open. In case the storm surge barriers fail the flood results mainly from the storm set-up. In the case with high river discharges the flood wave holds on several days perhaps even weeks after the storm set-up has ended resulting in higher river water levels. This means a difference in discharge flowing through the breach when comparing both cases (see h1 versus h2 in Figure 3-13).

Figure 3-13: Flood dominated by river and by storm at sea

Besides the distinction of separate scenario probabilities for an open and a closed state of the storm surge barriers also the correct or incorrect functioning of the closure regime of the barriers has to taken into account. With the distinction for different states of the storm surge barriers and the correct or incorrect functioning of the storm surge barriers the probability of only a breach at partial dike ring part 1 can be divided in 4 flood scenarios:

31

3 Failure probability analysis

P (Partial dike ring 1 fails and the other partial dike ring parts do not fail) = P (Failure ∩ hQ ≥ Closure Condition ∩ Correctly Closed) + P (Failure ∩ hQ ≥ Closure Condition ∩ Incorrectly Open) + P (Failure ∩ hQ < Closure Condition ∩ Incorrectly Closed) + P (Failure ∩ hQ < Closure Condition ∩ Correctly Open)

The first term refers to failure in case of a correctly closed barrier, the second term to failure in case of an incorrectly open barrier, the third term to failure in case of incorrectly closed barrier and the last term to failure in case of a correctly open barrier (Figure 3-14).

Figure 3-14: Graphical interpretation of the four states of the barrier 32

3 Failure probability analysis

System behavior The determination of the probability of a flood scenario means determining the probability a certain partial dike ring part fails while other partial dike ring parts don’t fail. In this analysis the physical condition has to be included. The influence of the physical situation is described with the criterion system behavior. In case of system behavior a breach in a partial dike ring part leads to lower water levels at other partial dike ring parts. The fraction of the total river discharge flowing through the breach is sufficiently large to have an impact on the water levels downstream of the breach. Loads on the surrounding partial dike ring parts reduce and therefore it is almost physically impossible more than one partial dike ring part fails. In case of no system behavior a breach in a partial dike ring part does not lead to lower water levels at other partial dike ring parts. No system behavior takes place in case of partial dike ring parts threatened by the sea. Then a breach does not lead to lower water levels at the neighboring partial dike ring parts. In a river system no system behavior can occur when the distance between the partial dike ring parts is so large a breach does not influence the water level at other partial dike ring parts [14].

As stated in IJsselmonde there are two possibilities to get extremely high river water levels: 1. Extremely high sea water levels and failure of the storm surge barriers (no closure). 2. High water levels at sea, closure of the storm surge barriers and high discharges at the rivers. In situation 1 the sea dominates the water levels at IJsselmonde, which means for this situation the criterion “no system behavior” is valid. In situation 2 the storm surge barriers are closed because of the storm at sea and high river discharges are present. When the storm surge barriers are closed the river water levels will rise, because the river water cannot pass the storm surge barriers. The river water is retained in the tidal river area. The larger the river discharge, the faster the river water levels will rise. A breach in this situation would not lead to lower water levels downstream. Also for situation 2 the criterion of “no system behavior” is used.

Intermezzo: In [42] flood simulations for dike ring 14 have been made with and without a breach. For these calculations water level developments were used with an exceedance frequency of 1/10.000. By coupling a fictive hinterland and subsequently modeling a breach at Rotterdam in this study the influence of a breach was determined. The results showed the breach led to a maximum water level drop of 10 cm at the breach location compared to the situation no breach was modeled [Figure 3-15]. The influence of this water level drop decreases at larger distances from the breach. The discharge through the breach is small compared to the river discharge and has

4 little influence on the

3.5 water levels at

3 surrounding partial

2.5 dike ring parts. In this

2 research boundary

1.5 conditions with even

1 smaller probabilities

0.5 are used. Water water level (NAP +m) water level 0 volumes will be

-0.5 greater compared to

-1 the 1/10000 situation; 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 the influence on the days other Partial dike ring

Rotterdam without breach Rotterdam with breach parts will also be less. Figure 3-15: Rotterdam with / without breach in case 1/10000 water level development 33

3 Failure probability analysis

The use of the criterion “no system behavior” in the calculations is a conservative approach. Scenarios with several breaches are possible which may lead to a high estimation of the risk. In this research use will be made of the physical relation “no system behavior” in the determination of the scenario probabilities. With the assumption of “no system behavior” the flood scenarios can be composed as in Table 3-2. IJsselmonde has been divided in eight partial dike ring parts (Table 3-1). This means in theory an eightfold breach can occur. In this research the probability of all single, all combinations of double, seven combinations of triple and one fourfold flood breach will be taken into account. In total 44 scenarios are defined.

Scenario Dike ring part

One Partial dike ring part fails Z1 < 0 ∩ Zi > 0 Two Partial dike ring parts fail Z1 < 0 ∩ Z2 < 0 ∩ Zi > 0 Three Partial dike ring parts fail Z1 < 0 ∩ Z2 < 0 ∩ Z3 < 0 ∩ Zi > 0 Four Partial dike ring parts fail Z1 < 0 ∩ Z2 < 0 ∩ Z3 < 0 ∩ Z4 < 0 ∩ Zi > 0 Table 3-2: Scenario table with criterion “no system behavior”

3.4.3 Results With the application “Scenariotool” the scenario probabilities for three states of the barriers have been calculated: the state with correctly closed barriers, incorrect open barriers and correct open barriers. Scenariotool does not calculate the state with the incorrectly closed barriers because the contribution to the flood scenario probabilities is negligible. Table 3-3 shows the 10 flood scenarios with the greatest probability of the 44 scenarios in case the barriers are correctly open and the case the barriers are open but should be closed. In these results the closure regime is not included, therefore the results for these two states are similar. In the last column can be seen the first 10 scenarios determine for more than 99% the flood scenario probabilities. Scenario 1 in which partial dike ring part 6 fails already takes 62%. It is so dominant the scenarios with multiple breaches with a breach at partial dike ring part 6 are found at place 2 to 5.

Scenario Failing partial Probability Reliability Cumulative Percentage dike ring areas index probability 1 6 1.18E-03 3.040 1.18E-03 62.38 2 5 en 6 2.58E-04 3.473 1.44E-03 75.97 3 6 en 7 2.20E-04 3.515 1.66E-03 87.56 4 5, 6 en 7 1.30E-04 3.652 1.79E-03 94.41 5 4, 5, 6 en 7 4.87E-05 3.897 1.84E-03 96.98 6 5 1.75E-05 4.139 1.86E-03 97.90 7 7 8.25E-06 4.308 1.87E-03 98.34 8 4, 5 en 6 7.39E-06 4.332 1.87E-03 98.73 9 6 en 8 5.22E-06 4.408 1.88E-03 99.00 10 5, 6 en 8 4.93E-06 4.420 1.88E-03 99.26 Table 3-3: Probability of flood scenario in case of incorrectly open barriers and correctly open barriers

Table 3-4 shows the first 10 flood scenarios in case the barriers are closed. Also in this case they determine the flood scenario probabilities for more than 99%. Also in these results the closure regime is not included.

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3 Failure probability analysis

Scenario Failing partial Probability Reliability Cumulative Percentage dike ring areas index probability 1 6 3.10E-07 4.985 3.10E-07 39.23 2 7 2.90E-07 4.998 6.00E-07 75.86 3 6 en 7 6.18E-08 5.288 6.62E-07 83.67 4 8 3.96E-08 5.369 7.01E-07 88.68 5 7 en 8 2.33E-08 5.464 7.25E-07 91.63 6 6 en 8 1.95E-08 5.496 7.44E-07 94.09 7 1 1.67E-08 5.523 7.61E-07 96.20 8 1 en 7 9.58E-09 5.620 7.70E-07 97.41 9 1 en 6 7.43E-09 5.664 7.78E-07 98.35 10 1 en 8 7.24E-09 5.668 7.85E-07 99.26 Table 3-4: Probability of flood scenario in case of correctly closed barriers

In the results of Table 3-3 and Table 3-4 the closure regime is not included. The next step in the procedure is to include the closure regime in the results. In PC-ring the probability of a certain state of the barriers is based on a stochastic function for the closure regime. Scenariotool bases the probability of occurrence of a state of the barriers on this stochastic function for the closure regime. Scenariotool takes the information needed from the PC-Ring output. The probability of occurrence of a state of the barriers can be combined with the scenario probabilities for a certain state of the barriers. The summation over the three states of the barriers results in the overall flood scenarios.

Scenariotool initially was developed for dike ring area 7, 14, and 36. For this research it was adapted to make it suitable for dike ring area 17. The adaptation succeeded for the determination of the partial dike ring probabilities and the flood scenario probabilities. These were presented before. The adaptation did not succeed for the determination of the overall flood scenario probabilities. For the combination of the flood scenario probabilities per state of the barrier with the probability of such a state the following pragmatic approach was used.

Besides the state incorrectly closed barrier the state correctly open barrier is neglected. In the PC-Ring output for all dike sections the failure probability for this state is several orders lower than the states incorrectly open barriers and correctly closed barriers. Only these two states remain in the analysis. Now the flood scenario probabilities in the state in which the barriers function correctly are multiplied with the probability the barriers function correctly and the flood scenario probabilities in the state in which the barriers fail is multiplied with the probability the barriers fail. This pragmatic solution results in an acceptable deviation [32]. The probability of failure of the barriers is 0.001; the probability the barriers function is 1- 0.001 = 0.999. This procedure results in the dominant flood scenarios that are presented in Table 3-5. As can be seen the flood scenario probabilities for an open barrier in Table 3-5 have decreased a factor 1000 with respect to the flood scenario probabilities in Table 3-3.

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3 Failure probability analysis

Scenario Failing partial State Barriers Scenario Cumulative Cumulative dike ring areas Probability probability Percentage 1 6 Incorrectly open 1.18E-06 1.18E-06 44.04 2 6 Correctly closed 3.10E-07 1.49E-06 55.59 3 7 Correctly closed 2.90E-07 1.78E-06 66.37 4 5 en 6 Incorrectly open 2.58E-07 2.04E-06 75.96 5 6 en 7 Incorrectly open 2.20E-07 2.26E-06 84.15 6 5, 6 en 7 Incorrectly open 1.30E-07 2.39E-06 88.98 7 6 en 7 Correctly closed 6.18E-08 2.45E-06 91.28 8 4, 5, 6 en 7 Incorrectly open 4.87E-08 2.50E-06 93.10 9 8 Correctly closed 3.96E-08 2.54E-06 94.57 10 7 en 8 Correctly closed 2.33E-08 2.57E-06 95.44 11 6 en 8 Correctly closed 1.95E-08 2.58E-06 96.16 12 5 Incorrectly open 1.75E-08 2.60E-06 96.81 13 1 Correctly closed 1.67E-08 2.62E-06 97.43 14 1 en 7 Correctly closed 9.58E-09 2.63E-06 97.79 15 7 Incorrectly open 8.25E-09 2.64E-06 98.09 16 1 en 6 Correctly closed 7.43E-09 2.64E-06 98.37 17 4, 5 en 6 Incorrectly open 7.39E-09 2.65E-06 98.65 18 1 en 8 Correctly closed 7.24E-09 2.66E-06 98.92 19 6 en 8 Incorrectly open 5.22E-09 2.66E-06 99.11 20 5, 6 en 8 Incorrectly open 4.93E-09 2.67E-06 99.29 Table 3-5: Dominant flood scenarios

These results show 10 scenarios with incorrectly open barriers and 10 scenarios with closed barriers. There is no dominant state. The first 20 scenarios contribute for more than 99% to the cumulative flood scenario probability. The cumulative flood scenario probability of the first 20 scenarios is 2.67E-06; for all 44 scenarios this is 2.69E-06. The dike ring failure probability is 2.99E-06. The cumulative flood scenario probability should arrive at this value. It comes close but there remains a difference. This difference can be explained by the fact only single, double, a few triple and only one fourfold scenarios have been calculated. Due to the criterion of “no system behavior” and the dominance of partial dike ring 6 multiple breaches do contribute to the flood scenario probabilities.

The pragmatic approach to determine the overall flood scenarios has the advantage the flood scenarios remain separated per state of the barrier. This is desirable with respect to the flood simulations. The output of Scenariotool for the overall scenario probabilities gives the summation of all states. Therefore it is not clear which state of the barriers contributes most to the overall flood scenario probability and what boundary conditions (open or closed state of the barriers) should be used for the flood simulation. In a next version of Scenariotool this separation would be an improvement.

3.4.4 Flood simulations From Table 3-5 follows flood simulations have to be made for in order of priority partial dike ring part 6, 7, 5, 4, 8 and 1. The breach locations have to be located at the weakest dike sections of these partial dike ring parts. At these locations flood simulations need to be made for an incorrect open and a correctly closed state of the barrier. In Figure 3-16 the breach locations are indicated with a red star and a letter. For example breach location A is situated at partial dike ring part 6.

36

3 Failure probability analysis

Figure 3-16: Breach locations of the necessary flood simulations

In the previous paragraph the ranking of the flood scenarios was only based on the flood scenario probabilities. This approach is too narrow. The impact of the consequences needs to be incorporated in this analysis. The ranking should be made on the risk of a flood scenario. It is possible a flood scenario with a slightly smaller probability passes another flood scenario simply because its consequences are more severe. The next chapter treats the consequences of the flood scenarios.

37

4 Consequences of a flood

38

4 Consequences of a flood

4 Consequences of a flood

In this chapter flood simulations of the dominant flood scenarios determined in the previous chapter are described. Paragraph 4.1 describes how the flood simulations have been modeled. Paragraph 4.2 presents the results of the flood simulations. These results consist of the hydraulic consequences as well as the translation of these hydraulic consequences to the expected economical damage and the expected number of casualties.

4.1 Modeling of the flood simulations

In the previous chapter the dominant flood scenarios have been determined. This paragraph describes how the modeling of the flood simulations is done. For the flood simulations use has been made of the flood simulation model for IJsselmonde that has been built by HKV [15]. The model has been built in Sobek version 2.09.003. Sobek solves the so-called two dimensional shallow water equations:

δζ ∂∂()uh () vh ++=0 (Equation 4-1) ∂∂tx ∂ y ∂∂∂∂uuuζ uV +++uvg + g + auu =0 (Equation 4-2) ∂∂∂txyxCh ∂ 2 ∂∂∂∂vvvζ vV +++uvg + g + avv =0 (Equation 4-3) ∂∂∂txyyCh ∂ 2

In which: u = Velocity in x-direction (m/s) v = Velocity in y-direction (m/s) V = Velocity: Vuv=+22 ζ = Water level above plane of reference (m) C = Chezy coefficient (√m/s) d = Depth below plane of reference (m) h = Total water depth:ζ+d (m) a = Wall friction coefficient (1/m)

Equation 4-1 is the continuity equation and ensures the conservation of fluid. Equation 4-2 and 4-3 are the momentum equations. They consist of acceleration terms: the horizontal pressure gradient, advective terms, bottom friction terms and wall friction terms [16]. To solve these equations information about bottom levels and friction of the flooded terrain is necessary. Furthermore water level developments at the river and the simulation of a breach are necessary to simulate a flood. These aspects are treated in the next paragraphs.

4.1.1 Spatial information This paragraph briefly discusses the spatial information that is included in the flood simulation model of IJsselmonde. The text in this paragraph is based on [15]. The spatial information used in the model is divided in a one-dimensional and a two-dimensional part. In the model it is possible to exchange data between the one- and the two-dimensional model by means of so-called connection nodes. The two-dimensional model covers the entire area of IJsselmonde and contains information about bottom levels relative to NAP. The information is recorded in a grid with a resolution of 100 meters and the presence of primary and secondary water defences and additional earth embankments such as roads and 39

4 Consequences of a flood

railways is included (Figure 4-1). The two-dimensional model furthermore contains information about the hydraulic friction of the terrain. The friction model is based on the land use. The area has been divided in several land use classes (Figure 4-2) and to each class a Nikuradse roughness factor has been attached.

Figure 4-1: Overview of IJsselmonde (yellow) with urban areas (pink), primary and secondary water defences (red), additional earth embankments (orange) and waterways (blue).

Figure 4-2: Classification of land use

The waterways (Figure 4-1) are schematized in the one-dimensional part of the flood simulation model. The waterways are modeled as line objects of which the hydraulic 40

4 Consequences of a flood

properties are defined. Each line object contains connection nodes. At these nodes the one- dimensional model is connected with the two dimensional model. At a connection node water from a canal can flood a grid cell.

In the two-dimensional model of the terrain levels elements such as secondary defences, roads and railways have been included. These elements are not continuous and often they are intersected by culverts or tunnels. The presence of a culvert or a tunnel influences the flood pattern. Therefore if an element is intersected by for example a tunnel this is included in the model. In the model it is assumed all passageways through secondary water defences are closed during high water. Therefore passageways through secondary water defences are not modeled. Only passageways through the additional earth embankments such as railways have been modeled, the locations of these passageways are shown in Figure 4-3. The passageways have been modeled as part of the one-dimensional model.

Figure 4-3: Modelled passages in earth embankments (culverts green, structures blue)

41

4 Consequences of a flood

4.1.2 Water level development at the river Besides the spatial information discussed in the previous paragraph water level developments at the river are necessary for a flood simulation. The development of the water level at the breach location determines for an important part the discharges flowing into the area and thus the damage that will occur. The link between the water level development and the actual flow of water into the area is formed by a breach. The modeling of a breach is discussed in the next paragraph.

There are two possibilities to get extremely high river water levels at IJsselmonde: 1. High sea water levels and failure of the storm surge barriers (incorrect open) 2. High water levels at sea, closure of the storm surge barriers and high discharges at the rivers (correctly closed).

Each situation has its own water level development. In Table 3-5 is presented which water level developments have to be generated for the dominant flood scenarios. At breach location A for example water level developments for both an incorrect open and a correctly closed barrier have to be generated.

Design points The determination of the water level developments is based on design points from the failure probability analysis. For each dike section design points are known, these are generated as a by-product in the PC-Ring calculation. The design points contain information over the most likely physical circumstances at which the dike section fails, the point with the greatest probability density. The breach locations are located at the weakest dike sections of the partial dike ring parts. Table 4-1 presents the design points of the dike sections at the breach locations for an incorrect open and a correctly closed state of the storm surge barriers.

Incorrect Open Barriers partial dike Breach Dike Height Norm. wind Discharge Discharge Water level Maas- Local Water Hs ring area Location (m+NAP) direction Lith (m3/s) Lobith (m3/s) mond (m+NAP) level (m+NAP) (m) 1 F 4.33 N.W. 433.4 2343 5.832 4.3 - 4 D 5.52 N.W. 318.4 1774 5.72 4.9 0.942 5 C 4.7 N.W. 335.8 1861 4.689 4.6 0.33 6 A 4.23 N.W. 354.4 1952 4.198 4.2 - 7 B 4.5 N.W. 413.6 2245 4.986 4.37 - 8 E 4.46 N.W. 933.7 4817 5.815 4.43 -

Correctly Closed Barriers partial dike Breach Dike Height Norm. wind Discharge Discharge Water level Maas- Local Water Hs ring area Location (m+NAP) direction Lith (m3/s) Lobith (m3/s) mond (m+NAP) level (m+NAP) (m) 1 F 4.33 N.W. 2650 12630 5.086 4.27 - 4 D 5.52 N.W. 2810 13280 6.279 4.61 1.05 5 C 4.7 N.W. 2756 13060 5.868 4.56 0.367 6 A 4.23 N.W. 2441 11790 5.127 4.15 - 7 B 4.5 N.W. 2412 11680 5.135 4.24 - 8 E 4.46 N.W. 2663 12680 4.982 4.41 - Table 4-1: Design points of the dike sections at the breach locations (taken from PC-Ring results)

The design points of breach location A, B, E and F correspond to the failure mechanism overtopping. At these locations the design point of the local water level (column 8) is practically similar to the crest level of the dike (column 2). The design points of breach location C and D are based on the failure mechanism wave overtopping. At these locations also the design points of the significant wave height Hs are shown (column 9). Because of the presence of the waves the local water level is significantly lower than the crest level at location C and D. 42

4 Consequences of a flood

The design points calculated for the incorrect open state of the barriers clearly show high water levels at the Maasmond (column 7) in combination with relatively low discharges of the Meus and the Rhine (column 5 and 6). The design points of the correctly closed barriers clearly show a combination of high water levels at the Maasmond and extremely high river discharges. The described situations to get high water at IJsselmonde correspond well with the values of the design points.

Intermezzo: The water level developments are based on the design points calculated for the normative wind direction. As can be seen in table 4-1 for partial dike ring part 1 a discharge of 12630 m3/s at Lobith is found as design point in case of correctly closed barriers for the normative North-West wind direction. At other wind directions higher values are found. Discharges varying from 30000 m3/s to 60000 m3/s can be seen. These discharges are surpassing the physical maximum. The physical maximum is the largest amount of water that safely can pass the Dutch river system. The value of the physical maximum is approximately 18000 m3/s. Discharges higher than the physical maximum are not possible because dikes upstream will fail. The existence of the physical maximum is not included in PC-Ring. For this research this is no problem while for none normative wind direction at any dike section the physical maximum is surpassed. However if the results would indicate a discharge higher than the physical maximum an over- estimation of the failure probability

would be made. This is explained by Figure 4-4. This figure explains the difference between the procedure in PC-Ring and the situation with a physical maximum by presenting both situations in a conceptual probability of exceedance curve, a cumulative density function and a probability density function. The red line indicates the procedure in PC- Ring, the black line represents the situation with a physical maximum. In the figure a design point for the local water level hd that is based on discharges higher than the physical maximum is chosen. In the probability density function of the situation with a physical maximum can be seen water levels based on discharges higher than the physical Figure 4-4: Design Point PC-Ring versus physical maximum maximum are censured. The probability mass of these water levels would be placed in a Dirac-function (indicated with a black arrow) and therefore these water levels can’t exist [39]. In the PC-Ring procedure no censuring of water levels based on discharges higher than physical maximum is applied. This would result in an overestimation of the failure probability.

43

4 Consequences of a flood

Generation of the water level developments The design points have to be translated to a water level development at the breach location. This translation can be made with the NDB-model. The NDB-model is a schematization of the tidal river area in Sobek. The storm surge barriers are included in the schematization. In the NDB-model boundary conditions have to be specified at sea and at the rivers. The boundary conditions at sea consist of the specification of a water level variation at the Maasmond and at the Hartelkering. This water level variation is a combination of a normal tide with a storm surge. The boundary condition at the river consists of the specification of a discharge at Hagestein, Lith and Tiel. With this information the NDB-model is capable of generating water level developments at each location in the tidal river area.

Water level developments for an incorrect open barrier In [15] the load combinations with the greatest probability of occurrence have been determined at several breach locations for the 1/4000 norm frequency. Figure 4-5 presents the 1/4000 water level development that was generated for breach location A at the Maashaven (Figure 3-16). It is indicated with the red line. This water level development is generated with the NDB-model and has been built up from a storm surge at the Maasmond of 3.36 m above NAP and a discharge at the Rhine of 2250 m3/s and an open state of the barriers. The storm surge lasts 35 hours and the top falls 4.5 hours behind the top of the tidal variation. This water level development does not correspond with the design points of the failure probability analysis. A new water level development had to be generated with the NDB-model. However the NDB-model was not available at the time. Therefore the following procedure was used in the determination of a water level development based on the design points. An extra 35 hours lasting storm surge with a triangular form was summed to the 1/4000 water level development. The maximum height of this extra storm surge corresponds with the difference of the design point of the local water level and the maximum water level of the 1/4000 water level development. The black line in Figure 4-5 represents this scaled water level development. The blue line presents the storm set-up of a boundary condition generated with the NDB-model for dike ring 14 with a similar design point of the local water level. The resemblance with respect to form between the scaled boundary condition and the boundary condition of dike ring 14 is quite good. Despite the fact the scaling method is not physically right and therefore introduces an error in the calculation it has been used for the determination of the water level developments for an incorrect open state of the barriers.

Water level development breach location A Maashaven 5 4 3 2 1 0 Water level (m+NAP) level Water -1 06/01/1991 08/01/1991 10/01/1991 12/01/1991 14/01/1991 Water level development incorrect open barriers (1/4000) Water level development incorrect open barriers (design point) Water level development incorrect open barriers dike ring 14

Figure 4-5: Water level development in case of incorrect open barriers

44

4 Consequences of a flood

Water level developments for a correctly closed barrier The development of the water level at the breach locations in case of correctly closed barriers has been calculated by running the NDB-model for the design points of Table 4-1. The blue line in Figure 4-6 represents the boundary condition in case of closed barriers. This water level development has been built up from a discharge at Lobith of 12000 m3/s and a storm surge at the Maasmond of 5m. It can be seen in Figure 4-6 that due to the closure of the barriers the tidal river area fills up rapidly due to the high river discharges. When the barriers are open again river water levels drop fast to the normal tidal variation. Due to the high river discharges the water levels reached in the normal tidal variation are higher compared to an incorrect open state of the barriers. The top water levels of the tidal variation in case of an incorrect open barrier are approximately 0.5 m above NAP, while in case of correctly closed barriers the top water levels in the normal tidal variation lay at approximately 1.5m above NAP. Breach discharges for a correctly closed state of the barrier will be higher after the storm surge has ended.

Water level development breach location A Maashaven 5 4 3 2 1 0 Water level (m+NAP) -1 06/01/1991 08/01/1991 10/01/1991 12/01/1991 14/01/1991

Water level development correctly closed barriers

Figure 4-6: Water level development in case of correctly closed barriers

45

4 Consequences of a flood

4.1.3 Modeling of the breach The modeling of the breach is part of the flood simulation model of IJsselmonde [15]. For this research the same model has been applied. The text in this paragraph is based on [15]. The location and height of the primary water defences is included in the two-dimensional model. The breach through which the water flows into the area is modeled at the location of the primary water defence. For the modeling of the breach use has been made of automatic breach growth in Sobek. Use has been made of the formula of Verheij - Van Der Knaap [17] that is formulated as follows:

For tstart < t <= t0: B(t) = B0 z(t) = zcrest-level – (zcrest-level – zmin) ⋅ (t/t0)

δ B For t > t0: B()tBtt=+Δ () ii+1 δt 1.5 ∂B ff {gh()up− h down } 1 And: ()t =⋅12 (Equation 4-4) i 2 fg⋅ δtuln10 c 2 1()+ tt10− uc In which: B0 = Initial width of the breach [m] B(t) = Width of the breach at point in time t [m] t = Actual computational point-in-time [hr] tstart = Point-in-time at which the breach starts to develop t0 = tstart + T0 = the point-in-time when the maximum breach-depth (zmin) is reached T0 = Time span over which the breach having a constant initial width (B0) is lowered from initial crest level (zcrest-level) to its final crest level (zmin) f1 = Factor1: constant factor (input parameter) [-] f2 = Factor 2: constant factor (input parameter) [-] g = Gravity acceleration [m/s2] hup = Upstream water level at point-in-time t [m] hdown = Downstream water level at point-in-time t [m] -1 uc = Constant critical flow velocity sediment/soil (input parameters) [m.s ] z(t) = Elevation of the dike-breach at point-in-time t [m] zcrest-level= Elevation of the crest-level of the dike at t=tstart (input parameter) [m] zmin = Elevation of the dike-breach at t=t0 (input parameter) [m]

The formula of Verheij – Van Der Knaap has been fitted on data of floods that occurred in the past and on laboratory tests. The development of the breach with the formula of Verheij –Van Der Knaap is described with Figure 4-7.

Figure 4-7: Breach growth formula Verheij – Van der Knaap 46

4 Consequences of a flood

In the flood simulations the variables for the development of the breach have been filled in as follows: - The initial width of the breach B0 is set to 5m. - The initial crest level is set to the crest level of the dike at which the breach occurs. - The bottom level of the breach is set equal to the surface level of the hinterland. - The time interval to reach to the bottom level of the breach (T0) is set to 10 minutes. - The critical flow velocity UC is dependent on characteristic bottom strength in the core of the dike. In case of a core of sand it is assumed UC = 0.2 m/s, in case of a core of clay it is assumed UC = 0.5 m/s.

For the breach locations that followed from the failure probability analysis (see Figure 3-16) the above mentioned procedure resulted in the values for the variables as presented in Table 4-2. partial dike Breach Initial width breach Time interval T0 Initial crest level Bottom level Crititical velocity ring area Location (m) (minutes) (m+NAP) Breach (m+NAP) (m/s) 1 F 5 10 4,33 0,5 0,5 4 D 5 10 5,52 0,78 0,5 5C 5 104,73 0,5 6 A 5 10 4,23 -0,53 0,5 7 B 5 10 4,5 -1,71 0,5 8 E 5 10 4,46 -1 0,5 Table 4-2: Values breach parameters

The values for the bottom level of the breach for breach location A, B and D have been taken from [15]. The bottom level of breaches C, E and F have been determined from the bottom level grid in the Sobek model. The bottom level of the breach at location C is significantly higher compared to the other locations. At the foreland of location C the port of Rotterdam is situated. The harbour terrains have been raised to a level of approximately 3.2m above NAP. This foreland is very wide and it is assumed the water is not capable to erode the breach to the level of the hinterland.

It is also possible a breach occurs in a secondary defence. In the flood simulation one breach in a secondary water defence has been modeled (see paragraph 4.2.2, extra flood simulation at IJsselmonde). At this location a breach has been implemented at a location where overtopping was more than 15 cm [15]. Such a secondary breach is used one time.

4.1.4 Economical damage With the spatial information and the description of the hydraulic loads and the breach growth the course of the flood can be simulated and the hydraulic consequences are known. The hydraulic consequences have to be translated to the economical damage. This is done with the computer program HIS-SSM version 2.1. HIS-SSM calculates the expected economical damage as a result of a flood. For this purpose HIS-SSM uses files with geographical data. The land is classified in functions; for example industry, low-rise buildings, high- rise buildings, agriculture, recreation etc. For each type of land use a damage function is defined. A damage function consists of the maximum damage that can occur at that type of land use, the unit in which the damage is expressed and the damage factor (and its corresponding damage function). The damage factor is a value between 0 and 1 dependent on the damage function. The damage function lays a relation between the water depth, the flow velocity, the flooding speed and the occurrence of a storm on the one side and the fraction of the maximal economical damage that occurs due to a particular flood on the other side. In case of maximal damage the damage factor is 1.

47

4 Consequences of a flood

The general form of a damage function is as follows:

n (Equation 4-5) SnS=⋅⋅∑αiii i=1

In which:

αi = The damage factor for category i. ni = Number of units in category i. Si = Maximum damage per unit in category i.

The damage in the here described situation is only because of the presence of the water. The water has not caused the buildings to collapse [18]. In HIS-SSM also is included that a building can collapse due to high flow velocities or due to waves. In the damage calculation first is determined which part of the buildings collapses due to high flow velocities. Then the maximum damage factor of 1 is attributed to these buildings. Subsequently is determined which part of the buildings collapses due to waves. To these buildings also the damage factor 1 is attributed. Then the damage to the buildings that remain standing is calculated with the damage functions. To implement the collapse of a building due to high flow velocities a critical flow velocity is introduced. For the implementation of the collapse of a building due to waves a shelter factor is included. The shelter factor has a range between zero and one. The larger the shelter factor, the larger the probability of collapse of a building due to storm waves. In this research the values for the critical flow velocity and the shelter factor have been taken from [15]. The critical flow velocity is set to 8 m/s and a shelter factor of 1 is used.

The economical damage consists of several categories of damage [19]: 1. Direct economical damage – material Direct material damage is defined as damage that occurs to objects, immovable properties and movable properties because of the direct contact with water. Here to belongs: - Repairing costs to immovable properties (either possessed or rented) like estates and buildings. - Repairing costs to means of production like machines, equipment, installations and means of transport. - Damage to household furniture. - Damage because of the loss of movable properties like base materials, auxiliary materials and products (including damage to the harvest). 2. Direct economical damage – because of business interruption This category is defined as losses that occur because businesses cope with a production standstill. 3. Indirect economical damage Indirect economical damage consists of damage that occurs at delivering and purchasing companies outside the flooded area. Also the increase in traveling time because of the not functioning of railways and highways in the flooded area is included in this category.

In paragraph 4.2 the expected total economical damage is presented for the simulated flood scenarios.

48

4 Consequences of a flood

4.1.5 Casualties HIS-SSM is also capable of translating the hydraulic consequences to an expected number of casualties. The expected number of casualties is dependent on the number of people in the flooded area. In this research use is made of dataset ‘SSM100NL2004’. In this dataset the number of people living in the area has been reduced with the people living in high-rise buildings, as these people are not in immediate danger. In the determination of the number of casualties a casualty function is used. The casualty function consists of the maximum number of casualties that can occur multiplied with a casualty factor that states which fraction of the people present is expected to drown. This factor is dependent on the water depth, the flow velocity and the flooding speed. The larger the water depth, the flow velocity and the flooding speed, the larger this factor is. The range of the factor lies between 0 and 1.

Furthermore the number of casualties is dependent on the number of people that have been evacuated because of the threatening flood. In HIS-SSM the number of people that have been evacuated can be included with help of an evacuation factor. In case of a preventive evacuation the number of casualties can be calculated by multiplying the number of casualties without an evacuation with (1- evacuation factor). In case of a flood wave at a dike ring area dominated by rivers warning times are relatively long, therefore there is time for a successful evacuation. For a flood at IJsselmonde always a storm surge at sea is necessary. This implies warning times are much shorter; therefore an evacuation needs to be executed in a relatively small time span. In this research the possibility of a preventive evacuation has not been taken into account. The calculated number of casualties therefore is an upper limit. In paragraph 4.2 the expected number of casualties is presented when no preventive evacuation takes place.

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4 Consequences of a flood

4.2 Results of the flood simulations

Figure 4-8 shows the breach locations. The locations indicated with a red star result from the failure probability analysis. At these points the weakest dike sections of the partial dike ring parts are located. Flood simulations have been made for each of these breach locations. Also at the locations indicated with a black star flood simulations have been made. These simulations serve to verify the quality of the division in partial dike ring parts.

Figure 4-8: Breach locations per partial dike ring part and compartment

The following paragraphs present the hydraulic consequences of the dominant flood scenarios. To illustrate the development of the hydraulic consequences use has been made of figures that present the flood progress in hours after the breach in the form of a strip. In these strips the intensity of the colours is coupled to a bottom level or a water depth as indicated in the legend presented in Figure 4-9.

Based on the hydraulic consequences the expected economical damage and the expected number of casualties has been determined. No measures that limit the damage have been used in the flood simulations. The flood simulation at breach location A will be described extensively. Only characteristic features of the flood simulations at the other breach locations will be described.

Figure 4-9: Legend

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4 Consequences of a flood

4.2.1 Breach location A at partial dike ring part 6 From Table 3-5 follows the first flood scenario is a scenario in which compartment 6 (Rotterdam-Zuid) is flooded. In scenario 1 the storm surge barriers are incorrectly open. The second scenario in the ranking from Table 3-5 is the scenario in which also compartment 6 is flooded, however in this scenario the barriers are correctly closed. The weakest section in partial dike ring part 6 is section 38 that is situated at the Maashaven. The breach is situated at location A in Figure 4-8. In Figure 4-10 the breach location is indicated with a red triangle.

Figure 4-10: Breach location at Maashaven

Incorrect open barriers Figure 4-11 presents the progress of scenario 1 in which the storm surge barriers are incorrectly open. In the top left corner the flood progress after one hour is presented. From left to right the progress after 1, 2, 6, 12, 24, 48, 96 and 120 hours is given. The surface level is indicated with the colour brown, the water depth is indicated with the colour blue. The intensity of the colour is coupled to a surface level or a water depth as indicated in Figure 4-9. The bottom level of the breach is situated at 0.53m below NAP [15]. In the first hours after the failure of the dike the discharges flowing through the breach are very high due to the presence of the storm set-up. After a while the storm set-up has subsided and the river water levels return to follow their normal tidal variation.

Figure 4-11: Flood after 1, 2, 6,12, 24, 48, 96 and 120 hours with incorrect open barriers 51

4 Consequences of a flood

The storm set-up subsides and discharges decrease and at low water the direction of the flow through the breach reverses (see Figure 4-12). The incoming volume of water spreads over Rotterdam-Zuid in the first hours.

Figure 4-12: Development of discharge through breach.

It can be seen Rotterdam-Zuid north of the A16 is completely flooded. The water is retained by the A16 (only after 24 hours the water passes the A16 through one of the tunnels) and also by the railway from Rotterdam - Dordrecht in the east.

Figure 4-13: Water level variation near Breach (left) and further from breach (right)

Figure 4-13 presents the development of the water level at a location near the breach and at a location further away from the breach. At both locations the water reaches the level of approximately 0.1m below NAP after 120 hours. This is the case throughout the flooded area. Due to the variation in bottom levels water depths vary from 0.5m to 2m in the flooded area. At the location near the breach it can be seen initially water levels rise high due to the high discharges. When the discharges decrease water levels near the breach drop, the water spreads over the area. Compared to the location near the breach the water level development at the location further from the breach is much smoother.

Two extra flood simulations have been made to get insight in the quality of the choice of partial dike ring parts. In these flood simulations the breach locations have been varied. 52

4 Consequences of a flood

The breach locations for these extra flood simulations are situated at the locations indicated with a black star in Figure 4-8. Figure 4-14 shows the progress of the flood after 120 hours for the original breach at the Maashaven (left), a breach at Feijenoord (middle), and a breach at the Brienenoord bridge (right).

Figure 4-14: Flood progress after 120 hours for three breach locations

In case of a breach at Maashaven the water does not pass the railway from Rotterdam to Dordrecht (black line in Figure 4-2). The breaches at Feijenoord and the Brienenoord bridge are situated east of the railway. Floods originating from these breaches flow over the railway and therefore flood a greater area. The expected total economical damage due to a flood with a breach at Maashaven is approximately 4.1 billion euro and the expected number of casualties is 600. For both breaches at Feijenoord and the Brienenoord bridge the expected damage is approximately 4.9 billion euro and the expected number of casualties is approximately 1500. The large difference in casualties can be explained with the fact that in case of a breach at Feijenoord or at the Brienenoord bridge first the basin east of the railway is flooded. This basin is relatively small. High flooding speeds occur here. The expected number of casualties is very sensitive for high velocities of water rise.

Correctly closed barriers The scenario with correctly closed barriers at location A in partial dike ring part 6 is second in the ranking of Table 3-5. Figure 4-15 shows the flood progress after 1, 2, 6, 12, 24, 48, 96 and 120 hours. The end result looks the same as in the case of an incorrectly open barrier.

Figure 4-15: Flood after 1, 2, 6, 12, 24, 48, 96 and 120 hours with correctly closed barriers 53

4 Consequences of a flood

However there are differences in the development of the flood. As can be seen in Figure 4-16 the initial discharges are significantly lower compared to the initial discharges in case of an incorrect open state of the barriers (see Figure 4-12) and the duration of these high discharges also is much shorter. This has to do with the choice of the breach moment (which is connected to the top water level) and especially with the form of the flood wave.

Figure 4-16: Development of discharge through breach

In case of incorrectly open barriers water levels remain high a longer period after the peak of the storm set up compared to the situation with correctly closed barriers. Because of the dominance of the initial discharges the development of the storm set up at sea and the choice of the top of the storm set up compared to the top of the tidal variation is crucial. In this research the water level developments for an incorrect open state of the barriers have been determined with a scaling procedure. This procedure was such that the top of the additional storm surge fell together with the top of the tidal variation. The top of the original storm surge fell 4.5 hours behind the top of the tidal variation. With this scaling procedure the top water level always falls together with the top water level of the tidal variation, giving an overestimation of the initial discharges. When the influence of the storm surges has ended the water levels are determined by a combination of a normal tidal variation and the occurring river discharges. In case of the correctly closed barriers these river discharges are high and thus river water levels remain relatively high. This results in breach discharges that remain high in every tidal cycle. Maxima of 120 m3/s in case of correctly closed barriers compared to maxima of 20 m3/s in case of incorrectly open barriers. Despite high river discharges and thus relatively high river water levels the flow in the breach reverses at low water.

Figure 4-17: Water level variation near Breach (left) and further from breach (right)

54

4 Consequences of a flood

Figure 4-17 presents the water level variation at a location near the breach (left) and the water level variation at a location further from the breach (right). At both locations the water reaches the level of approximately 0 m relative to NAP after 120 hours. This is 10 cm higher compared to the case of incorrectly open barriers (compare with Figure 4-13). When comparing the water level development at the locations further from the breach it can be seen in case of correctly closed barriers the water level develops more gradually.

The expected total economical damage due to a flood with a breach at Maashaven in case of correctly closed barriers is approximately 4 billion euro and the expected number of casualties is 504. Compared to the incorrect open state the economical damage is somewhat lower in spite of the higher water level. The number of casualties is significantly lower. This can be explained by looking at the development of the flood. Due to the higher and longer lasting initial discharges in case of an incorrect open state of the barriers higher water velocities and higher velocities of water rise occur. This has its effect on the economical damage and the number of casualties.

55

4 Consequences of a flood

4.2.2 Breach location B at partial dike ring part 7 The flood scenario with a single breach at location B in partial dike ring part 7 with a correctly closed state of the barriers is ranked at the third place in the list of dominant flood scenarios (see Table 3-5). The situation with an incorrect open state of the barriers is ranked at the fifteenth place. In Figure 4-18 breach location B is indicated with a red triangle.

Figure 4-18: Breach location B at Bolnes

Incorrect open barriers Figure 4-19 shows the flood progress at breach location B in case the barriers are incorrectly open. The flood progress after 1, 2, 6, 12, 24, 48, 96 and 120 hours is shown. The bottom level of the breach is situated at 1.71m below NAP, which is the lowest level of all breaches calculated. Discharges flowing through the breach are very high (see Figure 4-20). After a short period water levels in compartment 7 start to follow the tidal variation of the Nieuwe Maas. At locations further away from the breach top water levels in the flooded area reach approximately 0.4 m above NAP. Closer to the breach water levels can become higher. The flooded area surpasses compartment 7 as secondary defences are overtopped and water passes through culverts and tunnels. Parts of compartment 6 and 8 are flooded. Ridderkerk is not flooded as it is situated at higher grounds (right side in Figure 4-19). The expected economical damage is 2.5 billion euro and the expected number of casualties is 445.

Figure 4-19: Flood after 1, 2, 6, 12, 24, 48, 96 and 120 hours with incorrect open barriers 56

4 Consequences of a flood

Correctly closed barriers Similar to the flood simulation at breach location A in case of correctly closed barriers initial discharges are lower but discharges remain high longer; resulting in a more gradual flood progress (see Figure 4-20) and finally in a larger flooded area and higher water levels in the flooded area (because also here the river water levels remain higher). The expected economical damage therefore is higher (2.9 billion euro) and the expected number of casualties is lower (364).

Figure 4-20: Discharges through breach incorrect open (l) correctly closed barriers (r)

Extra breach location: IJsselmonde An extra flood simulation has been made at the location in partial dike ring part 7 indicated with a black star in Figure 4-8. In Figure 4-21 this breach location is indicated with a red triangle. Figure 4-22 shows the state of the flood after 1, 2, 6, 12, 24, 48, 96 and 120 hours. In this flood simulation first a small basin is filled. After two hours a breach in the secondary water defence has occurred (see paragraph 4.1.3) and the water has entered compartment 7 In the simulation with the breach at location B the water does not reach the small basin. The bottom level of the breach at this location is 0.78m below NAP. Compared to breach location B volumes of water entering partial dike ring 7 are smaller because of the higher bottom level of the breach.

Figure 4-21: Breach location at IJsselmonde

The expected economical damage in case of incorrectly open barriers is 1.3 billion euro and the expected number of casualties is 295. These consequences are smaller compared to the consequences calculated for a breach at location B. The consequences of a breach at location B can be seen as an upper limit. 57

4 Consequences of a flood

Figure 4-22: Flood after 1, 2, 6, 12, 24, 48, 96 and 120 hours with incorrect open barriers

4.2.3 Breach location C at partial dike ring part 5 From the list of dominant flood scenarios (Table 3-5) follows for breach location C at partial dike ring part 5 only simulations for an incorrectly open state of the barriers have to be made. The flood scenario with a single breach at location C can be found at the twelfth place. A breach at partial dike ring 5 comes back five times in scenarios with multiple breaches (at position 4, 6, 8, 17 and 20). Figure 4-23 shows the flood progress after 1, 2, 6 and 12 hours. After 6 hours a stable situation has been reached. The expected economical damage is 5 million euro and the expected number of casualties is 0. Consequences are relatively small. This can be explained with the high bottom level of the breach. At the fore land of the dike section at which the breach occurs the harbour of Rotterdam is situated. The harbour terrains have been raised to a level of approximately 3.2 m above NAP. These terrains are several 100 meters wide and covered with asphalt. Due to this high bottom level of the breach only the top water levels of the storm set-up flow through the breach. The consequences of a flooding at breach location C in the dike ring area are relatively small. However outside the primary water defences all the harbours will be flooded. The economical and environmental consequences of this are enormous.

Figure 4-23: Flood after 1, 2, 6 and 12 hours in case of incorrect open barriers

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4 Consequences of a flood

4.2.4 Breach location D at partial dike ring part 4 From the list of dominant flood scenarios (Table 3-5) follows for breach location D at partial dike ring part 4 only simulations for an incorrect open state of the barriers have to be made. As flood scenario with a single breach at partial dike ring part 4 does not appear in the dominant flood scenarios. A breach at partial dike ring part 4 only appears as part of a multiple breach (at position 8 and 17). In case of a breach partial dike ring part 4 is flooded completely as can be seen in the flood progress of Figure 4-25.

Figure 4-24: Breach location D at Hoogvliet

The expected economical damage is 1.1 billion euro and the expected number of casualties is 149. Hoogvliet has 35000 inhabitants. HIS-SSM bases its calculation on 27000 people that are in immediate danger of the flooding (people in high rise buildings are neglected). As practical rule is used that 0.1 to 1% of the people present in an area drown because of a flood. Applying this rule gives a range of 27 to 270 casualties.

Figure 4-25: Flood after 1, 2, 4, 6, 12 and 24 hours in case of incorrect open barriers

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4 Consequences of a flood

4.2.5 Breach location E at partial dike ring part 8 From the list of dominant flood scenarios (Table 3-5) follows for breach location E at partial dike ring part 8 flood simulations for both states of the barriers have to be made. As flood scenario with a single breach the situation with a closed state of the barrier comes back at the ninth place in the ranking. As part of a double breach the closed state comes back at place 10, 11 and 18. Simulations for an incorrect open state of the barriers only appear as part of a double breach (place 19, 20). Partial dike ring part 8 is divided in two by the railway Rotterdam – Dordrecht. In the flood progress (12 hours to 24 hours) can be seen the railway slows down the development of the flood but does not prevent the compartment 8 from flooding completely.

Figure 4-26: Flood after 1, 2, 6, 12, 24, 48, 72 and 120 hours with incorrect open barriers

The expected economical damage in case of incorrectly open barriers is 2.2 billion euro and the expected number of casualties is 524 when the bottom level of the breach lays at – 1m relative to NAP. When the bottom of the breach is varied and set to 0.5 above NAP the expected economical damage is 1.1 billion euro and the expected number of casualties becomes 187. In case of correctly closed barriers the expected economical damage is 4.4 billion euro and the expected number of casualties becomes 789. Also a significant part of compartment 7 is flooded.

4.2.6 Breach location F at partial dike ring part 1 From the list of dominant flood scenarios (Table 3-5) follows for breach location F at partial dike ring part 1 only simulations for correctly closed state of the barriers have to be made. A breach at this location gives the same view as a breach at partial dike ring part 4 (Hoogvliet); the compartment is flooded but the secondary water defences retain the water. The expected economical damage in case of correctly closed barriers is 0.4 billion euro and the expected number of casualties is 46. This number of casualties is relatively high compared to the practical 0.1% - 1% rule, this is caused by high flooding speeds.

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4 Consequences of a flood

4.3 Overview consequences of flood scenarios

Figure 4-27 summarizes all consequences per flood scenario from the previous paragraph. The consequences of a multiple breach follow from a summation of the consequences of the single breaches. The fault introduced by this simplification has no great impact as a result of the other water level developments that in fact would be necessary for the simulation of the multiple breaches. However this simplification does give an overestimation of the consequences when the floods from two breaches meet somewhere in the area. At these locations the consequences are counted twice. This situation however only occurs in flood scenario 10 and 18.

Flood Breach Failing partial State Economical damage Number of Scenario Location dike ring areas Barriers (Billion euro) Casualties 1 A 6 incorrect open 4.1 600 2 A 6 correctly closed 4 504 3 B 7 correctly closed 2.9 364 4 A and C 5 and 6 incorrect open 4.1 600 5 A and B 6 and 7 incorrect open 6.6 1045 6 A, B and C 5, 6 and 7 incorrect open 6.6 1045 7 A and B 6 and 7 correctly closed 6.9 868 8 A, B, C and D 4, 5, 6 and 7 incorrect open 7.6 1194 9 E 8 correctly closed 4.4 789 10 B and E 7 and 8 correctly closed 7.3 1153 11 A and E 6 and 8 correctly closed 8.4 1293 12 C 5 incorrect open 0.005 0 13 F 1 correctly closed 0.4 46 14 B and F 1 and 7 correctly closed 3.3 410 15 F 7 incorrect open 2.5 445 16 A and F 1 and 6 correctly closed 4.4 550 17 A, C and D 4, 5 and 6 incorrect open 5.1 749 18 E and F 1 and 8 correctly closed 4.8 835 19 6 and 8 incorrect open 6.3 1124 20 A, C and E 5, 6 and 8 incorrect open 6.3 1124 Figure 4-27: Overview consequences per flood scenario

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5 Determination of the flood risk

62

5 Determination of the flood risk

5 Determination of the flood risk

In this chapter flood scenario probabilities and their consequences are combined to the flood risk. Paragraph 5.1 focuses on casualties, paragraph 5.2 treats economical risk and paragraph 5.3 describes measures to reduce risks.

5.1 Flood risk concerning casualties

The combination of the flood scenario probabilities with their consequences as described in equation 5-1 results in the risk. In this paragraph the expected number of casualties forms the consequences.

N R ==⋅ES() S p (Equation 5-1) ∑ iFi i=1 In which: R = Risk

PFi = Flood scenario Probability

Si = Consequences of flood scenario i (there are N scenarios in total)

Table 5-1 gives an overview of the 20 dominant flood scenarios. These contribute for more than 99% in the cumulative flood scenario probability. The flood scenarios are multiplied with the expected number of casualties. In the determination of the expected number of casualties the possibility of a preventive evacuation was not taken into account. The risk of casualties therefore is an upper limit. Furthermore the consequences of a multiple breach simply follow from a summation of the consequences of the single breaches. The fault introduced by this simplification has no great impact via the other water level developments that in fact would be necessary for the simulation of the multiple breaches.

Flood Breach Failing partial State Scenario Number of Risk of Scenario Location dike ring areas Barriers Probability Casualties Casualties 1 A 6 incorrect open 1.18E-06 600 0.000710 2 A 6 correctly closed 3.10E-07 504 0.000156 3 B 7 correctly closed 2.90E-07 364 0.000105 4 A and C 5 and 6 incorrect open 2.58E-07 600 0.000155 5 A and B 6 and 7 incorrect open 2.20E-07 1045 0.000230 6 A, B and C 5, 6 and 7 incorrect open 1.30E-07 1045 0.000136 7 A and B 6 and 7 correctly closed 6.18E-08 868 0.000054 8 A, B, C and D 4, 5, 6 and 7 incorrect open 4.87E-08 1194 0.000058 9 E 8 correctly closed 3.96E-08 789 0.000031 10 B and E 7 and 8 correctly closed 2.33E-08 1153 0.000027 11 A and E 6 and 8 correctly closed 1.95E-08 1293 0.000025 12 C 5 incorrect open 1.75E-08 0 0.000000 13 F 1 correctly closed 1.67E-08 46 0.000001 14 B and F 1 and 7 correctly closed 9.58E-09 410 0.000004 15 F 7 incorrect open 8.25E-09 445 0.000004 16 A and F 1 and 6 correctly closed 7.43E-09 550 0.000004 17 A, C and D 4, 5 and 6 incorrect open 7.39E-09 749 0.000006 18 E and F 1 and 8 correctly closed 7.24E-09 835 0.000006 19 6 and 8 incorrect open 5.22E-09 1124 0.000006 20 A, C and E 5, 6 and 8 incorrect open 4.93E-09 1124 0.000006 Table 5-1: Flood risk concerning casualties 63

5 Determination of the flood risk

However this simplification does give an overestimation of the consequences when the floods from two breaches meet somewhere in the area. At these locations the consequences are counted twice. This situation however only occurs in flood scenario 10 and 18.

5.1.1 Group risk presented as FN-curve The sum of the last column gives the total risk is 0.001723 casualties per year. Besides the total risk with the information in Table 5-1 the probability density function of the number of casualties can be composed (Figure 5-1). In the determination of the probability density function is assumed the expected number of casualties is exactly known. The event in which no breach occurs has the greatest probability density and is not presented fully in Figure 5-1. The probability density of the situation with 0 casualties is 0.99999835.

1.2E-06 1.0E-06 8.0E-07 6.0E-07 4.0E-07 2.0E-07

Probability densityPN(X) 0.0E+00 0 46 364 410 445 504 550 600 600 749 789 835 868 1045 1045 1124 1124 1153 1194 1293 Number of casualties (N)

Figure 5-1: Probability density function number of casualties

From the probability density function (fN(x)) the cumulative probability density function (FN(X)) can be determined and ultimately the probability of exceedance (1-FN(X)) of the number of casualties can be determined. For the exact procedure is referred to [20]. Figure 5-3 presents the probability of exceedance (FN-curve) of the number of casualties on a double logarithmic scale. The FN-curve starts horizontally at 2.99⋅10-6. At approximately N=400 the curve begins to bend downward. The failure probability of the dike ring is small. However if a flood occurs the number of casualties immediately is great. Therefore dike ring IJsselmonde can be characterised as a dike ring with a small failure probability and great consequences.

Figure 5-2: Cartoon “IJsselmonde”

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1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 exceedance 1-FN(x) 1.0E-06 1.0E-07 1.0E-08 1.0E-09

Probability of of Probability 100 1000 10000 100000 Number of casualties (N) FN-curve dike ring IJsselmonde

Figure 5-3: Probability of exceedance of the number of casualties

5.1.2 Comparison with the external safety domain In Figure 5-4 the FN-curve of dike ring IJsselmonde is compared with the FN-curve of the external safety domain. Railway yards, companies that are obliged to conduct external safety reportages and airports belong to the external safety domain. The failure mechanisms overtopping, wave overtopping and damage to the revetment contribute to the presented FN- curve of dike ring IJsselmonde. The failure mechanisms piping and instability of the inside slope are not included in the FN-curve. The inclusion of these failure mechanisms can have an impact on the position of the FN-curve.

1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 FN(x) 1.0E-06 1.0E-07 1.0E-08

Probability of exceedance 1- 1.0E-09 100 1000 10000 100000 Number of casualties (N) FN-curve dike ring IJsselmonde FN curve external safety

Figure 5-4: Comparison with external safety domain

The FN-curve of dike ring IJsselmonde does not exceed the FN-curve of the external safety domain. The flood risk of IJsselmonde has been reduced significantly by the introduction of the Maeslantkering and the Hartelkering in the tidal river system. Therefore IJsselmonde probably is one of the safest dike ring areas in the Netherlands. Despite this the FN-curve of dike ring IJsselmonde does approach the FN-curve of the external safety domain for larger 65

5 Determination of the flood risk

numbers of casualties. From the difference in position of both curves the disaster potential becomes clear. If a flood occurs many casualties (hundreds, thousands) will fall, while in the external safety domain also smaller accidents (1 - 100 casualties) are expected to fall [20]. It should also be kept in mind that the FN-curve for the external safety domain is given for the Netherlands, while the FN-curve of dike ring IJsselmonde concerns only one dike ring, while there exist 52 other dike ring areas in the Netherlands. The total flood risk for the Netherlands will be even greater.

5.1.3 Comparison with the VROM standard In the Dutch external safety policy the VROM Standard for group risk is applied for chemical installations. In Figure 5-5 the position of the FN-curve of dike ring IJsselmonde is compared with the VROM standard. The VROM standard is defined as:

10−3 1()−

Ndij = The number of casualties at location j as a result of activity i.

The FN-curve of dike ring IJsselmonde exceeds the VROM standard amply. The question however is to what extent the VROM standard can be applied for dike ring areas. Fist of all the VROM standard is applied for approximately 1000 installations (n), while there are 53 dike ring areas in the Netherlands. If all dike ring areas and installations would satisfy the VROM standard the risks at national level for the installations would be much higher [20].

1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 xceedance 1- 1.0E-05 FN(x) 1.0E-06 1.0E-07 1.0E-08

Probability of e of Probability 1.0E-09 100 1000 10000 100000 Number of casualties (N) FN-curve dike ring IJsselmonde VROM standard

Figure 5-5: Comparison with VROM standard

Besides this an accident with an installation has a technical cause, while a flood partially is natural. The acceptability of risks is linked with the origin of an activity, at which a natural disaster is experienced as less serious. Because of this the VROM norm seems too strict for dike ring areas [20].

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5.2 Flood risk concerning economical damage

Besides loss of life economical damage forms an important part of the consequences. Table 5-1 the dominant flood scenarios are multiplied with their expected economical damage. Also in this case the consequences due to multiple breaches consist of a summation of the consequences of the scenarios with a single breach.

Flood Breach Failing partial State Scenario Economical damage Economical risk Scenario Location dike ring areas Barriers Probability (Billion euro) (Euro) 1 A 6 incorrect open 1.18E-06 4.1 4854 2 A 6 correctly closed 3.10E-07 4 1241 3 B 7 correctly closed 2.90E-07 2.9 840 4 A and C 5 and 6 incorrect open 2.58E-07 4.1 1057 5 A and B 6 and 7 incorrect open 2.20E-07 6.6 1453 6 A, B and C 5, 6 and 7 incorrect open 1.30E-07 6.6 858 7 A and B 6 and 7 correctly closed 6.18E-08 6.9 426 8 A, B, C and D 4, 5, 6 and 7 incorrect open 4.87E-08 7.6 370 9 E 8 correctly closed 3.96E-08 4.4 174 10 B and E 7 and 8 correctly closed 2.33E-08 7.3 170 11 A and E 6 and 8 correctly closed 1.95E-08 8.4 163 12 C 5 incorrect open 1.75E-08 0.005 0 13 F 1 correctly closed 1.67E-08 0.4 7 14 B and F 1 and 7 correctly closed 9.58E-09 3.3 32 15 F 7 incorrect open 8.25E-09 2.5 21 16 A and F 1 and 6 correctly closed 7.43E-09 4.4 33 17 A, C and D 4, 5 and 6 incorrect open 7.39E-09 5.1 38 18 E and F 1 and 8 correctly closed 7.24E-09 4.8 35 19 6 and 8 incorrect open 5.22E-09 6.3 33 20 A, C and E 5, 6 and 8 incorrect open 4.93E-09 6.3 31 Table 5-2: Flood risk concerning economical damage

Summing the last column gives the total risk is approximately 12000 euro per year. With the information in Table 5-2 a probability density function of the economical damage can be composed (Figure 5-6). In this probability density function the economical damage is modeled as a discrete stochastic variable, it is assumed the economical damage due to a flood scenario is exactly known [20]. The event in which no breach occurs has the greatest probability density and is not presented fully in Figure 5-6.

1.2E-06 1.0E-06 8.0E-07 6.0E-07 4.0E-07 2.0E-07

Probability density PD(X) 0.0E+00 4 0 0.4 2.5 2.9 3.3 4.1 4.1 4.4 4.4 4.8 5.1 6.3 6.3 6.6 6.6 6.9 7.3 7.6 8.4 0.01 Economical damage D (Billion euro)

Figure 5-6: Probability density function of the economical damage

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5 Determination of the flood risk

Similar to the situation with casualties from the probability density function (fD(x)) the cumulative probability density function (FD(X)) can be determined and ultimately the probability of exceedance (1-FD(X)) of the economical damage can be determined. For the exact procedure is referred to [20]. Figure 5-7 presents the probability of exceedance of the economical damage on a double logarithmic scale. The curve starts horizontally and starts to bend downward at an economical damage of approximately 3 billion euro. Probabilities are small but consequences are great.

1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 1.0E-06 1.0E-07 1.0E-08 1.0E-09 Probability of exceedance 1-FD(x) exceedance Probability of 0.01 0.1 1 10 Economical damage D (Billion euro)

Figure 5-7: Probability of exceedance of economical damage

5.3 Methods to reduce the flood risk

The calculation of the group risk is based on three elements: the flood scenario probabilities, the flood simulations (depth, water velocities, flight times) and data on the flooded area (population density). Measures to reduce flood scenario probabilities are effective in reducing the group risk of flooding. Besides this secondary defences can have influence on the course of a flood and accompanying hydraulic parameters. Measures that effect the arrangement of the area can also be effective in reducing the flood risk. With help of instruments in spatial planning it is possible to reduce the number of casualties in a flood. This is possible by prohibiting building at probable breach locations or at locations with great water depths in case of a flood. Also an evacuation can reduce the number of casualties significantly. The possibilities for an evacuation can be improved by formulating evacuation plans or by optimizing escape possibilities. The effect of two types of measures to reduce the group risk is presented in Figure 5-8 and Figure 5-9 [20].

Figure 5-8: Reduction of consequences left and failure probability right [20] 68

5 Determination of the flood risk

1.0E+00 1.0E-01 1.0E-02 Measures to 1.0E-03 reduce failure 1.0E-04 probability 1.0E-05 FN(x) 1.0E-06 1.0E-07 Measures to reduce the consequences of a 1.0E-08 1.0E-09 flood

Probability ofProbability exceedance 1- 100 1000 10000 Number of casualties (N)

Figure 5-9: Effect of measures presented in the form of a FN-curve [20]

5.3.1 Effect of the Maeslantkering and the Hartelkering An example of a measure to reduce the flood scenario probabilities is the construction of the Maeslantkering and the Hartelkering. These storm surge barriers significantly have reduced the flood risk in the tidal river area. Figure 5-10 presents the effect of the storm surge barriers on the flood risk of dike ring IJsselmonde in the form of a FN-curve.

1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 FN(x) 1.0E-06 1.0E-07 1.0E-08 1.0E-09 Probability of exceedance 1- 100 1000 10000 Failure probability barriers 0.001 per closure No barriers present Number of casualties (N) Failure probability barriers 0.01 per closure

Figure 5-10: Impact storm surge barriers presented in FN-curve

The blue line already was presented in paragraph 5.2 and is based on a failure probability of the Maeslantkering of 0.001 per closure. The red line presents the situation without the presence of the storm surge barriers and the green line is an indication of the position of the FN-curve in case the barriers have a failure probability of 0.01 per closure. The black arrow denotes the direction of decreasing failure probabilities.

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5 Determination of the flood risk

5.3.2 Compartmentation In this research was assumed secondary dikes retain water. Only at one location (see paragraph 4.2.2) a breach in a secondary water defence was modeled. Furthermore it was assumed all passageways in the secondary dikes are closed in case of a flood. These assumptions often result in compartments that are flooded completely while neighboring compartments are hardly affected. Only when secondary water defences are overtopped neighboring compartments can be flooded. Another assumption could be that secondary water defences have no water retaining function at all. This would result in larger areas affected by a flood, lower flooding speeds and lower water depths resulting in completely different consequences. A third description could be that secondary water defences function a while and only fail when loads become too great. This implies the worst features of the first two assumptions would be combined. First one compartment is filled to great water depths (many casualties, high economical damage), then a secondary water defense breaches somewhere and the water that already caused damage goes on to the next compartment causing losses there.

Compartmentation is a measure directed at the reduction of the consequences of a flood. It seems compartmentation has two effects; a positive and a negative. The positive effect is the reduction of the flooded area by restricting the flood to a compartment and the negative effect is an increase of damage in the flooded compartment. In case the positive effect is greater than the negative effect compartmentation is effective from a flood risk point of view (see Figure 5-11). The remainder of this thesis focuses on the impact of compartmentation on the flood risk.

1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 FN(x) Impact of compartmentation 1.0E-06 on the flood risk 1.0E-07 1.0E-08 1.0E-09

Probability ofProbability exceedance 1- 100 1000 10000 Number of casualties (N)

Figure 5-11: Possible Impact of compartmentation (negative in flooded compartment, positive in other compartments

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6 Impact of compartmentation on flood risk

This chapter focuses on the impact of compartmentation. Paragraph 6.1 is an introduction in compartmentation, paragraph 6.2 compares the application of compartmentation in different fields of engineering. In paragraph 6.3 characteristics that determine the impact of compartmentation in dike ring areas are identified. Paragraph 6.4 presents some cases that demonstrate the variation in the impact of compartmentation. In paragraph 6.5 a method is described to include compartmentation measures in an economical optimisation.

6.1 An introduction to compartmentation

Compartmentation can be defined as the dividing of the overall system in compartments resulting in isolation per compartment and therefore providing protection to the overall system by reducing the consequences of initial failure.

From this definition follows compartmentation is a method to reduce or even limit the consequences. In case of failure the damage is limited to a single component preventing greater damage to the overall system. Compartmentation is applied successfully in several fields of engineering. It is common use in ship engineering where watertight compartments are applied to reduce the probability of sinking and capsizing. Furthermore fire resistant compartments are used in high-rise buildings to reduce the impact of a spreading fire. Compartmentation has also been known for centuries as a method used in the protection against flooding. Already in the thirteenth century the Diefdijk was constructed protecting the the compartment of the Alblasserwaard against a flood from the compartment of the Betuwe, Tieler- and Culemborger- waard. Besides intended secondary water defences like the Diefdijk, artificial earth embankments of railways or roads are present in dike ring areas segregating the area in compartments. Little is known about their contribution to the protection against flooding in 1953. In the following the application of compartments in ships and of fire resistant compartments in high-rise buildings is briefly described. In paragraph 6.2 conditions that make the application of compartmentation in these fields successful are identified and compared with existing conditions present in flood protection.

Compartments in ship engineering The compartmentation of a ship acts as a barrier against fire and flooding, furthermore compartmentation has a positive effect on the stability of a ship (see intermezzo on next page). Ships are designed to withstand solid flooding of a number of compartments without sinking. By sacrificing a few compartments the complete loss of a ship is prevented or delayed. Compartmentation is effective in reducing the consequences and creating extra time to reach a port or start a rescue operation.

Fire resistant compartments in high-rise buildings No building is free from the threat of fire. However it can be ensured that only limited damage will result if fire breaks out by reducing the over-all fire risk. The single design feature that contributes most to the reduction of the over-all risk is the use of fire-resistant construction to separate a building into fire-resistant compartments. Figure 6-1: Ship compartmentation Fire-resistant construction may be described as construction that continues to fulfil its function during the course of a fire, and where walls, 71

6 Impact of compartmentation on flood risk

floors and partitions are involved preventing the transmission of fire beyond these boundaries. In all high-rise buildings staircases constitute fire-resistant compartments with direct access to the exterior of the building at ground level creating time to evacuate the storeys above the fire and thus reducing the probability of complete loss of life [23].

Intermezzo: Compartmentation has a positive impact on ship stability. This is illustrated with a case about the stability of a ballasted floating tunnel element. In the design of tunnel elements it has to be ensured the elements do not capsize during transport. In case of unstable elements waves can cause capsizing. Therefore a tunnel element has to be designed such that an initial distortion caused by an external source initiates a counteracting moment. The use of water for the sink down operation has a negative impact on the stability of the element (Same is true for water in a ship). In the figure an initial distortion causes the water depth at the left side to increase, while the water depth at the right side decreases. This results in a moment that positively influences the initial distortion. Compartmentation reduces the impact of the driving moment.

Figure 6-2: Ballasted tunnel element without / with compartmentation

The influence of the ballast water on the stability can be taken into account by defining the moment of inertia ( I ) as follows:

(Equation 6-1) I =−IIei∑

In which: I = Moment of inertia (m4) 4 Ie = Moment of inertia due to the surface crossed by water (m )

Ii = Moment of inertia ballast water with respect to the median of the compartment

Suppose the external width of the element in the figure is 10m and the internal width is 9m. A situation with a length of the element of 1m is considered (perpendicular to the surface of the figure). 1 1. Situation without compartmentation and ballast water: I =⋅⋅=1 1034 83.3m 12 1 2. Situation without compartmentation and with ballast water: I =−⋅⋅=83.3 1 934 22.5m 12 The use of a compartmentation has a positive impact on the stability. Suppose similar dimensions as in the previous case and a partition with a width of 0.4m: 1 3. Situation with compartmentation and ballast water: I =−⋅⋅⋅=83.3 2 1 4.334 70m 12 The use of more compartments increases the overall moment of inertia and therefore the stability by an eightfold reduction of the moment of inertia of the ballast water. Furthermore the impact of the compartments is greater in the direction along the tunnel element. The compartments have the following additional advantages; smaller spans and therefore smaller forces and moments. A concentrated force is distributed more effective over the element [24].

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6.2 Comparison of compartmentation in different engineering fields

Two conditions can be identified that make the application of compartmentation in ship engineering and in the fire resistant construction of high-rise buildings successful:

1. Compartmentation in these fields is very effective in preventing maximum loss.

This condition finds its origin in the course of the disaster. Both threats can be characterized by a feedback mechanism. The discharge through a leak in a ship will be constant (or increasing due to a growing leak) in case no compartmentation is present. The discharge of water into the ship causes a reduction of the stability of the ship. This instability increases with the volume of water entering. This “positive” feedback mechanism increases the probability of complete loss of the ship in case initial failure has occurred. Compartmentation limits the discharge of water into the ship and therefore interrupts the “positive feedback” mechanism that reduces the stability of the ship (See intermezzo). A similar feedback mechanism can be seen in the development of a fire [23]. Compartmentation in these fields is very effective in preventing maximum loss once initial failure has occurred.

2. Compartmentation in these fields is relatively easy to implement in the overall system.

The implementation of compartmentation to enhance safety can easily be combined with other systems. For example the layout of cabins in a ship and of apartments in a high-rise building only has to be upgraded to serve as compartmentation. Bulkheads in a ship are already a form of structural compartments. In this way multiple purposes are served. This makes compartmentation relatively easy to implement in these fields.

In case of a breach in a dike the development of the treat is different compared to the situation described under condition 1. The discharge entering a dike ring is amongst others dependent on the development of the water levels. Initial discharges will be high and will decrease when the storm surge or the flood wave passes. The question if maximum loss occurs depends on the volume of water entering the dike ring relative to the maximum volume of water that the dike ring could store. If the volume of water entering the dike ring already is small compared to the storage capacity of the dike ring no “positive” feedback mechanism as described before is present. This is completely different from a situation with a ship without compartmentation in which discharges continue till complete loss of the ship is fact.

Furthermore in case of compartmentation in dike ring areas synergy of combining compartmentation with other functions in the majority of cases is more difficult. The implementation of a new compartmentation in an area would probably be accompanied with long procedures and resistance from society.

The favorable conditions for successful compartmentation that are present in ship engineering and in the construction of fire-resistant compartments in high-rise buildings are less present for compartmentation in dike ring areas. The same is true for the design of airplanes. In the design of airplanes the strength of the system is concentrated in the exterior as compartmentation has a great impact on the scarce space and while the consequences probably would arrive so fast that no time is available to seal of compartments doors. The benefits of compartmentation in dike ring areas and airplanes therefore are less obvious. However even though conditions are less favorable for compartmentation in dike ring areas it is still possible compartmentation is effective in the protection against flooding.

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6.3 Compartmentation in dike ring areas

Historically, the primary flood defences are generally the ones that were constructed last in a successive series of flood defence systems. In most areas, historic flood defences are still present in the landscape and will influence the development of a flood. Also natural differences in terrain level and artificial earth embankments (roads, railroads) will affect the development of a flood. Ultimately the properties of the flood determine the direct flooding damage. In Figure 6-3 a conceptual model of the flooding of an area is presented. The model is not complete, but is intended to visualise the most important processes leading to flood damage after a part of the primary flood defence has failed. Starting in the right-hand side of Figure 6-3, the damage due to flooding is influenced by two factors; the size of the flooded area and the water level in the area. The size of the flooded area generally increases with increasing water level. The presence of secondary flood defences inside the area may limit the spatial scale of the flood. In that case, collapse of one or more flood defences inside the area causes an increase of the size of the flooded area. An increased size of the flooded area has a negative influence on the water level itself [25].

Figure 6-3: Conceptual model of the development of damage due to flooding

In paragraph 6.3.1 to 6.3.4 the following characteristics that influence the impact of a secondary defence will be described:

1. The distribution of flood scenario probabilities over the primary defences. 2. The hydraulic loads on a functioning secondary flood defence 3. The reliability of the secondary defences. 4. The spatial distribution of value over the compartments.

The combination of these characteristics determines the impact of compartmentation.

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6.3.1 Distribution of flood scenario probabilities Flood scenario probabilities are a measure for the frequency a partial dike ring area is breached. Therefore flood scenario probabilities also contain information over how often a secondary defence could have to fulfil a water retaining function. Therefore the distribution of flood scenario probabilities over the primary ring implicitly contains information over the partial dike ring part where a secondary defence could have the most impact. This makes the flood scenario probabilities very dominant in the determination of the impact of compartmentation. The construction of a new secondary defence or the removal of an old secondary defence has an impact on the division in partial dike ring parts and therefore on the determination of the flood scenario probabilities and the flood risk. In Appendix H the flood risk calculation scheme is presented with a feedback loop for the construction of or the removal of a secondary defence.

6.3.2 Hydraulic loading on a functioning secondary flood defence The impact of compartmentation is significant under the assumption of complete loss of all value in an area because of a breach and under the assumption of correct functioning of the secondary water defence. Under these assumptions compartmentation of an area in two equal parts reduces the consequences and therefore also the risk with a factor two. Failure of the primary flood defence however does not necessarily lead to complete loss of all value in the area. Incoming volumes of water simply may be too small to initiate a water retaining condition of the secondary defence. In this case the secondary defence does not reduce the consequences and the risk. Furthermore there is a probability of a double breach, one at each compartment. Also in this case the secondary defence has a marginal impact on the consequences. The assumption of complete loss of all value in a compartment in case of failure of the primary defence gives an overestimation of the impact of a functioning secondary defence. For a better understanding of the impact of secondary water defences the use of flood simulations is necessary. As can be seen in Figure 6-3 a functioning secondary defence initiates a feedback to the size of the flooded area and the water level inside the area. The impact of this feedback on a flood scenario can be investigated by looking at the volume of water flooding the area in case no secondary water defences would be present compared to the capacity of a compartment in case a functioning secondary defence is present. This relation is a measure for the prevention of additional damage caused by the impact of the secondary defence. The following indicator is introduced:

Vflood Isd = (Equation 6-2) Ccomp

In which:

Isd = Global indicator for the impact of a functioning secondary defence.

Vflood = The volume of water that enters the dike ring if no secondary 3 defence is present (m ). Vflood is determined by all parameters used in the flood simulation.

Ccomp = The volume of water that can be retained in the compartment in case of functioning secondary defences, the capacity of the compartment (m3).

In case Isd << 1 Vflood is small compared to Ccomp. The impact of a functioning secondary water defence will be negligible because the flood does not initiate the water retaining function of the secondary defence (Figure 6-4 left). In case Isd >> 1 Vflood is large compared to Ccomp. In this case the impact of a functioning secondary water defence on the course of a flood is significant. It should be noted however that whether the impact is positive or negative

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6 Impact of compartmentation on flood risk

depends on the spatial distribution of the value over the compartments (see paragraph 6.3.4). The indicator Isd can be used as a first assessment of the possible impact of a secondary defence. The value of the indicator lies in the ratio, which has as additional advantage that it useful in assessing both floods from a river and sea.

Figure 6-4: Graphical interpretation of the indicator Isd

6.3.3 Reliability of secondary defences In the previous paragraph implicitly a functioning secondary defence was assumed. However there always is a probability a secondary defence fails. The left side of Figure 6-5 presents a fictitious example of a dike ring separated in four compartments. The area has a square shape. The outer defence ring is split in four sections denoted I to IV. Inside the area, four inner flood defences are present, denoted 1 to 4. Due to the secondary defences the area is split into four compartments, denoted A to D. A flood scenario was defined as failure of one or more sections of the primary ring. Accounting for all possible combinations of failures of one, two, three or four sections of the outer ring leads in this case to a total of 15 scenarios. However, due to the presence of secondary flood defences inside the area, the direct damage in case of the occurrence of one scenario does not take a unique value. This is illustrated by the event tree for the scenario “failure of section I” in the right side of Figure 6-5. [25]

Figure 6-5: Event tree for failure of section I of the fictitious dike ring [25]

The scenario “failure of section I” in fact involves seven different sub-scenarios, ranging from flooding of area A only to flooding of all areas A to D. Similar trees can be developed for failure of other sections and for combinations of failure of more than one section of the primary defence ring. An analysis of all combinations of failures provides an estimate of the total number of distinct flood scenarios (see Figure 6-6).

Number of failures Number of scenarios Number of distinct Total number of primary sections primary ring scenarios inside ring scenarios 14 728 26 530 34 28 41 11 Total: 15 67 Figure 6-6: Number of distinct flooding scenarios for a simple dike ring [25]

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6 Impact of compartmentation on flood risk

In the analysis of scenarios inside the ring, only those scenarios that influence the spatial scale of the flood have been counted. For instance, in case of failure of sections I and II failure of section 4 does not influence the spatial scale of the flood and has therefore not been counted as a scenario. The fact that any flood defence may fail in different ways has been neglected. The total number of distinct scenarios is high, despite the fact that the example is very simple. [25]

The purpose of this example was to show the great variety in sub-scenarios introduced due to the functioning or not functioning of the secondary defences. In the example implicitly has been assumed the incoming volume of water is sufficient to fill the entire ring. This is not necessarily so (see paragraph 6.3.2). The impact of a secondary defence can be described with the ratio between the volume of water that would enter the dike ring if no secondary water defence would be present and the capacity of the compartment in presence of the secondary defence. In case of failure of a first secondary flood defence the impact of a second secondary water defence can be assessed with the indicator Isd by combining the capacities of both compartments (Ccomp =Ccomp1 + Ccomp2). Based on the value of the indicator Isd the necessity of the formulation of an event tree can be assessed.

The previous paragraph focused on the loading of secondary defences due to a flood. This paragraph focuses on the strength of the secondary defences for three variations of Isd. The strength of a secondary defence is uncertain amongst others because historic secondary defences often are intersected (for example by bicycle tracks). Figure 6-7 presents an overview of three different states of the secondary defence that could occur in case of a flooding for a simple case. In state A the consequences of failure of the primary defence in case of a functioning secondary defence (overtopping remains possible) are presented, state B denotes the consequences in case the secondary defence does not fulfil a water retaining function (is not there). State C is discussed later.

Figure 6-7: Three states of secondary water defences

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6 Impact of compartmentation on flood risk

The in Figure 6-7 presented water depths in the flooded areas are conceptual maxima that could occur during a flood given for three variations of Isd. Figure 6-7 does not give insight in water level variations at the river or sea and in the flooded area. The numbers used per state correspond to Figure 6-7. Ccomp1 is the left compartment, Ccomp2 the right compartment.

State A: The secondary defence remains intact, however overtopping remains possible (Ccomp = Ccomp1): 1. Isd << 1: Maximum water level in left compartment is lower than crest level secondary defence. 2. Isd = 1: Maximum water level in left compartment at best is equal to crest level secondary defence. 3. Isd >> 1: Maximum water level in left compartment could exceed crest level secondary defence. Flooding of right compartment depends on crest level secondary defence relative to occurring water level on river / sea and left compartment.

State B The secondary defence does not fulfil a water retaining function. (Ccomp = Ccomp1 + Ccomp2) 1. Isd << 1: Maximum water level is not dependent on secondary defence. 2. Isd = 1: Maximum water level is not dependent on secondary defence. 3. Isd >> 1: Maximum water level is not dependent on secondary defence.

State C The secondary defence initially functions and later on there occurs a breach. (Ccomp = Ccomp1): 1. Isd << 1: Not relevant as the secondary defence will not collapse. 2. Isd = 1: Initially maximum water level in left compartment at best is equal to crest level secondary defence. After the breach water spreads over both compartments. 3. Isd >> 1: Equal to situation B3, only the warning time for the second compartment is greater.

Situation C2 is special because the same volume of water causes damage twice, first because of high water depths in the first compartment and subsequently because of the increase of the flooded area to the second compartment. In this situation the flooding causes double negative consequences.

6.3.4 Spatial distribution of value over compartments The impact of a secondary defence is also determined by the spatial distribution of economical value and human life over the compartments. It needs no explanation that flooding of the left compartment in Figure 6-8 results in greater losses than flooding of the right compartment. Whether the impact of a secondary defense is positive or negative is dependent on which compartment is flooded.

Figure 6-8: Impact spatial distribution of value over compartments 78

6 Impact of compartmentation on flood risk

In case of flood scenario A in Figure 6-8 the impact of the secondary defence is positive as it prevents the compartment with the greater value from flooding. In this case the prevention of the flooding of the valuable compartment does compensate the extra damage due to the increase in water depth in the less valuable compartment. In case of scenario B there is a negative impact as the water depths in the valuable compartment are increased due to the presence of the secondary defence. In this case the prevention of the flooding of the less valuable compartment does not compensate the extra damage in the valuable compartment. In this example the positive or negative impact of a secondary defence depends on the flood scenario. To determine whether the overall impact of a secondary defence is positive or negative the impact of the secondary defence over all flood scenarios needs to be incorporated in the analysis. Once again this is a risk analysis. A secondary defence has a positive impact when the summation of the risk of each flood scenario (flood scenario probability times the consequences of the flood scenario) is lower compared to the same summation without the presence of the secondary defence.

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6 Impact of compartmentation on flood risk

6.4 Case study impact secondary defences

In the previous paragraph characteristics were identified that determine the impact of secondary defences. These determining characteristics are: 1. The distribution of flood scenario probabilities over the primary defences. 2. The hydraulic loads on a functioning secondary flood defence. 3. The reliability of the secondary defences. 4. The spatial distribution of value over the compartments. The quantity of these characteristics together with their variety in nature implies a great range of possible outcomes. This makes the question whether compartmentation is advantageous highly dependent on local characteristics (including breach growth and duration of flood waves). In this paragraph the impact of secondary defences at a variety of compartment sizes will be investigated.

6.4.1 Impact secondary defences on flood scenarios In this paragraph the impact of different states of the four secondary defences coloured red in Figure 6-9 on their corresponding flood scenarios is investigated. For this analysis flood simulations with a breach at location I, II, III and IV have been used resulting in flooding of compartments 3, 4, 7 and 9 and subsequent loading on the red secondary defences.

Figure 6-9: Locations investigated secondary defences

The states of the secondary defences correspond with the states described in Figure 6-7 and are as follows:

State A: The secondary defence remains intact, however overtopping remains possible. State B: The secondary defence does not fulfil a water retaining function (is not there). State C: The secondary defence initially functions and later on there occurs a breach.

Impact secondary defence on expected economical damage Figure 6-10 presents an overview of the change in economical damage caused by the presence of a functioning secondary defence compared with the situation no secondary defence is present. These results are based on flood simulations in which the flood progresses are presented in the form of a strip in Appendix I. In Figure 6-11 an example of 80

6 Impact of compartmentation on flood risk

such a strip is given for compartment 3. The left column indicates state A, the right column presents state B. State A: functioning State B:No secondary secondary defence defence present Breach Compartment Economical damage Economical damage Damage reduction caused Location ( Billion euro) (Billion euro) by secondary defence (%) I 9 0.782 1.286 39 II 3 0.103 0.537 81 III 4 0.7 1.3 46 IV 7 2.47 3.7 33 Figure 6-10: Reduction economical damage because of presence secondary defence.

For breach location I the greatest reduction in economical damage was expected as the secondary defence surrounds the smallest compartment. However significant overtopping over the secondary defence (see state A3 in Figure 6-7) occurs which explains the relatively small reduction. For breach location II the greatest reduction (81%) is found. Despite of the occurrence of overtopping (see state A3 in Figure 6-7) the presence of this functioning secondary defence significantly reduces incoming volumes of water preventing large scale flooding of compartment 5. For breach location III no overtopping over the secondary defence occurs corresponding with state A1 in Figure 6-7.

Figure 6-11: Flood progress compartment 3 with and without secondary defence

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6 Impact of compartmentation on flood risk

Based on the results of Figure 6-10 it can be concluded that the presence of a functioning secondary defence can have a significant impact on the flooded area and on the economical damage of a flood scenario compared to the situation no secondary defence is present. Often compartmentation results in a reduction of economical damage in a flood scenario (as was the case in all scenarios in Figure 6-10). However it remains possible that prevention of extra economical damage outside the compartment does not compensate the extra economical damage in the flooded compartment that is caused by greater water depths.

Impact secondary defence on expected number of casualties The same analysis can be done for the expected number of casualties instead of the expected economical damage. Figure 6-12 presents an overview of the change in the expected number of casualties caused by the presence of a functioning secondary defence compared with the situation no secondary defence is present. The results are based on the same flood simulations (See Appendix I and Figure 6-11).

State A: functioning State B:No secondary secondary defence defence present Breach Compartment Number of casualties Number of casualties Change in N caused Location (N) (N) by secondary defence (%) I 9 369 137 169 II 3 223 41 82 III 4 149 107 28 IV 7 268 511 -48 Figure 6-12: Change in number of casualties due to presence secondary defence

From Figure 6-12 can be concluded the presence of the secondary defence has a negative impact in case of a breach in compartment 3, 4 and 9. In these compartments high flooding velocities and greater water depths occur in the flooded compartment in case of a functioning secondary defence resulting in a higher expected number of casualties (notice the dark blue colour in compartment 3 four hours after the breach in Figure 6-11). For the flood scenario in compartment 4 the secondary defence has a positive influence on the expected number of casualties. This is due to the fact the secondary defence prevents the city of Zwijndrecht situated in compartment 8 from flooding. However in compartment 7 itself the expected number of casualties will be higher compared to the situation without a secondary defence.

It was already concluded that compartmentation can reduce the flooded area and therefore can have a serious impact on the economical damage. Often compartmentation results in a reduction of the economical damage of a flood scenario, however an increase in economical damage remains possible. Furthermore it can be concluded compartmentation results in higher flooding velocities and greater water depths in the flooded compartment resulting in a greater expected number of casualties. In the analysis for three flood scenarios (in compartment 3, 4 and 9) a decrease in expected economical damage (by flood area reduction) was coupled to an increase in expected number of casualties (by greater water depths and flooding velocities) and for one scenario (compartment 7) a reduction in both expected economical damage and number of casualties was found. It can be concluded that a positive impact of compartmentation on expected economical damage does not have to result in a similar positive impact on expected number of casualties.

6.4.2 Averaged impact of a secondary defence on flood scenarios The analyses in the previous paragraph were limited to the impact of a secondary defence on one flood scenario. However a secondary defence often affects more than one flood scenario. To determine whether the overall impact of a functioning secondary water defence is positive or negative the impact of the secondary defence over all flood scenarios needs to be incorporated in the analysis. There is a positive impact when the summation of the risk of each flood scenario with the presence of a functioning secondary defence (flood scenario 82

6 Impact of compartmentation on flood risk

probability times the consequences of the flood scenario) is less compared to the same summation without the presence of the secondary defence. This was done for the secondary defence that separates compartment 4 from 5 (see Figure 6-9). The analysis in this paragraph is limited to the expected economical damage. Besides the single flood scenarios corresponding with the flooding of compartment 4 or 5 also multiple flood scenarios that inhabit flooding of one of these compartments are incorporated in the analysis. Multiple scenarios in which both compartment 4 and 5 are flooded are neglected as the state of the secondary defence marginally influences the spatial scale of the flood. For the flood development strips is referred to appendix I. Figure 6-13 presents the expected economical damage corresponding with the flood scenarios for two states of the secondary defences. State A: functioning State B:No secondary secondary defence defence present Flood Failing partial State Scenario Economical damage Economical damage Scenario dike ring areas Barriers Probability (billion euro) (billion euro) 4 5 en 6 Incorrect open 2.58E-07 0.7 1.3 6 5, 6 en 7 Incorrect open 1.30E-07 0.7 1.3 8 4, 5, 6 en 7 Incorrect open 4.87E-08 - - 12 5 Incorrect open 1.75E-08 0.7 1.3 17 4, 5 en 6 Incorrect open 7.39E-09 - - 20 5, 6 en 8 Incorrect open 4.93E-09 0.7 1.3 20+ 4 Incorrect open 3.16E-10 1.11 0.9 Figure 6-13: Economical damage with and without functioning secondary defence

Figure 6-14 presents the flood risk for two states of the secondary defences.

State A: functioning State B:No secondary secondary defence defence present Flood Failing partial State Scenario Economical Risk Economical Risk Scenario dike ring areas Barriers Probability (Euro/year) (Euro/year) 4 5 en 6 Incorrect open 2.58E-07 180 335 6 5, 6 en 7 Incorrect open 1.30E-07 91 169 8 4, 5, 6 en 7 Incorrect open 4.87E-08 - - 12 5 Incorrect open 1.75E-08 12 23 17 4, 5 en 6 Incorrect open 7.39E-09 - - 20 5, 6 en 8 Incorrect open 4.93E-09 3 6 20+ 4 Incorrect open 3.16E-10 0.35 0.28 Total risk: 287.52 533.61 Figure 6-14: Flood risk with and without functioning secondary defence

From Figure 6-14 can be concluded that state A with a functioning secondary defence results in a total flood risk of 287 euro/year and state B where no secondary defence is present results in 534 euro/year. The presence of a functioning secondary defence results in 46% reduction in flood risk concerning economical damage. It can be concluded compartmentation is a possibility to reduce the economical flood risk.

The direct maintenance costs of the secondary defences at IJsselmonde for 2005 are estimated at 69000 euro and the indirect costs are estimated at 31000 euro, resulting in an estimated total maintenance costs of 100000 euro (Source Water Board Hollandsche Delta). The total length of the secondary defences in dike ring IJsselmonde is 40 km (Source province of South Holland). Assuming a linear relation the maintenance costs arrive at 2500 euro per km per year. The length of the secondary defence between compartment 4 and 5 is approximately 5 km, resulting in maintenance costs of 12500 euro per year. The risk reduction (247 euro/ year) by this secondary defence does not compensate its maintenance costs.

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6.5 Economical optimisation

In the previous paragraph was concluded compartmentation can have a positive impact on the economical flood risk. This paragraph handles the question whether it is cost-effective to rely on secondary defences compared to other measures like strengthening of the primary ring in the protection against flooding. When the choice is made to include secondary defences in the protection against flooding the state of the secondary defences needs to be ensured. This means safety standards need to be defined. Subsequently the secondary defences have to be adapted to satisfy these demands and a periodical assessment is necessary to ensure the secondary defences remain satisfying these demands. The updating of the secondary defences and maintaining them implies significant costs. When it is determined a secondary defence has a positive impact, an analysis is necessary to assess whether the application of a secondary defence is effective. In this paragraph a method will be introduced that makes it possible to include compartmentation measures in an economical optimisation.

6.5.1 Example economical risk optimisation by strengthening primary ring In Jonkman [20] a method to optimise the economical risk of a dike ring was described. This risk optimisation was limited to measures that strengthen the primary ring and thus reduce flood scenario probabilities. This paragraph describes the original simple case from Jonkman. This case has been taken over from Jonkman completely as it is a solid base for the more extensive risk optimisation in the next paragraph. Figure 6-15 presents the lay out of the conceptual dike ring in the simple case. The economical value in the studied dike ring is situated particularly in the eastern part of the polder, while the western part is agricultural. The bottom level in the polder decreases in western direction. In the figure the eastern borders of flooded areas for three single flood scenarios are indicated with lines. In Figure 6-16 the flood scenario probability and the economical damage corresponding with a flood scenario is presented.

Figure 6-15: Lay out conceptual dike ring

Scenario Flood scenario probability (beta) Economical damage (billion euro) 1 4.448 20 2 3.893 45 3 3.287 2.5 1 en 2 4.819 50 1 en 3 4.55 27.5 Figure 6-16: Initial situation dike ring area 84

6 Impact of compartmentation on flood risk

The risk in the initial situation (column 0 in Figure 6-18) is determined by multiplying the flood scenario probabilities with their corresponding economical damage and compensating for interest. The risk reduction is achieved in improvement rounds. The procedure is such that in every improvement round the flood scenario with the greatest contribution to the risk is improved. Figure 6-17 presents the development of the flood scenario probabilities due to the improvement rounds.

Improvement round ScenarioDamage0123456 1 20 4.448 4.448 4.353 4.353 4.3 4.829 4.69 2 45 3.893 4.346 4.232 4.646 4.551 4.558 4.888 3 2.5 3.287 3.23 3.672 3.624 4.027 4.026 4.352 1 and 2 50 4.819 5.039 4.936 5.153 5.066 5.012 5.116 1 and 3 27.5 4.55 4.496 4.638 4.591 4.763 4.779 4.847 Ring probability: 3.13 3.13 3.52 3.52 3.846 3.885 4.181 Figure 6-17: Development of flood scenario probabilities (beta) per improvement round

Figure 6-18 presents the development of the flood risk per scenario as a result of the applied improvement rounds. As stated the procedure is such that in every improvement round the flood scenario with the greatest contribution to the risk is improved. When in Figure 6-18 scenario 2 in improvement round 0 (initial situation) has the greatest risk this scenario will be improved in improvement round 1. In these figures can be seen the weakest dike section regarding flood scenario probability does not correspond to the weakest section regarding flood risk.

Improvement round ScenarioDamage0123456 1 20 5.8 5.8 9.0 9.0 11.4 0.9 1.8 2 45 148.6 20.8 34.8 5.1 8.0 7.8 1.5 3 2.5 84.4 103.2 20.1 24.2 4.7 4.7 1.1 1 and 2 50 2.4 0.8 1.3 0.4 0.7 0.9 0.5 1 and 3 27.5 4.9 6.4 3.2 4.0 1.8 1.6 1.2 Total Risk: 246.1 136.9 68.3 42.7 26.6 15.9 6.2 Figure 6-18: Development of net present flood scenario risks in million euro per improvement round

Figure 6-20 indicates the measures and the costs of the measures (see Figure 6-19) applied in the improvement rounds. (O) is a measure to reduce the probability of overtopping (increase in dike height of 0.5 m, while (P) is applied to reduce the probability of piping (thickening top layer of 1 m). The last columns indicate the costs of the measures.

Measure Dike section 1 Dike section 2 Dike section 3 Dike heightening (0.5m) 20 10 15 Thickening top layer (1m) 25 20 - Figure 6-19: Improvement costs per dike section in million euros.

Improvement Measure at Compartment Beta-ring Cost Cumulative Round primary ring measure (million euro) cost 0- -3.130 0 1 2(O) - 3.13 10 10 2 3(O) - 3.52 15 25 3 2(O) - 3.52 10 35 4 3(O) - 3.85 15 50 5 1(P) - 3.89 25 75 6 2 en 3 (O) - 4.18 25 100 Figure 6-20: Improvement rounds at risk optimisation

Figure 6-21 presents the risk as a function of the costs of the measures of Figure 6-20. In the economical optimisation the total costs have to be minimized. The total costs (Ctot) consist of the investments (I) and the present value of the risk (R). The risk is a function of the investments (R(I)). The total costs therefore are a function of the investments.

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CItot ()=+ IRI () (Equation 6-3)

In the optimal situation the total costs are minimal. The optimum can be found as follows [20]: dC() I tot = 0 (Equation 6-4) dI

dR() I 10+= (Equation 6-5) dI dR() I =−1 (Equation 6-6) dI

The economical optimum in Figure 6-21 is situated at the point where the derivative of the risk to the investments is equal to –1. In this example the optimum lays at an investment of 100 million euro, this corresponds with a risk of 50 million and ring probability of beta 3.85.

300 250 200 150 100

Risk (millions) 50 0 0 20406080100120 Investments (millions)

Risk optimization (only strengthening primary ring)

Figure 6-21: Risk as a function of investments in a risk optimisation

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6.5.2 Inclusion of compartmentation measures in a economical optimisation In the previous paragraph only measures that reduce flood scenario probabilities were included in the optimisation. However it is also possible to include measures that reduce the consequences. In the case in the previous paragraph the procedure is such that in every improvement round the flood scenario with the greatest contribution to the risk is improved. In the optimisation method described in this paragraph this procedure remains intact. The difference lays in the fact that in the new optimisation method in every improvement round a choice is introduced in which way risk reduction can be achieved: by reducing the flood scenario probabilities (strengthening primary ring) or by reducing the consequences (compartmentation). The most effective measure should be applied in the improvement round. The here-described procedure is illustrated by means of the same conceptual dike ring as used in Jonkman [20] and in the previous paragraph. For the analysis it is necessary to extend the range of measures from Figure 6-20 with options for the implementation of secondary defences at the locations with a red dotted line indicated in Figure 6-22.

Two situations can be identified in case of implementation of a secondary defence in the system as a measure in the protection against flooding:

1. The construction of a completely new secondary defence 2. The upgrading of a historical secondary defence or an earth embankment

A completely new secondary defence will be significantly more expensive then the upgrading of an historical defence. Both situations will be investigated. For the construction costs and the upgrading costs of secondary defences and also for their impact on the consequences of a flood rough assumptions have been made in this optimisation case. However the purpose of this paragraph is to explain the risk optimisation procedure.

Figure 6-22: Conceptual dike ring with secondary defences

Construction of new secondary defences The procedure is such that the scenario with the greatest contribution to the risk has to be improved. Column 0 in Figure 6-18 shows the scenario with the greatest contribution to the flood risk is scenario 2. There exist two options to reduce the risk of scenario 2:

A. The strengthening of primary dike section 2 (first measure applied in previous paragraph) B. The introduction of a new secondary defence in the eastern part of the dike ring.

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Suppose this new secondary defence always fulfils its water retaining function and has a length of 2 km. Furthermore suppose the secondary defence reduces the consequences of flood scenario 2 from 45 billion euro to 5 billion euro and the consequences of double scenario 1 and 2 to 25 billion euro. The costs of the implementation of a completely new secondary defence in the landscape will be significantly higher than strengthening of the primary defence. The costs of dike strengthening in the previous paragraph correspond to 5 million euro/km [20]. Suppose the new secondary defence costs 20 million euro/km resulting in a total investment of 40 million euro.

The impact of strengthening the primary ring and the impact of a secondary defence on the risk can be plotted as a function of the investments in the measures (left graph in Figure 6-23). The inclination of the lines is a measure for the effectiveness of the measure. In this case the measure strengthening of primary dike section 2 has the steepest inclination and is the most effective measure. Therefore strengthening of primary dike section 2 will be applied in the first improvement round.

300 300 250 250 200 200

150 150

100 100 Risk (millions) Risk (millions) 50 50

0 0 02040600204060 Investments (millions) Investments (millions)

Strengthening primary dike section 2 Strengthening primary dike section 3 Introduction new secondary defence Introduction new secondary defence

Figure 6-23: Strengthening primary dike section versus new secondary defence

After the first improvement round the situation is similar to the case in the previous paragraph as strengthening of the primary dike section proved to be the best option. After updating the changes in the scenario risks due to improvement round 1 scenario 3 turns out to have the greatest contribution to the risk. Again the choice between strengthening the primary ring or implementing a secondary defence has to be made. Despite the implementation of a secondary defence to reduce the consequences of scenario 3 on first sight will not be effective because of the relatively low consequences of scenario 3 still a measure concerning the implementation of a secondary defence is defined to continue the procedure correctly. Suppose the introduction of a secondary defence in the western part of the dike ring (see Figure 6-22) reduces the consequences of scenario 3 from 2.5 billion euro to 1.0 billion euro and the investment costs are 40 million euro. In the right graph of Figure 6-23 the choice between strengthening primary dike section 3 and the introduction of the new secondary defence is presented. Strengthening primary dike section 3 appears to be most effective and will be applied in improvement round 2. The procedure can be continued until the optimal economic situation is reached (at an inclination of –1).

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Upgrading historic secondary defences Now a variation will be presented in which already a historic defence is situated at the eastern part of the dike ring. Suppose the upgrading of this historic defence costs 10 million euro. Now the choice between strengthening of dike section 2 and upgrading the historic defence becomes different (see left graph in Figure 6-24). In this case the upgrading of the historic secondary defence is most effective and will be applied in improvement round 1. After updating the scenario risks the choice for the measure in improvement round 2 has to be made. In the right graph the choice is presented for the dike strengthening of primary dike section 3 or the construction of the new secondary defence in the western part of the dike ring. Strengthening of primary section 3 is most effective etc.

300 300

250 250

200 200

150 150

100 100 Risk (millions) Risk (millions) 50 50

0 0 0204060 0204060 Investments (millions) Investments (millions)

Strengthening primary dike section 2 Strengthening primary dike section 3 Upgrading of historic secondary defence Introduction new secondary defence

Figure 6-24: Strengthening primary dike section versus upgrading secondary defence

Every succession of measures forms an improvement strategy. The optimal improvement strategy is the strategy that results in the greatest reduction of the risk for the lowest investments. The optimal improvement strategy has the steepest downward inclination indicated with the thicker line in Figure 6-25.

Figure 6-25: Investment strategies

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6.5.3 Economical risk optimisation case IJsselmonde In Appendix J the risk optimisation method as described in the previous paragraph is applied at dike ring IJsselmonde. The results of this optimisation are interpreted in this paragraph. Figure 6-26 presents the risk as a function of investments in several measures. The blue line indicates the development of the risk after four investment rounds in which the primary dike sections with the greatest contribution to the flood risk are improved. The green and the red line indicate the choice in improvement round 1 for implementing a secondary defence to reduce the risk of the dominant scenario. The location of this secondary defence is indicated in Appendix figure Y. In the red line also the net present maintenance costs are processed. As can be seen this has little effect and they can be neglected. The black line is an indicator for an inclination of -1. As can be seen significant investments have to done to achieve a small reduction in the flood risk. All measures presented in Figure 6-26 have an inclination flatter than –1, which indicates those measures are not cost-effective. This is largely due to the fact that the failure probabilities at IJsselmonde are already dominated by the impact of the Maeslantkering and the Hartelkering.

0.90 0.80 0.70 0.60 0.50

(Millions) 0.40 0.30

Risk 0.20 0.10 0.00 0 10203040506070 Investments (Millions) Measures strengthening primary ring Measure implementation secondary defence without maintenance costs Measure implementation secondary defence with maintenance costs Example of inclination -1

Figure 6-26: Economical flood risk as function of investments in measures in improvement rounds

The impact of the secondary defence on the flood risk in Figure 6-26 is overestimated, because the introduction of this secondary defence should result in a new definition of the partial dike ring parts (see Appendix H). This means partial dike ring part 6 should have been divided in three new partial dike ring parts. This has not been done resulting in an overestimation of the impact of the new secondary defence. It can be concluded that in this case the implementation of a secondary defence is less effective than dike strengthening.

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6.5.4 Example economical optimisation as a function of two variables The previous paragraphs showed that investments can be done in two kinds of measures in the dike ring to reduce the flood risk. Those investments (I) can consist of measures that reduce the flood scenario probabilities (Pf) and of measures that reduce the consequences (D). In this paragraph a concept is proposed for an economical optimisation as a function of two variables. Therefore a distinction in investments in the primary ring and investments in the secondary defences will be introduced. Investments in the primary ring (IP) result in a reduction of the flood scenario probabilities (see left graph in Figure 6-27) and investments in secondary defences (Is) result in a reduction of the expected economical damage (D) (See right graph in Figure 6-27). This means now two optimisation parameters are present adding an extra dimension to the economical optimisation. The concept first will be described with general mathematical expressions. Then these expressions will be applied in a simple conceptual case. For this case the original economical optimisation of the Delta Committee will be used.

Figure 6-27: Two methods to reduce flood risk

General description concept with mathematical expressions Suppose total investments (I) in the dike ring are a summation of the investments in the primary ring (Ip) and the investments in the secondary defences (Is):

I =+IIP S (Equation 6-7)

In an economical optimisation the optimal situation is found by minimizing the total costs. The total costs (Ctot) consist of investments (I) and the present value of the risk (R). The risk is a function of the investments R(I) [20]:

CItot ()=+ IRI () (Equation 6-8)

As the investments (I) consist of Ip and Is the equation for the total costs can be written as:

CIItot(,) p s=++ I p I s RII (,) p s (Equation 6-9)

As stated in the optimal situation the total costs are minimal. The optimum can be found as follows [20]: dC() I tot = 0 (Equation 6-10) dI()

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Equation 6-10 written as a function of Ip and Is becomes a function of two variables. This means the partial derivatives have to be determined. To find the global minimum of a function of two variables both partial derivatives (to Ip and Is) should equal zero. Figure 6-28 presents both partial derivatives of equation 6-9. Furthermore in Figure 6-28 the partial derivatives are set equal to zero.

Partial derivative of Ctot(Ip,Is) to Ip Partial derivative of Ctot(Ip,Is) to Is

∂∂∂CII(,) I∂I RII ( ) ∂CII(,)∂∂ I∂I RII ( ) tot p s=++ ps p, s =0 tot p s= p++s p, s =0 ∂∂∂∂IIIIpppp ∂∂∂∂IIIIssss

(Equation 6-11) (Equation 6-12)

∂RI(,) I ∂RI(,) I 10+=ps 10+ ps= ∂I p ∂Is

∂RI(,) I ∂RI(,) I ps=−1 ps= −1 ∂I p ∂Is

Figure 6-28: Partial derivatives to Ip and Is

These partial derivatives can be interpreted as follows. Suppose the choice is made only to invest in strengthening of the primary ring (Ip). This means no investments in the secondary ring are made. In this case the economical optimisation only uses the partial derivative to Ip. Optimising the system only via this partial derivative returns the original economical optimisation as presented by Jonkman [20]. However by introducing the new parameter Is that influences the damage (D) of a scenario an extra dimension is introduced in the economical optimisation. Now it becomes possible to optimise the system only by investing in Ip, or by investing only in Is or by investing in both. This will be illustrated with an example based on two simple investment functions for Ip and Is.

Case Delta Committee This example is based on the original economical optimisation of South Holland (by Van Dantzig). However now the total investments (I) are a summation of investments in the primary ring (Ip) and investments in the secondary defences (IS). For the investments in Ip the original investment function (equation 6-16) has been sustained and for the investments in Is a linear damage reduction function (equation 6-18) has been assumed.

Van Dantzig formulated the following economical decision problem. Suppose the probability of exceedance of the sea water level can be described with an exponential distribution:

−−()/hA B Fhh ()=− 1 e (Equation 6-13)

In which: h = Sea water level and h ≥ A [m+NAP] A = Location parameter exponential distribution [m+NAP] = 1.96 m+NAP. B = Scale parameter exponential distribution [m]= 0.33 m.

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The probability of the high water level (h) exceeding the crest height of the dike (hd) becomes:

−−()/hABd Phfd{}>= h e (Equation 6-14)

The sum of the present values of the expected costs of flood damage per year (the risk) can be written as:

D Re= 0 −−()/hABd (Equation 6-15) r '

In which: r’ = Reduced interest rate [-] = 0.015 per year. 10 D0 = Damage that occurs without investments in secondary ring [g]= 2.4⋅10 gulden

Suppose investments (I) to reduce this risk, consist of investments in the primary ring (Ip) and of investments in the secondary defences (Is). The investments in strengthening the primary ring can be written as a linear function of the dike heightening:

I pvd=+⋅IIhh00() − (Equation 6-16)

In which: 8 I0 = Constant costs [gulden] = 1.1⋅10 gulden. 7 Iv = Variable costs [gulden/m] = 4.0⋅10 gulden h0 = Original dike height before heightening [m+NAP] = 3.25 m+NAP

The other way around the dike heightening of the primary ring can be written as a function of investments in the primary ring:

IIp − 0 hhd =+0 (Equation 6-17) Iv

Until now the analysis has followed the analysis of van Dantzig. Now suppose by investing in secondary defences the expected damage of a flood can be reduced. Suppose the expected damage can be written as a linear function of the investments in secondary defences:

DD=−⋅0 cIs (Equation 6-18)

In which: 10 D0 = Damage that occurs without investments in secondary ring [g] = 2.4⋅10 gulden D = Damage that occurs after a certain investment in secondary defence [gulden] c = Factor for effectiveness of investments in secondary defences [-]

The other way around the investments in secondary defences can be written as a function of the damage reduction:

()DD− I =− 0 (Equation 6-19) s c

Because of the introduction of Ip and Is as optimisation parameters the expression for the risk from equation 6-15 changes. The probability of flooding (Pf) is written as a function of Ip 93

6 Impact of compartmentation on flood risk

(instead of hd) and the expected damage becomes a function of Is. This means the risk now can be written as follows:

IIp − 0 −+−()/hAB0 −−()/hABdv I PIbp()⋅ DI () s eDcIeDcI⋅()−⋅ ⋅ () −⋅ RI(, I )==00s = s (Equation 6-20) sp rr'' r '

As stated the total costs (Ctot) consist of the investments and the risk:

IIp − 0 −+−()/hAB0 eDcIIv ⋅−⋅() CII(,)=++ I I 0 s (Equation 6-21) tot p s p s r '

As described previously for the economical optimisation now the partial derivatives to Ip and Is of Ctot are necessary. The partial derivative of equation 6-21 to Ip becomes:

IIp − 0 −+−()/hAB0 1 Iv −⋅()eDcI ⋅−⋅ (0 s ) ∂CIItot(,) p s IB⋅ =+1 V (Equation 6-22) ∂Irp '

The partial derivative of equation 6-21 to Is becomes:

IIp − 0 −+−()/hAB0 Iv ∂CIItot(,) p s ec⋅− =+1 (Equation 6-23) ∂Irs '

As a check the second order mixed partial derivatives are determined, when these are equal the derivation is correct. Both second order mixed partial derivatives arrive at:

IIp − 0 1 −+−()/hAB0 −⋅()ecIv ⋅− ∂∂CIItot(,) p s CII tot (,) p s IB⋅ ==v (Equation 6-24) ∂∂IIps ∂∂ II sp r'

Now these equations will be presented graphically. In this presentation all values of the parameters corresponding with investments in the primary ring have been taken from the economical optimisation of Van Dantzig [34]. The values of the parameters corresponding to investments in the secondary defences are speculative and a linear damage reduction function has been assumed (equation 6-18). Probably a linear function is too simple and a function that better suits the relation should be found. However the purpose of this example is to illustrate the concept of an optimisation with two optimisation parameters is possible. The parameter c in equation 6-18 is a parameter that reflects the impact of Is on the expected damage reduction. Now suppose c = 100, then Figure 6-29 presents the total costs as a 94

6 Impact of compartmentation on flood risk

function of Ip and Is. Figure 6-29 is a graphical presentation of equation 6-21. Figure 6-30 presents the risk as a function of Ip and Is and corresponds to equation 6-20.

Total costs as function of Ip and Is

4.5E+08 4.0E+08 4E+08-4.5E+08 3.5E+08 3.5E+08-4E+08 3.0E+08 3E+08-3.5E+08 2.5E+08 Ctot 2.5E+08-3E+08 2.0E+08 2E+08-2.5E+08 1.5E+08 1.0E+08 1.5E+08-2E+08 7.5E+7 5.0E+07 5.0E+7 1E+08-1.5E+08 0.0E+00 2.5E+7 5E+07-1E+08 0 0-5E+07 Is 1.8E+08 2.0E+08 2.1E+08 2.3E+08 2.4E+08 Ip 2.6E+08

Figure 6-29: Total costs as a function of Is and Ip for c = 100

For a value of Is = 0 (on the Ip axis) the well known original economical optimisation of Van Dantzig is returned. In the Van Dantzig optimisation the possibility of risk reduction by investing in secondary defences is not utilised. However for a value of c is 100 in the damage reduction function (equation 6-18) investments in secondary defences are not necessary as the minimum of the total costs is situated at a value of Is = 0. For a value of c = 100 investments in secondary defences (along the Is axis) will reduce the risk (see Figure 6-30), however the risk reduction is smaller than the investments in the secondary defences resulting in an increase in total costs along the Is axis (see Figure 6-29).

Risk as function of Ip and Is

4.5E+08

4.0E+08 4E+08-4.5E+08 3.5E+08 3.5E+08-4E+08 3.0E+08 3E+08-3.5E+08 2.5E+08 R 2.5E+08-3E+08 2.0E+08 2E+08-2.5E+08 1.5E+08 1.5E+08-2E+08 1.0E+08 7.5E+7 1E+08-1.5E+08 5.0E+07 5.0E+7 5E+07-1E+08 0.0E+00 2.5E+7 0-5E+07 0 Is 1.8E+08 2.0E+08 2.1E+08 2.3E+08 2.4E+08 Ip 2.6E+08

Figure 6-30: Risk as a function of Is and Ip for c = 100

A value of c is 100 in the linear damage reduction function (equation 6-18) would mean investments in secondary defences only result in increasing total costs. Suppose the damage 95

6 Impact of compartmentation on flood risk

reduction can be achieved more effectively. Suppose a value of c is 250 is substituted in the damage reduction function. Figure 6-31 presents the total costs and Figure 6-32 the risk as a function of Ip and Is.

Total costs as function of Ip and Is

4.5E+08 4.0E+08 4E+08-4.5E+08 3.5E+08 3.5E+08-4E+08 3.0E+08 3E+08-3.5E+08 2.5E+08 Ctot 2.5E+08-3E+08 2.0E+08 2E+08-2.5E+08 1.5E+08 1.0E+08 1.5E+08-2E+08 7.5E+7 5.0E+07 5.0E+7 1E+08-1.5E+08 0.0E+00 2.5E+7 5E+07-1E+08 0 0-5E+07 Is 1.8E+08 2.0E+08 2.1E+08 2.3E+08 2.4E+08 Ip 2.6E+08

Figure 6-31: Total costs as a function of Is and Ip for c=250

Of course the original economical optimisation by Van Dantzig at Is = 0 remains the same. Along the Is axis in Figure 6-32 a steeper risk reduction can be seen. As can be seen in Figure 6-31 at a value of c = 250 the risk reduction by investing in secondary defences outweighs the investment costs resulting in a downward slope of the total cost function along the Is axis. However the minimum of the total costs remains situated at Is = 0 as investments in the primary ring remain more effective.

Risk as function of Ip and Is

4.5E+08

4.0E+08 4E+08-4.5E+08 3.5E+08 3.5E+08-4E+08 3.0E+08 3E+08-3.5E+08 2.5E+08 R 2.5E+08-3E+08 2.0E+08 2E+08-2.5E+08 1.5E+08 1.5E+08-2E+08 1.0E+08 7.5E+7 1E+08-1.5E+08 5.0E+07 5.0E+7 5E+07-1E+08 0.0E+00 2.5E+7 0-5E+07 0 Is 1.8E+08 2.0E+08 2.1E+08 2.3E+08 2.4E+08 Ip 2.6E+08

Figure 6-32: Risk as a function of Is and Ip for c = 250

The optimisation only via Ip (thus Is = 0), which was done by Van Dantzig results in a minimum on the Ip axis. Theoretically an optimisation only via Is (Ip = 0) could result in a minimum on the Is axis. In principle the global minimum of the total costs will be optimal. The 96

6 Impact of compartmentation on flood risk

global minimum of the total costs is the point where both partial derivatives equal zero. In Figure 6-29 and Figure 6-31 no global minimum where both partial derivatives equal zero can be seen. The minimum of the total costs is situated at Is =0 indicating that for these cost functions (equation 6-16 and equation 6-18 for c = 100 and c = 250) investing only in the primary ring is most effective.

In this example a linear damage reduction function (equation 6-18) has been chosen which means that when investing enough in Is the damage could be reduced to zero. In this example it has no use to apply higher values of c then 250, as the linear damage reduction function would arrive at negative values of the damage. This is not realistic. A more reasonable assumption could be that the damage could be reduced to a certain minimum value. However the value of such a minimum value is unknown and also the path towards such a minimum value is unknown, see Figure 6-33 in which the linear damage reduction function and two possible damage reduction functions with a minimum value of the damage are presented.

When looking at Figure 6-29 and Figure 6-31 it becomes clear that investing in secondary defences only would become effective when it is possible to achieve significant damage reduction for relatively low investments in the secondary ring as for example could possible be achieved by the damage reduction function with the sharpest inclination at Is = 0 in Figure 6-33.

Figure 6-33: Different paths to unsure minimum value

The form of the damage reduction function should be based on the actual situation in South Holland. Furthermore if this concept would be made acceptable per flood scenario in the economical risk optimisation from the previous paragraphs further research is required into how effectively the damage of a possible flood could be reduced by investing in secondary defences.

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6 Impact of compartmentation on flood risk

6.5.5 Qualitative analysis In this chapter some remarks are placed at aspects of the compartmentation problem that deserve further attention.

Cost-effectiveness Despite the fact in paragraph 6.5.2 and 6.5.3 rough assumptions of the costs of constructing a secondary defence have been made and in paragraph 6.5.4 rough assumptions about the effectiveness with which a secondary defence can prevent flood damage have been made, compartmentation-measures only seem cost-effective under special system characteristics.

As long as weak spots occur in the primary ring the risk can be reduced with relatively effective investments in the primary ring. It is difficult for compartmentation measures to compete, as a significant reduction in dike section failure probabilities is easier to achieve than a similar reduction in consequences. Heightening a primary dike section by 0.5 meter results in a dike section failure probability that relatively fast is an order lower, while implementing a secondary defence that reduces the consequences that much would be very expensive. In case all dike sections in a primary ring have more or less the same failure probability an integral dike strengthening is necessary to reduce the flood risk further. An integral dike strengthening means the complete primary ring has to be strengthened, which is very expensive (See Figure 6-34). As an alternative for integral dike strengthening the implementation or upgrading of a secondary defence system could be an option. In an economical risk optimisation these measures only will be cost-effective when the risk reduction is greater than the investments (steeper than –1). Therefore integral dike strengthening and the implementation or upgrading of a secondary defence system has a greater probability to become cost-effective in a dike ring with a relatively low safety standard and a great economical value as in such a dike ring it is easier to create a significant risk reduction for the same investment. However even then it is quite possible the risk reduction is not compensated by the investments.

Figure 6-34: Integral strengthening primary ring

Consequence reducing potential To become cost-effective compartmentation measures should at least result in a significant reduction of consequences. For example in the case in the paragraph 6.5.3 the eastern secondary defence was very effective in reducing the consequences, as it prevents not only the city from flooding, but also the complete conceptual dike ring (because of the downward slope). Seen from the consequence reducing potential it can be substantiated a secondary defence system in the form of a ring (see Figure 6-35) is more effective than a secondary defence system in the form of a cross (in case the value is concentrated in the centre of the ring). This statement is confirmed by the results of a study towards the impact of the secondary defences in the Hoeksche Waard in which the influence of various secondary defence layouts on the flood risk was investigated [40]. 98

6 Impact of compartmentation on flood risk

Figure 6-35: Secondary defence system in form of ring versus cross

Economical damage versus casualties As was shown in paragraph 6.4.1 the consequences as a result of compartmentation are not univocal. Compartmentation can have a positive impact on the expected economical damage; while at the same time there can be a negative impact on the expected number of casualties. By including the possibility of evacuation in the analysis the negative impact on the number of casualties could be reduced. However the discrepancy between economical damage and number of casualties will remain and should be included in the analysis. A possibility could be by valuating the cost of a human life, however this is a difficult topic.

Failure of the secondary defences There exists a possibility also the secondary defence fails in case the primary defence fails. In this case the damage is not prevented, it is even possible the consequences increase as the water first causes great damage in the first compartment as a result of great water levels and then continues causing losses in the second compartment (see state C in Figure 6-7). Failure of the secondary defences can be included in the flood risk analysis by defining the following event tree.

Figure 6-36: Event tree for state of secondary defence

Failure of the secondary defence can be described with a conditional probability (Ps). The condition corresponds to failure of the primary defence. In this case the flood risk can be defined by:

RP=⋅⋅f ((1)) PDs failure +−⋅ PD S functioning (Equation 6-25)

In which:

Dfailure = Damage that occurs in case of failure of the secondary defence [Euro]

Dfunctioning = Damage that occurs in case of a functioning secondary defence [euro]

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7 Conclusions and recommendations

7 Conclusions and recommendations

In this chapter the conclusions (paragraph 7.1) and the recommendations (paragraph 7.2) of this research are presented.

7.1 Conclusions

The objective of this research was to assess the flood risk of dike ring IJsselmonde using flood scenario probabilities and flood simulations of these scenarios in a case study. Furthermore the objective was to study the impact of compartmentation as a measure to reduce the flood risk. The conclusions are categorized per sub-objective as they were described in paragraph 1.4:

Sub-objective 1: Determination of flood scenario probabilities.

- The combined ring failure probability for the failure mechanism wave overtopping and the failure mechanism damage to the revetment and erosion of the dike body is calculated to be 2.99 E-06 per year (approximately 1 / 334000 per year). - The presence of the Maeslantkering and the Hartelkering in the tidal river area has a large influence on the failure probabilities. - The implementation of the Maeslantkering and the Hartelkering in the tidal river area results in two possibilities to get extremely high river water levels at dike ring Ijsselmonde: - Extremely high water levels at sea in combination with failure of the storm surge barriers (incorrect open barriers). - Extremely high water levels at sea in combination with closure of the storm surge barriers and high discharges at the rivers (correctly closed barriers). - In the list of dominant flood scenarios that contribute for more than 99% to the ring failure probability (see Table 3-5) flood scenarios with an incorrect open barrier as well as flood scenarios with correctly closed barriers are present.

Sub-objective 2: Determination of corresponding flood simulations.

- The expected economical damage corresponding with the dominant flood scenarios ranges from 5 million euro to 8.4 billion euro dependent on the breach location or whether the flood scenario is a single or a multiple scenario (see Figure 4-27). - The expected number of casualties corresponding with the dominant flood scenarios ranges from 0 to 1293 casualties dependent on the breach location or whether the flood scenario is a single or a multiple scenario (see Figure 4-27). - The water level development at a breach location for a flood scenario with incorrect open barriers is different compared with the flood scenario with correctly closed barriers. River water levels in case of correctly closed barriers remain high longer often resulting in greater losses. - Secondary defences and other earth embankments (roads / railways) have a significant impact on the development of a flood.

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7 Conclusions and recommendations

Sub-objective 3: Determination of flood risk.

- The flood risk concerning casualties for the failure mechanism wave overtopping and the failure mechanism damage to the revetment and erosion of the dike body is calculated to be 0.0017 casualties per year (see paragraph 5.1). - The economical flood risk for the failure mechanism wave overtopping and the failure mechanism damage to the revetment and erosion of the dike body is calculated to be approximately 12000 euro per year (see paragraph 5.2). - The calculated group risk for dike ring IJsselmonde exceeds the standard for chemical installations applied in the external safety domain (presented in a FN- curve in Figure 5-5). - The presence of the Maeslantkering and the Hartelkering results in extremely low flood scenario probabilities. IJsselmonde therefore is a very special dike ring and is not representative for other dike ring areas, where the flood scenario probabilities are expected to be significantly higher. Due to the great population density and the enormous protected value at IJsselmonde the consequences immediately are very extreme if a breach occurs. However at IJsselmonde even the extreme consequences are dominated by the flood scenario probabilities resulting in an extremely low flood risk.

Sub-objective 4: The impact of compartmentation

- Conditions for effective compartmentation in dike ring areas are less favorable compared to the conditions for compartmentation in ships and high-rise buildings. - The impact of compartmentation can be described with the following characteristics: the distribution of flood scenario probabilities over the primary defences, the hydraulic loads on a functioning secondary flood defence, the reliability of the secondary defences and the spatial distribution of value over the compartments. - Compartmentation can result in a reduction of the expected economical damage and the expected number of casualties of a flood scenario (see paragraph 6.4.1). However it is also possible compartmentation results in a reduction of the expected economical damage and simultaneously results in an increase of the expected number of casualties of a flood scenario. The increase in expected number of casualties is caused by greater water depths and higher flooding velocities in the flooded compartment. In this case the increase of the number of casualties in the flooded compartment outweighs the prevention of casualties in neighboring compartments. Of course a change in expected economical damage and expected number of casualties can be related directly to the change in economical flood risk and risk of casualties. - The previous conclusion can be extended to the flood risk averaged over multiple flood scenarios. Compartmentation can result in a reduction of the economical risk and the risk of casualties averaged over all flood scenarios that could possibly influence a secondary defence. However it is also possible the economical flood risk averaged over multiple scenarios decreases, while the risk of casualties increases (see paragraph 6.4.2). - The economical risk optimisation is an effective method to present the impact of measures on the flood risk. In this thesis a method is introduced that describes how compartmentation measures or in general all measures that reduce the consequences of a flood can be included in an economical risk optimization (see paragraph 6.5.2). The new method makes it possible to compare the effect of investments in the primary ring with the effect of investments in secondary defences.

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7 Conclusions and recommendations

- Compartmentation can reduce the economical flood risk, however it probably is not the most effective measure as conditions for an effective risk reduction due to investments in secondary defences are less favorable compared to risk reduction by investments in the primary ring. By strengthening a primary dike section a flood scenario probability relatively fast is reduced by an order while reducing the consequences of a flood with an order by investing the same amount in secondary defences in general is harder to accomplish. - In this thesis (see paragraph 6.5.4) a concept is proposed that separates the total investments (I) in investments in the primary ring (Ip) and investments in secondary defences (Is). This distinction makes it possible to extend the original economical optimisation in Ip of Van Dantzig with an extra optimisation parameter Is. This results in an extra dimension in the optimisation problem conceptually making it possible to compare the effectiveness of a wider range of possible protection strategies, as investments in secondary defences can be included.

7.2 Recommendations

The recommendations are divided in recommendations concerning the method to determine the flood risk and recommendations concerning compartmentation:

The calculated flood risk is based on a great number of variables, simplifications and schematizations and therefore only is an approximation of the actual flood risk. As a result of this research the following recommendations are formulated to improve the calculation method as to be able to give a better approximation of the actual flood risk in the future:

- To achieve a complete view of the flood risk of IJsselmonde it is recommended to extend the calculation with the failure mechanisms piping, instability of the inside slope and all mechanisms concerning civil engineering structures. - The presence of the Maeslantkering and the Hartelkering is an important factor in the determination of the flood risk. It is recommended to investigate whether the failure probability of the Maeslantkering and the Hartelkering that is used in the calculation model is correct. - It is recommended to improve the piping model that is applied in the failure probability analysis. - Investigate the impact of the closure of the Maeslantkering and the Hartelkering on the system behavior in the tidal river area. - As to now the Scenariotool gives as end result a combined flood scenario probability. The contribution of the flood scenario probabilities per state (incorrect open, correctly closed etc) to the combined flood scenario probability is not clear. It is recommended to extend Scenariotool such that is capable of including the flood scenario probabilities per state of the barrier in the output. - The results of the expected number of casualties are very sensitive for flooding velocities. It is recommended to further investigate the influence of the flooding speed on the number of casualties. - It is recommended to improve the breach growth model. - The consequences of recent hurricanes in New Orleans learn not all consequences are foreseen. For example the failure of gas pipes occurred on a large scale causing buildings to burn even when flooded. Furthermore the effects of chemical substances washing through the city and the temporary closure of oil manufacturing companies on the global economy turned out to have a significant impact. It is recommended to investigate what would the impact of these and similar “forgotten” consequences in the Dutch situation. - After the storm set up has subsided water levels return to normal tidal variations. At low water the flow direction in the breach is reversed. Relatively fast after the 102

7 Conclusions and recommendations

subsidence of the storm set up slack water occurs. At slack water efforts could be made to close the breach. If these efforts could succeed in the first slack water the extent of the consequences could be somewhat reduced. It is recommended to investigate the impact of these efforts. - It is recommended to include the effect of evacuation in the flood risk analysis.

The recommendations concerning compartmentation are as follows:

- It is recommended to investigate the strength of secondary defences under the hydraulic loading that occurs in case of a flood. Therefore the behavior of secondary defences could be included in a failure probability analysis. Therefore the concept of conditional failure of a secondary defence could be used. - It is recommended to further investigate the impact of secondary defences on the expected economical damage and the expected number of casualties and the discrepancy between them. In this analysis also the possibility should be included that a breach in the secondary defence occurs after the first compartment is flooded completely and then continues to cause damage in the second compartment resulting in extra losses. - It is recommended to use the economical risk optimisation in the assessment of risk reducing measures. The economical risk optimisation is a very clear method to present the effect of measures on the flood risk and is very suitable to compare the effectiveness of flood risk reducing measures, whether they reduce the consequences of a flood scenario or the flood scenario probabilities. - It is recommended to do further research into system configurations in which compartmentation could be cost-effective.

103

References

104

References

References

[1] Technical Advisory Committee on Water Defences (TAW), Fundamentals on water defences, TAW, Delft, 1998.

[2] Technical Advisory Committee on Water Defences (TAW), Van Overschrijdingskans naar overstromingskans, TAW, Delft, 2000.

[3] Grashoff, P.S., Gebruikershandleiding PC Ring V4.3, TNO, Delft, 2004.

[4] Vrouwenvelder, A.C.W.M., Steenbergen, H.M.G.M., Gebruikershandleiding PC Ring V4.0, TNO, Delft, 2003.

[5] Vrouwenvelder, A.C.W.M., Steenbergen, H.M.G.M., Theoriehandleiding PC Ring Deel A: Mechanismebeschrijvingen V4.0, TNO, Delft, 2003.

[6] Vrouwenvelder, A.C.W.M., Steenbergen, H.M.G.M., Theoriehandleiding PC Ring Deel B: Statistische modellen V4.0, TNO, Delft, 2003.

[7] Vrouwenvelder, A.C.W.M., Steenbergen, H.M.G.M., Theoriehandleiding PC Ring Deel C: Rekentechnieken V4.0, TNO, Delft, 2003.

[8] Projectbureau VNK, Dijkringrapport 16: Rekenresultaten overstromingskansen (concept), DWW, Delft, 2003.

[9] Diermanse F., Thonus B., Lammers I., den Heijer F., De veiligheid van Nederland in kaart: Inventariseren en inbouwen van hydraulische randvoorwaarden in PC Ring , DWW, Delft, 2003.

[10] Directoraat – Generaal Rijkswaterstaat, Hydraulische Randvoorwaarden 2001 Voor het toetsen van primaire waterkeringen, DWW, RIZA, RIKZ, Delft, 2001.

[11] Beijersbergen J.A., Rapportage veiligheid dijkringgebied 17 Ijsselmonde, Provincie Zuid-Holland, Den Haag, 1999.

[12] Geodelft, Schematisering en gegevensverzameling IJsselmonde en Pernis in het kader van VNK, Delft, 2004.

[13] Kuijper, H.K.T., Vrijling, J.K., Probabilistic approach and risk analysis, TU Delft, Delft, 1998.

[14] Manen van S.E. et al, PiCasO (Pilot Case Overstromingsrisico (part 1 to 6), Bouwdienst Rijkswaterstaat, Delft, 2001.

[15] Tonk A., Kolen B., Overstromingsmodel IJsselmonde, HKV lijn in water, Lelystad, 2005.

[16] WL/ Delft Hydraulics, Manual Delft-1D2D Sobek Overland Flow Module Version 2.0, Delft 2000.

[17] Verheij, H.J., Formula Verheij-vdKnaap: Modification breach growth model in HIS-OM, WL/| Delft Hydraulics, Delft 2002.

105

References

[18] Huizinga H.J., Dijkman M., Barendrecht A., Waterman R., Gebruikershandleiding HIS-SSM, DWW, Delft 2004.

[19] Holterman S., Brinkhuis-Jak M., Cappendijk-de Bok P., Wouters K., Schade na een grootschalig overstroming, DWW, Delft, 2003.

[20] Jonkman S.N., Overstromingsrisico’s: Een onderzoek naar de toepasbaarheid van risicomaten, afstudeerrapport TU Delft, Delft, 2001.

[21] Snijders W., Investigation: The Oude Maas, prospects for natural features, an approach based on functional use, Provincie Zuid-Holland, Papendrecht, 1999.

[22] Projectbureau VNK, Schematisering en gegevensverzameling van dijken en duinen, Handleiding ten behoeve van de bepaling van overstromingskansen van dijkringen, DWW, Delft, 2002

[23] McGuire J.H., Fire and the Compartmentation of Buildings, CBD-33 Canadian building digest, 1962.

[24] Baars Van S., Kuijper H.K.T., Handboek Constructieve Waterbouw, Collegedictaat Constructieve Waterbouw, TU Delft, Delft 2002.

[25] Voortman H.G., Risk-based design of large-scale flood defence systems, TU Delft, Delft 2002.

[26] Egmond van N.D., Risico’s in bedijkte termen, Milieu- en Natuurplanbureau (MNP) van het Rijksinstituut voor Volksgezondheid en Milieu (RIVM), Bilthoven, 2004.

[27] CUR onderzoekscommissie “risico analyse” (E10), Kansen in de Civiele techniek, CUR, 1997

[28] Horst ten W.L.A., The safety of dikes during flood waves, Afstudeerrapport TU Delft, Delft, 2005.

[29] Vermijmeren P., Gevolgen van overstromen, een onderzoek naar maatregelen ter reductie van Overstromingsschade, Afstudeerrapport TU Delft, 2002.

[30] Thonus B.I., Investeren om te reduceren, een probabilistisch model waamee het verband tussen de investeringskosten en een overstromingskansreductie kan worden bepaald, Afstudeerrapport TU Delft, Delft 2000.

[31] Baan P., Spankrachtstudie: kosten van maatregelen, RIZA and WL/ Delft Hydraulics, Delft, 2002.

[32] Thonus B.I., Gebruikershandleiding Scenariokans Versie 1.0, HKV lijn in water, DWW Delft, 2004.

[33] Thonus B.I., Duits M.T. Waterstandsverloop benedenrivieren, HKV lijn in water, DWW, Delft, 2002.

[34] Noortwijk van J.M., Kok M., Thonus B.I., Overzicht van methoden voor kosten-baten- analyse voor maatregelen ter beperking van overstromingsrisico’s, HKV lijn in water, DWW, Delft, 2005.

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[35] Jonkman S.N., Kok M., Vrijling J.K., Economic optimisation as a basis for the choice of flood protection strategies in the Netherlands, HKV lijn in water, TU Delft, DWW, Delft, 2004.

[36] Ebregt J., Eijgenraam C.J.J., Stolwijk H.J.J., Kosteneffectiviteit van maatregelen en pakketten: Kosten-batenanalyse voor Ruimte voor de Rivier deel 1 en 2, CPB, Den Haag, 2005.

[37] Verhaeghe R.J., Plan and Project evaluation (impact assessment methods), Collegedictaat TU Delft, Delft, 2002.

[38] Gemeente Rotterdam, Rotterdam Waterstad 2035, Waterschap Hollandsche Delta, Hoogheemraadschap Schieland en de Krimpenerwaard, Rotterdam, 2005.

[39] Vrijling J.K., Gelder van, P.H.J.A.M., Probabilistic design in hydraulic engineering, Collegedictaat TU Delft, Delft, 2002.

[40] Meer van der M.T., Onderzoeksrapport secundaire waterkeringen Hoeksche Waard, Fugro, Nieuwegein, 1997.

[41] Knoeff J.G., Effectiviteit tweede waterkeringen, GeoDelft, Delft, 2002.

[42] VNK, Overstromingsrisico dijkring 14, DWW, Delft 2005.

Software

PC Ring, version 4.3 Sobek rural, version 2.09 Scenariokans, version 1.1

107

Appendices

Appendices

108

Appendices

A. Dike ring areas in the Netherlands

The figure presents the division in dike ring areas in the Netherlands with its accompanying safety standard. Dike ring 17 IJsselmonde is situated near Rotterdam.

Appendix figure A: Division in dike ring areas

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Appendices

B. Schematization of dike sections

Appendix figure B presents the division in and the length of these dike sections. Graphs and photos of the profiles of these dike sections are presented on the following pages.

Dike Length Dike Length Section (m) Section (m) 1 117 38 706 2102039696 3148140797 4 270 41 495 5 427 42 395 6124043837 7254044226 810714528 9 350 46 2676 10 267 47 411 11 884 48 200 12 800 49 600 13 200 50 100 14 1750 51 700 15 300 52 400 16 400 53 350 17 450 54 1392 18 350 55 158 19 551 56 500 20 978 57 1499 21 1671 58 466 22 500 59 685 23 1500 60 348 24 101 61 1100 25 401 62 1100 26 398 63 595 27 601 64 1605 28 1554 65 700 29 2148 66 1400 30 800 67 550 31 900 68 1261 32 2999 69 489 33 501 70 3994 34 1097 71 302 35 702 72 283 36 2000 73 218 37 500 --

Appendix figure B: division in dike sections

110

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Dike section profiles:

111

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112

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113

Appendices

114

Appendices

115

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116

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117

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Appendix figure C: Graphs of dike profiles

118

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Dike section pictures:

Dike section 5 Dike section 11 Dike section 12

Dike section 20 Dike section 23 Dike section 24

Dike section 37 Dike section 39 Dike section 40

Dike section 51 Dike section 66 Dike section 70 Appendix figure D: Some pictures of dike sections

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C. PC-Ring calculation lay-out

The failure probability of dike ring areas due to failure of a dike section can be determined with PC-Ring. PC-Ring calculates the failure probability of a series of water defences and the contribution of each element and / or each parameter to this probability. To determine the failure probability of a dike ring area PC-Ring uses the calculation scheme as depicted in Appendix figure E.

Appendix figure E: Calculation scheme PC-Ring

Several failure mechanisms can cause a dike section to fail. Appendix figure H gives the fault tree for failure of dike section. Here after the calculation steps in the calculation scheme will be described:

Step 1: The first step is to determine the failure probability of a dike section for one wind direction, for one tide, due to one (partial) failure mechanism. For the calculation of the failure probability due to on (partial) failure mechanism the following input is required: 1. A model describing the failure mechanism and its corresponding Limit State Function 2. Strength parameters of the dike section 3. Load parameters applied at the dike section 4. Probabilistic parameters applied at the dike section

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Ad 1: A description of the failure mechanism is given in paragraph 3.1.2 and the corresponding Limit State Functions are described in Appendix D.

Ad 2 and 3: The resistance and load parameters of the dike section consist of: - Geometrical data: slope, profiles (See Appendix B), orientation, fetch, etc. - Material properties: weight, shear stresses, cohesion, etc. - Hydraulic loading: waves, water level, duration, etc.

Ad 4: The probabilistic parameters mainly consist of: - Mean value and standard deviation of a random variable - Spatial correlation within a dike section - Correlation in time

With the help of several calculation techniques (FORM, Directional Sampling) the failure probability of a dike section for one wind direction, for one tide, due to one (partial) failure mechanism can be determined based on the above described input parameters. A brief explanation of FORM and Directional Sampling is given on the next page and a more extensive explanation is given in [7].

Step 2: The second step is to determine the failure probability of a failure mechanism due to several partial failure mechanisms. For example the failure mechanism overtopping can be caused by erosion of the inner slope or saturation. To determine the failure probability due to overtopping based on the two partial failure mechanisms the Hohenbichler-Rackwitz method is applied. The Hohenbichler-Rackwitz method is a general method to approximate the failure probability of a system. In PC-Ring the Hohenbichler-Rackwitz method is only used for the calculation of the probability:

PF()=<∩< P{ Z12 0 Z 0}

This formula indicates the failure of a parallel system of two elements. For a detailed description to determine this probability is referred to [7].

Step 3: In the third step the failure probabilities due to one failure mechanism for all wind directions are combined. Also for this procedure the Hohenbichler-Rackwitz method is used.

Step 4: The fourth step is to determine the failure probability due to one failure mechanism for one dike section for the total regarded period. The Borges castanheta model is used to transform the failure probability for one tide into a failure probability for the total regarded period. For the functioning of the Borges Castanheta model is referred to [6].

Step 5: In the fifth step the failure probabilities for all failure mechanisms and all dike sections can be determined by combining the various failure probabilities. The underlaying calculation model is again the Hohenbichler-Rackwitz method. However it is used in a different way now as the dike ring can be referred to as a serial system. The failure probability of a serial system of two elements can be written as:

121

Appendices

PF( )=<∪<=<+<−<∩< PZ (12 0 Z 0) PZ ( 1 0) PZ ( 2 0) PZ ( 12 0 Z 0)

The first two terms are already determined in a previous step and the last term can be solved with Hohenbichler-Rackwitz method resulting in the failure probability of a serial system of two elements. In case more than two elements are present in the serial system the procedure is to combine two elements into one “equivalent replacing element”. The original number of elements (n) than has been reduced with one element to (n-1). When repeating this procedure the whole system is winded up resulting in one element and one dike ring failure probability. In the case of IJsselmonde this procedure has been executed for three states of the barriers and then summed to arrive at an overall failure probability. For a detailed description to determine this probability is referred to [7].

Calculation techniques Under step 1 it was stated there are various calculation techniques to determine the failure probability of a dike section for one wind direction, for one tide, due to one (partial) failure mechanism: FORM, SORM, Directional sampling, numerical integration etc. Each calculation strategy has advantages and disadvantages. Therefore a short description of the characteristics of the calculation techniques that are applied in this research (FORM and directional sampling) will be given. For a more detailed description of (all) calculation techniques is referred to [7].

- FORM (First order reliability method): FORM transforms all stochastic functions and the Limit State Function to standard normal distributed space (U-space). The failure probability is determined by the position of a design point. The design point is the point on the Limit State Function (Z=0) with the largest contribution to the failure probability. In U-space this point has the smallest distance to the origin. With a minimization procedure the design point can be found. Often a small amount of iterations is necessary to find the design point, which makes FORM a fast method.

u2

Design Point Z < 0 ud,2 = - α2 β

Z = 0

ud,1 = - α1 β u1

Appendix figure F: Definition design point

A disadvantage of FORM is that sometimes no convergence takes place. In a number of cases the Limit State Function is curved in such a way the iteration process doesn’t convert to a definitive value. FORM can’t find a solution in such a case and another calculation technique should be used. Furthermore the results are inaccurate when the Limit State Function is strongly curved. FORM determines the failure probability by means of a linearization of the Limit State Function in the design point. When the Limit State Function is curved strongly the approximation with a linearization is insufficient. Furthermore sometimes a local minimum is found instead of a global minimum. In such a case FORM calculates an inaccurate design point. By executing the iteration process with different initial values

122

Appendices

(starting point of the iteration process) a control exists that checks the occurrence of a local minimum.

- DS (Directional sampling): Directional Sampling is a calculation technique quite similar to a Monte-Carlo analysis. Random drafts are done for every stochastic function. The failure probability can be determined by calculating the frequency of the samples in the failure domain (Z < 0). The number of samples determines the accuracy of the calculated failure probability. More samples means more accuracy. When calculating small probabilities many samples are necessary for an accurate approximation. Computer times are significantly higher than for a FORM calculation. Another disadvantage is the lack of a design point. This disadvantage is overcome be combining introducing the technique DS+FORM in which DS calculates the failure probability for one cross-section and the FORM method is used for determination of the design point. The design point then is used for the rescaling of the failure probability.

1000000

NI MC 100000 β=4 DS 10000 MC β=3 DS 1000 MC DS β=2

100 number of samples of number

10 0 20 40 60 80 100 120 number of variables Appendix figure G: Relation between number of stochastic functions and number of samples

For the failure probability analysis of IJsselmonde the following calculation strategy has been followed: - First calculations with FORM have been made for two different initial values (different starting points of the iteration process) to detect the occurrence of local minima. - Calculations with DS (5000 samples) have been made in case of differences between both FORM-calculations. 5000 samples is insufficient for an accurate calculation, but it gives an indication which one of the FORM calculations is correct. - To verify the results design point analyses haven been executed. See also appendix E.

123

Appendices

D. Failure mechanisms This appendix describes the models used to describe the failure mechanisms used in the calculation of the failure probability of a dike section. Structural failure of a dike section can be described as presented in the fault tree in Appendix figure H. Calculations have been made for the failure mechanisms (Wave) overtopping, damage to revetment and erosion of the dike body and piping. For these mechanisms the Limit State functions used in the PC- Ring calculations will be discussed briefly. The remaining mechanisms will not be discussed here. The text in this appendix is based on Part A: Description of the failure mechanisms of the PC-Ring manual [5].

Appendix figure H: Fault tree structural failure dike section

Overtopping / Wave overtopping In the failure mechanism overtopping / wave overtopping the dike fails due to great quantities of water running over the dike crest. Failing occurs when the quantities of water overtopping the dike are greater then that what the inner slope can endure. When the wave height is less then 1 mm this failure mechanism is called overtopping, otherwise it is called wave overtopping. Overtopping occurs when offshore wind is present or no wind at all. Two sub failure mechanisms have been implemented in PC-Ring to describe the failure of the inner slope: erosion of the inner slope and saturation. A dike section fails if one of these mechanisms occurs, so in the fault tree a ‘if’-statement is shown. In this research calculations have been made with PC-Ring wave overtopping model 1 in which no use is made of residual strength (time to erode the top clay layer) and the sub failure mechanism saturation (which therefore is not described here).

124

Appendices

Appendix figure I: overtopping

Sub failure mechanism erosion of the inner slope due to wave overtopping: In case of wave overtopping the dike fails when the combination of overtopping due to water level and waves is larger then the inner slope can withstand. Erosion starts, a breach starts to grow and large quantities flow into the hinterland. The load in this model is formed by the wave overtopping discharge qo. The strength of the dike is formed by the critical discharge qc at which the inner slope fails. The Limit State function is described as:

Z =−mqqc c mq qo o/ P t

This Limit State Function contains two model factors mqc and mqo that describe the uncertainty in the models that determine qc and qo. Pt takes into account the part of the time that overtopping occurs to cope with the pulsating character of wave overtopping. In case of overtopping Pt is set to 1. The occurring overtopping discharge qo is determined according to Van der Meer. The critical wave overtopping discharge qc can be entered directly or can be determined with a model for the strength of grass in PC-Ring. In this research calculations have been made with PC-Ring wave overtopping model 1 in which the critical wave overtopping discharge qc is entered directly.

Sub failure mechanism erosion of the inner slope due to overtopping: In case of offshore wind or waves smaller than 1mm the sub failure mechanism overtopping is used. In this research calculations have been made with PC-Ring wave overtopping model 1. The Limit State Function for overtopping in model 1 is as follows:

Z =−hhd

In which hd is the crest level of the dike and h is the local outside water level. By applying this Limit State Function no use is made of the residual strength of the grass on the inner slope. To cope with the residual strength of grass a model that describes failure when the local outside water level h exceeds the critical crest level of the dike hkd should be used. In such a case the Limit State function would become:

Z =−hhkd

In which hkd is the critical crest level of the dike and h is the local outside water level. The critical crest level is the sum of the crest level of the dike hd and a critical height height difference Δhc. The critical height difference is a function of the critical overtopping discharge qc. Using the concept of complete overflow the relation between qc and Δhc is:

125

Appendices

5 1 24 3 vkc 3,8 qghcc=⋅⋅Δ=0, 6 3 and: vfcg= 10 4 (1+ 0, 8 logt ) 125tanαi e

In these formulas g is the gravitational acceleration, k is the roughness factor according to

Strickler, αi is the angle of the inner slope, vc is the critical flow velocity at which after a time te failing of the grass on the inner slope occurs. The Limit State function in such a can be described as:

q2 Z =hhhhhh −=+Δ−=+3 c − h kd d c d 0.36g

Damage to revetment and erosion of the dike body In the failure mechanism damage to the revetment and erosion of the dike body wave attack damages the revetment after which the cross-section of the dike is reduced due to erosion. A dike with a grass revetment fails when the time needed to damage the grass revetment tRT and to erode the rest of the dike body tRK+tRB is shorter than the duration of the storm tS. In case of a grass revetment the Limit State function can be described as:

Z =++−ttttRT RK RB S

In which:

dw 0, 4⋅⋅LcK RK 0, 4 ⋅ LcBRB⋅ tRT = and tRK = 22 and tRB = 22 Eg rH⋅ S rH⋅ s in which:

22 rH⋅ S Eg = cg

In these formulas dw is the depth of the grass roots, Eg is the velocity of erosion of the grass revetment, r is the reduction factor for the wave angle, HS is the wave height, LK is the width of the clay cover layer, cRK is a factor representing the erosion sensitivity of the clay cover, LB is the width of the dike body and cRB is a factor representing the erosion sensitivity of the dike body.

Appendix figure J: Damage to revetment (left), piping (right)

126

Appendices

Uplifting and piping In the failure mechanism uplifting and piping the dike fails due to washing away of sand from under the dike. If this mechanism occurs the pressure of the water firstly lifts up the if present impermeable top layer, after which pipes start to develop which transport the sand from under the dike. The complete failure mechanism consists of two sub failure mechanisms. Failure occurs when for both sub failure mechanisms the loads are higher then the strength. In a fault tree this is indicated with a ‘AND’-statement.

Sub failure mechanism uplifting: In the sub mechanism uplifting the pressure of the water lifts up the impermeable clay top layer. The pressure the top layer just can withstand can be denoted with a critical water level. The top layer lifts up if the difference between the local outside water level h en the inside water level hb exceeds the critical water level hc. The Limit State function is described as:

Z =−mh0 ch m() h − h b

This Limit State function contains two model factors m0 and mh. The model factor m0 represents the uncertainty in the determination of the critical water level for uplifting. The model factor mh represents the amount of damping. The critical water level hc is a function of the volumetric weight of the wet top layer γwet , the volumetric weight of water γw and the thickness of the top layer d:

γ wet−γ w hdc =>0 γ w

Sub failure mechanism piping: In the sub mechanism piping pipes start to develop as the pressure of the water level outside increases. The pressure the sand layer just can withstand can be denoted with a critical water level. The dike will fail due to piping when the difference between the local outside water level h and the inside water level hb reduced with a part of the vertical seepage length exceeds the critical water level hp. If the difference is somewhat smaller, there may develop pipes, but these pipes do not lead to failure of the dike. The Limit State function is described as:

Z =−−−mhpp() h0.3 d h b

This Limit State function contains the model factors mp. This factor mp represents the uncertainty in the determination of the critical water level for piping. The critical water level hp is described with the Sellmeijer model, which can be expressed as follows:

⎛⎞γ k hcLp =−−αθ⎜⎟10.680,1lntan0() c > ⎝⎠γ w

The critical water level hp is a function of the factor α, the coefficient c, the length of the leakage way (the width of the defense), the resistance angle for rolling of the sand θ, the 3 volumetric weight of water γw and the volumetric weight of the sand grains γk [27 kN/m ]. The factor α incorporates the effect of the finite thickness of the sand layer through which water is transported. α is described as:

127

Appendices

0,28 ⎛⎞D ((DL / )2,8 − 1) α = ⎜⎟ ⎝⎠L

The coefficient c is determined by the properties of the exposed sand layer:

1 ⎛⎞1 3 cd=η 70 ⎜⎟ ⎝⎠κ L

In which η [-] is the drag force factor (constant of White), d70 [m] is a representative grain fraction (the sieve through which 70% of the weight of the fraction passes), κ is the intrinsic permeability [m2] and L [m] is the leakage length. The intrinsic permeability can be determined in several ways. In this research the intrinsic permeability is determined from the specific permeability k [m/s] with the relation:

ν κ = k g

In which ν is the kinematic viscosity (1,33⋅10-6 m2/s for water of 10° C) and g is the acceleration of gravity (9,81 m/s2). In PC-Ring this relation is incorporated in strength model 1 (c determined with specific permeability k). This model has not been compared with model 2 (c determined with the Constant of Bear CBear ) because of lack of data.

128

Appendices

E. PC-Ring output and design point analysis

In this appendix the PC-ring output for two dike sections, section 38 and section 70 is presented completely. Appendix figure K presents the PC-Ring A-Output that contains statistical information (alpha coefficients and reliability indexes) for section 38. Appendix figure L partially presents the A-output for section 70. Appendix figure M presents the PC-Ring B-output that contains information about the design points for section 38. After each of these figures a short explanation about their contents is given.

Appendix figure K: PC-Ring A-Output for dike section 38 (alpha coefficients and reliability indexes)

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Berekeningen dijkvak id 1170035038: 17-14-4

locatie(stat1/stat2/%) = 1001002 1001002 100. richting dijknormaal = 29.0 [graden] dijkhelling (boven) = 0.166 [tan] dijkhoogte tov NAP = 4.23 [m] blokgrootte debiet = 10.00 [dagen]

------Mech. Windr. F d KsKr alfa waarden 1, ..., aantal stochasten betaM betaW betaX beta Pf [km] [m] [-] [-] [-] [-] [-] [-] [voor 1 berekeningsperiode] [-] ------OVER NOORD 0.00 0.0 1.00 0.1991 0.0000 0.0000 0.0000 0.0000 6.474 6.918 6.389 6.833 0.417E-11 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2987 0.0000 -0.8364 -0.0064 -0.4143 0.0000 0.0000 OVER N.N.O. 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER N.O. 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER O.N.O. 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER OOST 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER O.Z.O. 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER Z.O. 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER Z.Z.O. 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER ZUID 0.00 0.0 1.00 0.2159 0.0000 0.0000 0.0000 0.0000 9.917 9.917 9.846 9.846 0.364E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3239 0.0000 0.0000 0.0000 -0.9211 0.0000 0.0000 OVER Z.Z.W. 0.00 0.0 1.00 0.1968 0.0000 0.0000 0.0000 0.0000 9.475 9.556 9.408 9.489 0.119E-20 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2952 0.0000 0.0000 -0.0412 -0.9341 0.0000 0.0000 OVER Z.W. 0.00 0.0 1.00 0.0988 0.0000 0.0000 0.0000 0.0000 7.375 7.675 7.334 7.634 0.115E-13 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1482 0.0000 -0.6166 0.0152 -0.7667 129

Appendices

0.0000 0.0000 OVER W.Z.W. 0.00 0.0 1.00 0.1300 0.0000 0.0000 0.0000 0.0000 6.850 7.184 6.794 7.128 0.512E-12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1950 0.0000 -0.8467 -0.0442 -0.4756 0.0000 0.0000 OVER WEST 0.00 0.0 1.00 0.1434 0.0000 0.0000 0.0000 0.0000 6.202 6.594 6.138 6.530 0.331E-10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2151 0.0000 -0.8239 0.0000 -0.5043 0.0000 0.0000 OVER W.N.W. 0.00 0.0 1.00 0.1409 0.0000 0.0000 0.0000 0.0000 5.890 6.342 5.826 6.277 0.173E-09 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2113 0.0000 -0.8100 0.0000 -0.5286 0.0000 0.0000 OVER N.W. 0.00 0.0 1.00 0.1388 0.0000 0.0000 0.0000 0.0000 5.639 6.127 5.574 6.062 0.674E-09 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2083 0.0000 -0.8006 0.0000 -0.5444 0.0000 0.0000 OVER N.N.W. 0.00 0.0 1.00 0.1421 0.0000 0.0000 0.0000 0.0000 5.919 6.392 5.854 6.327 0.125E-09 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2131 0.0000 -0.8175 -0.0168 -0.5155 0.0000 0.0000 ------Bovengrens faalkans: 5.997 0.101E-08 Ondergrens faalkans: 6.062 0.674E-09 Maatgevende windrichting N.W. (315.0 [graden]) Resultaat combinatieprocedure: 5.997 0.101E-08

Faalkans voor totale periode: 4.960 0.354E-06

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Berekeningen dijkvak id 1170035038: 17-14-4

locatie(stat1/stat2/%) = 1001002 1001002 100. richting dijknormaal = 29.0 [graden] dijkhelling (boven) = 0.166 [tan] dijkhoogte tov NAP = 4.23 [m] blokgrootte debiet = 7.81 [dagen]

------Mech. Windr. F d KsKr alfa waarden 1, ..., aantal stochasten betaM betaW betaX beta Pf [km] [m] [-] [-] [-] [-] [-] [-] [voor 1 berekeningsperiode] [-] ------OVER NOORD 0.00 0.0 1.00 0.0926 0.0000 0.0000 0.0000 0.0000 4.866 5.439 4.819 5.392 0.349E-07 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1389 0.0000 -0.9819 -0.0050 -0.0889 0.0000 0.0000 OVER N.N.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER N.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER O.N.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER OOST 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER O.Z.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER Z.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER Z.Z.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER ZUID 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 130

Appendices

-0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER Z.Z.W. 0.00 0.0 1.00 0.1965 0.0000 0.0000 0.0000 0.0000 9.501 9.582 9.434 9.515 0.927E-21 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2948 0.0000 0.0000 -0.0412 -0.9342 0.0000 0.0000 OVER Z.W. 0.00 0.0 1.00 0.1170 0.0000 0.0000 0.0000 0.0000 6.059 6.425 6.005 6.372 0.939E-10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1755 0.0000 -0.9728 -0.0589 -0.0756 0.0000 0.0000 OVER W.Z.W. 0.00 0.0 1.00 0.1021 0.0000 0.0000 0.0000 0.0000 5.176 5.607 5.126 5.557 0.138E-07 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1532 0.0000 -0.9775 -0.0675 -0.0783 0.0000 0.0000 OVER WEST 0.00 0.0 1.00 0.0889 0.0000 0.0000 0.0000 0.0000 4.455 4.980 4.408 4.933 0.405E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1334 0.0000 -0.9820 -0.0665 -0.0749 0.0000 0.0000 OVER W.N.W. 0.00 0.0 1.00 0.0904 0.0000 0.0000 0.0000 0.0000 4.183 4.792 4.135 4.743 0.105E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1356 0.0000 -0.9833 -0.0271 -0.0766 0.0000 0.0000 OVER N.W. 0.00 0.0 1.00 0.0814 0.0000 0.0000 0.0000 0.0000 3.961 4.622 3.917 4.578 0.235E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1221 0.0000 -0.9863 -0.0168 -0.0732 0.0000 0.0000 OVER N.N.W. 0.00 0.0 1.00 0.0854 0.0000 0.0000 0.0000 0.0000 4.259 4.888 4.213 4.843 0.642E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1281 0.0000 -0.9846 -0.0107 -0.0827 0.0000 0.0000 ------Bovengrens faalkans: 4.440 0.449E-05 Ondergrens faalkans: 4.578 0.235E-05 Maatgevende windrichting N.W. (315.0 [graden]) Resultaat combinatieprocedure: 4.440 0.449E-05

Faalkans voor totale periode: 2.952 0.158E-02

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Berekeningen dijkvak id 1170035038: 17-14-4

locatie(stat1/stat2/%) = 1001002 1001002 100. richting dijknormaal = 29.0 [graden]

dijkhelling (boven) = 0.166 [tan] dijkhoogte tov NAP = 4.23 [m] blokgrootte debiet = 7.81 [dagen]

------Mech. Windr. F d KsKr alfa waarden 1, ..., aantal stochasten betaM betaW betaX beta Pf [km] [m] [-] [-] [-] [-] [-] [-] [voor 1 berekeningsperiode] [-] ------OVER NOORD 0.00 0.0 1.00 0.0926 0.0000 0.0000 0.0000 0.0000 4.866 5.439 4.819 5.392 0.349E-07 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1389 0.0000 -0.9819 -0.0050 -0.0889 0.0000 0.0000 OVER N.N.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER N.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER O.N.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER OOST 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER O.Z.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER Z.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 131

Appendices

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER Z.Z.O. 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER ZUID 0.00 0.0 1.00 0.2155 0.0000 0.0000 0.0000 0.0000 9.941 9.941 9.871 9.871 0.284E-22 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.3232 0.0000 0.0000 0.0000 -0.9215 0.0000 0.0000 OVER Z.Z.W. 0.00 0.0 1.00 0.1965 0.0000 0.0000 0.0000 0.0000 9.501 9.582 9.434 9.515 0.927E-21 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2948 0.0000 0.0000 -0.0412 -0.9342 0.0000 0.0000 OVER Z.W. 0.00 0.0 1.00 0.1170 0.0000 0.0000 0.0000 0.0000 6.059 6.425 6.005 6.372 0.939E-10 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1755 0.0000 -0.9728 -0.0589 -0.0756 0.0000 0.0000 OVER W.Z.W. 0.00 0.0 1.00 0.1021 0.0000 0.0000 0.0000 0.0000 5.176 5.607 5.126 5.557 0.138E-07 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1532 0.0000 -0.9775 -0.0675 -0.0783 0.0000 0.0000 OVER WEST 0.00 0.0 1.00 0.0889 0.0000 0.0000 0.0000 0.0000 4.455 4.980 4.408 4.933 0.405E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1334 0.0000 -0.9820 -0.0665 -0.0749 0.0000 0.0000 OVER W.N.W. 0.00 0.0 1.00 0.0904 0.0000 0.0000 0.0000 0.0000 4.183 4.792 4.135 4.743 0.105E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1356 0.0000 -0.9833 -0.0271 -0.0766 0.0000 0.0000 OVER N.W. 0.00 0.0 1.00 0.0814 0.0000 0.0000 0.0000 0.0000 3.961 4.622 3.917 4.578 0.235E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1221 0.0000 -0.9863 -0.0168 -0.0732 0.0000 0.0000 OVER N.N.W. 0.00 0.0 1.00 0.0854 0.0000 0.0000 0.0000 0.0000 4.259 4.888 4.213 4.843 0.642E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1281 0.0000 -0.9846 -0.0107 -0.0827 0.0000 0.0000 ------Bovengrens faalkans: 4.440 0.449E-05 Ondergrens faalkans: 4.578 0.235E-05 Maatgevende windrichting N.W. (315.0 [graden]) Resultaat combinatieprocedure: 4.440 0.449E-05

Faalkans voor totale periode: 2.952 0.158E-02

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Berekeningen dijkvak id 1170035038: 17-14-4

locatie(stat1/stat2/%) = 1001002 1001002 100. richting dijknormaal = 29.0 [graden] dijkhelling (boven) = 0.166 [tan] kruinhoogte tov NAP = 4.23 [m]

------Mech. alfa waarden 1, ..., aantal stochasten beta Pf [-] [-] [-] [-] [-] [voor totale periode] ------Falen 1 0.1618 0.0000 0.0000 0.0000 0.0000 4.960 0.354E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2427 0.0000 -0.6524 -0.0023 -0.6201 0.0000 0.0000 -0.3236 SlReg 1 0.0000 0.0000 0.0000 0.0000 0.0000 1.322 0.930E-01 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.8682 -0.0332 -0.0599 0.0000 -0.1681 -0.4618 Combin 1 0.1618 0.0000 0.0000 0.0000 0.0000 4.960 0.353E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2427 0.0000 -0.6525 -0.0023 -0.6201 0.0000 0.0000 -0.3236 Kans -3.091 0.999E+00 Regime 1 0.1618 0.0000 0.0000 0.0000 0.0000 4.960 0.353E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2427 0.0000 -0.6525 -0.0023 -0.6201 0.0000 0.0000 -0.3236 132

Appendices

Falen 2 0.1425 0.0000 0.0000 0.0000 0.0000 2.952 0.158E-02 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2137 0.0000 -0.8694 -0.0223 -0.1262 0.0000 0.0000 -0.4023 SlReg 2 0.0000 0.0000 0.0000 0.0000 0.0000 1.322 0.930E-01 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.8682 -0.0332 -0.0599 0.0000 -0.1681 -0.4618 Combin 2 0.1425 0.0000 0.0000 0.0000 0.0000 2.952 0.158E-02 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2137 0.0000 -0.8694 -0.0223 -0.1262 0.0000 0.0000 -0.4023 Kans 3.091 0.999E-03 Regime 2 0.1425 0.0000 0.0000 0.0000 0.0000 4.661 0.158E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2137 0.0000 -0.8694 -0.0223 -0.1262 0.0000 0.0000 -0.4023 Falen 3 0.1425 0.0000 0.0000 0.0000 0.0000 2.952 0.158E-02 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2137 0.0000 -0.8694 -0.0223 -0.1262 0.0000 0.0000 -0.4023 Combin 3 0.4063 0.0000 0.0000 0.0000 0.0000 5.446 0.258E-07 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.6093 0.0000 -0.3918 -0.0008 -0.1629 0.0000 0.5141 -0.1391 Kans -9.000 0.100E+01 Regime 3 0.4063 0.0000 0.0000 0.0000 0.0000 5.446 0.258E-07 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.6093 0.0000 -0.3918 -0.0008 -0.1629 0.0000 0.5141 -0.1391 ------Sluitingsregime 0.1547 0.0000 0.0000 0.0000 0.0000 4.616 0.195E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2317 0.0000 -0.8456 -0.0188 -0.2256 0.0000 0.0080 -0.3949

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Berekeningen dijkring: 17 IJsselmonde

------Dijkvak dijkhoogte alfa waarden 1, ..., aantal stochasten beta Pf [m] [-] [-] [-] [-] [-] [voor totale periode] ------38 4.230 0.1547 0.0000 0.0000 0.0000 0.0000 4.616 0.195E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2317 0.0000 -0.8456 -0.0188 -0.2256 0.0000 0.0080 -0.3949 ------Bovengrens faalkans: 4.616 0.195E-05 Ondergrens faalkans: 4.616 0.195E-05 Maatgevende dijkvak 38 Resultaat combinatieprocedure: 4.616 0.195E-05

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Omschrijving stochasten per mechanisme

------Mechanisme: OVER Stochast Omschrijving ------1 Dijkhoogte h_d 2 Bermhoogte h_B 3 Bermbreedte B 4 Teenhoogte h_t 5 Helling buitentalud (boven) 6 Helling buitentalud (onder) 7 Helling binnentalud 8 Modelfactor kritiek overslagdebiet m_qc 9 Ruwheid binnentalud k 10 Factor voor bepaling Q_b f_b 11 Factor voor bepaling Q_n f_n 12 Modelfactor optredend overslagdebiet m_q 13 Fout in bodemligging 14 Modelfactor Bretschneider voor Hs 15 Modelfactor Bretschneider voor Ts 16 Fout in locale waterstand 17 Stormduur t_s 133

Appendices

18 Waterstand Maasmond 19 Windsnelheid Schiphol/Deelen |MM 20 Debiet Lobith 21 Debiet Lith 22 Voorspelfout waterstand MK ------PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Resultaten Overslag/overloop berekeningen dijkring: 17 IJsselmonde

betrouwbaarheidsindex = 4.616 faalkans = 0.195E-05

------Stochast Omschrijving Alfa waarde [-] ------1 Dijkhoogte h_d 0.155 2 Bermhoogte h_B 0.000 3 Bermbreedte B 0.000 4 Teenhoogte h_t 0.000 5 Helling buitentalud (boven) 0.000 6 Helling buitentalud (onder) 0.000 7 Helling binnentalud 0.000 8 Modelfactor kritiek overslagdebiet m_qc 0.000 9 Ruwheid binnentalud k 0.000 10 Factor voor bepaling Q_b f_b 0.000 11 Factor voor bepaling Q_n f_n 0.000 12 Modelfactor optredend overslagdebiet m_qo 0.000 13 Fout in bodemligging 0.000 14 Modelfactor Bretschneider voor Hs 0.000 15 Modelfactor Bretschneider voor Ts 0.000 16 Fout in locale waterstand -0.232 17 Stormduur t_s 0.000 18 Waterstand Maasmond -0.846 19 Windsnelheid Schiphol/Deelen |MM -0.019 20 Debiet Lobith -0.226 21 Debiet Lith 0.000 22 Voorspelfout waterstand MK 0.008 23 Windrichting -0.395 ------

The colored items in the following text correspond to the colored parts in the PC-Ring A- output of section 38. The reliability index β of dike section 38 is 4.616 and the corresponding failure probability is 1.95E-06 per year. This failure probability is a summation of the correctly closed state (3.53E-07 per year), the incorrectly open state (1.58E-06 per year) and the correctly open (0.258E-07 per year) of the storm surge barriers. For dike section 38 the incorrect open state of the storm surge barriers has the greatest contribution to the failure probability.

Appendix figure L: PC-Ring A-output for dike section 70 PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 28-11-2005 Tijd: 11:35:38 ======

Berekeningen dijkvak id 1170035070: 17-25-2

locatie(stat1/stat2/%) = 1020979 1020979 100. richting dijknormaal = 152.0 [graden] dijkhelling (boven) = 0.129 [tan] dijkhoogte tov NAP = 4.55 [m] blokgrootte debiet = 2.48 [dagen]

======

Berekeningen dijkvak id 1170035070: 17-25-2

locatie(stat1/stat2/%) = 1020979 1020979 100. richting dijknormaal = 152.0 [graden] dijkhelling (boven) = 0.129 [tan] kruinhoogte tov NAP = 4.55 [m]

------Mech. alfa waarden 1, ..., aantal stochasten beta Pf [-] [-] [-] [-] [-] [voor totale periode] ------Falen 1 0.1667 0.0000 0.0000 0.0000 0.0000 5.196 0.102E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1785 0.0000 -0.5786 -0.0148 -0.7138 0.0000 0.0000 -0.3096 134

Appendices

SlReg 1 0.0000 0.0000 0.0000 0.0000 0.0000 1.322 0.930E-01 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.8682 -0.0332 -0.0599 0.0000 -0.1681 -0.4618 Combin 1 0.1666 0.0000 0.0000 0.0000 0.0000 5.197 0.102E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1785 0.0000 -0.5789 -0.0149 -0.7135 0.0000 -0.0001 -0.3098 Kans -3.091 0.999E+00 Regime 1 0.1666 0.0000 0.0000 0.0000 0.0000 5.197 0.101E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1785 0.0000 -0.5789 -0.0149 -0.7135 0.0000 -0.0001 -0.3098 Falen 2 0.1314 0.0000 0.0000 0.0000 0.0000 4.556 0.261E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1407 0.0000 -0.7894 -0.0396 -0.4691 0.0000 0.0000 -0.3439 SlReg 2 0.0000 0.0000 0.0000 0.0000 0.0000 1.322 0.930E-01 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.8682 -0.0332 -0.0599 0.0000 -0.1681 -0.4618 Combin 2 0.1314 0.0000 0.0000 0.0000 0.0000 4.556 0.261E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1407 0.0000 -0.7894 -0.0396 -0.4691 0.0000 0.0000 -0.3439 Kans 3.091 0.999E-03 Regime 2 0.1314 0.0000 0.0000 0.0000 0.0000 5.841 0.261E-08 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1407 0.0000 -0.7894 -0.0396 -0.4691 0.0000 0.0000 -0.3439 Falen 3 0.1314 0.0000 0.0000 0.0000 0.0000 4.556 0.261E-05 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1407 0.0000 -0.7894 -0.0396 -0.4691 0.0000 0.0000 -0.3439 Combin 3 0.2659 0.0000 0.0000 0.0000 0.0000 7.299 0.147E-12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2847 0.0000 -0.2236 -0.0368 -0.8296 0.0000 0.3288 -0.0228 Kans -9.000 0.100E+01 Regime 3 0.2659 0.0000 0.0000 0.0000 0.0000 7.299 0.147E-12 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2847 0.0000 -0.2236 -0.0368 -0.8296 0.0000 0.3288 -0.0228 ------Sluitingsregime 0.1659 0.0000 0.0000 0.0000 0.0000 5.192 0.104E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1777 0.0000 -0.5856 -0.0156 -0.7078 0.0000 -0.0001 -0.3112

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 28-11-2005 Tijd: 11:35:38 ======

Berekeningen dijkring: 17 IJsselmonde

------Dijkvak dijkhoogte alfa waarden 1, ..., aantal stochasten beta Pf [m] [-] [-] [-] [-] [-] [voor totale periode] ------70 4.550 0.1659 0.0000 0.0000 0.0000 0.0000 5.192 0.104E-06 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.1777 0.0000 -0.5856 -0.0156 -0.7078 0.0000 -0.0001 -0.3112 ------Bovengrens faalkans: 5.192 0.104E-06 Ondergrens faalkans: 5.192 0.104E-06 Maatgevende dijkvak 70 Resultaat combinatieprocedure: 5.192 0.104E-06

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 28-11-2005 Tijd: 11:35:38 ======PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 28-11-2005 Tijd: 11:35:38 ======

Resultaten Overslag/overloop berekeningen dijkring: 17 IJsselmonde

betrouwbaarheidsindex = 5.192 faalkans = 0.104E-06 135

Appendices

------Stochast Omschrijving Alfa waarde [-] ------1 Dijkhoogte h_d 0.166 2 Bermhoogte h_B 0.000 3 Bermbreedte B 0.000 4 Teenhoogte h_t 0.000 5 Helling buitentalud (boven) 0.000 6 Helling buitentalud (onder) 0.000 7 Helling binnentalud 0.000 8 Modelfactor kritiek overslagdebiet m_qc 0.000 9 Ruwheid binnentalud k 0.000 10 Factor voor bepaling Q_b f_b 0.000 11 Factor voor bepaling Q_n f_n 0.000 12 Modelfactor optredend overslagdebiet m_qo 0.000 13 Fout in bodemligging 0.000 14 Modelfactor Bretschneider voor Hs 0.000 15 Modelfactor Bretschneider voor Ts 0.000 16 Fout in locale waterstand -0.178 17 Stormduur t_s 0.000 18 Waterstand Maasmond -0.586 19 Windsnelheid Schiphol/Deelen |MM -0.016 20 Debiet Lobith -0.708 21 Debiet Lith 0.000 22 Voorspelfout waterstand MK 0.000 23 Windrichting -0.311 ------

Omschrijving stochasten per mechanisme

------Mechanisme: OVER Stochast Omschrijving ------1 Dijkhoogte h_d 2 Bermhoogte h_B 3 Bermbreedte B 4 Teenhoogte h_t 5 Helling buitentalud (boven) 6 Helling buitentalud (onder) 7 Helling binnentalud 8 Modelfactor kritiek overslagdebiet m_qc 9 Ruwheid binnentalud k 10 Factor voor bepaling Q_b f_b 11 Factor voor bepaling Q_n f_n 12 Modelfactor optredend overslagdebiet m_q 13 Fout in bodemligging 14 Modelfactor Bretschneider voor Hs 15 Modelfactor Bretschneider voor Ts 16 Fout in locale waterstand 17 Stormduur t_s 18 Waterstand Maasmond 19 Windsnelheid Schiphol/Deelen |MM 20 Debiet Lobith 21 Debiet Lith 22 Voorspelfout waterstand MK

The colored items in the following text correspond to the colored parts in the PC-Ring A- output of section 70. The reliability index β of dike section 38 is 5.192 and the corresponding failure probability is 1.04E-07 per year. This failure probability is a summation of the correctly closed state (1.01E-07 per year), the incorrectly open state (2.61E-09 per year) and the correctly open (1.47E-12 per year) of the storm surge barriers. For dike section 70 the correctly closed state of the storm surge barriers has the greatest contribution to the failure probability. Analyzing the PC-Ring A-output for all sections it can be seen that at the western dike sections (near the sea) the incorrect open state has the greatest contribution the failure probability of a dike section. In eastward direction this dominance decreases. At the most eastern dike sections (for example section 70) the correctly closed state becomes dominant.

Appendix figure M: Example PC Ring B-Output for section 38 (Design points) PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Designpunt dijkvak id 1170035038: 17-14-4

locatie(stat1/stat2/%) = 1001002 1001002 100. richting dijknormaal = 29.0 [graden] dijkhelling (boven) = 0.166 [tan] dijkhoogte tov NAP = 4.23 [m]

------136

Appendices

Mech. Windr. Xd waarden 1, ..., aantal stochasten qovsl hloc Hs Ts [m2/s] [m] [m] [s] ------OVER NOORD 4.101E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.10E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 2.900E-01 7.276E+00 5.154E+00 2.682E+01 1.007E+04 2.038E+03 0.000E+00 OVER N.N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.264E+00 6.318E+00 6.183E+04 1.490E+04 0.000E+00 OVER N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.246E+00 7.474E+00 6.183E+04 1.490E+04 0.000E+00 OVER O.N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.233E+00 7.553E+00 6.183E+04 1.490E+04 0.000E+00 OVER OOST 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.244E+00 6.556E+00 6.183E+04 1.490E+04 0.000E+00 OVER O.Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.276E+00 5.792E+00 6.183E+04 1.490E+04 0.000E+00 OVER Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.270E+00 6.212E+00 6.183E+04 1.490E+04 0.000E+00 OVER Z.Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.244E+00 6.481E+00 6.183E+04 1.490E+04 0.000E+00 OVER ZUID 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.818E-01 7.276E+00 1.221E+00 7.351E+00 6.183E+04 1.490E+04 0.000E+00 OVER Z.Z.W. 4.044E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.04E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.195E-01 7.276E+00 1.195E+00 9.854E+00 5.843E+04 1.405E+04 0.000E+00 OVER Z.W. 4.157E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.16E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.639E-01 7.276E+00 2.903E+00 2.700E+01 2.736E+04 6.317E+03 0.000E+00 OVER W.Z.W. 4.141E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.14E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 2.004E-01 7.276E+00 4.656E+00 4.198E+01 1.264E+04 2.653E+03 0.000E+00 OVER WEST 4.141E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.14E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 2.001E-01 7.276E+00 4.916E+00 3.748E+01 1.205E+04 2.505E+03 0.000E+00 OVER W.N.W. 4.147E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.15E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.867E-01 7.276E+00 4.957E+00 3.435E+01 1.199E+04 2.490E+03 0.000E+00 OVER N.W. 4.152E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.15E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.762E-01 7.276E+00 5.127E+00 3.155E+01 1.179E+04 2.441E+03 0.000E+00 OVER N.N.W. 4.146E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.15E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.892E-01 7.276E+00 5.208E+00 3.011E+01 1.171E+04 2.421E+03 0.000E+00 ------

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Designpunt dijkvak id 1170035038: 17-14-4

locatie(stat1/stat2/%) = 1001002 1001002 100. 137

Appendices

richting dijknormaal = 29.0 [graden] dijkhelling (boven) = 0.166 [tan] dijkhoogte tov NAP = 4.23 [m]

------Mech. Windr. Xd waarden 1, ..., aantal stochasten qovsl hloc Hs Ts [m2/s] [m] [m] [s] ------OVER NOORD 4.185E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.18E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.014E-01 7.276E+00 4.276E+00 2.217E+01 2.255E+03 4.156E+02 0.000E+00 OVER N.N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.264E+00 6.318E+00 6.182E+04 1.489E+04 0.000E+00 OVER N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.246E+00 7.474E+00 6.182E+04 1.489E+04 0.000E+00 OVER O.N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.233E+00 7.553E+00 6.182E+04 1.489E+04 0.000E+00 OVER OOST 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.244E+00 6.556E+00 6.182E+04 1.489E+04 0.000E+00 OVER O.Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.276E+00 5.792E+00 6.182E+04 1.489E+04 0.000E+00 OVER Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.270E+00 6.212E+00 6.182E+04 1.489E+04 0.000E+00 OVER Z.Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.244E+00 6.481E+00 6.182E+04 1.489E+04 0.000E+00 OVER ZUID 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.221E+00 7.351E+00 6.182E+04 1.489E+04 0.000E+00 OVER Z.Z.W. 4.043E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.04E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.201E-01 7.276E+00 1.195E+00 9.858E+00 5.841E+04 1.404E+04 0.000E+00 OVER Z.W. 4.159E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.16E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.595E-01 7.276E+00 3.861E+00 3.988E+01 2.311E+03 4.268E+02 0.000E+00 OVER W.Z.W. 4.177E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.17E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.190E-01 7.276E+00 3.909E+00 3.515E+01 2.196E+03 4.036E+02 0.000E+00 OVER WEST 4.190E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.19E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 8.912E-02 7.276E+00 4.035E+00 3.137E+01 2.044E+03 3.729E+02 0.000E+00 OVER W.N.W. 4.192E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.20E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 8.508E-02 7.276E+00 4.106E+00 2.895E+01 2.015E+03 3.671E+02 0.000E+00 OVER N.W. 4.198E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.20E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 7.254E-02 7.276E+00 4.198E+00 2.659E+01 1.952E+03 3.544E+02 0.000E+00 OVER N.N.W. 4.194E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.19E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 8.183E-02 7.276E+00 4.247E+00 2.501E+01 2.083E+03 3.807E+02 0.000E+00 ------

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======138

Appendices

Designpunt dijkvak id 1170035038: 17-14-4

locatie(stat1/stat2/%) = 1001002 1001002 100. richting dijknormaal = 29.0 [graden] dijkhelling (boven) = 0.166 [tan] dijkhoogte tov NAP = 4.23 [m]

------Mech. Windr. Xd waarden 1, ..., aantal stochasten qovsl hloc Hs Ts [m2/s] [m] [m] [s] ------OVER NOORD 4.185E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.18E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.014E-01 7.276E+00 4.276E+00 2.217E+01 2.255E+03 4.156E+02 0.000E+00 OVER N.N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.264E+00 6.318E+00 6.182E+04 1.489E+04 0.000E+00 OVER N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.246E+00 7.474E+00 6.182E+04 1.489E+04 0.000E+00 OVER O.N.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.233E+00 7.553E+00 6.182E+04 1.489E+04 0.000E+00 OVER OOST 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.244E+00 6.556E+00 6.182E+04 1.489E+04 0.000E+00 OVER O.Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.276E+00 5.792E+00 6.182E+04 1.489E+04 0.000E+00 OVER Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.270E+00 6.212E+00 6.182E+04 1.489E+04 0.000E+00 OVER Z.Z.O. 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.244E+00 6.481E+00 6.182E+04 1.489E+04 0.000E+00 OVER ZUID 4.016E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.02E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.820E-01 7.276E+00 1.221E+00 7.351E+00 6.182E+04 1.489E+04 0.000E+00 OVER Z.Z.W. 4.043E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.04E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 4.201E-01 7.276E+00 1.195E+00 9.858E+00 5.841E+04 1.404E+04 0.000E+00 OVER Z.W. 4.159E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.16E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.595E-01 7.276E+00 3.861E+00 3.988E+01 2.311E+03 4.268E+02 0.000E+00 OVER W.Z.W. 4.177E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.17E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 1.190E-01 7.276E+00 3.909E+00 3.515E+01 2.196E+03 4.036E+02 0.000E+00 OVER WEST 4.190E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.19E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 8.912E-02 7.276E+00 4.035E+00 3.137E+01 2.044E+03 3.729E+02 0.000E+00 OVER W.N.W. 4.192E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.20E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 8.508E-02 7.276E+00 4.106E+00 2.895E+01 2.015E+03 3.671E+02 0.000E+00 OVER N.W. 4.198E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.20E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 7.254E-02 7.276E+00 4.198E+00 2.659E+01 1.952E+03 3.544E+02 0.000E+00 OVER N.N.W. 4.194E+00 3.400E+00 0.000E+00 3.400E+00 1.660E-01 4.19E+00 0.000E+00 5.639E-01 8.944E-01 1.455E-02 5.200E+00 2.600E+00 8.944E-01 0.000E+00 9.889E-01 9.889E-01 8.183E-02 7.276E+00 4.247E+00 2.501E+01 2.083E+03 3.807E+02 0.000E+00 139

Appendices

------

PC-Ring Project: VNK Dijkring: 17 IJsselmonde Berekening: Overslag/overloop Berekeningsmethode: FORM Versie: 4.2 Datum: 6-12-2005 Tijd: 14:31:18 ======

Omschrijving stochasten per mechanisme

------Mechanisme: OVER Stochast Omschrijving ------1 Dijkhoogte h_d 2 Bermhoogte h_B 3 Bermbreedte B 4 Teenhoogte h_t 5 Helling buitentalud (boven) 6 Helling buitentalud (onder) 7 Helling binnentalud 8 Modelfactor kritiek overslagdebiet m_qc 9 Ruwheid binnentalud k 10 Factor voor bepaling Q_b f_b 11 Factor voor bepaling Q_n f_n 12 Modelfactor optredend overslagdebiet m_q 13 Fout in bodemligging 14 Modelfactor Bretschneider voor Hs 15 Modelfactor Bretschneider voor Ts 16 Fout in locale waterstand 17 Stormduur t_s 18 Waterstand Maasmond 19 Windsnelheid Schiphol/Deelen |MM 20 Debiet Lobith 21 Debiet Lith 22 Voorspelfout waterstand MK ------

The design points calculated for dike section 38 for the failure mechanism overtopping have the following characteristics: 1. The normative wind direction is northwest (N.W.) 2. The design point of the crest level (dijkhoogte h_d) is practically similar to the local water level (hloc). 3. Different design points are found for easterly en westerly winds. The loading model causes this difference. In the tidal river area a correlation between the wind statistics and the sea water levels is included for the westerly winds, while no such correlation is included for the easterly winds. 4. For the dominant northwest wind direction the following design points are found: Correctly closed state barriers: Discharge Lobith (11790 m3/s), Water level Maasmond (5.127 m). Incorrectly open state barriers: Discharge Lobith (1952 m3/s), Water level Maasmond (4.198 m). 5. Analyzing B-output for all dike sections it can be seen that for easterly non dominant wind directions the design points consist of extremely high discharges at Lobith (40000 – 60000 m3/s) and Lith (13000 –15000 m3/s), low wind speeds (4 – 9 m/s) and low sea water levels at the Maasmond (1-1.5 m/s). 6. The design points calculated for the non dominant westerly wind directions have the following characteristics: Lower discharges at Lobith (12000 –30000 m3/s) and Lith (2000 – 8000 m3/s), Extemely high wind speeds (10 – 40 m/s) and high sea water levels at the Maasmond (5 – 7 m).

The design points calculated for the failure mechanism damage to revetment share the following characteristics: 7. The discharges at Lobith (order 6000 m3/s)and Lith (700 m3/s) are extremely low, wind speeds are extremely high (order 50 m/s) and sea water levels are extremely high (order 7m).

The extreme values for discharges, wind speeds and sea water levels can be explained by the extremely small probabilities that are calculated. PC-Ring extrapolates until a load combination is found at which the dike fails. If a dike section is over dimensioned for the loads it has to withstand the extrapolation ends at extreme circumstances. 140

Appendices

Appendix figure N: Design Point PC-Ring versus physical maximum

The water level developments at the breach locations are based on the design points calculated for the normative wind direction. As can be seen in table 4-1 for partial dike ring part 1 a discharge of 12630 m3/s at Lobith is found as design point in case of correctly closed barriers for the normative North-West wind direction. At other wind directions higher values are found. Discharges varying from 30000 m3/s to 60000 m3/s can be seen. These discharges are surpassing the physical maximum. The physical maximum is the largest amount of water that safely can pass the Dutch river system. The value of the physical maximum is approximately 18000 m3/s. Discharges higher than the physical maximum are not possible because dikes upstream will fail. The existence of the physical maximum is not included in PC-Ring. For this research this is no problem while for none normative wind direction at any dike section the physical maximum is surpassed. However if the results would indicate a discharge higher than the physical maximum an over-estimation of the failure probability would be made. This is explained by Appendix figure N. This figure explains the difference between the procedure in PC-Ring and the situation with a physical maximum by presenting both situations in a conceptual probability of exceedance curve, a cumulative density function and a probability density function. The red line indicates the procedure in PC-Ring, the black line represents the situation with a physical maximum. In the figure a design point for the local water level hw that is based on discharges higher than the physical maximum is chosen. In the probability density function of the situation with a physical maximum can be seen water levels based on discharges higher than the physical maximum are censured. The probability mass of these water levels would be placed in a Dirac-function (indicated with a black arrow) and therefore these water levels can’t exist. In the PC-Ring procedure no censuring of water levels based on discharges higher than physical maximum is applied. This would result in an overestimation of the failure probability.

141

Appendices

F. Water level developments at breach locations

In this appendix water level developments at the river for a number of breach locations are presented. These water level developments are based on design points from the PC-Ring calculation.

Water level development breach location A Maashaven 5

4 3

2 1 0 Water level (m+NAP) level Water -1 06/01/1991 08/01/1991 10/01/1991 12/01/1991 14/01/1991

Boundary condition closed barriers (design point)

Water level development breach location A Maashaven 5 4 3 2 1 0 Water level (m+NAP) -1 06/01/1991 08/01/1991 10/01/1991 12/01/1991 14/01/1991 Water level development incorrect open barriers (1/4000) Water level development incorrect open barriers (design point) Water level development incorrect open barriers dike ring 14

Water level development breach location D Hoogvliet

6 5 4 3 2 1 0 -1 04/01/1991 06/01/1991 08/01/1991 10/01/1991 12/01/1991 14/01/1991

Water level development incorrect open barriers

Water level development breach location E Zwijndrecht

5 4 3 2 1 0 -1 04/01/1991 06/01/1991 08/01/1991 10/01/1991 12/01/1991 14/01/1991

Water level development incorrect open barrier Water level development correctly closed barrier

Appendix figure O: Water level developments at breach locations

142

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G. Output HIS-SSM

The next table presents the HIS-SSM output for the dominant flood scenario at breach location A at partial dike ring part 6.

Globale parameters Storm : J Kritieke stroomsnelheid [m/s] :8.0 ------Wegingset : standaard ======totaal Schaderelatie Soort Schade(gew) Aantal "nat" Reductie ------Landbouw direct 1,915,731 Euro 2,389,776 m2 1.00 Glastuinbouw direct 600,328 Euro 35,019 m2 1.00 Stedelijk Gebied direct 7,387,762 Euro 7,127,976 m2 1.00 Recreatie Extensief direct 4,620,445 Euro 2,546,716 m2 1.00 Recreatie Intensief direct 2,830,320 Euro 70,745 m2 1.00 Vliegvelden direct 0 Euro 0 m2 1.00 Rijkswegen direct 123,015 Euro 550 m 1.00 Autowegen direct 0 Euro 0 m 1.00 Overige wegen direct 21,229,780 Euro 229,208 m 1.00 Spoorwegen direct 42,148,381 Euro 6,256 m 1.00 Vervoermiddelen direct 9,262,680 Euro 39,086 stuk 1.00 Gemalen direct 0 Euro 0 stuk 1.00 Zuiveringsinstallaties direct 0 Euro 0 stuk 1.00 Eengezinswoningen direct 82,620,017 Euro 20,293 stuk 1.00 Laagbouwwoningen direct 1,415,475,341 Euro 12,713 stuk 1.00 Hoogbouwwoningen direct 171,123,681 Euro 3,122 stuk 1.00 Middenbouwwoningen direct 1,069,537,165 Euro 14,527 stuk 1.00 Boerderijen direct 0 Euro 0 stuk 1.00 Delfstoffen direct 1,659,840 Euro 10 abp 1.00 Bouw direct 1,324,366 Euro 1,100 abp 1.00 Handel/Horeca direct 11,224,038 Euro 5,147 abp 1.00 Transport/Communicatie direct 39,748,155 Euro 795 abp 1.00 Banken/Verzekeringen direct 26,013,409 Euro 2,800 abp 1.00 Overheid direct 12,205,284 Euro 1,915 abp 1.00 Industrie direct 10,006,664 Euro 303 abp 1.00 Nutsbedrijven direct 7,450,255 Euro 91 abp 1.00 Zorg/Overige direct 7,420,330 Euro 2,919 abp 1.00 Landbouw indirect 517,247 Euro 2,389,776 m2 0.25 Glastuinbouw indirect 14,971 Euro 35,019 m2 0.25 Rijkswegen indirect 13,786 Euro 550 m 0.25 Spoorwegen indirect 36,031 Euro 6,256 m 0.25 Delfstoffen indirect 26,448 Euro 10 abp 0.25 Bouw indirect 860,838 Euro 1,100 abp 0.25 Handel/Horeca indirect 491,052 Euro 5,147 abp 0.25 Transport/Communicatie indirect 165,823 Euro 795 abp 0.25 Banken/Verzekeringen indirect 505,816 Euro 2,800 abp 0.25 Overheid indirect 111,882 Euro 1,915 abp 0.25 Industrie indirect 627,658 Euro 303 abp 0.25 Nutsbedrijven indirect 489,674 Euro 91 abp 0.25 Zorg/Overige indirect 584,351 Euro 2,919 abp 0.25 Vliegvelden b.u. 0 Euro 0 m2 1.00 Spoorwegen b.u. 253,058 Euro 6,256 m 1.00 Delfstoffen b.u. 76,608 Euro 10 abp 1.00 Bouw b.u. 5,959,647 Euro 1,100 abp 1.00 Handel/Horeca b.u. 4,209,014 Euro 5,147 abp 1.00 Transport/Communicatie b.u. 5,935,725 Euro 795 abp 1.00 Banken/Verzekeringen b.u. 4,046,530 Euro 2,800 abp 1.00 Overheid b.u. 1,871,477 Euro 1,915 abp 1.00 Industrie b.u. 2,223,703 Euro 303 abp 1.00 Nutsbedrijven b.u. 1,345,852 Euro 91 abp 1.00 Zorg/Overige b.u. 1,261,456 Euro 2,919 abp 1.00 Slachtoffers direct 600 Pers 96,993 pers 1.00 ------totalen Schade (gewogen) ------4,137,555,634 Euro 600 Pers ------143

Appendices

H. Flood risk calculation scheme

The figure presents the flood risk calculation scheme with a feedback loop for a change in the system of secondary defences.

Appendix figure Q: flood risk calculation scheme (including feedback for change in secondary defence)

144

Appendices

I. Impact functioning secondary defences on flood scenarios

In this appendix the impact of functioning flood defences on flood scenarios in compartment 3, 4, 5, 7 and 9 is presented. Appendix figure R shows the flood progress at compartment 3 in case of a functioning secondary defence and in case no secondary defence is present. In this figure can be seen the critical moment is four hours after the breach. In case of a functioning secondary defence the compartment is flooded to great depths, while without a secondary defence the flood is spread over a larger area.

Appendix figure R: Flood progress compartment 3 with and without secondary defence

145

Appendices

In Appendix figure S can be seen also in case of compartment 4 the available secondary defence has a significant influence on the flood progress. In the flooded compartment extra damage occurs due to the functioning secondary defence, while the neighbouring compartment is spared.

Appendix figure S: Flood progress compartment 4 with and without secondary defence

146

Appendices

In Appendix figure T can be seen the secondary defence between compartment 4 and 5 also functions at also has a significant influence in case of flood in compartment 5.

Appendix figure T: Flood progress compartment 5 with and without secondary defence

147

Appendices

Appendix figure U shows the various developments for a flood in compartment 7. In this case a functioning secondary defence prevents a great volume of water entering the area, as the bottom level of the breach is very low.

Appendix figure U: Flood progress compartment 7 with and without secondary defence

148

Appendices

Appendix figure V shows the difference in flood progress for compartment 9. Due to the small size of the compartment and the high crest level of the secondary defence the secondary defence (when it functions) prevents significant economical damage. However the flooding velocities in compartment 9 are very high resulting in a great number of casualties. In case the secondary defence functions HIS-SSM calculates 369 casualties, while without a secondary defence 137 casualties are calculated. A small compartment has a negative influence on the number of casualties.

Appendix figure V: Flood progress compartment 9 with and without secondary defence

149

Appendices

J. Risk optimisation IJsselmonde

In this appendix the underlying calculation results of the risk optimisation for dike ring IJsselmonde from paragraph 6.5.3 are presented. The risk in the initial situation (see Appendix figure X) is determined by multiplying the flood scenario probabilities with their corresponding economical damage and compensating for interest. The risk reduction is achieved in improvement rounds. The procedure is such that in every improvement round the flood scenario with the greatest contribution to the risk (indicated in yellow in Appendix figure X) is improved. Appendix figure W presents the development of the flood scenario probabilities due to four improvement rounds that strengthen the primary ring. Appendix figure Y presents the measures (and their investment costs) that are applied in the improvement rounds. Scenario Probability Flood Breach Failing partial State Initial Improvement Improvement Improvement Improvement Scenario Location dike ring areas Barriers Situation Round 1 Round 2 Round 3 Round 4 1 A 6 incorrect open 1.18E-06 2.70E-07 1.91E-07 2.19E-07 1.39E-07 2 A 6 correctly closed 3.10E-07 1.07E-07 1.02E-07 1.02E-07 9.86E-08 3 B 7 correctly closed 2.90E-07 3.51E-07 3.51E-07 2.51E-08 2.51E-08 4 A and C 5 and 6 incorrect open 2.58E-07 9.80E-08 8.39E-08 1.07E-07 8.67E-08 5 A and B 6 and 7 incorrect open 2.20E-07 1.13E-07 9.62E-08 6.75E-08 5.55E-08 6 A, B and C 5, 6 and 7 incorrect open 1.30E-07 1.26E-07 1.21E-07 9.95E-08 9.28E-08 7 A and B 6 and 7 correctly closed 6.18E-08 4.88E-11 2.07E-11 2.61E-12 1.34E-12 8 A, B, C and D 4, 5, 6 and 7 incorrect open 4.87E-08 4.94E-08 4.92E-08 4.51E-08 4.49E-08 9 E 8 correctly closed 3.96E-08 5.90E-08 5.90E-08 8.03E-08 8.03E-08 10 B and E 7 and 8 correctly closed 2.33E-08 5.09E-08 5.09E-08 3.29E-08 3.29E-08 11 A and E 6 and 8 correctly closed 1.95E-08 1.23E-11 4.97E-12 6.84E-12 3.55E-12 12 C 5 incorrect open 1.75E-08 3.74E-08 4.62E-08 5.10E-08 6.53E-08 13 F 1 correctly closed 1.67E-08 2.41E-08 2.41E-08 3.43E-08 3.43E-08 14 B and F 1 and 7 correctly closed 9.58E-09 2.31E-08 2.31E-08 1.63E-08 1.63E-08 15 F 7 incorrect open 8.25E-09 2.49E-08 2.95E-08 5.43E-09 7.65E-09 16 A and F 1 and 6 correctly closed 7.43E-09 5.17E-12 2.07E-12 3.18E-12 1.64E-12 17 A, C and D 4, 5 and 6 incorrect open 7.39E-09 7.71E-09 7.47E-09 9.49E-09 9.01E-09 18 E and F 1 and 8 correctly closed 7.24E-09 1.58E-08 1.59E-08 4.06E-08 4.06E-08 19 6 and 8 incorrect open 5.22E-09 4.01E-09 3.50E-09 3.93E-09 3.22E-09 20 A, C and E 5, 6 and 8 incorrect open 4.93E-09 3.39E-09 3.21E-09 3.79E-09 3.54E-09 Ring probability: 2.66E-06 1.37E-06 1.26E-06 9.43E-07 8.36E-07 Appendix figure W: Development of flood scenario probabilities per improvement round

Economical risk

Flood Breach Failing partial State Initial Improvement Improvement Improvement Improvement Scenario Location dike ring areas Barriers Situation Round 1 Round 2 Round 3 Round 4 1 A 6 incorrect open 323601 73829 52169 59824 37962 2 A 6 correctly closed 82746 28541 27192 27196 26292 3 B 7 correctly closed 56004 67947 67953 4851 4852 4 A and C 5 and 6 incorrect open 70475 26786 22944 29168 23705 5 A and B 6 and 7 incorrect open 96861 49752 42306 29694 24424 6 A, B and C 5, 6 and 7 incorrect open 57206 55495 53187 43781 40821 7 A and B 6 and 7 correctly closed 28427 22 10 1 1 8 A, B, C and D 4, 5, 6 and 7 incorrect open 24693 25026 24937 22857 22753 9 E 8 correctly closed 11611 17316 17318 23547 23548 10 B and E 7 and 8 correctly closed 11353 24789 24794 16012 16013 11 A and E 6 and 8 correctly closed 10899 7 342 12 C 5 incorrect open 6 12 15 17 22 13 F 1 correctly closed 445 644 644 916 916 14 B and F 1 and 7 correctly closed 2108 5075 5076 3583 3584 15 F 7 incorrect open 1374 4147 4911 905 1275 16 A and F 1 and 6 correctly closed 2180 2 110 17 A, C and D 4, 5 and 6 incorrect open 2513 2622 2541 3227 3065 18 E and F 1 and 8 correctly closed 2316 5072 5073 12993 12994 19 6 and 8 incorrect open 2194 1685 1470 1651 1351 20 A, C and E 5, 6 and 8 incorrect open 2070 1425 1346 1593 1485 Total risk: 789082 390194 353889 281821 245065 Appendix figure X: Development of net present flood scenario risks in euro per improvement round in case of only measures that strengthen the primary ring

150

Appendices

Improvement Strengthening of Length dike Costs dike streng- Total investments Cum. investment Round prim. dike section section (m) thening (euro/km) measure (euro) costs (euro) 0- - - 0 0 1 38 706 5000000 3530000 3530000 2 36 2000 5000000 10000000 13530000 3 54 1392 5000000 6960000 20490000 4 40 797 5000000 3985000 24475000 Appendix figure Y: Measures for strengthening primary ring applied per improvement round

Appendix figure AA presents the change in net present flood scenario risks in case in improvement round 1 a new secondary defence is introduced near breach location A (indicated with a red line in Appendix figure Z) that reduces the consequences of flood scenario 1 from 4.1 billion dollar to 0.25 billion dollar. This damage reduction is also processed in the multiple scenarios. The cost of this measure including net present maintenance costs is indicated in Appendix figure BB. The direct maintenance costs of the secondary defences at IJsselmonde for 2005 are estimated at 69000 euro and the indirect costs are estimated at 31000 euro, resulting in an estimated total maintenance costs of 100000 euro (Source Water Board Hollandsche Delta). The total length of the secondary defences in dike ring IJsselmonde is 40 km (Source province of South Holland). Assuming a linear relation the maintenance costs arrive at 2500 euro per km per year.

Appendix figure Z: New secondary defence (red) Economical risk

Flood Breach Failing partial State Initial Improvement Improvement Improvement Improvement Scenario Location dike ring areas Barriers Situation Round 1 Round 2 Round 3 Round 4 1 A 6 incorrect open 323601 19732 2 A 6 correctly closed 82746 5172 3 B 7 correctly closed 56004 56004 4 A and C 5 and 6 incorrect open 70475 70475 5 A and B 6 and 7 incorrect open 96861 40359 6 A, B and C 5, 6 and 7 incorrect open 57206 57206 7 A and B 6 and 7 correctly closed 28427 12977 8 A, B, C and D 4, 5, 6 and 7 incorrect open 24693 24693 9 E 8 correctly closed 11611 11611 10 B and E 7 and 8 correctly closed 11353 11353 11 A and E 6 and 8 correctly closed 10899 6033 12 C 5 incorrect open 66 13 F 1 correctly closed 445 445 14 B and F 1 and 7 correctly closed 2108 2108 15 F 7 incorrect open 1374 1374 16 A and F 1 and 6 correctly closed 2180 322 17 A, C and D 4, 5 and 6 incorrect open 2513 2513 18 E and F 1 and 8 correctly closed 2316 2316 19 6 and 8 incorrect open 2194 853 20 A, C and E 5, 6 and 8 incorrect open 2070 2070 Total: 789082 327622 Appendix figure AA: Development of net present flood scenario risks in euro per improvement round in case of implementation new secondary defence near breach location A

151

Appendices

Improvement Implementation Length seconda- Costs secondary Net present maint- Total investments Total costs inc. Round secondary defence ry defence (km) defence (euro/km) enance costs (euro) measure (euro) maintenance (euro) 0- - - 0 0 1 Sec. Def. near A 3 20000000 500000 60000000 60500000 Appendix figure BB: Measure to reduce flood scenario risk by implementing a new secondary defence

0.90 0.80 0.70 0.60 0.50

(Millions) 0.40 0.30

Risk 0.20 0.10 0.00 0 10203040506070 Investments (Millions) Measures strengthening primary ring Measure implementation secondary defence without maintenance costs Measure implementation secondary defence with maintenance costs Example of inclination -1

Appendix figure CC: Economical flood risk as function of investments in measures in improvement rounds

Appendix figure CC presents the economical risk as a function of the investments in improvement rounds. In paragraph 6.5.3 the interpretation of this graph is given.

152