Development of a wave flume for the centrifuge

1. Development of a wave flume for the centrifuge Dr Tim Newson / Dr Ping Dong University of Dundee

2. Geo-fluids Research Group Academic staff • Dr. T.A. Newson • Dr. P. Dong • Dr M.F. Bransby • Professor Kenichi Sato • Professor M.C.R. Davies Research interests Coastal engineering, offshore engineering, in situ testing, numerical modelling, constitutive modelling, centrifuge modelling, element tests

3. Requirements for Appropriate Scaling in Physical Modelling • Requirement for similitude between material properties in prototype and model • Stress-strain behaviour of geomaterials is highly non-linear, stress level dependent and stress history dependent

4. The centrifuge ‘technique’

5. Gravity stress Gravity stress g ‘nth’ Scale Model g Prototype hm hp Depth Depth Stress Similitude in Model & Prototype

6. Inertia stress w w2. r Gravity stress g ‘nth’ Scale Model Prototype hm hp Depth Depth Stress Similitude in Model & Prototype

7. prototype: p     hp g  m    model:  (ng)    hp g hp n i.e. p = m Stress Similitude in Model & Prototype acceleration = r x  = n.g

8. Centrifuge Modelling Laws - Defined Quantities Physical quantity Prototype Model Macroscopic length 1 1/n Stress 1 1 Strain 1 1 Pore water pressure 1 1 Time : 1 2 diffusion processes 1 1/n inertial effects 1 1/n 2 Force 1 1/n Interstitial water velocity 1 n Heat flux 1 n

9. Centrifuge modelling Drum centrifuge Fixed beam centrifuge

10. Wave flumes on the centrifuge 50 g tests, 4m water depth, 4.5 m sand Sekiguchi et al. (2000) Viscous pore fluid - simultaneous scaling of consolidation & inertia

11. Centrifuge modelling Ultrasonic generator Wave Paddle Slotted partition Strong box Fluid 250 mm PWP transducers Soft soil 550 mm

12. Standing wave Progressive wave Anti-node Slotted partition Node Centrifuge modelling Wave Paddle Fluid PWP transducers Soft soil

13. Progressive waves (co = 0.13) Sub-liquefaction behaviour umax = 4 kPa

14. Standing waves (co = 0.20) Liquefaction behaviour umax = svo’

15. Critical wave loading for liquefaction Progressive Standing

16. Post wave loading behaviour Post wave pore pressures Surface settlement

17. Theoretical Basis Wave surface elevation where S0 is the displacement of the board at the water level The dispersion relationship where

18. Wave pressure at flume base Amplitude of wave pressure

19. Limitations 1. The real soil is not an ideal poro-elastic body 2. The theoretical model is applicable to semi- infinite soil, but the model soil in the centrifuge is of finite depth. 3. The influence of structures is not accounted for 4. Particle movement not accounted for

20. Scaling factors in centrifuge Basic parameters Acceleration g: N Model length scale, H, h, etc: 1/N Prototype soil materials used in the model Density ρ: 1 Particle size d: 1

21. Scaling factors in centrifuge Derived parameters Wave period T: 1/N Wave number k: N Fluid pressure: 1 Fluid flow velocity: 1 Inertia time scale: 1/N Laminar flow time scale: 1/N2 By using pore fluid with a high viscosity (N times higher) such as silicone oil, the laminar flow scale can be made to be 1/N

22. Paddle Design Dimensions of the strong box Japan Dundee (Sekiguchi et al. 1998) Length (mm) 550 1600 Height (mm) 250 680 Width (mm) 100 276 Wave generator Quasi-Flap Type Quasi-Flap Type

23. Dundee flume dimensions

24. Paddle and operation (1) AC servo motor (4) Crank shaft (2) Reduction wheel (5) Wave paddle (3) Attachment wheel (6) Wave channel

25. Typical operating conditions Japan Dundee Wave height: 10-23 mm 5-40 mm Wave frequency: 11 Hz 5-15 Hz Water depth: 90 mm 100-300 mm Sand bed thickness: 100mm 100-200mm Centrifugal accel.: 50 25-50 (? less)

26. Applications / Collaboration • Validation against large flume data • Validation/calibration of numerical models • Different soils: sand/silt/clayey/gassy? • Small structures: cylinder/sphere/cube (surface & buried) • Large structures: caisson/breakwater/cliff