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					Scale effects related to small scale physical modelling of
       overtopping of rubble mound breakwaters



                           Coastal Structures 2007, Venice



            Burcharth, H. F., Aalborg University, Denmark
           Lykke Andersen, T., Aalborg University, Denmark




      SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
              OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                          Burcharth & Lykke Andersen
                                                                   1 of 18
                   Coastal Structures 2007, Venice, July, 2007
                                               Contents

• The problem

• Scale and model effects

• Experimental set-up

• Verification of scaling of model experiments

• Video from experiments

• Results and conclusion




      SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
              OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                          Burcharth & Lykke Andersen
                                                                   2 of 18
                   Coastal Structures 2007, Venice, July, 2007
                                          The problem
• Admissible overtopping of breakwaters is an important design parameter
as it - roughly speaking - determines the crest level.

• In case of roads, sheds, storage areas etc. just behind the structure we
are dealing with very small limiting overtopping discharges characterized
by average values less than 1 litre/sm.

• The EU-CLASH project
showed that normal
size small scale rubble
mound models under
estimate smaller                                                                            app. 1 l/sm
overtopping discharges
compared to prototype
measurements.



                                         Comparison of model and prototype overtopping for antifer cube
                                         armoured breakwater at Zeebrugge (CLASH, 2006)
      SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
              OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                          Burcharth & Lykke Andersen
                                                                                                      3 of 18
                   Coastal Structures 2007, Venice, July, 2007
                                         The problem



• Note that small overtopping discharges are caused by very few
waves in a storm.


• Therefore, important to model these few waves kinematically
and statistically correct.




     SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
             OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                         Burcharth & Lykke Andersen
                                                                  4 of 18
                  Coastal Structures 2007, Venice, July, 2007
                           Scale and model effects
Deviations between model and prototype results are due to scale
and model effects

Scale effects due to incorrect reproduction of ratios between
forces in the model
  Inertia forces
                    Froude
                      U
                      gL
                                               Reynolds
                     Surface waves
  Gravity forces                                                   Cauchy
                                                  UL
                                                                   U²
                                               Porous flow                        Weber
                                                                   Wave slamming
  Viscous forces                                                                   U² L
                                                                                     
                                                                                   Air content


  Elastic forces



  Surface tension
        SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
                OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                            Burcharth & Lykke Andersen
                                                                                                 5 of 18
                     Coastal Structures 2007, Venice, July, 2007
                         Scale and model effects
Model effects
• Deviations in wave kinematics (directionality, wave height
distribution, succession of waves, degree of instability)

• Methods in wave recording (pressure gauge, accelerometer
buoy, acoustic, staff)

• Methods of wave analysis

• Geometrical differences (width of overtopping tanks, sea bed
topography, ……)

• Lack of wind and currents

Impossible to separate and quantify scale and model effects for
small overtopping discharges by comparing model and prototype
results.
      SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
              OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                          Burcharth & Lykke Andersen
                                                                   6 of 18
                   Coastal Structures 2007, Venice, July, 2007
                                                                  Flow regimes
  Some scale effects can be studied by comparing small and large scale
  models (typical length scale ratios 1:5 – 1:10) because similar incident
  waves or flows can be generated due to the controlled environment.

  Regimes of scale effects in run-up on rubble slopes:
                                                                             Surface flow upper part of wedge
Wave propagation                           Wave breaking and impact
                                                                             (Reynolds, Weber)
                                           (Reynolds, Weber, Cauchy)               4
                    1                                2
                                                                 3


                                                          e
                                                       edg
                                                rt of w
                                               a
                                       w   er p
                                  w lo
                         fac e flo                                                                    Porous flow
                     Sur nolds)                                                                       (Reynolds)
                      (R ey                                                                                         Illustration of surface flow and
                                                                                                                    porous flow domains during
                                                                                                                    run-up (Burcharth, 2004)


  The run-up height determines the overtopping. The CLASH project showed
  bigger overtopping deviations between model and prototype for flatter
  slopes. This could be due to increased flow resistance in the upper part of
  the run-up wedge. Here the run-up has the characteristics of a flow
  between obstacles for which drag coefficients can be very dependent on
  the Reynolds number.
                   SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
                           OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                                                    Burcharth & Lykke Andersen
                                                                                                                                               7 of 18
                                            Coastal Structures 2007, Venice, July, 2007
   Investigation of scale effects in the upper part
      of the run-up wedge by physical models
Reynolds effect
The larger the drag force on the armour the smaller will be the run-up.

The drag coefficients in Morison and Forcheimer equations decreases with
increasing Reynolds number in the actual range of fully turbulent flow.

                                                            CD



                 Schematic illustration
                 of drag variation with
                 Reynolds’ number
                                                                                            UL
                                                                                        Re = 




                                                                            prototype
                                                                    model
As the reduction in drag coefficients are less for sharp edged objects it
was chosen to use cubes as armour elements in order to demonstrate a
lower limit for the scale impact. Consequently, the scale effect on rock
armour is expected to be larger than seen in the present tests.
       SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
               OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                           Burcharth & Lykke Andersen
                                                                                                 8 of 18
                    Coastal Structures 2007, Venice, July, 2007
 Investigation of scale effects in the upper part
    of the run-up wedge by physical models
Surface tension effect
The surface tension is relatively much smaller in large scale
models and prototypes than in the small scale models. This cause
very different air bubble structures with many more smaller air
bubbles in larger scale models and especially in salt water
prototypes (Bullock et al., 2001)

The Reynolds and surface tension scale effects cannot be
separated in the tests.




     SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
             OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                         Burcharth & Lykke Andersen
                                                                  9 of 18
                  Coastal Structures 2007, Venice, July, 2007
                                                   Test set-up
   A jet-like up-slope flow on a cube armoured impermeable ramp
   was generated by instant removal of a hatch to a reservoir.
                                                                       Cross section

                                                                     16.7 L                           Cube side length L


                                                                                                           p




                                                                                h = 10.9 L
                                                                                                     Ram 5
                                                                                                           7
                                                                    Reservoir                         1:2.
                                                                                             Hatch             L
Two geometrically absolute                                                                   2.5 L      20.8
similar models of length
ratio 1:5 were used:                                                Plane view of ramp

  18.0 mm small scale
L
  90.0 mm large scale
                                           Hatch




                                                                                                           7L
Porosity = 0.42
Width between cubes = 0.3 L
         SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
                 OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                             Burcharth & Lykke Andersen
                                                                                                                10 of 18
                      Coastal Structures 2007, Venice, July, 2007
       Determination of minimum size of model

The flow must imitate as closely as possible wave run-up on an armour
slope.

Critical Reynolds’ number for armour stability:
Re 
     UL
      
           app. 3.5  10 4        
                            U  g Hs                  
Outflow from reservoir:
U  2gh

with small scale cube side length l = 18 mm and  = 10-6 m2/s
=> head h in reservoir  0.193 m




       SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
               OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                           Burcharth & Lykke Andersen
                                                                    11 of 18
                    Coastal Structures 2007, Venice, July, 2007
       Scaling law for initial outflow of reservoir

For the instant flow through the sharp edge hatch opening only gravity
and inertia forces dominates (Froude model) when according to Hager
(1998) the hatch opening time top  1.25(h/g)0.5, which

                          0.17 s small scale
t op  1.25 h / g 0.5  
                          0.39 s large scale




        SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
                OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                            Burcharth & Lykke Andersen
                                                                     12 of 18
                     Coastal Structures 2007, Venice, July, 2007
                 Photos of the two models




SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
        OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                    Burcharth & Lykke Andersen
                                                             13 of 18
             Coastal Structures 2007, Venice, July, 2007
                Video – small scale model




SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
        OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                    Burcharth & Lykke Andersen
                                                             14 of 18
             Coastal Structures 2007, Venice, July, 2007
                Video – large scale model




SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
        OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                    Burcharth & Lykke Andersen
                                                             15 of 18
             Coastal Structures 2007, Venice, July, 2007
                       Photos of max run-up



Small scale




Large scale



 SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
         OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                     Burcharth & Lykke Andersen
                                                              16 of 18
              Coastal Structures 2007, Venice, July, 2007
             Results and conclusions
The run-up tongue reaches 3 cube length further in the
large model than in the small model.

The vertical run-up height is 1L larger in the large scale
model than in the small scale model.

This shows a significant scale effect solely related to run-
up in the upper part of the wedge and probably explain
to a large extent why small scale models underpredict
small overtopping discharges.

Equivalent changes in run-up correspond to typical
overtopping discharges is increased by approximately a
factor of 5 to 10 in a large scale model.



SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
        OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                    Burcharth & Lykke Andersen
                                                             17 of 18
             Coastal Structures 2007, Venice, July, 2007
    Difference in mean overtopping discharge
     equivalent to run-up height difference L
•   h=9m
•   Hs = 5 m
•   s0p = 0.04
•   L = 2 m (KD = 4)
•   Gc = 3L = 6 m
•   Slope 1:2


Ac = Rc = 6.5 m            =>         q = 1 l/sm (CLASH NN)
Ac = Rc = 4.4 m            =>         q = 10 l/sm (CLASH NN)


Ac,Rc increased by 1 L
Ac = Rc = 8.5 m =>                    q = 0.15 l/sm (CLASH NN)
Ac = Rc = 6.4 m =>                    q = 1.1 l/sm (CLASH NN)


     SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
             OVERTOPPING OF RUBBLE MOUND BREAKWATERS
                         Burcharth & Lykke Andersen
                                                                  18 of 18
                  Coastal Structures 2007, Venice, July, 2007