Simulating Overtopping of seawall defences

B.D. Rogers*, M.V. McCabe, P.K. Stansby, D.A. Apsley

*RCUK Research Fellow

School of MACE

OutlineIntroduction to Overtopping: • The need for numerical models

Numerical Model 1:• Boussinesq-type model• Modification for Seawall

Numerical Model 2: • Smoothed Particle Hydrodynamics (SPH)• Effect of the recurve wall

Results:• Overtopping events and volumes

Prediction of Wave Overtopping

• Physical Models • Empirical Data

• Numerical Modelling?

Nonlinear Shallow Water Equations

hpu hp

Boussinesq – type equationsIntermediate depths

NLSW equationsShallow water only

Shallow Water and Boussinesq Equations with a Vertical Wall

231

31

0

2

22

3

33

2

32

2

breakpre

breakposte

b

xBgd

txhu

xdd

xuh

xxBgd

txhudB

xz

ghxhgh

xhu

thu

xhu

th

Continuity Equation

Momentum Equation

Boussinesq Terms Dissipation Terms

Fwallu

hwalldxuhk wallwall

2

Force Imposed by a Wall

0 200 400 600 800 1000 12000

1

2

3

4

5

6

7

Time (s)

Cum

ulat

ive

Volu

me

(m3

/m)

Wave Overtopping Volumes, Prototype ScaleHm0 = 3.41m, H0 / L0 = 0.04

SWAB Modelwith Force at

Seawall

Laboratory Data

Field Data(from EA)

SWAB Modelwithout Force

at Seawall

Shallow Water And Boussinesq (SWAB) Model Validation

ExampleOvertopping and Beach Level at Walcott Link to

Movie

2007 Storm – Overtopping Rates

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 82.35

2.4

2.45

2.5

2.55

2.6

Hm0 (

m)

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 81

1.5

2

2.5

3

3.5

Time (hours)

Wat

er L

evel

(maO

D)

3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 80

0.5

1

1.5

Mea

n O

verto

ppin

g R

ate

(l/s/

m)

Hourly Mean Overtopping Rates - SWAB Model vs Neural Network Tool

SWAB ModelNeural Network - No SetupNeural Network + Setup

Smoothed Particle Hydrodynamics (SPH)

Plunger

Splashup

(Photo courtesy of F. Raichlen)

Overtopping, flooding and inundation

Very complex multi-phase multi-scale

highly nonlinear problems

Breaking waves on beaches

W(r-r’,h)

Compact supportof kernel

WaterParticles

2h

Radius ofinfluence

rRadius of influence

Detailed modelling requires SPH

The Future: (Multi) Hybrid Chips• Dual-SPHysics (cpu & gpu) – SPEEDUPS of 100 for a Desktop machine = Supercomputer of

1000’s cores• Crespo et al.

SPH simulation

SPH simulation

SPH simulation

SPH simulation

SPH simulation

SPH simulation

3m

In SPH, we know that overtopping is dependent on resolution, so with a much finer resolution this could well produce higher values

Overtopping volumes from SPH Simulations

Results:• With the same bathmetry from the Boussinesq simulations:

overtopping events of 2400 litres/m• With the Recurve wall: overtopping event of 540 litres/m

Comparison with Boussinesq & Eurotop

Thank you

Acknowledgements:• Maurice McCabe• Nicolas Chini• Peter Stansby

• SeaZone – bathymetry below the low water line• Environment Agency (EA) – beach profile above the low water line