Royal Society Publishing

Uncertainties and constraints on breaching and their implications for flood loss estimation

Robert Muir Wood , William Bateman

Abstract

Around the coasts of the southern North Sea, flood risk is mediated everywhere by the performance of natural and man-made flood defences. Under the conditions of extreme surge with tide water levels, the performance of the defences determines the extent of inland flooding. Sensitivity tests reveal the enormous increase in the volume of water that can pass through a defence once breaching is initiated, with a 1 m reduction in sill elevation doubling the loss. Empirical observations of defence performance in major storm surges around the North Sea reveal some of the principal controls on breaching. For the same defence type, the maximum size and depth of a breach is a function of the integral of the hydraulic gradient across the defence, which is in turn determined by the elevation of the floodplain and the degree to which water can continue to flow inland away from the breach. The most extensive and lowest floodplains thereby ‘generate’ the largest breaches. For surges that approach the crest height, the weaker the protection of the defence, the greater the number of breaches. Defence reinforcement reduces both the number and size of the breaches.

Keywords:

1. Introduction

Modern flood defences are engineered to provide protection against floods of a specified return period and elevation. Beyond this design level, the defence can expect to be subject to partial overtopping leading to flow down the inner face of the embankment. High water levels can also lead to infiltration through the materials of the defence. For all but the strongest reinforced concrete defences, once a defence is significantly overtopped, or infiltrated, some form of breaching is almost inevitable.

In modelling risk in the coastal floodplain, the most critical component concerns predicting potential breaching behaviour (Muir Wood et al. 2005). Once overtopping becomes replaced by significant breaching, the volume of water that passes into the floodplain can increase by several orders of magnitude.

(a) The sensitivity of flood loss to breaching

In order to determine the sensitivity of flood loss to breach size, the Risk Management Solutions (RMS) UK storm surge flood modelling platform (Muir Wood et al. 2005) was used to simulate the same surge time-history for breaches of different sizes. As the results of such an experiment will be influenced by the disposition of the building stock relative to the floodplain topography, an urban area, the city of Hull, was chosen in which the whole floodplain and its margins have a similar exposure density. An extreme surge tide combination was chosen for the simulation with a return period greater than 5000 years—and with the potential to flood large parts of the city, should a major breach develop.

A number of simplifications were made in the modelling approach: the weir equation was used to determine the flow rate through the defence, neglecting the impact of ponding in reducing the hydraulic gradient (see Muir Wood et al. 2004). The height of the surge with tide is time-stepped through the whole flood event for that period in which the surge with tide remains higher than the sill height of the defence. The water volume is then dispersed into the floodplain in the form of half a cone, from a maximum height at the coast equal to the average water height through/over the defence during the high water of the surge with tide, down to the maximum semicircular flood extent, assuming a constant water surface gradient sloping away from the breach.

The depth of floodwater was derived at each postcode unit by deducting the ground elevation from the elevation of the sloping water surface. Losses were then calculated based on modelled exposure values and standard vulnerabilities for the building stock of the city.

The results of one set of simulations are shown in figure 1, with respect to the influence of the sill elevation of a large breach on the resulting monetary flood loss for Hull. Losses were found to be approximately doubled with every 1 m reduction in sill height. However, once the width of a breach reaches a dimension of 20–30 m, loss was found to be less sensitive to further lateral expansion.

Figure 1

Modelled loss in the city of Hull versus the depth of the sill elevation (relative to sea level) for a single breach of 100 m in width, for a 0.02% annual probability of exceedance water level, involving a spring tide with a 3.5 m, 30 h half-wavelength, storm surge.

This modelling shows how critical it is to know not only the probability that breaching is initiated, but also how large a breach will grow, and in particular how deep it becomes eroded. Once the conditions are ripe for the formation of a breach at one location, it is likely that other breaches may start to form on neighbouring sea defences, and hence it is also important to understand the constraints on the density and dimensions of breaching along a specific section of sea defence. For this purpose, a survey was undertaken to determine what could be learnt from the experience of breaching in past storm surges around the North Sea.

(b) The controls on breaching

Breach growth is a function of two distinct erosional processes: hydraulic erosion and slumping (Morris & Hassan 2002). As water begins to move over or through the defence, unconsolidated materials of the defence (typically sand or clay) become eroded and transported into the floodplain. As the gap enlarges, flow velocities increase along with the rate of erosion. As erosion undercuts the defence, rotational shear failures develop in the neighbouring defence wall with the slumped material being carried away by the flow. Experiments have shown that with a 3–4 m hydraulic head, a breach in an unconsolidated sand embankment can expand at several metres a minute.

Any defence armour resistant to erosion, such as concrete paving or asphalt (or even well-rooted grass), can restrict the initiation of breaching by reducing significant erosion and downcutting. Even when an opening has been eroded, such materials can also limit breach expansion by resisting the propagation of the cracks on which the slumping occurs. Breach expansion is also resisted by encountering less readily erosible materials at the base of the defence, such as a concrete foundation or harder geological substrate.

Once a breach has opened, flow is initially driven by the hydraulic gradient across the defence, as determined by the difference in elevation of the high water levels of the surge with tide relative to the elevation of the protected floodplain. The larger the difference in elevation, the faster the flow and the more rapid the erosion. Repeated cycles of slumping and erosion continue until flow velocities eventually decline owing to a reduction in hydraulic gradient.

Outside the defence, while the storm surge can be considered of infinite extent, the sea water elevation changes at rates of 0.1–1 m h−1. However, the principal determinant of a reduction in hydraulic gradient is the degree to which flow becomes distributed away from the breach. In a smooth, flat, effectively infinite floodplain, water will rapidly drain away from the opening and the hydraulic gradient can be maintained. However, real floodplains tend to shelve inland, may have a second line of defences or other obstructions, all of which restrict the ability of water to become distributed. The smaller the floodplain and the more constricted flow beyond the defence (as by a second embankment for example), the more rapid the ponding and the faster the rate of breach erosion slows. This means, for modelling purposes, that the size of the floodplain determines the maximum size of a breach. In effect, the size of the floodplain thereby dictates the extent of the flood.

2. Observations of breaching behaviour

The aftermath of breaching has been observed in a number of surge events around the North Sea over the last half century: most importantly in the 1953 storm surge along the coasts of eastern England and southwestern part of the Netherlands (Wolf 1953; Cooling & Marsland 1954; Snell 1954; Spalding 1954). More localized breaching also occurred on the coast of North Wales in the storm of 26 February 1990, as well as in the windstorm ‘Anatol’ on the southwest coast of Jutland on 3 December 1999, which was the object of a field survey by RMS engineers. However, all breaching is ephemeral as repairs are begun within hours or days of the passage of the storm. In none of these incidents was there a comprehensive survey of breaching populations and dimensions. While the width of individual breaches can be mapped, the all-important depth of the ‘sill height’ is often unknown or can only be inferred.

(a) Geological context

In evaluating all the observations of breaching around the North Sea coasts, the need to understand the geographical and geological context of the original flood defences became clear.

The very existence of the Netherlands is predicated on the construction of embankments to protect large areas below high-tide levels. The defences are built on geologically recent, unconsolidated Holocene sediments transported by the distributaries of the River Rhine (in some areas reworked by the wind or sea). Long-term geological subsidence and compaction of the thick quaternary deltaic sequence of sediments has meant that defences have had to be continually raised since the rich farmland was first protected from the advancing sea in the Middle Ages.

The geological situation in the Netherlands contrasts with eastern England where there has been no long-term Quaternary subsidence and much of the coastal geology comprises a range of consolidated and older Tertiary clays or mid-Quaternary glacial sediments. With access to higher land to the west, the protected coastal floodplains in eastern England are rarely situated below mean sea level (with some exceptions in areas protected by Dutch hydraulic engineers: as at Canvey Island in the Thames estuary and around the Wash). The modal elevation in the eastern England coastal floodplain is 2–3 m above Ordnance Datum and only approximately 7% of all the postcode units below 5 m elevation are less than 1 m above sea level. In consequence, coastal floodplains are significantly smaller and at higher average elevation than in the Netherlands.

This difference in settlement geography and coastal geology helps explain the difference in the maximum dimension of breaches found in the 1953 storm surge flood. In the Netherlands, the largest breach size was 520 m wide and 36 m deep, i.e. with a cross-sectional area of around 10 000 m2 (see figure 2). (Once a deep breach had formed on the Netherlands coast it became employed at every tide, in some cases remaining open for several months.) Along the eastern coast of England, the largest known breaches were around 100 m in width and eroded to an estimated 12 m below sea level (as along the south bank of the River Crouch in Essex and at one location along the Lincolnshire coast) with estimated cross-sectional areas of around 600 m2. The large majority of breaches along the coast of England did not erode below low water level (see figure 3). This order of magnitude difference in cross-sectional area reflects the reduced hydraulic gradient at breach initiation and the more rapid reductions in hydraulic gradient owing to ponding. This confirms the manner in which the maximum anticipated breach size is constrained by the elevation and extent of the floodplain into which the water can flow. The bigger and lower the floodplain, the larger the breach.

Figure 2

Typical breach in the 1953 storm surge along defences protecting extensive floodplain polders in southwest Netherlands. Note deep downcutting of the breach through the defence as a result of the low elevation and large size of the floodplain. Also note the initiation of other breaches along the unarmoured upper sections of defences in the background. Photo source ‘De Ramp’ February 1953, Amsterdam.

Figure 3

Typical breach in the 1953 storm surge along the eastern coast of the England at Dersingham, Norfolk. Erosion has not proceeded below sea level, as the defence is built on a relatively resistant substratum and the floodplain does not extend far inland. Photo: Professor Peter Wolf (from Wolf 1953).

(b) The population of breaches

For any section of defence, the number of breaches increases the closer the water levels of the surge with tide and associated waves approach the defence crest elevation. Inevitably, given the different degree to which breaching proceeds, the population of breaches in a long length of similar defences shows a range of sizes (potentially a fractal distribution up to the maximum breach in that stretch of defence). In 1953, along the Scheldt estuary in Belgium, where land beyond the defences was 1–2 m above low-water mark (comparable to the situation in eastern England), most of the unprotected earth defences along the river were overtopped, leading to 180 breaches, five of which were eroded below the low-water mark (J. Blockmans, pp. 56–57 in discussion preceding Cooling & Marsland 1954). Along the north coast of Kent, with similar unreinforced defences, there were 400 complete breaches of all sizes from a few metres to more than 200 m in width. Along the estuaries of Essex, there were 839 breaches up to 45 m in width and extending from 1.5 to 6 m depth below the former defence crest (Cooling & Marsland 1954).

The exact point at which a breach is initiated may reflect some small flaw in the defence: the largest breach on the Ouse estuary embankments, close to Kings Lynn, in 1953 was blamed on the presence of a thorn hedge that had fallen over, exposing the material of the defence to further erosion (Doran 1954). On the island of Rørøy, Denmark, in December 1999 the principal breach formed at an outer corner in the defences (see figure 4) (Michael Drayton, personal communication).

Figure 4

Breaching in defences at the northeast edge of the island of Rørøy, Jutland, Denmark in the ‘Windstorm Anatol’ of 3 December 1999. Note: (i) deep scour hole at the corner of the island, (ii) defence removed by wave action while clay substrate remains, (iii) channel cut in foreshore of the defence as water flowed out of the flooded island when the tide and surge receded, (iv) other breaches initiated further along the defence, (v) sand deposited inland of the breaches as water velocities slowed. Photo: Michael Drayton, Risk Management Solutions.

Neighbouring breaches can also be in competition with one another, as the water that arrives behind the defence from the initial breach will tend to reduce the hydraulic gradient and hence erosion rates of subsequent breaches. For this reason, all else being equal, the first breach to form in a section of defence will tend to be the largest.

(c) Defence protection

Armouring of the defence reduces the probability of a breach forming and can also limit the degree to which the breach can expand through erosion and slumping. In 1953, along the Lincolnshire coast, the town of Mablethorpe was protected by stepped concrete frame defences founded on unreinforced sand-dunes (Wolf 1953). While at a number of locations erosion of the supporting dunes caused the concrete structures to collapse, the concrete debris was resistant to being washed away and obstructed the further downcutting or slumping associated with typical breach expansion.

3. Conclusions

For all risk quantification and risk mitigation investigations relating to storm surge flooding, breaching remains the most critical source of uncertainty. It is therefore important to understand the constraints on potential breaching behaviour so that these can be incorporated into the modelling. These can be stated as follows:

  1. For any given design and situation of a sea defence, the probability of breach initiation rises as the water level (from the surge and associated waves) approaches the defence crest.

  2. For similar relative water levels and wave exposure, the probability of breaching decreases the more that the defence is armoured and protected against erosion.

  3. Once formed, the maximum size of a breach in a given defence type is determined principally by the elevation and extent of the interior floodplain, as this determines the degree to which the original hydraulic gradient across the breach persists during breach expansion.

The key to the reliable modelling of the risk of breaching comes in quantifying these interdependencies.

Footnotes

  • One contribution of 14 to a Theme Issue ‘The big flood: North Sea storm surge’.

References

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