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# Chapter 5: Use of Theory

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5. Use of Theory

5. Use of Theory

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• 1. Chapter 5: use of theoryct5308 Breakwaters and Closure DamsH.J. VerhagenFebruary 1, 2012 1Faculty of Civil Engineering and GeosciencesVermelding onderdeel organisatieSection Hydraulic Engineering
• 2. Theoretical background needed • waterlevels (tides) • flow trough gaps • stability of floating objects • waves • basics • refraction, shoaling, breaking, diffraction, reflection • wave statistics • short term statistics (Rayleigh) • long term statistics • Geotechnics • sliding • squeeze • liquefactionFebruary 1, 2012 2
• 3. Initial tidal wave by the moon andthe sunFebruary 1, 2012 3
• 4. Adding semi-diurnal constantsresulting in spring and neap tideFebruary 1, 2012 4
• 5. Adding diurnal to semi-diurnalconstantFebruary 1, 2012 5
• 6. Amphidromy in the North SeaFebruary 1, 2012 6
• 7. typical tidesFebruary 1, 2012 7
• 8. adding the fortnightly constantFebruary 1, 2012 8
• 9. flow pattern in a gapFebruary 1, 2012 9
• 10. Flow over a sill subcritical flow Q  mBh 2 g ( H  h) Q h u m 2 g ( H  h) Ba a critical flow 1 Q = mBa 2g H 3 2 1 Q  m B( H ) 2 g ( H ) and um 2 3 3 2 1 1 Q  m B( H ) 2 g ( H ) and u  m 2 g ( H ) 3 3 3February 1, 2012 10
• 11. modellingQ H + Bx = 0x t Q  (  Q u) H g Q Q  g A  2 W x  0t x x C AR Solving these equation by: •physical model •mathematical model •2 d model •1 d model •storage area approachFebruary 1, 2012 11
• 12. Physical modelFebruary 1, 2012 12
• 13. two dimensional modelOosterscheldewerken, Waqua, Rijkswaterstaat/WL Korea, Gaduk port, Mike21, DHI February 1, 2012 13
• 14. one-dimensional modelFebruary 1, 2012 14
• 15. storage/area approach Q H + Bx = 0 x tFebruary 1, 2012 15
• 16. validity of storage/area approach length of tidal wave: L= c*T = gh * T = 10*10 *12*3600 = 432 km basin < 0.05 L = 20 kmFebruary 1, 2012 16
• 17. equations for storage/area approach dh3  Ag 2 g ( H1  h2 )  B  QR (t ) dt 2 h2  h3 for h3  H1 3 2 2 h2  H1 for h3  H1 3 3 Ag and B can be combined to one input parameterFebruary 1, 2012 17
• 18. parameters needed• water level in the sea• river discharge• ratio between storage area and width of closure gap• sill height• discharge coefficient of the gapAssume for the time being that the river discharge is zero and that the tide is always semi-diurnalSet the discharge coefficient of the gap to 1Remaining parameters:• tidal difference• ratio storage area/gap width• sill heightFebruary 1, 2012 18
• 19. design graph for the velocityFebruary 1, 2012 19
• 20. example of the use of a design graphFebruary 1, 2012 20
• 21. velocity as a function of the closureFebruary 1, 2012 21
• 22. Stability of a submerged objectFebruary 1, 2012 22
• 23. Stability of a floating object I MC  V .5b 1 I  yx 2 dx  LB3 .5b 12 G V gFebruary 1, 2012 23
• 24. Definition of a regular wave H H wave height H cos  2 x  2 t   2  T wave period   L T  L wave length gL  2 h  c tanh   2  L  gT 2 c  ghL0   1.56T 2 2February 1, 2012 24
• 25. validity for wave theoriesFebruary 1, 2012 25
• 26. breakingby steepness H/L< 0.14by depth H/h < 0.78 but…………….February 1, 2012 26
• 27. Irregular waveFebruary 1, 2012 27
• 28. Rayleigh graph paper   H 2   2     Hs   P( H  H )  e  February 1, 2012 28
• 29. characteristic wave heightsName Notation H/m0 H/HsStandard deviation free surface =m0 1 0.250RMS height Hrms 22 0.706Mean Height H = H1 2ln 2 0.588Significant Height Hs= H1/3 4.005 1Average of 1/10 highest waves H1/10 5.091 1.271Average of 1/100 highest waves H1/100 6.672 1.666Wave height exceeded by 2% H2% 1.4February 1, 2012 29
• 30. characteristic wave periods Name Notation Relation to spectral T/Tp moment Peak period Tp 1/fp 1 Mean period Tm (m0/m2) 0.75 to 0.85 Significant period Ts 0.9 to 0.95February 1, 2012 30
• 31. typical types of wave statisticspatternsFebruary 1, 2012 31
• 32. H/T-diagramFebruary 1, 2012 32
• 33. waves in shallow water shoaling H 1 1    ksh refraction H0 tanh  2 h / L  1  4 h / L  breaking sinh  4 h / L  diffraction reflectionFebruary 1, 2012 33
• 34. the iribarren number(surf similarity parameter) tan   H L0 tan  slope of the shoreline/structure H wave height L0 wave length at deep waterFebruary 1, 2012 34
• 35. breaker types (2) spilling  < 0.5 plunging 0.5 <  < 3 collapsing  = 3 surging  > 3February 1, 2012 35
• 36. breaking waves  2  H b  0.142 L tanh  h  L  Hb  0.78 ( solitarywave) h Hs  0.4  0.5 hFebruary 1, 2012 36
• 37. change of distribution in shallowwaterFebruary 1, 2012 37
• 38. Battjes Jansen method    H 2   F1 ( H )  1  exp      H  H tr    H    1 Pr  H  H       H 3.6   F2  H   1  exp      H  H tr     H2     February 1, 2012 38
• 39. Influence of shallow water on thewave heightFebruary 1, 2012 39
• 40. Wave refraction  c2  sin  2    sin 1  c1  H2 b1  H1 b2February 1, 2012 40
• 41. Diffraction behind a detachedbreakwaterFebruary 1, 2012 41
• 42. reflection HRKr   0.1 2 HI     tot i r  1  r  Hi 2     H    cos 2 x *cos 2 t  1  r  i sin 2 x *sin 2 t L T 2 L T  February 1, 2012 42
• 43. Example with Cress run demo Cress refraction shoaling, etc diffraction y (-200,200) x(50-200;4)February 1, 2012 43
• 44. The effect of shoaling on waveparametersFebruary 1, 2012 44
• 45. Typical wave record of the North Sea  t    a cos  2 f t    i i i  S    1  ai2  2 H s  4 m0  H13.5%February 1, 2012 45
• 46. Spectral wave periodsThe use of different wave parameters to obtain better results for wavestructure interaction  mn   f S  f  df n 0ct5308 Breakwaters and closure damsH.J. VerhagenFebruary 1, 2012 46Faculty of Civil Engineering and GeosciencesVermelding onderdeel organisatieSection Hydraulic Engineering
• 47. Example wave record 28 waves, Hs = "13% wave", Hs= wave nr 4, Hs ≈ 3.8 28 waves in 150 seconds, so Tm = 5.3 sFebruary 1, 2012 47
• 48. composition of the record H1 = 0.63 m T1= 4 sec H2 = 1.80 m T2 = 5 sec H3 = 1.55 m T3 = 6.67 sec H4 = 0.90 m T4 = 10 sec Tm = 5.3 secFebruary 1, 2012 48
• 49. Spectrum discretised spectrum energy density spectrum1 2 a  S  f 7 72 6 6 energy density (m 2s) energy density (m 2s) 5 5 4 4 3 3 2 2 1 1 0 0 0,1 0,15 0,2 0,25 0 0,1 0,2 0,3 0,4 frequency (Hz) frequency (Hz) H2 1.552H  8S  f S   6 [m 2 s ] 8f 8  0.05 February 1, 2012 49
• 50. Calculation of m0 discretised spectrum 7 6 energy density (m 2s) 5 4 3 0.05*2 0.10 2 1 0.05*6 0.30 0 0,1 0,15 0,2 0,25 frequency (Hz) 0.05*3 0.15 0.05*1 0.05 0.60 4 m0  3.1 m mn   f n S  f  df 0 February 1, 2012 50
• 51. Calculation of m1 discretised spectrum 7 6 energy density (m 2s) 5 4 dist * Sf 3 2 0.10*0.10 0.010 1 0 0.15*0.30 0.045 0,1 0,15 0,2 0,25 frequency (Hz) 0.20*0.15 0.030 0.25*0.05 0.013 0.098 mn   f n S  f  df 0 February 1, 2012 51
• 52. Calculation of m2 discretised spectrum 7 6 energy density (m 2s) 5 4 dist2 * Sf 3 2 0.102*0.10 1.00 10-3 1 0 0.152*0.30 6.75 10-3 0,1 0,15 0,2 0,25 frequency (Hz) 0.202*0.15 6.00 10-3 0.252*0.05 3.12 10-3 m0 0.60 T  10  5.69sec 1.69 10-3 m2 1.69 mn   f n S  f  df 0 February 1, 2012 52
• 53. Calculation of m-1 discretised spectrum 7 6 energy density (m 2s) 5 4 1/dist * Sf 3 2 1/0.10*0.10 1.0 1 0 1/0.15*0.30 2.0 0,1 0,15 0,2 0,25 frequency (Hz) 1/0.20*0.15 0.75 1/0.25*0.05 0.20 m1 3.95 Tm1,0    6.58 sec 3.95 m0 0.60 mn   f n S  f  df 0 February 1, 2012 53
• 54. Overview Usual assumptions: Tm0 = Tp•Hm0 = 3.1 m(1.55+1.10+0.90+0.63=4.18) T1/3 = Tm•Tm0 = 5.69 sec•Tm-1,0 = 6.58 sec•Tpeak = 6.67 sec For standard spectra: Tm 1,0 6.58 Goda: Tp=1.1 T1/3•   1.16 PM: Tp=1.15 T1/3 T m0 5.69•Tm = 5.35 sec Jonswap: Tp=1.07 T1/3 Tm 0 5.69 TAW (vdMeer): Tp=1.1Tm-1,0•   1.06 Tm 5.35 Old Test (vdMeer): Tp=1.04 Tm-1,0 Also: Tm-1,0=1.064T1/3February 1, 2012 54
• 55. Overview to determine shallow water wavecondition• Determine deep water wave condition, this gives wave height, peak period and spectrum shape type (e.g. Jonswap)• Calculate shallow water condition using spectral model (e.g. with SWAN), this gives Hm0, Tm0 and Tm-1,0• Use Battjes-Jansen method to determine H2%February 1, 2012 55
• 56. Why these parameters ? 0.2 0.18  S  s  H 2% 0.25  c pl P   m 1,0 cot  for plunging waves d n50  N 0.2 0.13  S  s    H 2% 0.25 P  0.5  cs P   m 1,0 s 1,0 for surging waves d n50  NFebruary 1, 2012 56
• 57. stress relations determined by soiltestingFebruary 1, 2012 57
• 58. Dam profile after the slideFebruary 1, 2012 58
• 59. SqueezeFebruary 1, 2012 59
• 60. Liquefied sandFebruary 1, 2012 60