INTEGRATING RELIABLE FLOOD MODELLING WITH PROBABILISTIC ANALYSIS IN PRACTICE

Transcription

1 INTEGRATING RELIABLE FLOOD MODELLING WITH PROBABILISTIC ANALYSIS IN PRACTICE PAUL SAYERS 1 MICE, IAN MEADOWCROFT 2 AMICE, ALASTAIR MOODY 3 BEN GOULDBY 1 and MATT CROSSMAN 1 1 HR Wallingord, Howbery Park, Wallingord, OX10 8BA, UK 2 Environment Agency, National Centre or Risk Analysis and Options Appraisal 3 Arup Water Consultancy, Raety House, Surrey ABSTRACT In recent years there have been a number o advances in modelling lood events. This has been matched by simultaneous advances in probabilistic techniques to evaluate loading and response. The reliability o a lood risk assessment, however, remains constrained by the ability to determine the likelihood o deence ailure and test multiple ailure and load scenarios. In addition, conventional analysis has diiculty resolving lood risk resulting rom multiple breach/ailure locations and load combinations. Thereore, it oten remains ocused on the impact o a breach on discrete areas o the lood plain; rather than considering the potential damage resulting rom a broader perspective o multiple ailures arising in any given system o deences. As a result, the improvements in lood inundation modelling and probabilistic analysis techniques have been largely incompatible in practice. For simple lood plains protected by a limited number o discrete deences subjective techniques based on expert judgement supported by limited modelling and sensitivity analysis oer robust and appropriate solutions to determining lood risk. However, in complex situations, a more advanced physically-based approach is required. Thereore, to improve decision making in these complex situations and achieve reliable lood risk mapping, a probabilistic systems based approach that integrates lood inundation modelling with deence perormance and economic analysis is presently under development. The methodology is being developed in tandem with a number o Coastal and Tidal Deence Strategy Studies and combines large quantities o synthetic data rom joint probability analysis with system thinking on deence perormance, to enable economic damages to be directly and consistently assessed. The outline procedure presented in this paper is generic and could be applied to many situations to provide a consistent evaluation o dierent options. However, this level o analysis would not be appropriate in cases where the risk and investment levels are low or where decisions are clear cut. INTRODUCTION The preparation o strategies or the management o luvial, tidal and coastal deences is becoming increasingly dependent on probabilistic analysis o lood deences. A problem central to the development o robust strategic options is to understand the way in which lood deence systems behave, the likelihood o ailure and the resulting inundation and damage. Recent advances in probabilistic design provide the potential or a large number o deence and load realisations and hence a risk-based approach to the assessment o uture deence management scenarios. This paper explores these techniques and present thinking in terms o combining loading and response using probabilistic techniques. The discussion included within the paper is evolving and is by no means complete. However, it seeks to demonstrate that probabilistic risk assessment can be applied in practice. αβχδ

2 Outline o the Paper This paper describes on-going research and its practical application in terms o reliably establishing lood risk. The techniques discussed have been developed through application and extension o techniques outlined in FCDPAG4 (MAFF, 2000) and in three strategy studies: Thames Tidal Embayments (Environment Agency, 2000, being undertaken by Arup); Folkestone to Rye (Environment Agency, 2001a, undertaken by HR Wallingord); and Thames Tidal Walls (West); (Environment Agency, 2001b, being undertaken by HR Wallingord). The paper is structured in three sections: Deence perormance and system ailure Integrated lood inundation modelling Conclusions DEFENCE PERFORMANCE AND SYSTEM FAILURE Assessing the Likelihood o Deence Failure Many authors have grappled with the thorny issue o assessing the likelihood o deence ailure (Sayers and Simm, 1997; Hall et al, 2001). Typically, single deterministic values o residual lie that represent a judged best estimate have been, and are oten still, used to provide a representation o the likelihood o ailure. In more recent studies, deences have been categorised into bands that indicate their Estimated Useul Lie (e.g less than 1 year, 1-5 years, etc). Mid value estimates are then oten used to inorm decision making; at least with regard to assigning annual ailure probability values. To move towards a probabilistic assessment o lood risk a better ounded probabilistic description o the likelihood o ailure is clearly required. However, this is extremely diicult given the complex interactions between load, hydraulic response and deence structural deterioration. To address this issue, a simpliied probabilistic methodology has been developed or use in the Thames, west o Dartord, jointly by Arup and the Environment Agency (Environment Agency, 2000) that oers a practical way o determining annual ailure probabilities or individual deences. The approach adopted utilises the Condition Grade categories developed by the Environment Agency (Environment Agency, 1999) and is briely outlined below in three steps. Step 1 - Establish the Lie Expectancy or each generic deence type Maximum lie expectancies or various structures within the Thames Tidal Embayments Study 1 area (Teddington Weir to Dartord Creek/Mar Dyke) have been developed through consensus based on engineering judgement and experience. Typically, these range rom 50 years or an embankment through to 75 years or steel sheet piling and up to 300 years or a masonry wall. In establishing these values it was assumed that the structure is subjected to average environmental and loading conditions throughout its lie and never exposed to extremes. It was also assumed that the structure is unmaintained, i.e. no actions are undertaken (such as grass mowing, painiting, grouting, etc.) to prolong the lie o the deence. Step 2 - Establish an Age: Failure Probability relationship For each generic deence type, a generic deterioration curve was then developed. These socalled Age: Failure Probability relationships are shown in Figure 1 and based on an exponential unction as given below. 1 An embayment is an area o the tidal Thames loodplain deined by the limit to which loodwater would extend in the event o a breach in the deences. Tributaries, high ground or artiicial constraints extending to the River Thames separate embayments rom each other. A total o 23 separate embayments have been identiied between Teddington Weir and Mar Dyke/Dartord Creek. αβχδ

3 Probability o deence ailure = p = e a + blnl Where p = probability o ailure o a single deence length independent o its neighbours perormance, L is the remaining lie o the deence element and a and b are constants which depend on the maximum lie expectancy o the generic deence type. It was o course recognised that the deterioration o lood deence structures may not ollow an exponential curve. For example, large earth embankments may experience early rapid deterioration to a relatively stable condition beore experiencing urther rapid deterioration to ailure. However, in the absence o empirical evidence on which to base alternative deterioration proiles, more realistic decay unctions cannot at present be deined. Step 3 Establish the deence speciic Annual Failure Probability and Condition Grade The Condition Grade (rom 1 to 5) provided by the Environment Agency Flood Deence Management System (FDMS) is then utilised to establish an equivalent ailure probability range or each deence as given below and shown in Figure 1. Condition Grade CG1 CG2 CG3 CG4 CG5 p Thus, a rontage designated CG1 would be assigned an annual ailure probability (p) o between and It should be noted that these probability intervals are essentially arbitrary and are not supported by empirical data but, through extensive debate, are considered an appropriate translation o the Condition Grade, assigned on inspection, to an annual ailure probability. To determined a precise annual ailure probability in any given year the Condition Grade is then combined with knowledge on the age o the deence as discussed below. Step 4 Establish the Annual Failure Probability in any year For the purposes o decision making it is not suicient to simply determine the present day conditions o a deence, but an estimate o how a particular deence may perorm in the uture is required. Thereore, the annual ailure probability assigned to any deence element in any particular year depends on the age o the element and on the condition o the element under consideration at the time o inspection as described by the Condition Grade. These two criteria (Steps 2 and 3) are combined to give an eective age o the deence to enable uture changes in annual ailure probability to be determined. For example, a concrete deence element may be expected to have a useul lie o 100 years. I constructed sixty years ago it might be expected to have a remaining lie o 40 years. This would lead to an anticipated annual ailure probability o (using the exponential deterioration curve or a concrete deence given in Figure 1) and hence be expected to receive a Condition Grade o 2 in a present day inspection (see Table above). However, i the Condition Grade assigned by an experienced inspector was CG4 (and hence the deence was in worse condition than may have been expected based on the generic age:ailure probability relationship) its eective age would be 82 leaving a remaining lie o only 18 years (equivalent to an annual ailure probability o in Year 0; the lower limit o the CG4 equivalent ailure probability). This approach provides some practical irst steps towards determining a probabilistic description o a varying uture annual ailure probability. However, it attempts only to deal with intrinsic uncertainties in deence perormance based on condition o structural elements; uncertainties in uture load sequences and severity are αβχδ

4 ignored. This is an issue that will need to be addressed in order to relate the likelihood o ailure to the drivers o ailure; i.e. the extreme wave, water level and low conditions. It will also be important to reine the assumed deterioration curves as empirical evidence becomes available. Deence System Failure The above is ocused towards establishing an annual ailure probability within any year or one deence length. Within FCDPAG3 (1999) the appraisal o breach ailure is also based on an individual, sel-contained, deence or which annual ailure probabilities can be interpolated. In reality this assumption is oten undamentally lawed. Flood plains are typically protected by a myriad o deences o varying condition and residual structural strength (see Figure 2). In this case, ailure o any one or more deences may lead to inundation o some or all o the lood plain. Thereore, a particularly diicult issue in any lood risk assessment is to determine the likelihood o ailure o any particular deence length (as discussed above) and, based on these individual assessments, the likelihood o a ailure occurring somewhere within the system o deences. Within FCDPAG4 (MAFF, 2000) two scenarios are presented or assessing the probability o system ailure (P system ) where deences are similar in length: Assume deences are ully independent In this case it is assumed that a particular deence length will behave in accordance with its own intrinsic qualities such as construction material and residual structural strength. Under this assumption the probability o system ailure is easily described as: P system = 1-( (1-p 1 ). (1-p 2) (1-p n-1 ), (1- p n )) (e.g rom Figure 2, where n=6, P system = 0.32) where n = the number o discrete deence lengths Assume deences are ully dependent In this case it is assumed that there is a tendency or deences exposed to similar loading to behave in a similar way. For example, or each deence length, ailure is most likely to occur during a major storm. Under this assumption the probability o system ailure is easily described as: P system = Maximum p i i=1 to n (e.g. rom Figure 2 P system = 0.10) In reality it is likely that P system will lie somewhere between 0.32 and 0.10 and the degree o correlation between deences will depend on their proximity, structural orm and ailure mechanisms, as well as their exposure to extreme loads that may lead to ailure. The most complex part o this process is to determine the correlation between these components and hence the system ailure probability. To determine the value o P system a number o possible methodologies are available to achieve a more realistic representation o partial dependence between deences. These are discussed below. Approximate methods to introduce a degree o dependence A simpliication made within the Thames Tidal Embayments Studies was to separate the deences into two classes: strong deences with a low probability o ailure; and weak deences with a high probability o ailure. I the strong sub-system ails then it is assumed that the weaker sub-system also ails. To determine the overall 'system' ailure probability a mixed correlation approach is then adopted. First or each sub-system (i.e strong and weak deences) the statistical independence assumption is made, i.e. P sub-system = αβχδ

5 1-((1-p 1 ).(1-p 2 )...(1-p n )). Then, the two sub-system ailure probabilities are combined assuming statistical dependence, enabling the system ailure probability to be deined as P system = maximum o P weak sub-system and P strong sub-system. Within this above approach, however, the ailure probability assigned to a deence length remains uninluenced by the condition o its immediate neighbours or the sequence and severity o the loading. Develop correlation matrices that describe relationships between deences The approximate methods can be improved to enable the condition o the immediate neighbours to a deence to inluence the likelihood o its ailure by using a Conditional Probability Relationship as discussed in PAG4. This involves the establishment o a correlation matrix to describe conditional ailure probability relationships (i.e inormation on the change in the likelihood o ailure o a particular deence assuming its neighbouring deence ails or a severe storm is encountered). However, although this is relatively simple in theory, application o this approach in practice is constrained due to the limited understanding o the interaction o deences and their structural perormance under extreme loads. Thereore, although a promising approach, it will require urther thinking and research to develop evidence based correlation matrices. As with the approximate methods, this approach would continue to rely on deterioration curves based on average loading to determine uture annual ailure probabilities and thereore would take no account o the sequence or severity o uture loading. Develop ull simulation based approaches o deence perormance The most powerul approach is one o ull simulation that seeks to combine evidence on deence perormance, loading and response. These techniques are starting to be explored through the use o simulation tools that consider the reliability o deence system as a whole with built-in correlation between deence elements and loading. This type o approach is currently being developed by the Dutch or managing dyke rings (PC Ring Project) that includes correlation between loading and condition assessments (Vrijling and van Gelder, 2000). Similar approaches are presently being considered or application in the UK where the deence system and lood plain is complex, although it will require considerable research eort to develop useable and scaleable methodologies. INTEGRATED FLOOD INUNDATION AND ECONOMIC DAMAGE MODELLING Establishing deence perormance is diicult but, unortunately, only one part o the equation. The lood orcing unctions are also oten complex and include hydraulic loading (waves, surges, luvial lows), deence ailure (i.e. overtopping and overlow) and lood propagation across the lood plain. In the past it has been convenient to consider lood risk in terms o single hazards, i.e extreme water levels, wave induced overtopping or luvial lows. Then use discrete return periods o these hazards (i.e. the 1:100 year water level) and assume these relate well to discrete lood inundation return periods, or even, incorrectly, economic losses o the same return period. Over the past ew years this view has been challenged and recent work by HR Wallingord as part o the Thames Tidal Walls Strategy development (Environment Agency, 2000) has adapted and extended the joint probability methodologies that are traditionally used to derive hydraulic load conditions, to the broader question o economic damage that recognises waves, surges, luvial lows and various deence ailure scenarios as potentially important contributors to lood risk (see Figure 3). Although the Thames Tidal Walls (West) Strategy Study study (Environment Agency, 2000) is on-going, and the methodology continues to be developed through associated research at αβχδ

6 HR Wallingord, the key elements o the approach are outlined in Figures 4 and 5 and are discussed below in nine steps. Steps 1 to 3 Establishing the hydraulic loading conditions (see Figure 5) Joint probability methods have been developed over many years and are now common place in most assessments o hydraulic loads (HR Wallingord, 1994). More recently these methodologies have been extended to directly consider the response o deences to those loads, or example in terms o wave run-up or overtopping and, where suitable relationships are known, structural response such as rock stability. HR Wallingord 1998, demonstrates a discrepancy between the joint exceedance return period o the load and the return period o the response derived rom it. Comparisons suggest that i the target response return period is used to select the joint exceedance load, then the response return period could be underestimated by a return period actor o up to 2 to 3 times. Thereore, the need to adopt a joint probability method to establish the extremes o a response o interest is clear. In seeking to select the preerred lood deence option, the primary driver used in England and Wales is one o comparing potential costs and damages associated with each option. However, to determine potential economic loss, spatial changes in both loading and deence response (i.e overtopping) are important intermediate steps that need to be understood and represented within the lood model i it is to reproduce well the lood inundation characteristics o the lood plain; a eature o particular signiicance in determining lood risk in the Thames estuary where the lood plain is extensively interconnected. For example, exposure o deences to hydraulic loading along the Thames varies signiicantly at any one time depending on the wind direction and surge. Also luvial lows are important in raising water levels west o Dartord Creek Barrier. To account or all these inluences on deence loading and to understand their spatial variation, within the Thames Tidal Walls (West) Strategy it is proposed to extend an existing isis model o the Thames estuary (developed by the Thames Region, Environment Agency) to include the southern bank lood plain east o Dartord Creek. The hydraulic boundary conditions or this integrated model o the estuary and lood plain will then be provided by a simulated datatset o approximately 700,000 high tide events (i.e. equivalent to 10,000 years) o simultaneous water level and wind speeds predicted at Southend-on-Sea (assuming a continuation o the present day climate) using the JOIN-SEA sotware (HR Wallingord, 1998), see Figure 6. It is noteworthy that luvial lows were shown to have little inluence on extreme water levels east o Dartord Creek and are thereore excluded rom the JOIN-SEA analysis. It is also noteworthy that wind speeds at Southend-on-Sea are used as a proxy or wave conditions through the study area. The use o wind speed as the second variable in the joint probability analysis at Southend-on-Sea, instead o wave conditions, enables simultaneous wave conditions to be predicted at any location within the estuary, with the correct joint relationship with predicted water levels at Southend-on-Sea. This relationship can then be used determine simultaneous, but varying, combinations o wave and water levels throughout the study area as discussed below. Step 4, 5 and 6 Establish lood inundation and resulting economic damage (see Figure 5) The JOIN-SEA simulation is equivalent to more than 10,000 years o high tide data. It is thereore impractical to run a hydraulic model and determine the lood inundation and resulting economic damage or a range o deence ailure scenarios in all o these events. Instead, it is proposed to adopt a representative sub-set o the ull population o joint hydraulic loading conditions to drive the integrated isis model o estuary and lood plain. αβχδ

7 For a range o deence ailure scenarios, economic damages can then easily be assessed using the isis results or the sub-set o hydraulic conditions. It is also interesting to note that the predicted lood inundation automatically includes the variations in hydraulic loading during any single storm event (or combination o events i required) along the estuary. Variations in wave conditions can be derived independently rom isis based on wind speeds at Southendon-Sea provided by the JOIN-SEA simulation, and the resulting wave conditions included explicitly within the isis model. Variations in water levels are predicted within the isis hydraulic model directly rom the water level boundary condition provided at Southend-on- Sea. Steps 7 and 8 Derive directly extremes o economic loss (see Figure 5) Within FCDPAG 3 it is assumed that the practitioner has a number o discrete results o economic damage (1:1 year, 1:10 year etc) taken rom a small set o lood inundation results. Using the approach discussed above in Steps 4 to 6, the ull population o wind speed and water level conditions may be represented by a selected sub-set o conditions. For each o these conditions the economic damage can be established based on the predicted inundation. Using contouring methods developed at HR Wallingord (HR Wallingord, 2001) it is possible to extend this relatively small number o realisations o economic damage to the ull population o joint probability conditions o wind speed and water levels predicted at Southend-on-Sea (see Figure 7). The extended dataset provides a 10,000 year population o economic damage rom which extremes may be directly extracted; including an Annual Average Damage or any other statistical parameter. Step 9 Repeat various scenarios o deence system ailure and climate change (Figure 5) A key innovation o the methodology proposed or the Thames Tidal Walls (West) Strategy is its ability to be run or many combinations o deence ailure realisations and uture climate scenarios. For example, a change in mean sea level can easily be incorporated within the joint distribution o waves and water levels by simply re-scaling the marginal extremes or uture water levels and re-contouring the economic loss results to establish uture marginal extremes o economic damage without the need or urther inundation modelling. Equally, more subtle changes in wind/wave climate can be incorporated and their signiicance tested in a similar manner. CONCLUSIONS A new approach to lood risk assessment is presently under development or making better decisions where the loading, deence system and lood plain is complex and the decisions to be made are diicult to determine. The methodology described in outline in this paper: Enables the changing annual ailure probability o a deence due to deterioration to be incorporated in a simple way. More advanced methodologies to enable deence deterioration to be linked to possible realisations o uture loading are now required. Recognises that lood plains are deended by a system o deences. Present practical methodologies in both the UK and overseas are immature in this area. However, key advances towards a more realistic representation o the deence systems and the risks they pose are emerging. Implicitly recognises that deences and interconnected lood plains are exposed to a combination o extreme water levels (luvial and surge) and wave conditions. αβχδ

8 Avoids the assumption that links extremes o economic damage to particular events. Instead, it enables a ull distribution, and hence direct extraction o extremes and other statistical descriptions, o economic damage to be calculated using well tried and tested joint probability methodologies. There is considerable development work still required to enable a consistent and objective risk assessment methodologies to be developed or use when decision making complex. However, many o the oundation stones are now in place. ACKNOWLEDGEMENTS The authors wish to thank members o the Embayments Methodology Steering Group, especially Arup (Duncan Hay), Environment Agency, MAFF and Andrew Pepper (ATPEC Ltd), who have contributed considerably to the conceptual development o the Thames Region's Tidal Embayment Studies. Also the advice provided by Dr Peter Hawkes and Robert Cheetham o HR Wallingord and Mike Turville o Environment Agency (Southern Region) in developing the approach proposed or use in the Thames Tidal Walls (West) Strategy Study is grateully acknowledged. REFERENCES Environment Agency, National Sea and River Deence Surveys Condition Assessment Manual Environment Agency, Thames Tidal Embayments Strategy Appraisal Methodology Guidance Note Drat 2. RKL Arup Water Consultancy Environment Agency, 2001b. Thames Tidal Walls (West) Strategy Study Scoping Report. HR Wallingord EX 4256 Environment Agency, 2001a. Folkestone to Rye Coastal Deence Strategy Study. - Main Strategy Report. HR Wallingord EX 4142 Hall J, Davies J, Taylor C, Durgaprasad J, Dawson R, Baker E, Perormance-based assessment management or complex inrastructure. 8th International Conerence o Structural Saety and Reliability, Newport Beach, CA, June 18-22, 2001 HR Wallingord, Validation o joint probability methods or large waves and high water levels. SR 347 HR Wallingord, Joint probability o waves and water levels: JOIN-SEA. SR 537 November 1998 HR Wallingord, 2001 Joint probability o luvial lows and tidal levels or predicting extreme water levels in estuaries. In press MAFF, Flood and Coastal Deence Project Appraisal Guidance 3 Economic Appraisal MAFF, Flood and Coastal Deence Project Appraisal Guidance 4 Approaches to risk Sayers P B and Simm J D, Residual lie: Its assessment and importance in terms o coastal management and beneit analysis. MAFF Conerence, 1997 Vrijling and van Gelder, Policy implications or uncertainty integration in design. 8 th Symposium, Stochastically hydraulics International αβχδ

9 1.000 Embankments Steel sheet piling p (Logarithmic) Concrete walls CG5 Assumed threshold o structural ailure CG4 CG Age CG2 CG1 Figure 1 Deterioration o dierent generic deence types in the tidal Thames Key 1 = Individual deence lengths P = Probability o ailure in Year Old masonary wall P = New concrete wall P = New concrete wall P = Earth embankment P = Earth embankment P = Earth embankment P = 0.1 Flood plain LAND WATER Figure 2 Schematic o deence lengths protecting a single lood plain αβχδ

10 Wind Wind Dartord Creek Flow Waves Southend-on-Sea Tide + Surge Wind Wind Figure 3 Thames Tidal Walls Study Area Dartord Creek to Southend-on-Sea: Complex loading and an interconnected lood plain Establish hydraulic drivers (winds, waves, water levels, lows) Establish deence response (overtopping or overlow) Establish lood plain response and inundation Repeat or many deence and load scenarios and combine Establish associated economic loss Figure 4 Overview o approach to the integrated lood inundation and economic modelling αβχδ

11 Step 1 Predict population o joint water level, luvial and wind boundary conditions (JOIN-SEA) Step 2 Predict simultaneous wave conditions at selected locations Step 3 Predict simultaneous water levels throughout the study area or selected loading conditions Step 4 Establish overtopping / overlow o all deences or a given deence ailure/improvement scenario under the selected loading conditions Step 5 Establish lood inundation or each o the selected loading condition using an appropriate model (isis/telemac) Step 6 Establish lood depth across the lood plain and distribution o associated economic loss or each o the selected loading conditions Step 7 Establish population o economic loss based on popolutaion o loading conditions (modiied by climate change i required) Step 8 Derive directly marginal extremes o economic loss or each deence 'system' ailure scenario rom the population o results Step 9 Repeat or many dence ailure and climate scenrios Figure 5 Flow chart showing the probabilistic economic damage assessment methodology αβχδ

12 Southend water level v's UKMO wind speeds 24 Wind speed (m/s) Southend water level (modn) Figure 6 Population o joint wind and water levels at Southend-on-Sea Figure 7 Indicative contours o economic damage based on results rom selected ull model runs αβχδ