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