Using vegetation properties to predict flow resistance and erosion rates. Nick Kouwen University of Waterloo Waterloo, Canada

Transcription

1 1/37 INTERNATIONAL WORKSHOP o RIParia FORest Vegetated Chaels: Hydraulic Morphological ad Ecological Aspects Treto, Italy, February 2003 Usig vegetatio properties to predict flow resistace ad erosio rates Nick Kouwe Uiversity of Waterloo Waterloo, Caada

2 US Dept. of Agriculture, Stillwater Okla. Lab Test chaels 5% slope (This ru 1.7 m 3 /s 60 cfs) 2/37

3 Measuremet of soil profile ad cout of grass desity 3/37

4 View through side after approximately 5 day ru 4/37

5 5/37 UW Lab plastic model of grass Circa 1969 Use of pitot tube as referece to measure height

6 Click o isert to view movie 6/37

7 Defiitio of variables 7/37

8 Dimesioal Aalysis (List of everythig by Fezl): ( ρ µ, σ, h, b, J, k, λ, λ, λ,... λ, θ, θ, β, V, y, g, S ) 0, 1 2 p s f = After applyig the Buckigham Π theorem (by NK) f = k y, k h, h MEI τ Oly the most importat variables are retaied o 1 4 M =stem desity = EI f y k h =vegetatio stiffess =D - W frictio factor =depth of flow =roughess height i flow =vegetatio legth τ o = shear stress = γals D 2 λλ 1 2 (NOTE: k < h ad k < y ) 8/37

9 9/37 From Experimets: k h f h MEI = τ 0 1/4 So: = h k, y k f f Kouwe, Uy & Hill, ASCE J. of the Hydraulics Divisio, May, 1973,

10 Kouwe, Li & Simos, Tras. ASAE, 24(3), 1981, & /37

11 11/37

12 12/37 i.e. f = f (relative roughess, smoothess) I practical terms, this meas: 1 f = a + b log 10 y k where a ad b are coefficiets that vary with the value of k/h - or smoothess (re: Keulega, 1938) a k = f h k 1 b = f2 h

13 13/37 S y h S y MEI 0.14h y blog a 8g V γ + = All we ow eed is MEI for atural vegetatio

14 14/37 So how do we get values for MEI for atural vegetatio? Assume values for MEI ad fit computed -VR to observed data. Doe for approx. 150 Experimets (1980) Kouwe & Li, ASCE J. of the Hydraulics Divisio, Jue, 1980,

15 Field methods to obtai MEI 15/37

16 16/37 Board drop test (for MEI) Eastgate, 1966 Eastgate data Kouwe, IAHR J. Hydraulic Research, 1988, Vol. 26,

17 17/37 MEI ca also be based o the vegetatio height: A compariso of the two methods of Estimatig MEI yields similar results. Kouwe, IAHR J. Hydraulic Research, 1988, Vol. 26,

18 Kouwe, ASCE J. of the Irrigatio ad Draiage Divisio, Sept./Oct. 1992, /37

19 Stability: As log as y has some value, there is little shear at the bed ad chael is stable 19/37

20 20/37 It turs out that roughly : y goes to zero whe k/h ~ 0.35 Expect erosio rate to icrease dramatically at this poit O

21 21/37 O O O O O O

22 Scour hole developed i 250 mm log Bermuda Grass after 5 day ru Slope 5% Flow 1.7 m 3 /s k/h for this case was ~ /37

23 23/37 Erosio Model: τ = ρgy S (1 s 2 e CF )( ) Er = kk( τ τ ) a' e c Effective shear (Temple) Duboys sedimet trasport equatio to estimate detachmet

24 24/37

25 25/37 Coclude: Oset of istability ca be predicted by Temple-Duboys model kk ad a i Duboys eq. the same for all plots Oly the Cover Factor C f adjusted Details: Samai & Kouwe. ASCE J. Hyd. Eg. Ja. 2002

26 Drag o trees 26/37

27 Straight, level road with o cross-wid km/hr i 10 km/hr icremets Cedar, Spruce, Austria ad White pie trees Up to 3.5 m i height. Freshly cut. (please ote: i Caada we ormally drive o the right) 27/37

28 Sapligs of cedar, spruce ad two species of Pie were tested i water ad air. Drag was measured ad recorded for a period of time usig force balace tables ad a load cell. I water, the additive priciple was tested. Differet patters were used. Dese cedar sapligs i a flume with oe tree i the force balace Fathi-Moghadam & Kouwe ASCE J. Hydraulic Eg. Ja pp /37

29 29/37 I water: I air:

30 30/37 ( ) 1 1 d l...,,l,,,h,,j,g, y,,v, A f C ω φ ξ µ ρ = ο 0 V y, gy V, Vy, J y V, y h, y l, y l, y A,,, C f d 2 = ω µ ρ ρ φ ξ f C A h Vh J Vy V gy y V d ( ),,,, = ρ ξ ρ µ ω C A h f V h J d = ρ ξ f V E = α ξ ρ β ξ E Nf m h 1 2 s = f C A a d = 4

31 f = 4C A d a A = Mometum Absorbig Area a = horizotal area of caopy f = α V ξe ρ β ξ = parameter to accout for plat deformatio due to flow velocity ξe = vegetatio idex ξ E = Nf 2 1 m h s (Nickas & Moo, 1988) Nf 1 = atural frequecy of the tree m s = total tree mass h = height of the tree (or caopy) Kouwe & Fathi-Moghadam, ASCE J. Hydraulic Eg., Oct. 2000, /37

32 32/37 Trolley ad load cell to measure Force o a tree Accelerometer to obtai Natural Frequecy Shaker table ad spectrum aalyzer to Obtai atural frequecy of the tree.

33 Kouwe & Fathi-Moghadam, ASCE J. Hydraulic Eg., Oct. 2000, /37

34 34/37 Kouwe & Fathi-Moghadam, ASCE J. Hydraulic Eg., Oct. 2000, (Streamliig) (Species)

35 frictio facter f Air ad Water Tests Coclude: Effect of trees o f ca be represeted by submerged biomass ad atural frequecy of trees usig McMaho (1975) self-similarity cedar spruce white pie Austria pie Combied 1.0 Kouwe & Fathi-Moghadam, ASCE J. Hydraulic Eg., Oct. 2000, V / ( ξ E) / ρ /37

36 36/37 Summary Dimesioal aalysis provides a uified approach to flow resistace due to vegetatio. The flexural characteristics of vegetatio have a major effect o resistace. The biomechaical properties of grass as they affect flow resistace are i essece a equivalet to plastic stiffess.

37 Thak you Presetatio at 37/37