Observations of wave-induced porepressure gradients and bed level response on a surf zone sandbar

Transcription

1 Observations of wave-induced porepressure gradients and bed level response on a surf zone sandbar Dylan Anderson 1, Dan Cox 1, Ryan Mieras 2, Jack Puleo 2, Tom Hsu 2 Oregon State University 1 University of Delaware 2 OS32A-06

2 Physical mechanisms driving sandbar migration Offshore migrations Large waves break on the sand bar Undertow currents directed offshore Bar moves offshore 1 (adapted from Hoefel & Elgar 2003)

3 Physical mechanisms driving sandbar migration Onshore migrations As = u t3 u t 2 3/2 Calmer wave conditions, weak currents Asymmetric wave shapes Bar moves onshore 2 (adapted from Hoefel & Elgar 2003)

4 Sheet flow θ = 0.8 Shields parameter τ θ = b ρ s ρ w gd 50 τ b 3 (adapted from Jack Puleo)

5 Considering pressures within the sediment bed: horizontal forcing Shields parameter τ θ = b ρ s ρ w gd 50 Sleath parameter S = p x ρ s ρ w g τ b p p + p x dx 4

6 Considering pressures within the sediment bed: horizontal forcing Shields parameter τ θ = b ρ s ρ w gd 50 Sleath parameter S = p x ρ s ρ w g p p + p x dx 5 Bed failure plug flow S f = 0.1 (Foster et al. 2006) (adapted from Sleath 1999)

7 1 p ρ f x = u t + u u x + w u z As = u t3 u t 2 3/2 Shields parameter τ θ = b ρ s ρ w gd 50 Sleath parameter S = p x ρ s ρ w g τ b p p + p x dx 6

8 Can we develop a more holistic understanding of the forces within the bed? Oscillatory flow Wave propagation 7 spatial and temporal gradients in the flow

9 8 Long Wave Flume Length: 104m Width: 3.7m Depth: 4.6m Piston-type wavemaker: -Regular, Irregular, Tsunami -Max wave: 5 seconds

10 Hybrid profile construction - limits large-scale bathymetrichydrodynamic feedbacks - isolates small-scale bed response to varying wave forcing d 50 = 0.17 mm d 50 = 0.27 mm 9

11 Hybrid profile construction - limits large-scale bathymetrichydrodynamic feedbacks - isolates small-scale bed response to varying wave forcing OS23B-2039 From the sand bed to the free surface: an experimental study of wave induced sediment transport over a sandbar (Ryan Mieras)

12 Pore-Pressure Transducer Array - Buried within sediment bed - Druck PDCR 81s, sampling at 100 Hz - Finite differencing 10

13 Pore-Pressure Transducer Array Horizontal p γ P xi = 2P i 1 3P i + 6P i+1 P i+2 = 2x 2 3x 3 + 6x 4 x 5 6 x x 6 x = Vertical p γ = P zi = 3P i + 4P i+1 P i+2 = 3x 3 + 4z 1 z 2 2 z z 2 z 11

14 Conductivity Concentration Profiler - Buried within sediment bed - Instantaneous bed levels - 32 mm window, sampling at 100z 12

15 13 62 trials consisting of 26 different wave conditions

16 Ensemble averaging to create pressure gradient vector p shore 14

17 Rotations of p with each wave cycle shore 15

18 16 Steep, short period waves can produce same onshore S as less steep long period waves with larger As values

19 1 p ρ f x = u t + u u x + w u z Advective terms account for 14% of the horizontal pore pressure gradient 17

20 Shields parameter τ θ = b ρ s ρ w gd 50 Sleath parameter S = p x ρ s ρ w g 18

21 Erosion depth is function of both shear and pressure gradient Shields parameter τ θ = b ρ s ρ w gd 50 Sleath parameter S = p x ρ s ρ w g 4 mm 24 grain diameters 18

22 19 Bed failures coincident with spikes in onshore-directed S

23 S f is not universal, and has no clear dependence on As 20 Initiation of erosion likely depends on a combination of shear and pressure gradients competing to secure or destabilize sediment skeleton (Foster et al. 2006; Frank et al. 2015; Cheng et al. 2016)

24 Obtained a pore pressure gradient, p, within the sediment bed beneath complicated hydrodynamics over a surf zone sandbar Oscillatory flow Magnitude of onshore-directed Sleath not directly related to As Rapid drops in bed level were coincident with spikes in pore pressure gradient, but not at a universal critical failure point dp dx τ s h b > KC ρ s ρ g + K dp dz 21 (Sleath [1999], Foster et. al. [2006])

25 Natural Hazards Engineering Research Infrastructure (NHERI) program Daniel Cox NHERI Project PI Pedro Lomonaco HWRL Director Oregon State Univ. of Delaware Myongji University (Korea) Dan Cox (PI) Jack Puleo (PI) Hyun-Doug Yoon Dylan Anderson Tom Hsu (PI) Wei Cheng Ryan Mieras Yokohama University (Japan) Hyoungsu Park Yeulwoo (Yaroo) Kim Takayuki Suzuki Jose Pintado Patino O.H. Hinsdale Lab Zheyu (Nancy) Zhou Kyoto University (Japan) Pedro Lomonaco Patricia Chardon William Pringle Tim Maddux Doug Kraft Cooper Pierson Wang Yanhong (National Hydraulic Research Institute of China)

26 1 p ρ f x = u t + u u x + w u z

27 Deriving gradients by finite difference approximations P i 1 = P i xp xi x2 P xxi 1 6 x3 P xxxi + O x 4 P i = P i P i+1 = P i + xp xi x2 P xxi x3 P xxxi + O x 4 P i+2 = P i + (2 x)p xi (2 x)2 P xxi (2 x)3 P xxxi + O x 4 P xi 1 x α j P j j = α i 1 + α i + α i+1 + α i 1 x P i = α i 1 + α i+1 + 2α i P xi = 1 2 α i α i α i xp xxi = 1 6 α i α i α i x 2 P xxxi α i 1 α i α i+1 α i+2 = α i 1 α i α i+1 α i+2 = Horizontal p γ x = P xi = 2P i 1 3P i + 6P i+1 P i+2 6 x = 2x 2 3x 3 + 6x 4 x 5 6 x Vertical p γ z = P zi = 3P i + 4P i+1 P i+2 2 z = 3x 3 + 4z 1 z 2 2 z