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2D Hydrodynamic Modelling: Mobile Beds, Vehicle Stability and Severn Estuary Barrage

Prof. Roger A. Falconer Cardiff University Prof. Binliang Lin Cardiff University Dr Junqiang Xia Cardiff University

March 2012 Project Website: www.floodrisk.org.uk

2D Hydrodynamic Modelling: Mobile Beds,

Vehicle Stability and Severn Estuary Barrage

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Document Details

Statement of Use

This report is intended to be used by researchers, model developers and modellers

who wish to understand and potentially use the advances in 2D modelling developed

during WP1.1 of the FRMRC2. The report presents an enhanced approach to

determining stability of vehicles during flooding. It also provides details of linked 2D

hydraulics and sediment modelling and results from modelling of a potential barrage

in the Severn Estuary.

Acknowledgements

The research reported above was conducted as part of the Flood Risk Management

Research Consortium (Phase II), supported by the UK Engineering and Physical

Sciences Research Council (GR/S76304). The bathymetric data for the Boscastle

study were provided by the Environmental Agency, with the post flood surveys being

undertaken by Halcrow Group Limited. The contributions of both the organizations

and individuals involved are gratefully acknowledged.

Disclaimer

This document reflects only the authors’ views and not those of the FRMRC Funders.

The information in this document is provided ‘as is’ and no guarantee or warranty is

given that the information is fit for any particular purpose. The user thereof uses the

information at its sole risk and neither the FRMRC Funders nor any FRMRC Partners

is liable for any use that may be made of the information.

© Copyright 2012 The content of this report remains the copyright of the FRMRC Partners, unless

specifically acknowledged in the text below or as ceded to the Funders under the

FRMRC contract by the Partners.



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Summary

This report provides a summary of research undertaken in work package 1.1 of the

FRMRC2. The focus is on aspects of 2D modelling of flooding and the report covers

the following topics:

• Development of a 2D morphodynamic model in which the processes of flow

routing, sediment transport and corresponding bed evolution are simulated

using a coupled approach, with a refined wetting and drying approach.

• Development of incipient velocity formulas for flooded vehicles. Two

incipient velocity formulae under different scenarios are proposed for

assessing stability criteria of vehicles in floodwaters, and the accuracy of these

formulas are validated using flume-based experimental data and observed data

from real events.

• Development of an integrated numerical model for flood risk management.

The developed model can be used to predict the inundation of flash floods and

the corresponding flood hazards to people and property. The model was

validated using observations obtained from three flash floods, which indicates

the enhanced numerical model can be used as an approximate assessment tool

to assist in flood risk management.

• Simulations of the impacts of a potential Severn Barrage on flood risk.



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Table of Contents

1 Introduction ............................................................................................................ 1

2 Relevance of the Research ..................................................................................... 2

2.1 Modelling of dam-break floods over mobile beds ........................................... 2

2.2 Estimation of flood risk to people and vehicles in urban areas ....................... 2

2.3 Estimation of future coastal flooding in the Severn Estuary ........................... 2

3 Literature Review ................................................................................................... 4

3.1 Algorithms for 2D flood inundation modelling ............................................... 4

3.2 Modelling flash flood routing over mobile beds .............................................. 4

3.3 Safety criteria of people and property in floodwaters ...................................... 5

3.3.1 Assessment method for people safety .................................................... 5

3.3.2 Assessment method for vehicle safety ................................................... 7

3.3.3 Estimation of flood risk to buildings ..................................................... 7

3.4 Flood risk associated with the proposed Severn Barrage ................................ 8

3.5 References ........................................................................................................ 9

4 Summary of the Key Findings ............................................................................. 12

4.1 Modelling flood routing with the refined wetting and drying method .......... 12

4.2 Modelling of dam-break flows over mobile beds using a coupled approach 13

4.3 Incipient velocity formula for fully submerged vehicles ............................... 15

4.4 Incipient velocity formula for partially submerged vehicles ......................... 18

4.5 2D modelling of flood hazard ........................................................................ 23

4.6 Estimation of future coastal flood risk in the Severn Estuary ....................... 24

5 Conclusions and Recommendations .................................................................... 26

6 List of Publications .............................................................................................. 28

6.1 Peer-reviewed journal papers ......................................................................... 28

6.2 Conference papers .......................................................................................... 28



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1 Introduction

Work Package 1.1 of FRMRC2 was entitled “Hydrodynamic Modelling to

Support Enhanced Flood Risk Estimation” and was conducted in the Hydro-

environmental Research Centre, at Cardiff University, with Prof. Roger A. Falconer

being the leader of this work package. This report provides a summary of the main

outputs of the research – further information is published in a series of papers (as

listed in Chapter 6).

This report includes the following sections:

• relevance of the research

• literature review

• summary of the key findings

• conclusions and recommendations

• list of publications



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2 Relevance of the Research

The research conducted mainly covers three aspects of flood analysis: numerical

methods for predicting flood routing over mobile beds, the stability criterion of

flooded vehicles, and the effect of barrage construction on the coastal flooding in the

Severn Estuary. The relevance of this research for each aspect is presented in this

section.

2.1 Modelling of dam-break floods over mobile beds

Many numerical models pertaining to dam-break floods can be found in the

literature, and they have been successfully used to predict the flood inundation extent

and velocity distributions. However, the majority of these models are only applicable

to dam-break floods over fixed beds. In some catastrophic flood events, flood flows

have induced severe sediment movements in various forms: debris flows, mud flows,

floating debris and sediment-laden currents. Due to the interaction between the

sediment-laden flow and mobile bed, river channels, floodplains and other flood-

prone areas undergo frequent morphological changes. For example, severe sediment

deposition in a local reach caused by a dam-break flood would lead to reduced

channel conveyance; in some extreme cases, the volume of entrained material could

reach the same order of magnitude as the volume of water initially released from the

failed dam, and this material usually includes large-size boulders, and even vehicles,

which could block local hydraulic structures, such as bridges or culverts. For dam-

break floods, the processes of flood wave propagation and associated bed evolution

are usually very significant. In order to accurately predict these processes, it is

necessary to develop a morphodynamic model using a sediment-water coupled

approach to take into account the effects of bed level change and sediment

contractions on the process of flood inundation.

2.2 Estimation of flood risk to people and vehicles in urban areas

The risk to vehicles and people caused by a flood varies both in time and place

across a flood-prone area, and also changes with different body shapes and weights.

The variation in the hazard degree for people in floodwaters needs to be understood

by managers for urban floods. Therefore, it is important to assess the degree of people

stability in floodwaters. Vehicles in urban areas usually tend to be unstable by losing

their resistance (frictional instability) or becoming buoyant (floating) in flash floods,

which further leads to various hazards, including causing injuries or mortality to

passengers and bystanders, damage to buildings and infrastructure, and even

exacerbation of a flood event by blocking local hydraulic structures, such as bridges

or culverts. Therefore, it is necessary to investigate vehicle stability conditions in

floodwaters and to develop appropriate formulations for engineers to estimate such

conditions.

2.3 Estimation of future coastal flooding in the Severn Estuary

The Severn Estuary is an ideal site for tidal renewable energy projects, since

this estuary has the third highest tidal range in the world. The UK Government

recently considered many proposals for tidal renewable energy projects for the

estuary. The Severn Barrage was one of the proposals submitted. If the barrage were

to be built as proposed, the higher tide levels would be reduced significantly inside the

barrage but the extent of reduction would depend on the mode of barrage operation. In

order to prevent future coastal flooding in the basin, the barrage could also be



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operated so as to reduce higher tide levels caused by storm surges. These disasters

may cause great damage to life and properties along the estuary. Climate change is set

to increase the potential impacts. An assessment of future coastal flood risk along the

Severn Estuary needs to account for the effect of the potential barrage construction

and various open seaward boundary scenarios.



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3 Literature Review

3.1 Algorithms for 2D flood inundation modelling

For a flood induced dyke failure or dam break event, or a sudden opening of a sluice

gate in a flood detention basin, a shock wave usually forms and then propagates forward

on an initially dry bed. The processes of flood routing on dry beds caused by dam-break

flows can usually be simulated by two-dimensional (2D) hydrodynamic models. Flood

inundation studies based on 2D numerical model simulations and laboratory experiments

for dam-break flows are one of the most widely studied topics in the current

computational hydrodynamics research field (Bellos et al., 1992; Fraccarollo and Toro,

1995; Bradford and Sanders, 2002; Lin et al., 2003; Zhou et al., 2004; Yoon and Kang,

2004; Liao et al., 2007; Soares-Frazao, 2007; Liang et al., 2007). In the literature, many

numerical methods are available for simulating dam-break flows. Zhao et al. (1996)

presented a detailed review of a range of numerical methods developed for simulating

dam-break flows, based on solving the 2D shallow water equations (SWEs). Bradford

and Sanders (2002) presented a robust procedure for modelling urban floods and applied

it to simulate the movement of a wetting and drying wave front. Among these numerical

methods the finite volume method (FVM) with a total variation diminishing (TVD)

scheme is considered to be one of the most successful methods for simulating the

propagation of shock waves (Sleigh et al., 1998; Bradford and Sanders, 2002; Zhou et al.,

2004; Liao et al., 2007). In a FVM solver, the depth-integrated 2D SWEs are solved in

each computational cell with mass and momentum being automatically conserved, even

in the presence of a discontinuity for some flow parameters. The normal fluxes across the

cell faces are often evaluated using an approximate Riemann solver, instead of an exact

Riemann solver. Such a method is computationally more efficient, yet it is still able to

accurately capture shock wave fronts. In addition, numerical oscillations that sometimes

occur at the flood wave front, including a hydraulic jump, can be suppressed by

introducing a suitable flux limiter. For predicting dam-break flows it is necessary to

employ a specific approach to simulating the evolution of wetting and drying fronts. In a

practical study of flooding over a real topography or terrain, both positive and negative

bed slopes generally exist, as well as different structures and obstacles, such as buildings,

trees and roads, etc. The presence of steep bed slopes and/or sharp changes along the

horizontal model boundary often results in challenging difficulties for numerical models,

as an inaccurate treatment of wetting and drying fronts may lead to significant prediction

errors. Therefore, it is necessary to propose an appropriate method to deal with the

wetting and drying problem.

3.2 Modelling flash flood routing over mobile beds

Earlier studies on flood routing were primarily based on analytical solutions for

idealised conditions. With the advancement of computer technology and numerical

solution methods of the shallow water equations, hydrodynamic models based on one-

dimensional (1D) and two-dimensional (2D) approaches are increasingly being used for

predicting dam-break flows. Currently, numerical solutions of the shallow water

equations type are one of the most active topics in the field of hydraulics research.

Several numerical models pertaining to dam-break flows can be found in the literature,

and they have been successfully used to predict flood inundation extent and velocity

distributions. However, the majority of these models are only applicable to dam-break

flows over fixed beds (Lin et al., 2003; Zhou et al., 2004; Liang et al., 2007). In some

catastrophic flood events, particularly those caused by dam or dike failures, flood flows



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have induced severe sediment movements in various forms: debris flows, mud flows,

floating debris and sediment-laden currents (Costa et al., 1988). Capart et al. (2001)

pointed out that in some extreme cases, the volume of entrained material could reach the

same order of magnitude as the volume of water initially released from the failed dam. It

is thus often necessary to account for the process of morphological changes when

simulating such severe dam-break flows. Currently, two approaches are often used to

simulate the morphodynamic processes: uncoupled and coupled solutions (Zhang and Xie,

1993). In order to model the morphodynamic processes caused by dam-break flows, the

second method may be more acceptable. This is due to the rate of bed evolution often

being comparable to the rate of water depth variation. Early numerical models for

simulating dam-break flows over mobile beds often adopted uncoupled solutions that did

not account for the effects of sediment transport and bed deformation on the movement of

flow (Ferreira and Leal, 1998; Fraccarollo and Armanini, 1998; Fagherazzi and Sun,

2003).

Although many 2D dam-break flow models over non-mobile, or fixed, beds have

been developed over the past decade (Lin et al., 2003; Liao et al., 2007; Zhou et al., 2004;

Liang et al., 2007; Begnudelli and Sanders, 2007; Gallegos et al., 2009; Fraccarollo and

Toro, 1995; Zhao et al., 1996), 2D models for dam-break flows over mobile beds using

the coupled solution are seldom reported due to the complexity of flow-sediment

transport and bed evolution. Simpson and Castelltort (2006) extended an existing 1D

coupled model of Cao et al. (2004) to a 2D model for the free surface flow, sediment

transport and morphological evolution. This model used a Godunov-type method with a

first-order approximate Riemann solver, and was verified by comparing the computed

results with the documented solutions. As commented by Cao (2007), the first-order

numerical scheme in solving the governing equations may have limitations in modelling

water levels and sediment concentrations with gradient discontinuities. The model was

applied to test cases with some idealized flat bed channels, without the need to consider

the wetting and drying fronts. Therefore, it is necessary to develop a morphodynamic

model for simulating dam-break flows over mobile beds with more advanced solution

schemes and wider applicability.

3.3 Safety criteria of people and property in floodwaters

3.3.1 Assessment method for people safety

Previous studies on the assessment method of people safety have been carried

using two different approaches: (i) based on empirical or semi-quantitative criteria

(NSWG, 2005; Penning-Rowsell et al., 2005; Defra and EA, 2006; Ishigaki et al., 2005,

2008), and (ii) based on formulae derived from mechanical principles, i.e. balance of

forces, linked with experiments (Foster and Cox, 1973; Abt et al., 1989; Keller and

Mitsch, 1992; Karvonen et al., 2000; Lind et al., 2004; Jonkman and Penning-Rowsell,

2008).

Empirical or semi-quantitative criteria were usually used to evaluate the degree of

hazard to people by organisations of flood management or related departments of a

government. Defra and the EA (2006) reported a simple method to determine the rating

of flood hazard based on flow velocity, depth and the presence of debris. Formulae

derived from a more mechanics-based experimental approach were obtained from studies

by Abt et al. (1989) and Karvonen et al. (2000). Abt et al. (1989) reported experiments of

human stability on one concrete monolith and 20 healthy, lightly dressed human subjects

walking and standing in water of various depths. Karvonen et al. (2000) conducted

further tests on people stability in the Rescdam project, in which seven people, age



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ranging from 17 to 60 year old, were involved. Both these studies proposed a critical

depth-velocity product, indicating that the combination of a certain depth and a

corresponding velocity would lead to human instability. The empirical formula obtained

is expressed as ( , )c p p

hU f m h= , where h is the depth of the incoming flow; c

U is the

critical velocity for reaching human instability; and ( , )p p

f m h is an empirical function

related to the height (p

h ) and mass (p

m ) of a person.

The studies on people safety in floodwaters by Foster and Cox (1973), Keller and

Mitsch (1993), and Takahashi et al. (1992) adopted alternative criteria for people

stability, and major differences between these studies in the methodologies used for

developing the criteria exist (Cox and Ball, 2001). Foster and Cox (1973) based their

criteria on physical tests in a laboratory flume, and presented the safe and unsafe flow

conditions for standing children. Keller and Mitsch (1993) established a force balance

equation for a person standing on a flooded street against sliding, linking the buoyant

force, weight, frictional resistance and drag force due to flowing water. The formula is

given by:

2 / ( )c r f d

U F C Aρ= (1)

where f

ρ is the density of the flowing fluid; d

C is the drag coefficient; r

F is the

restoring force due to the friction with r v

F Fµ= ; v

F is the magnitude of the normal force

acting on the surface; µ is the friction coefficient; and A is the submerged area projected

normal to the flow. This criterion of people stability (Keller and Mitsch, 1993) was based

on a computational analysis of potential flow conditions, rather than on any laboratory

experiments.

Fig. 1 Instability curves for a child and adult in floodwaters (Keller and Mitsch, 1993)

In this analysis, the dimensionless coefficient of friction between the child’s shoes

and the road surface was assumed to be 0.30 under sliding, and a conservative value for

dC of 1.2 was adopted with the assumption that the body shape of a child was idealised to

the shape of a vertical cylinder (Cox and Ball, 2001). According to Eq. (1), two curves

were presented between the product of the flow velocity (c

U ) and the incoming depth ( h )

at the point of human instability versus h , for a five year old child with the height and

weight of 1.11 m and 19 kg respectively and an adult, under the condition of sliding

equilibrium. Fig. 1 shows the instability curves for a child and an adult in floodwaters,

and it can be seen that there is a significant difference between the critical velocities for

the child (0.5 m/s) and the adult (2.2 m/s) as the incoming depth is equal to 0.6 m. It



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should be noted that whether a person standing in floodwaters is in danger or not depends

on the objective condition (such as the local flow pattern, terrain and visibility) and the

objective condition (such as the physical and psychological status of a person). Therefore,

the curves in Fig. 1 just present a rough estimate of the risk to a generic person in

floodwaters, and these curves have been used in the following numerical assessment of

people stability in floodwaters.

3.3.2 Assessment method for vehicle safety

Existing studies on the stability criteria of vehicles in floodwaters are limited.

Gordon and Stone (1973) investigated the stability of a Morris Mini car with the two back

wheels being locked to prevent any movement. The vehicle stability condition was

obtained when the horizontal force was just balanced by the product of the measured

vertical reaction force and the coefficient of friction. In this approach it was important to

estimate the appropriate value of the friction coefficient for sliding. Bohham and

Hattersley (1967) suggested a sliding friction value of 0.3, while Gordon and Stone (1973)

indicated that the friction coefficient ranges from 0.3 to 1.0. Keller and Mitsch (1993)

conducted a theoretical investigation into the stability conditions for idealised cars, and

developed a simple method for estimating the forces exerted on a stationary vehicle in

floodwaters and an incipient velocity formula for a partially submerged vehicle.

In the latest report by AR&R (Shand et al., 2010), existing guidelines and

recommendations for the limits of vehicle stability were compared with experimental and

analytical results, with a marked difference being obtained between these two sets of

results. Therefore, interim criteria for stationary vehicle stability were proposed for three

vehicle classes, including small passenger and large passenger vehicles, as well as 4WD

(four wheel drive) vehicles. In the recent study conducted by the authors (Xia et al.,

2011ab), all of the forces acting on a flooded vehicle were analysed and the

corresponding expression for incipient velocity was derived for commonly used vehicles

parking on flooded roads or streets. The proposed formulas can account for two scenarios:

(i) the inside space of a vehicle would be filled by the floodwater; and (ii) the inside

space would not be filled quickly by the flood water, and the vehicle would start to float

for a relatively high depth. More details can be seen in section 4.

3.3.3 Estimation of flood risk to buildings

Buildings are potential places of refuge during floods and are frequently used by

people in flood-prone areas. A partial or complete failure of buildings in which people

might shelter to provide safe refuge is consequently a significant factor in determining the

potential number of deaths resulting from flooding in extreme circumstances (Defra and

EA, 2006). Buildings can collapse because of water pressure, scour of foundations, or a

combination of these events. In addition, debris carried by a flood in the form of trees,

boulders or vehicles, can cause severe damage to buildings. Kelman and Spence (2004)

presented an overview of flood characteristics with respect to their applicability for

estimating and analysing direct flood damage to buildings. Flood actions on buildings

include: hydrostatic actions, hydrodynamic actions, and erosion actions, etc. However,

the main flood actions are the depth difference between water levels outside and inside a

building and the velocity near the building walls. Kelman (2002) proposed matrices for

damage to buildings based on the maximum flood depth difference and the maximum

flood velocity. Five potential levels of damage were assigned to different combinations of

depth differences and velocities, from minor water contact and infiltration to irreparable



8

structural damage. However, such complex matrices for damage to buildings are not

necessary in the initial assessment of flood risk.

Therefore, a simplified assessment matrix for the flood risk to buildings was

presented by Defra and the EA (2006). This matrix adopted an average of hazard scale

for each building type in each combination of depth difference and velocity (Kelman,

2002). The assessment matrix can also be approximately expressed by regression into a

simple formula: 0.14 0.340.7HD U h= ∆ (2)

where U = velocity near the building walls; h∆ = depth difference between water levels

outside and inside a building; and HD = hazard degree of the building in floodwaters.

The hazard degrees have been grouped into three damage categories, including some

damage (HD ≤ 0.5), severe damage (0.5 < HD < 0.98) and irreparable damage (HD ≥

0.98). It should be pointed out that such a matrix is an indicative assessment of the

damage that would occur to buildings in urban areas, and it can not include the effect of

different types of building. However, it is often accepted for a preliminary assessment of

flood risk in local organisations such as Environment Agency.

3.4 Flood risk associated with the proposed Severn Barrage

Coastal flooding is generally caused by a combination of high water levels, which

may be caused by spring tides and storm surges, together with high waves (Townsend,

1981), which can lead to overtopping of coastal defences and inundation of low-lying

areas, potentially causing damage to life and properties. Waves and storm surges are

caused by storm events with high winds blowing over the adjacent sea. Tsunamis, caused

by undersea earthquakes, landslides, volcanic eruptions and meteorites can also be

important in causing coastal flooding in some parts of the world. Defra (2005)

commissioned a study into the tsunami risk to the UK, which concluded that the risk of a

tsunami higher than storm surge levels of 2 m could be extremely low and that although

further study and upgrading of warning systems was recommended, no specific tsunami

flood defences were required. The value of the UK’s assets at risk from flooding by the

sea has significantly increased in recent years. In England and Wales alone, over 4

million people and properties valued at over £200 billion are at risk (Office of Science

and Technology, 2004). The expected annual damage in England and Wales due to

coastal flooding is predicted to increase from the current £0.5 billion to between £1.0 and

£13.5 billion, depending on the scenario of climate and socio-economic changes (Hall et

al., 2006). At the current stage it is difficult to predict the exact magnitude of sea level

rise in a specified estuary in the future, and different values of sea level rise have been

predicted by researchers. According to the prediction by Hansen (2007), a sea level rise

of several meters will be a near certainty if greenhouse gas emissions keep increasing

unchecked. Using results from the Hadley Centre’s HadCM3, Hulme et al. (2002)

predicted that by the 2080s relative sea level may reach over 70 cm above the current

level in Wales and southwest England in the case of high CO2 emissions scenario.

Therefore, it is necessary to pay more attention to the changes of coastal flooding caused

by future sea level rise due to climate change from global warming, or occurrence of

extreme sea levels caused by meteorologic or geological disasters.

The hydrodynamic processes in the Bristol Channel and Severn Estuary are highly

complex due to the irregular land boundaries and the extremely high tidal range, and the

hydrodynamic processes of astronomic tides in the Severn Estuary have been studied

extensively by researchers and organisations using numerical models (Uncles, 1983;

Evans et al., 1990; Harris et al., 2004; DE et al., 1989). These models need to be refined



9

further and can be then used to analyse the potential risk of coastal flood in case of

extreme sea levels. Bates et al. (2005) applied a simple two-dimensional hydraulic model

to assess the coastal flood risk due to sea level rise in various areas at different scales.

Purvis et al. (2008) presented a methodology to estimate the probability of future coastal

flooding given uncertainty over possible values of sea level rise, and applied this

methodology to a 32 km coastal stretch of the Severn Estuary in South-West England. To

simulate the tide propagation in an estuary caused by storm surges or tsunamis, it is

necessary to incorporate additional terms into the governing equations defining the

hydrodynamic processes. For example, the time evolution of the bottom displacement is

usually included in the continuity equation of flow when simulating tsunami propagation,

and the wind stress needs to be calculated and the corresponding term needs to be

included in the momentum equations of flow when predicting the development of storm

surges (Jain et al., 2006; Wolf, 2009).

3.5 References

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[2] Bates PD, Dawson RJ, Hall JW, Horritt MS, Nicholls RJ, Wicks J, Hassan, MAAM. (2005)

Simplified two-dimensional numerical modelling of coastal flooding and example applications.

Coastal Engineering 52: 793-810.

[3] Begnudelli L and Sanders BF (2007). Conservative wetting and drying methodology for

quadrilateral grid finite-volume models. ASCE Journal of Hydraulic Engineering 133(3): 312–

322.

[4] Bellos V, Soulis JV and Sakkas JG (1992). Experimental investigations of two dimensional dam-

break-induced flows. IAHR Journal of Hydraulic Research 30(1): 47-63.

[5] Bonham AJ and Hattersley RT (1967). Low level causeways. University of New South Wales,

Water Research Laboratory, Technical Report No. 100.

[6] Bradford SF and Sanders BF (2002). Finite-volume model for shallow water flooding of arbitrary

topography. ASCE Journal of Hydraulic Engineering 128(3): 289-298.

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[11] Cox RJ and Ball EJ (2001). Stability and safety in flooded streets. In: Proceedings of conference

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[12] Defra (2005). The threat posed by tsunami to the UK. Study report commissioned by Defra Flood

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10

[15] Evans GP, Mollowney BM and Spoel NC (1990). Two-dimensional Modelling of the Bristol

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[16] Fagherazzi S and Sun T (2003). Numerical simulations of transportational cyclic steps.

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European Concerted Action on Dam-Break Modeling, Munich, pp. 175-222.

[18] Foster DN and Cox R (1973). Stability of children on roads used as floodways. Technical Report

No. 73/13, Water Research Laboratory, The University of New South Wales, Manly Vale, NSW,

Australia.

[19] Fraccarollo L and Armanini A (1998). A semi-analytical solution for the dam-break problem

over a movable bed. Proceedings of the European Concerted Action on Dam-Break Modeling,

Munich, pp 145-152.

[20] Fraccarollo L and Toro EF (1995). Experimental and numerical assessment of the shallow water

model for two-dimensional dam-break type problems. IAHR Journal of Hydraulic Research

33(6): 843-864.

[21] Gallegos HA, Schubert JE and Sanders BF (2009). Two-dimensional, high-resolution modeling

of urban dam-break flooding: A case study of Baldwin Hills, California. Advance in Water

Resources 32: 1323-1335

[22] Gordon AD and Stone PB (1973). Car stability on road floodways. The University of New South

Wales, Water Research Laboratory, Technical Report 73/12.

[23] Hall JW, Sayers PB, Walkden MJA and Panzeri M (2006). England and Wales: 2030 -2100

Impacts of climate change on coastal flood risk. Philosophical Transactions of the Royal Society

A, 364: 1027-1049.

[24] Hansen JE (2007). Scientific reticence and sea level rise. Environmental Research Letters, 2,

024002 (1-6).

[25] Harris EL, Falconer RA and Lin BL (2004).Modelling hydroenvironmental and health risk

assessment parameters along the South Wales Coast. Journal of Environmental Management 73:

61-70.

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12

4 Summary of the Key Findings

4.1 Modelling flood routing with the refined wetting and drying method

Significant refinements have been made to a two-dimensional hydrodynamic

model, based on a TVD finite volume method, to predict rapid flood flows on initially dry

beds. A Roe’s approximate Riemann solver, with the MUSCL scheme, has been used in

this model. The scheme is second-order accurate in both time and space and is free from

spurious oscillations. The model deploys unstructured triangular grids and adopts a

refined wetting and drying approach originally developed for a regular grid finite

difference model, DIVAST. This approach can be summarised as follows:

(1) Firstly, each cell is checked at the start of each time step to decide its type. In

this method, the computational cells are divided into three types. A cell is considered to

be active and wet if the water depth at the cell centre i

h is greater than a small value of

water depth, minh . A cell is considered dry with its velocity being set to zero, if i

h is less

than minh . Further, a dry cell can be classified as an inactive dry one if all of the three

surrounding cells are dry, and as an active dry cell if one of the three surrounding cells is

wet. The inactive dry cells will be removed temporarily out of the computational domain,

and this treatment can accordingly decrease the computer time in the case of lots of

inactive dry cells.

(2) Then, each wet cell or active dry cell is checked after each time step for possible

drying. If the predicted depth at the end of each time level i

h becomes less than minh ,

then this cell is set as a dry cell. In addition, the cell i is also treated as a dry cell, even if

ih is greater than minh but the maximum water depth Max( )

jh of the three surrounding

cells, around the cell i , is less than set

h . Here set

h is a preset small water depth, typically

of a value of 2 - 2.5 minh . However, the water elevation retained at this dry cell is set to

the value at the previous timestep when the cell was still wet.

(3) Finally, each inactive dry cell from step (1) is checked after each time step for

possible wetting. An inactive dry cell i is considered as being flooded and to be an active

dry cell if the water level at a neighbouring wet cell j around the dry cell is greater than

both the bed elevation at the centre of cell i and the midpoint bed elevation of the

common edge of cells i and j . An active dry cell will be returned to the computational

domain at the start of the next time step. Outflow of flow flux is not permitted from an

active dry cell, and the active dry cell can be re-introduced into a wet one only if one of

the surrounding cells is wet, provided that the flow flux entering this dry cell is large

enough.

The model has been applied to several cases, including the Glasgow flood in the UK

and a flood event in the Yellow River in China. Numerical model tests were undertaken

to investigate the sensitivity of model predictions to the value of a minimum depth as

required for treating the wetting and drying fronts. It has been found that the selection of

the minimum water depth has a significant impact on the speed of the flood wave

propagation on an initially dry bed. For a given time step, an excessively large value of

the minimum water depth will lead to inaccurate predictions of the wetting and drying

wave fronts, but a very small value will result in numerical instability (Fig. 2).



13

Fig. 2 Water depth profiles along the channel under different minimum depths

4.2 Modelling of dam-break flows over mobile beds using a coupled approach

Dam-break flows usually propagate along rivers and floodplains, where the

processes of fluid flow, sediment transport and morphological changes are closely linked.

However, the majority of existing 2D models used for simulating dam-break flows are

only applicable to a fixed bed. The hydrodynamic model described above has been

extended to include sediment transport and bed level changes to enable the prediction of

dam-break flows over mobile beds. In this model 2D shallow water equations are

modified to account for the effects of sediment concentration and bed evolution on flood

wave propagation, with the non-equilibrium transport equation for graded sediments

being used to represent the sediment transport processes. In addition, the model can take

account of the adjustment process of bed material composition during the morphological

evolution process. The sediment transport equation is solved in a semi-implicit manner.

The predictor-corrector scheme is used in time stepping, leading to a second-order

accurate solution in both time and space.

(1) Governing equations for flow and sediment transport

The hydrodynamic governing equations used are based on the two-dimensional

shallow water equations, but with additional terms being included to account for the

sediment effects on the fluid density and bed level change. The shallow water governing

equations of the 2D hydrodynamic model comprise the mass and momentum

conservation equations for the water-sediment mixture flow. The modified continuity and

momentum equations in the x and y directions can be expressed in detail as follows:

( ) ( ) ( ) bZh hu hv

t x y t

∂∂ ∂ ∂+ + = −

∂ ∂ ∂ ∂ (3)

2 2 2

2 2 012 2 2

( ) ( ) ( ) ( ) ( )2

m bbx fx t

s m m

u Zu u gh Shu hu gh huv gh S S hv

t x y x y x t

ρ ρρ

ρ ρ ρ

− ∂∂ ∂ ∂ ∂ ∂ ∆ ∂+ + + = − + + − +

∂ ∂ ∂ ∂ ∂ ∂ ∂ (4)

2 2 22 2 01

2 2 2( ) ( ) ( ) ( ) ( )

2

m bby fy t

m s m

v Zv v gh Shv huv hv gh gh S S hv

t x y x y y t

ρ ρρ

ρ ρ ρ

− ∂∂ ∂ ∂ ∂ ∂ ∆ ∂+ + + = − + + − +

∂ ∂ ∂ ∂ ∂ ∂ ∂ (5)

where t = time; h = water depth; u and v = velocity components in the x and y

directions, respectively; g = gravitational acceleration; t

ν = turbulent viscosity

coefficient; s f

ρ ρ ρ∆ = − , in which f

ρ = clear water density and s

ρ = sediment density;



14

mρ = density of water-sediment mixture 0ρ = density of saturated bed material,

0ρ = (1 / )s f

ρ ρ ρ ρ′ ′− + , in which ρ′ = dry density of bed material; S = total

concentration of graded sediments. The bed slope terms (bx

S ,by

S ) and friction slope

terms (fx

S ,fy

S ) are written as /bx b

S Z x= −∂ ∂ , /by b

S Z y= −∂ ∂ and

2 2 2 4/3/fxS n u u v h= + , 2 2 2 4/3/fyS n v u v h= + , in the x , y directions, respectively,

where b

Z = bed elevation; n = Manning’s roughness coefficient.

For the suspended load, the 2D non-equilibrium transport equation is given as:

*( ) ( ) ( ) ( ) ( ) ( )k k

k k k s s sk sk k k

S ShS huS hvS h h S S

t x y x x y yε ε α ω

∂ ∂∂ ∂ ∂ ∂ ∂+ + = + − −

∂ ∂ ∂ ∂ ∂ ∂ ∂ (6-1)

For the bed load, the 2D non-equilibrium transport equation is given as:

*( ) ( ) ( ) ( )bk bk bk bk bk bk b khq huq hvq q qt x y

α ω∂ ∂ ∂

+ + = − −∂ ∂ ∂

(6-2)

where sε = turbulent diffusion coefficient of sediment; subscript k represents the kth

sediment fraction; k

S , *kS , and skω represent, respectively, the sediment concentration,

sediment transport capacity and effective settling velocity for the kth fraction; sk

α = non-

equilibrium adaptation coefficient of suspended load, which is an empirical coefficient

associated with the rate of bed evolution. bk

q = amount of bed load in a unit volume of

water, in kg/m3;

bkω = setting velocity of bed load; *b k

q = transport capacity of bed load

in a unit volume of water, in kg/m3; and

bkα = non-equilibrium adaptation coefficient of

bed load.

The equation used to represent the suspended load induced during bed evolution is

written as:

*( )sksk sk k k

ZS S

tρ α ω

∆′ = −

∆ (7-1)

The equation used to represent the bed load induced during bed evolution is written as:

*( )bk

bk bk bk b k

Zq q

tρ α ω

∆′ = −

∆ (7-2)

where sk

Z∆ and bk

Z∆ = thicknesses of bed deformation caused by suspended load and

bed load, respectively, in one time step; and tZ∆ = total thickness of bed evolution in one

time step, given by:

t

1 1

s

s

N N

sk bk

k k N

Z Z Z= = +

∆ = ∆ + ∆∑ ∑ (7-3)

in which N = total number of fractions of non-uniform sediments; ands

N = number of

fractions of non-uniform suspended sediments. The model was used to study the

influence of using different sediment size distributions on the flood flow and channel bed

changes.

(2) Predicted results for a partial dam-breach flow in a mobile channel

Model studies were undertaken to investigate the differences in the speed of flood

wave propagation over fixed and mobile beds. The model results indicate that there is a

significant difference between dam-break flow simulations over fixed and mobile beds.

For a dam-break induced flow at the initial stage, the rate of bed evolution is comparable



15

to the rate of water depth variation near the dam site (Fig. 3). For mobile beds, the

erosion extent over a bed made up of uniform sediment is less than that over a non-

uniform sediment bed, while the maximum erosion depth obtained over the former is

greater than that over the latter (Fig. 4). The planar shape of the scour hole is

approximately elliptical over the uniform sediment bed and it is almost circular over the

non-uniform sediment bed, which indicates an increase in the erosion extent in the lateral

direction.

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

0 600 1200 1800 2400 3000 3600

Time (s)

Wa

ter

/ B

ed

le

ve

l (m

)

Case 0

Case 1

Case 2

Case 0

Case 1

Case 2

( a)-0.5

-0.1

0.3

0.7

1.1

1.5

0 600 1200 1800 2400 3000 3600

Time (s)

Wa

ter

/ B

ed

le

ve

l (m

)

Case 0

Case 1

Case 2

Case 0

Case 1

Case 2

( b)W

ate

r

Wate

r

Bed

Bed

Fig. 3 Water level and bed level variations downstream of the dam for (a) P1 and (b) P2

Fig. 4 Contours of bed levels after 1h for (a) uniform sediment; and (b) non-uniform sediment

4.3 Incipient velocity formula for fully submerged vehicles

Flash floods propagate rapidly, which can lead to a significant hazard to human life

and property. However, parked and unattended vehicles can also cause a hazard even in

slowly propagating urban floods when they move as floating debris.

A formula has been derived to predict the incipient velocity of flooded vehicles

according to the mechanical condition of sliding balance, with a key assumption being

made that the inside space of a prototype vehicle would be filled quickly by the

floodwater. A series of flume experiments were conducted using three types of scaled

die-cast model vehicles, with two scales being tested for each type of vehicle (Fig. 5).

More attention was focused on the case of fully submerged condition in these

experiments. The experimental data obtained for the small-scale model vehicles were

used to determine the two parameters in the derived formula (Fig. 6 and Table 1) and the

prediction accuracy of this formula was validated using the experimental data obtained

-1.4

-1.4

-1.2

-1

-1

-0.8

-0.6

-0.4

-0.4

-0.2

-0.2

-0.2

-0.1

-0.1

-0.1

X(m)

Y(m

)

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

-0.1

-0.2

-0.4

-0.6

-0.8-1

-1.2

-1.4

-1.6

Scour depth(m) (a)

-1

-0.8

-0.6

-0.6-0.4

-0.2

-0.2

-0.2

-0.2

-0.1

-0.1

-0.1

X(m)

Y(m

)

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

-0.1

-0.2

-0.4

-0.6-0.8

-1

-1.2

-1.4-1.6

Scour depth(m) (b)



16

for the large-scale model vehicles (Fig. 7). Finally, the corresponding incipient velocities

under various incoming depths were computed using this formula for these three

prototype vehicles (Fig. 8). It is found that for a specified vehicle the value of incipient

velocity reaches its minimum as the incoming flow depth approaches the height of the

vehicle. The smaller and lighter the vehicle, the easier for it to start sliding in floodwaters.

The results can be used as a preliminary assessment to define the hazard to vehicles

parking on flooded streets or roads.

Fig. 5 Fully and partially submerged vehicles in the flume

(1) Formula derivation and parameter determination

The incipient velocity formula for flooded vehicles has been derived, giving:

2 ( )f c f

c c

c f

hU g h

h

βρ ρ

αρ

− = × ×

(8)

in which f

h and c

h = water depth and vehicle height, respectively; c

ρ and f

ρ =

densities of the vehicle and water, respectively; g = gravitational acceleration; and α

and β = parameters related to the shape of a vehicle, the type of its tyres and the

roughness of road surface, which were determined in this study from flume experiments

using die-cast model vehicles.

Table 1 Different parameter values in the formula of incipient velocity

Flooding Degree Partially Submerged Fully Submerged

Parameters α β α β

Pajero Jeep 1.492 -0.731 0.737 0.532

BMW M5 1.116 -0.558 0.816 0.264

Mini Cooper 1.225 -0.708 0.932 0.121



17

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.00 0.02 0.04 0.06 0.08 0.10 0.12

h (m)

Uc (

m/s

) h > hch < hc (a) Pajero Jeep (1:43)

Fl ow di r ect i onh = incoming depth

hc = vehicle height=0.042

m

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.00 0.02 0.04 0.06 0.08 0.10 0.12

h (m)

Uc (

m/s

) h > hch < hcFl ow di r ect i onh = incoming depth

hc = vehicle height=0.038

m

(b) BMW M5 (1:43)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.00 0.02 0.04 0.06 0.08 0.10 0.12h (m)

Uc

(m

/s) h > hch < hc Fl ow di r ect i on

h = incoming depth

hc= vehicle height=0.032 m

(c) Mini Cooper (1:43)

Fig. 6 Incoming depths and corresponding incipient velocities of different vehicles

(For parameterisation)

(2) Formula validation and application



18

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.05 0.10 0.15 0.20 0.25

h (m)

Uc (

m/s

)

Pajero Jeep

BMW M5

Mini Cooper

Pajero Jeep

Mini Cooper

BMW M5

Fig. 7 Validation of Eq. (8) using the experimental data for 1:18 scaled vehicles

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

h (m)

Uc (m

/s)

Pajero Jeep

BMW M5

Mini Cooper

Fig. 8 Application of Eq. (8) in calculating the incipient velocities of prototype vehicles

4.4 Incipient velocity formula for partially submerged vehicles

Vehicles parking in urban areas can often cause various degrees of hazard to people

and buildings when they are swept away by flash floods. Therefore, it is necessary to

investigate the appropriate criteria of vehicle stability in floodwaters, especially under

partially submerged conditions.

In the present study different forces acting on partially submerged vehicles have

been analysed, with the corresponding expressions for these forces being presented, to

derive a mechanics-based formula of incipient velocity for partially submerged vehicles

parking in urban areas, with an important assumption being made that the inside space of

a prototype vehicle would not be filled quickly by floodwaters and the vehicle would

start to float when the outside water depth exceeds a specified depth. About 100 runs

of flume experiments were conducted to obtain the combinations water depth and the

velocity when a vehicle is at the threshold of instability for three typical types of die-cast

model vehicles of the same scale ratio of prototype-to-model dimensions (Fig. 9). The

experimental data from these model vehicles studies were then used to determine two key

parameters in the derived formula (Fig. 10, Fig. 11 and Table 2).

(1) Formula derivation and parameter determination



19

The formula of incipient velocity for partially submerged vehicles in floodwaters can

be expressed as:

2f c c

c c f

c f f

h hU gl R

h h

βρ

αρ

= −

(9)

where c

l = vehicle length; / ( )f c c k fR h hρ ρ= in which k

h = critical water depth at which

the vehicle starts to float. The values of α and β are related to the shape of a vehicle, the

tyre type and the roughness of the road surface, which are determined in this study by the

experimental studies using die-cast model vehicles in a flume.

Fig. 9a Different vehicle orientation angles undertaken in the experiments

Fig. 9b Partially submerged model vehicles in flume

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.01 0.02 0.03 0.04h (m)

U(m

/s)

180°

0°

(a) Ford Focus

Uc

(m/s

)

hf (m)

U

U



20

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0.01 0.02 0.03 0.04h (m)

U(m

/s)

180°

0°

(b) Ford Transit Uc

(m/s

)

hf (m)

U

U

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.01 0.02 0.03 0.04h (m)

U(m

/s)

180°

0°

(c) Volvo XC90

Uc (

m/s

)

hf (m)

U

U

Fig. 10 Depth-incipient velocity relationships for partially submerged model vehicles


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Measured (m/s)

Cal

cula

ted (

m/s

)

Ford Focus

Ford Transit

Volvo XC90

Fig. 11 Comparison between the calculated and measured velocities for different model vehicles




21

Table 2 Different parameter values for incipient velocity Formula Eq. (9)

Vehicles Parameters

α β

Ford Focus 0.500 -0.178

Ford Transit 0.227 -0.764

Volvo XC90 0.394 -0.630

(2) Formula validation and application

The flow conditions were regarded as being similar to those in the prototype if the

model displays similarity of form (geometric similarity), similarity of motion (kinematic

similarity) and similarity of forces (dynamic similarity) (Shen 1979, Zhang and Xie

1993).

The size of the model vehicles were required to strictly follow geometric similarity,

and three typical model vehicles were selected, therefore, with the same geometric scale

ratio of 18. The tests were designed in an undistorted scale model, due to the use of vivid

die-cast models, with the scale ratio of length λL being equal to that of height λH, namely

λL = λH = 18. According to the conditions for kinematic similarity, the scale ratio of the

inertia force to gravity gives the relationship between the scale ratios of velocity λU and

length λL, which can be expressed by λU = (λL)0.5

.

Dynamic similarity implies that the ratios of the prototype to model forces are equal to

the same scale ratio of λF, which is also equivalent to (λL)3. Herein, the selected density of

a model vehicle was nearly equal to that of the corresponding prototype, so that λFg = λF

and λFb = λF were also satisfied. Although vivid die-cast model vehicles were used, the

location of the model mass centre was likely to be different from that of a corresponding

prototype vehicle. It was thus assumed that all of the wheels were locked, and only the

motion pattern of vehicle sliding was considered. Therefore, the difference in the location

of the centre of mass between the model and prototype vehicles was neglected.

Furthermore, with such a scenario not being considered herein, then the uneven mass

centre distribution over the axles could lead to the back of the vehicle becoming buoyant

earlier and the frictional effect of the back wheels ceasing to contribute to stability. The

stability criteria under these specific scenarios needs to be investigated in the future. With

the relatively high values of the Reynolds number in the flume tests, the drag coefficient

was considered constant for a specified shape (Chanson 2004), so that Cd for the model

was nearly equal to that of the prototype. The measured depth-averaged velocities mainly

varied from 0.2 to 1.4 m/s, and the mean vehicle width was about 0.1 m, which led to

larger Reynolds numbers Re, ranging from 2.0×104

to 1.4×105, where Re = Ubc/ν; and ν is

the kinematic viscosity for water. Therefore, the similarity principle for the drag

coefficient was guaranteed for all of the model and prototype vehicles used, resulting in

λFD = λF.

The friction coefficient between the tyre and wet carpet for various model vehicles

was measured in the flume. A model vehicle was put in the horizontal flume with the bed

covered with a wet carpet, and with the vehicle then being pulled manually by a spring

balance. The value of the force shown on the balance was recorded as the vehicle started

to move. The value of the friction coefficient was equated to the ratio of the force

recorded on the spring to the vehicle’s weight. The measured values of the friction



22

coefficient were 0.39, 0.50 and 0.68 for the Ford Transit, Ford Focus and Volvo XC90,

respectively. Therefore, the range of friction coefficients for the model vehicles

corresponded well with the prototype ranges of between 0.25 and 0.75 (Kurtus 2005,

Gerard 2006). It was concluded that the friction coefficients for the models were nearly

equal to those for the prototypes, so that λFR = λF.

Since these model experiments strictly followed the principles of geometric,

kinematic and dynamic similarity, the incipient velocity obtained under a specified water

depth for a model vehicle could be directly used to estimate the critical condition for the

corresponding prototype vehicle according to the scale ratios. These scale ratios can be

expressed by:

fp fm Lh h λ= × and cp cm LU U λ= × (10)

where the subscripts p and m refer to prototype (full-scale) and model parameters

respectively; and L

λ = scale ratio of length .

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7hf (m)

Uc (

m/s

)

Eq.(12)(Ford Focus)

Eq.(12) (Ford Transit)

Eq.(12)(Volvo XC90)

Eq.(14)(Ford Focus)

Eq.(14)(Ford Transit)

Eq.(14)(Volvo XC90)

2004 Boscastle flood, UK

Ford Transit

Ford Focus

Volvo XC90

2010 Var flood, France

Visual Observations

Eq.(9) (Ford Focus)


Eq.(9) (Volvo XC90)

Eq.(10) (Ford Focus)


Eq.(10) (Volvo XC90)

Fig. 12 Comparisons between estimated incipient velocities for prototype vehicles using two

different approaches (Sources of visually-observed data: BBC (2004). Dozens rescued from flash floods.

BBC News < http://news.bbc.co.uk/2/hi/uk_news/england/cornwall/3570940.stm>; and BBC (2010). French flash

flood toll up to 25. BBC News < http://www.bbc.co.uk/news/10337433>)

Incipient velocities for partially submerged prototype vehicles in floodwaters were

estimated using two different approaches, including the predictions using the model scale

ratios and computations based on the derived formula (Fig.12). These critical conditions

in the prototype using the scale ratios compared well with the calculations using the

derived formula, and the derived formula was also validated by the visually-observed

data of swept vehicles in flash floods, which provided some degree of verification of the

estimation reliability of the incipient velocity formulation derived for partially submerged

prototype vehicles (Fig.12). Further details on the verification are available in Shu et al

(2011).



23

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(a) Maximum hazard degree of Pajero Jeeps

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(b) Maximum hazard degree of Mini Coopers

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(c) Maximum hazard degree of children

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(d)Maximum hazard degree of adults

References Chanson, H. (2004). The hydraulics of open channel flow: an introduction, 2

nd ed. Elsevier

Butterworth-Heinemann, Oxford UK.

Gerard, M. (2006). Tyre-road friction estimation using slip-based observers. Master thesis. Dept.

Automatic Control, Lund University, Lund Sweden.

Shu C, Xia J, Falconer R A, Lin B, (2011). Incipient velocity for partially submerged vehicles in

floodwaters, Journal of Hydraulic Research , 49 (6) 709-717 10.1080/00221686.2011.616318

Shen, H.W. (1979). Modeling of rivers. Wiley, New York.

Kurtus, R. (2005). Coefficient of friction values for clean surfaces. School for Champions, Oregon

USA. <http://www.school-for-champions.com/science/friction_coefficient.htm>.

Zhang, R.J., Xie, J.H. (1993). Sedimentation research in China. China Water & Power Press, Beijing.

4.5 2D modelling of flood hazard

Flash flooding often leads to extremely dangerous conditions due to its short

timescale, giving limited opportunity for issuing warnings, and hence can result in deaths.

Many past extreme flood events have been accompanied by flash floods, and they are one

of the main sources of serious loss of human life among natural disasters. Flash floods

can also cause heavy loss of property, such as the damage to a bridge and loss of vehicles

in the 2004 Boscastle flood in the UK. Therefore, flash floods often lead to casualties and

can cause damage to vehicles, especially in densely populated urban areas.

In flood risk management studies, it is desirable to be able to predict the degree of

safety of people and vehicles during flash floods using a numerical model. In the current

study, an algorithm for assessing the degree of safety of people and property has been

linked with an existing two-dimensional hydrodynamic model capable of simulating flash

floods, which comprises of a 2D integrated numerical mode for flood risk management.

In this algorithm, empirical functions relating water depths and corresponding critical

velocities for children and adults, developed from previous studies, are used to assess the

degree of people safety (Eq. (1) or Fig.1), and a new incipient velocity formula is used to

evaluate the degree of vehicle safety (Eq. (8) or Fig. 8).

Fig. 13 Distributions of maximum hazard degrees for different people groups and vehicles

The refined model was then applied to three real case studies, including: the

Glasgow and Boscastle floods in the UK, and the Malpasset dam-failure flood in France.

According to model predictions, the following conclusions have been drawn: (i) model



24

results for the Glasgow flood showed that children would be in danger of standing in the

flooded streets in some areas (Fig. 13); (ii) for the Boscastle flood model results indicated

that vehicles in the car park would be flushed away by the flow with a high velocity,

which indirectly testified the predictive accuracy of the incipient velocity formula for

vehicles (Fig. 14); and (iii) for the Malpasset dam-failure flood model results showed that

the adopted method for the assessment of people safety was applicable, and some local

people living below the dam would have been swept away, which corresponded well with

the report of casualties. Therefore, the enhanced model can be used to evaluate the flood

hazard degree of safety prediction for people and vehicles in flash floods.

Fig. 14 Distribution of maximum hazard degrees for the Pajero Jeep vehicle

4.6 Estimation of future coastal flood risk in the Severn Estuary

The Bristol Channel and Severn Estuary constitute a large, semi-enclosed body of

water in the southwest part of the UK. Communities have settled in the coastal lowlands

of this estuary for many centuries, and many of these lowlands and settlements have been

subject to the risk of coastal flooding and have relied on the protection of artificial sea

defences. According to the predicted future sea level rise and possible occurrence of

extreme sea levels due to climate change and storm surge events, the probability of

coastal flooding in the Severn Estuary will increase accordingly. On the other hand, the

Severn Estuary is an ideal site for tidal renewable energy projects, since this estuary has

the third highest tidal range in the world. Therefore, it is appropriate to predict the future

status of coastal flooding in this estuary for various scenarios combining the effects of

climate change and potential barrage construction. In this study, the finite volume

algorithm hydrodynamic model was modified to predict the hydrodynamic processes

associated with the operation of a tidal barrage. Three scenarios at the open seaward

boundary were considered, including the observed time series of water level as the

current baseline (Scenario I), the current level hydrograph plus a sea level rise of 1.0 m

(Scenarios II) and the current level hydrograph in Scenario I with a surge height of 1.0 m

(Scenarios III). Finally, the numerical model was used to simulate the hydrodynamic

processes in the Severn Estuary using three seaward boundary scenarios for the

conditions without and with the Severn Barrage (Fig. 15), and the flood risk in a small

coastal floodplain was assessed with these predictions and documented data.

Model predictions show that: (i) without the barrage, the maximum water levels

along the estuary could rise by 1.0-1.2 m due to sea level rise, and the effect of extreme

sea levels on the maximum water level would be noticeable only in the outer estuary

reach; (ii) with the barrage, the maximum water level could reduce by 0.5-1.2 m upstream



25

of the barrage, even if a sea level rise of 1.0 m were to occur, and extreme sea levels

could not influence the maximum water level upstream of the barrage; and (iii) the future

flood risk in a small coastal floodplain would reach £6.5 M/yr due to sea level rise

without the barrage, and such a coastal flood risk could be avoided completely if the

barrage were to be built as proposed.

(a) Scenario I

(b) Scenario II



26

Fig. 15 Predicted maximum levels with the barrage

5 Conclusions and Recommendations

The research has developed:

• a morphodynamic model to simulate the processes of flood routing,

sediment transport and corresponding bed evolution using a coupled

approach, with a refined wetting and drying approach,

• incipient velocity formulae for flooded vehicles under different scenarios for

assessing stability criteria of vehicles in floodwaters;

• an integrated numerical model to predict the inundation of flash floods and

the corresponding flood hazards to people (including children and adults)

and property (vehicles and buildings). The model was validated using some

observations obtained from three flash floods, which indicates the enhanced

numerical model can be used as an approximate assessment tool assist in

flood risk management.

Concerning the stability criteria of vehicles in floodwaters, the research proposed

two sets of incipient velocity formulae for different assumptions about the sealing

capacity of inside space of a vehicle. It should be pointed out that the current study was

based on relatively ideal circumstances that the direction of the incoming flow was

always facing the rear or front side of a vehicle and the channel bed was flat. For the

assessment of instability thresholds of flooded vehicles under real and more complex

circumstances, further studies need to be conducted in order to enable a more practical

application of the derived formulae, which should include: (i) the effect of different

incoming flow directions; (ii) the effect of different bed slopes; and (iii) the potential

prototype experiment with full-scale vehicles.

Concerning the integrated numerical model for predicting the flood risk to people

and property in urban areas, the additional algorithm developed for hazard degree

estimations is proposed as a valuable tool for flood risk managers responsible for

planning and issuing flood warnings etc., associated with flash floods in urban and

mountainous environments. However, a further calibration process is required in the

(c) Scenario III



27

future to check the reliability of the integrated model as more observed data become

available.



28

6 List of Publications

6.1 Peer-reviewed journal papers

[1] Xia JQ, Falconer RA and Lin BL (2011). Numerical assessment of flood hazard

risk to people and vehicles in flash floods. Environmental Modelling and Software

26(8): 987-998.

[2] Xia JQ, Falconer RA and Lin BL (2011). Modelling of Flash Flood Risk in Urban

Areas. Proceedings of the Institution of Civil Engineers-Water Management,

164(WM6): 267-282.

[3] Xia JQ, Falconer RA and Lin BL (2011). Estimation of future coastal flood risk in

the estuary due to the Severn Barrage. Journal of Flood Risk Management, 1-13

(DOI:10.1111/j.1753-318X.2011.01106.x).

[4] Xia JQ, Falconer RA and Lin BL (2010). Numerical model assessment of tidal

stream energy resources in the Severn Estuary, UK. IMECH, Part A, Journal of

Power and Energy 224(7): 969-983.

[5] Xia JQ, Falconer RA, Lin BL and Tan GM (2010). Modelling floods routing on

initially dry beds with the refined treatment of wetting and drying. International

Journal of River Basin Management 8(3-4): 225-243.

[6] Xia JQ, Fang YT, Lin B L and Falconer RA (2011). Formula of incipient velocity

for flooded vehicles. Natural Hazards, 58(1): 1-14.

[7] Xia JQ, Lin BL, Falconer RA and Wang GQ (2010). Modelling Dam-break Flows

over Mobile Beds using a 2D Coupled Approach. Advances in Water Resources

33(2): 171-183.

[8] Xia JQ, Falconer RA and Lin BL (2010). Impact of different operating modes for a

Severn Barrage on the tidal power and flood inundation in the Severn Estuary, UK.

Applied Energy 87(7): 2374-2391.

[9] Xia JQ, Falconer RA and Lin BL (2010). Impact of different tidal renewable energy

projects on the hydrodynamic processes in the Severn Estuary, UK. Ocean

Modelling 32(1-2): 86-104.

[10] Xia JQ, Falconer RA and Lin BL (2010). Hydrodynamic Impact of a Tidal Barrage

in the Severn Estuary, UK. Renewable Energy 35(7): 1455-1468.

[11] Falconer RA, Xia JQ, Lin BL and Ahmadian R (2009). The Severn Barrage and

Other Tidal Energy Options: Hydrodynamic and Power Output Modelling. Science

in China (Ser. E) 52(11): 3413-3424.

[12] Shu CW, Xia JQ, Falconer RA and Lin BL (2011). Estimation of Incipient Velocity

for Partially Submerged Vehicles in Floodwaters. Journal of Hydraulic Research (in

press).

[13] Xia JQ, Falconer RA and Lin BL (2011). Estimation of annual energy output from a

tidal barrage using two methods. Applied Energy (Under review).

[14] Xia JQ, Lin BL, Falconer RA and Wu BS (2011). 2D hydrodynamic Modelling of

Flood Flows in the Lower Yellow River. Proceedings of the Institution of Civil

Engineers, Water Management (Under review).

6.2 Conference papers

[15] Xia JQ, Falconer RA and Lin BL (2011).Theoretical Estimation and Numerical

modelling of annual energy output from a tidal barrage. Proceedings of 34th

IAHR

Congress, Brisbane, Australia, pp.1247-1254.

[16] Falconer RA, Xia JQ and Lin BL (2010). The Severn Barrage Project: Modelling



29

Comparisons for Power Generation and Hydrodynamic Impact. In: Proceedings of

the Second International Conference on Coastal Zone Engineering and

Management (Arabian Coast 2010), Sultan Qaboos University Press, Muscat-

Sultanate of Oman, pp. 41-50 (ISSN: 2219-1283).

[17] Xia JQ, Falconer RA and Lin BL (2010). Numerical assessment of people and

vehicles safety in flash floods. Proceedings of the first European IAHR conference,

Edinburgh.

[18] Xia JQ, Falconer RA and Lin BL (2010). Predicting the future coastal flooding in

the Severn Estuary. Proceedings of the first European IAHR conference, Edinburgh

(Keynote Lecture).

[19] Falconer RA, Xia JQ and Lin BL. (2010). Severn Barrage and other tidal energy

options: Environmental hydraulics studies. Proceedings of 6th

International

Symposium on Environmental Hydraulics, Athens, Greece. CRC Press, Vol. 1, 13-

26. (Keynote Lecture).

[20] Falconer RA, Xia JQ, Lin BL and Ahmadian R (2009).The Severn Barrage and

Fleming Lagoon: Hydro-environmental Impact Assessment Modelling. IWRSD

Forum in China.

[21] Xia JQ, Lin BL, Falconer RA and Wang GQ (2009). 2D Morphodynamic

Modelling of Dam-break Flows over Mobile Beds. Proceedings of 33rd

IAHR

Congress, Vancouver, Canada, IAHR, A-4, August 2009, pp.543-553.

[22] Falconer RA, Lin BL, Ahmadian R and Xia JQ. (2009). The Severn Barrage:

Hydro-environmental Impact Assessment Studies. Proceedings of 33rd

IAHR

Congress, Vancouver, Canada, IAHR, S-8, August 2009, pp.2075-2082.

[23] Xia JQ, Lin BL, Falconer RA and Wu BS (2008). An unstructured finite volume

algorithm for predicting man-made flood routing in the Lower Yellow River，

p289-295. Proceedings of the BHS 10th

National Hydrology Symposium. British

Hydrological Society (ISBN 1-903741-16-5).

2D Hydrodynamic Modelling: Mobile Beds, Vehicle Stability ...fcerm.net/sites/default/files/resources/wp1-1... · Vehicle Stability and Severn Estuary Barrage 4 3 Literature Review

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