1. Institute of Oceanology Polish Academy of Sciences Groundwater flow induced by surface waves on a permeable beach S. R. Massel, A. Przyborska, M. Przyborski Institute of Oceanology of the Polish Academy of Sciences Sopot, Poland

2. Institute of Oceanology Polish Academy of Sciences Institute of Oceanology

3. Polish Academy of Sciences

4. Institute of Oceanology Polish Academy of Sciences Importance of groundwater flow Sustaining the productivity of shallow water transporting organic matter and dissolved oxygen to beach body support the solar radiation into organic carbon with high efficiency (about 67 g C m -2 per year) support the beach action as effective biological filters and beach self-cleaning enhance the decomposition of dead organic matter in beach body influence on sediment transport at shallow waters influence on stability of engineering structures

5. Institute of Oceanology Polish Academy of Sciences GWK Hannover (Germany)

6. Institute of Oceanology Polish Academy of Sciences GWK Hannover (Germany)

7. Institute of Oceanology Polish Academy of Sciences Beach sand characteristics (a)

8. Institute of Oceanology Polish Academy of Sciences Beach sand characteristics (b)

9. Institute of Oceanology Polish Academy of Sciences Arrangement of pore pressure recording systems

10. Institute of Oceanology Polish Academy of Sciences Arrangement of wave gauges

11. Institute of Oceanology Polish Academy of Sciences Pore pressure sensors

12. Institute of Oceanology Polish Academy of Sciences Layout of the pressure system

13. Institute of Oceanology Polish Academy of Sciences Test 01 System 4 : H=0.4 [m],T=8 [s] 00.511.522.5 x 10 4 -15 -10 -5 0 5 10 15 20 test01 P1 P2 P3 P4

14. Institute of Oceanology Polish Academy of Sciences Test 01 System 1 : H=0.4 [m],T=8 [s] 00.511.522.5 x 10 4 -2 0 2 4 6 8 10 12 14 16 test01 P1 P2 P3 P4

15. Institute of Oceanology Polish Academy of Sciences Pore pressure components:  phase-resolving component of pore pressure  (fast varying) - outside of breaking zone  phase-averaged component of pore pressure  (slowly varying) - within breaking zone

16. Institute of Oceanology Polish Academy of Sciences Test 07 System 2 : H=0.2 [m],T=8 [s] 051015 x 10 4 -4 -2 0 2 4 6 8 10 12 14 test07 P1 P2 P3 P4 Red pressure range is growing up; sensor become out of sand

17. Institute of Oceanology Polish Academy of Sciences

18. Institute of Oceanology Polish Academy of Sciences Model 1: non-deformable porous bed and incompressible fluid (a)  porous bed is rigid and non-deformable  isotropic permeability  fluid is incompressible  fluid motion is expressed by Darcy’s law

19. Institute of Oceanology Polish Academy of Sciences Model 1: non-deformable porous bed and incompressible fluid (b) Governing equation and its solution due to periodic surface waves: Pressure is independent of the permeability of the bed material

20. Institute of Oceanology Polish Academy of Sciences

21. Institute of Oceanology Polish Academy of Sciences Model 2: grain skeleton is rigid and water is compressible - bulk modulus of water -governing equation -continuity equation

22. Institute of Oceanology Polish Academy of Sciences Model 3: elastic deformation of porous bed and compressible fluid (a) bed skeleton and water are elastic media - Young modulus of water without air content - influence of air content E s = 1.5·10 9 - coarse sand = 0.5 - 5·10 8 - fine sand = 0.5·10 5 - 0.2·10 7 - sandy clay - water compressibility - skeleton compressibility

23. Institute of Oceanology Polish Academy of Sciences Biot’s two phase model Linearised momentum eqs. solid skeleton: fluid:

24. Institute of Oceanology Polish Academy of Sciences Model 3: elastic deformation of porous bed and compressible fluid (b)

25. Institute of Oceanology Polish Academy of Sciences Normalised pore pressure (amplitudes)

26. Institute of Oceanology Polish Academy of Sciences Solid skeleton displacements (amplitudes)

27. Institute of Oceanology Polish Academy of Sciences Normalised pore pressure (amplitude)

28. Institute of Oceanology Polish Academy of Sciences Normalised pore pressure (arguments)

29. Institute of Oceanology Polish Academy of Sciences Solid skeleton displacements (amplitudes)

30. Institute of Oceanology Polish Academy of Sciences Solid skeleton displacements (arguments)

31. Institute of Oceanology Polish Academy of Sciences Conformal mapping technique

32. Institute of Oceanology Polish Academy of Sciences Velocity patterns

33. Institute of Oceanology Polish Academy of Sciences Components of pore water velocity

34. Institute of Oceanology Polish Academy of Sciences Film

35. Institute of Oceanology Polish Academy of Sciences Conclusions  Using the excellent laboratory conditions, a large number of high quality data has been collected  Two components of the pore pressure have been detected in the recorded pressures  The phase-averaged pressure component is clearly seen only for the pressures within the breaking and run-up zone  The phase-resolving component of pore pressure dominates  outside of breaking zone. The Biot’s theory provides good  prediction of the pressure  The collected data will serve as a reference material for theoretical models which are under preparation