BED, BANK & SHORE BED, BANK & SHORE PROTECTION - CHAPTER 6 doc

BED, BANK & SHORE BED, BANK & SHORE PROTECTION PROTECTION Lecturer: Pham Thu Huong Lecturer: Pham Thu Huong Faculty of Coastal Engineering Faculty of Coastal Engineering Chapter 6 Chapter 6 Waves Waves - - Loads Loads (6 class hours) Content Content 6.1 Introduction 6.2 Non breaking waves 6.3 Breaking waves 6.4 Wave on the slope 6.4 Reduction of wave loads 6.5 Summary Wave issues Wave issues 1. Wave generation 2. Wave hydrodynamics 3. Wave statistics Generation: H, T characteristic = f (u wind , h, fetch) Hydrodynamics: u, p, τ = f (H,T,h) Statistics: p(H) = f (H characteristic , distribution function) Examples of wave loads Examples of wave loads In which: In which: (A) (A) - - standing wave standing wave (B) (B) - - breaking wave on a mild slope breaking wave on a mild slope (C) (C) - - breaking wave on a steeper slope breaking wave on a steeper slope Wave motion in periodic, Wave motion in periodic, unbroken wave unbroken wave Validity of wave theories Validity of wave theories Application of linear theory Application of linear theory gradient in filter under breakwater gradient in filter under breakwater Friction under waves Friction under waves [...]... sinh kh ω : angular frequency in waves (=2π/T) ˆ u = ub sin ω t cf = e 2 b ⎡ − 6. 0 + 5.2 ( a / k )−0.19 ⎤ b r ⎢ ⎥ ⎣ ⎦ with: c f max = 0.3 Near -shore effects Shoaling Near -shore effects Shoaling Refraction Near -shore effects Shoaling Refraction Diffraction Near -shore effects Shoaling Refraction Diffraction Reflection Near -shore effects Shoaling Refraction Diffraction Reflection Breaking breaking waves... ⎠ limits: 0 .6 < γB < 1 and -1 < dh /Hs < 1 Shallow foreshore γf = H2% / 1.4Hs run-down Battjes formula, 1994: Rd = Ru (1 − 0.4 ξ ) = = H (1 − 0.4 ξ ) ξ Rd 2% = − 0.33 H s ξ p ( Rd 2% max = −1.5 H s ) Example A dike with concrete block revetment, slopes 1:3 and a 2 m berm at design level is attacked by perpendicular (swell) waves with Hs = 1 m and a steepness of 0.01 What is the wave run-up? HS = 1... distribution in shallow water run up Run-up calculation Hunt’s Formula (for regular waves) Ru =ξ H CUR/TAW, 1992 (for Irregular waves) Ru 2% = 1.5 γ rγ β γ Bγ f H s ξ p correction factors: • γr roughness • γβ approach angle berm reduction • γB • γf foreshore reduction ( Ru 2% max = 3 H s ) Wave run-up irregular wave Hs = significant wave height ξ0 = breaker parameter based on Tm-1,0 For smooth slope friction... Asphalt, concrete, smooth blocks, grass, Sand-asphalt Blocks in asphalt or concrete matrix, blocks with grass Placed block revetment 0.95 0.90 0.80 0.70 0.55 riprap penetrated with asphalt Single layer of riprap Double layer of riprap Angle of attack For long crested waves (swell) γβ = √cos β (with minimum of 0.7) For short crested waves (wind wave) γβ = 1 - 0.0022 (β in degrees) (with a minimum of 0.8)... α slope of the shoreline/structure H wave height L0 wave length at deep water breaker types breaker types spilling ξ < 0.5 (sóng vỗ bờ) plunging 0.5 < ξ < 3 (Sóng cuộn đổ) collapsing ξ = 3 (sóng đổ) surging ξ > 3 (sóng cồn, sóng dâng) bore and hydraulic jump reflection Battjes, 1974 HR Kr = ≈ 0.1ξ 2 HI small ξ Kr = 1 less reflection seawall (standing wave) Loads due to breaking Breaker-depth γb = H/h... 2m 1:3 Ru ? solution Starting point is equation for run-up irregular wave Ru2% Ru 2% = 1.5 γ rγ β γ Bγ f H s ξ p γr = 0.9 2 ⎛ ⎡ hB ⎤ ⎞ B γ B = 1 − B ⎜1 − 0.5 ⎢ ⎥ ⎟ LB ⎜ ⎣ Hs ⎦ ⎟ ⎝ ⎠ ( Ru 2% max = 3 H s ) hB = 0 hence, γB = 0.75 LB = 2Hscotα + 2 = 8 m γβ = 1 and γf = 1 The surf similarity parameter is tanα/0.1 = 3.33 > 2, hence ξ = 2 The wave run-up, finally, is then: Ru2% = 1.5*0.9*0.75*1*2 ≅ 2m above . BED, BANK & SHORE BED, BANK & SHORE PROTECTION PROTECTION Lecturer: Pham Thu Huong Lecturer: Pham Thu Huong Faculty of Coastal Engineering Faculty of Coastal Engineering Chapter 6 Chapter. 6 Chapter 6 Waves Waves - - Loads Loads (6 class hours) Content Content 6. 1 Introduction 6. 2 Non breaking waves 6. 3 Breaking waves 6. 4 Wave on the slope 6. 4 Reduction of wave loads 6. 5 Summary Wave. (=2π/T) Near Near - - shore effects shore effects ¾ ¾ Shoaling Shoaling Near Near - - shore effects shore effects ¾ ¾ Shoaling Shoaling ¾ ¾ Refraction Refraction Near Near - - shore effects shore effects ¾ ¾ Shoaling Shoaling ¾ ¾ Refraction Refraction ¾ ¾ Diffraction Diffraction Near Near - - shore