Sediment Transport & Channel Design

Transcription

1 DEPARTMENT OF WATERSHED SCIENCES Sediment Transport & Channel Design Peter Wilcock 4 August 2016

2 The stable channel The regime channel The hydraulic geometry A basis for channel design?

3 The width of channels increases consistently with the square root of discharge. The flow that moves the most sediment, over time, tends to just fill the channel and occurs ever year or two. At the core of these observations is a correlation between channel geometry, flow, and sediment supply The correlation requires that the channels have adjusted to their water and sediment supply. But what if channel is currently adjusting, or perpetually adjusting?

4 Using the stable channel or the equilibrium channel for design? Streams are never in equilibrium! Especially those we judge to be unacceptably out of adjustment The forcing is (always) changing How do we connect with specific, local, non sediment objectives? (if we build it like this good things will happen. Surely this is better, right?) A rational approach: break problem down into its pieces: specify drivers, quantify channel response. A design approach : specify objectives and design to meet them (rather than specify design and hope that it solves the problem) An empirical stable channel is inevitably an intellectual black box. We need to connect objectives to actions, through specific mechanisms Unfortunately, for a rational design approach (A) We can never forecast future conditions (e.g. water & sediment supply) with a high degree of accuracy (B) We will never know the exactly correct channel geometry for a river channel (because there probably isn t one) Can we develop a design approach that (1) Specifies desired channel behavior (2) Incorporates sediment transport with uncertainty (3) Accommodates typical conditions

5 What is the supply of water and sediment? and What do you want to do with them? (1) Do you want the bed and banks to be static at a design flow? (2) Do you need to match transport capacity to sediment supply? (3) Both of the above Specified equilibrium dimensions Channel Design Account for uncertainty & risk Accommodate typical dimensions Specified channel behavior

6 Estimating uncertainty In sediment transport (i) Threshold channel (critical discharge for incipient motion Q c ) (ii) Alluvial Channel (estimate transport rate Q s from a formula) Threshold Channel Find critical discharge Q c using critical Shields Number Replace with c ( s1) gd rearrange and solve for critical discharge Q * c a * Qc ( 1) 7/6 c s D ns 1 5/3 1b Replace h in ghs using Q h BU continuity b B aq hydraulic geometry U h S 2/3 h n nq b 2/3 aq Sh c 1 3/5 b nq h so a S 1b 3/5 nq 0.7 g S a Manning s eqn. Replace in Qs * c c B ( s 1) gd ( s1) gd o 1 3/ b nq S * s o ( 1) c Q cb s gd The hydraulic problem Alluvial Channel Find transport rate using M P&M a ( s1) D 3/2 3/2

7 Application of sediment transport concepts: Stream response to increased fines input There are many reasons why sand supply to a gravel-bed river might be increased fire, urbanization, reservoir flushing, dam removal What is the effect on transport rates? Channel dynamics? Stream ecology? Previous Experiments Jackson & Beschta (1984) Ikeda & Iseya (1988) Adding sand increases gravel mobility East Fk R., near Boulder WY, bl confluence of Muddy Ck. 7

8 Some experimental evidence J06 5 sediments, add sand to gravel Sand: mm Gravel: mm Sand Content: 6, 14, 21, 27, & 34% 9 or 10 runs with each sediment, wide range of transport rates Depth & width held constant, primary variables are sand content & flow strength J14 J21 J27 BOMC y y

9 Effect of sand content on gravel transport rate 1000 Gravel transport rate [g / (m s)] J06 J14 J21 J27 BOMC 66% Gravel 94% Gravel Transport increases even though proportion of gravel in bed decreases Bed Shear Stress (sidewall-corrected; Pa) How do we capture effect of sand content on gravel transport rates? 9

10 The sand effect on transport is captured by a reduced critical shear stress for incipient motion of the gravel 0.1 * c 0.01 Shear stress (Pa) No Motion < 10% sand 1 Motion Motion ~18% sand c No Motion * rg Grain Size D (mm) S * >34% sand quartz in water Framework Supported Sand Content of Bed * c c ( s1) gd For D > 4 mm Matrix Supported

11 We have captured the effect of sand on gravel transport by reducing the critical shear stress for the gravel Gravel transport rate [g / (m s)] * Reducing c by a factor of four increases the transport rate by much, much more J06 J14 J21 J27 BOMC 34% sand 6% sand Bed Shear Stress (sidewall-corrected; Pa) q* E-05 M-P&M 2t*c (t*)^ * 11

12 Framework Supported Matrix Supported (a) * rg Field Lab This changes our approach to predicting sediment transport rates: A fundamental parameter depends on bed grain size Sand Content of Bed (also found in the many fraction surface-based model) * rg ( s rg 1) gd Wilcock, P.R. and Kenworthy, S.T., 2002, A two fraction model for the transport of sand/gravel mixtures, Water Resources Research, 38(10). Wilcock, P.R., Kenworthy, S.T. and Crowe, J.C., Experimental study of the transport of mixed sand and gravel, Water Resources Research Wilcock, P.R., Two-fraction model of initial sediment motion in gravelbed rivers, Science 280:

13 Pay attention to this slide Test sand effect in a sediment feed flume Feed gravel (2-32 mm) at same rate in each run; Increase sand feed rate from much less to much more than gravel Results As sand feed increases, bed gets sandier & slope decreases: less stress required to carry same gravel load & increased sand load Gravel Feed Rate Sand Feed Rate Feed Bed Surface Bed Slope Total Feed Rate (g/ms) 13

14 The point? Adding sand can have a huge effect on gravel transport rates most of this is captured in a changed critical Shields Number There are a number of ways to increase sand supply to a gravel-bed river fire, urbanization, reservoir flushing, dam removal A two fraction approach captures this effect in a tractable framework 0.05 * rg Sand Content of Bed 14

15 (I) Threshold Channel Design Under Uncertainty 15

16 Step 1 Determine design bed material gradation/channel boundary. Step 2 Determine preliminary width. Step 3 Estimate critical shear stress/velocity. Step 4 Determine flow resistance (Manning s n). Step 5 Calculate depth and slope. Step 6 Determine planform. Step 7 Assess for failure and sediment impact.

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18 h n1 lim * 0 c Given QB,,, D and D, n find, nru,, and Sfrom c ( s-1) gd c 50 1/6 * c R R log D84 2 3/5 Bo 2hn 1m nq S B mh A h Bo mh R P B 2 h 1 m o Q U A S c gh o 2 n 2/5 Given discharge Q, grain size D, m Finding Normal Depth - Trapezoidal Channel Manning's eqn: Q where mh Bo mh 1 h 5/3 S hb ( o mh) n 2/3 2 Bo 2h 1m 2 2 B Bo 2 mh, A Boh mh h Bo mh, P Bo 2h 1m Finding nq,, or Sis easy; to find hrequires iteration 2/5 2 3/5 Bo 2hn 1m nq Try Manning arranged as hn 1 S Bo mhn where n and n1 subscripts indicate successive approximations * c critical Shields Number, Limerinos roughness & trapezoidal channel shape, find slope S producing incipient motion. 18

19 Given discharge Q, grain size D, Limerinos roughness & trapezoidal channel shape, find slope S producing incipient motion. * Specify B 12.5 m and c 0.047, solution is S with depth h0.54 m Depth Slope Depth (m) S v Slope Bottom Width (m) 0 * c

20 * Other values of n, c, and D could be chosen * Changing c and D 45 mm 32 mm Depth D = 32 mm, t* = 0.03 Slope D = 32 mm, t* = Depth (m) Calculated slope 3x bigger! = RISK S v Slope Bottom Width (m) 6( b1) b1 7 * 10/7 c c ( 1) aq S s D n 0 20

21 Strategy What is probability of failure? What probability are you willing to accept? P( failure) PQ ( ) PQ ( Q) D D c Choose width, slope combination to match acceptable risk. For example, for a 25yr Q and a channel design with 10% failure probability, D P( failure) PQ ( ) PQ ( Q) (0.04)(0.1) D D c giving a 0.4% chance of failure in any year. Q c

22 (II) The Armoring Problem 22

23 1. Stream bed armoring surface composition & the problem of predicting transport rates

24 Stream bed armoring is pervasive in gravel bed steams Armor Ratio = D50 (surface) D50 (subsurface) Bed surface composition determines: Frequency Streambed Armoring Armor Ratio Mean: 2.80 Std. Deviation: 2.06 Median: grains available for transport hydraulic roughness bed permeability living conditions for bugs & fish

25 The armor problem We can measure the bed surface size at low flow, but not at flows moving sediment We don t know what the bed surface looks like at the flows that create it Does the armor layer stay or go during floods?

26 Flume studies do not resolve the issue Q % Q Q Qs Qs Q Grain Size Sediment Feed Qs Q Sediment Recirculation Both Cases D50 Bed Transport D50 Bed Transport Transport D50 Surface D50 Flow, Transport Rate Flow, Transport Rate 0 Flow, Transport Rate Mobility driven armoring Zero divergence Kinematic sorting

27 To address the armor problem, we first tackle the transport problem Transport rates depend on transport of grains available for transport on bed surface But nearly all transport data provide composition of the bed subsurface, not surface! This means that the resulting transport models must somehow implicitly account for surface sorting (armoring)

28 Transport Modeling Basics 1 Given fully rough flow with boundary stress, sediment of mean size D m, with individual fractions of size D i and proportion f i. Transport rate q bi depends on q fn ( f, D, D,, sed) ri fn 2 ( D m bi, D i / D i m i where sed = other sediment properties. We search a transport model of form q where bi ri is a fn1 (, ri) reference value of fi near the onset of sediment motion,sed) But, what size distribution should we use for f i? ans: surface m

29 There were essentially no surfacebased transport observations, so we made some % J06 Sand Gravel 5 sediments, add sand to gravel Sand: mm Gravel: mm Sand Content: 6, 14, 21, 27, & 34% 9 or 10 runs with each sediment, wide range of transport rates Depth & width held constant, primary variables are sand content & flow strength % % % % J14 J21 J27 BOMC y y Grain Size (mm)

30 Transport Modeling Basics 2 To develop a general transport model, we nondimensionalize q F in the form of a similarity collapse where W * i ( s F i 1) gq 3/ 2 / F i surface proportion; g gravity; water density; s sed spec. gr. bi bi i fn (, 1 ri * W i fn ) 3 ri The Point: The transport function does not contain grain size!

31 Building a surface based transport model * W i * W r Sediment = J tref tr fn (Pa) * W i * W r Sediment = J ri

32 It remains to explain ri 100 Sediment = J14 ri Grain Size Di (mm)

33 10 Surface Based Transport Model All sizes, All runs, All sediments * W i / ri

34 Values of ri for all sizes and all sediments ri 100 J06 J21 BOMC Surface Dm J14 J27 Shields D i Grain Size (mm)

35 Values of ri collapse nicely when divided by values at the mean size D sm 10 ri rsm D i D sm J06 J14 J21 J27 BOMC A 'hiding' function Relative size effect weaker for larger sizes (absolute size effect makes ri increase with D i ) Wilcock, P.R. & Crowe, J.C., J. Hydr. Eng., 2003

36 It remains to explain rm Sand Interaction Function The sand interaction function completes the surface based transport model

37 Surface based transport model can be used in both forward & inverse forms Forward: predict transport rate & grain size as function of and bed surface grain size Inverse: predict and bed surface grain size as function of transport rate & grain size Don t try this with a subsurface based model! The inverse model provides a useful tool for considering armor persistence because we do have good transport data from the field To the field!

38 Transport grain size increases with flow! isbtm not only predicts a persistent armor layer, it also predicts the surface grain size observed in the field! (a) Percent Finer (b) Median Grain Size (mm) Oak Ck, OR Grain size of transport (measured) and bed surface (calculated) Surface Grain Size (mm) Transport Rate (kg/ms) Surface D50 Transport D Transport Rate (kg/ms) Solid symbols: predicted surface grain size

39 Again, transport grain size increases with flow! Again, isbtm predicts a persistent armor layer. This time it overpredicts the surface grain size observed in the field! Reason: dunes! (a) Percent Finer (b) Median Grain Size (mm) Goodwin Ck MS Grain size of transport (measured) and bed surface (calculated) SURF Grain Size (mm) Transport Rate (kg/ms) Surface D50 Transport D Transport Rate (kg/ms) Solid symbols: predicted surface grain size

40 At reach and storm scales of space and time Armor layer grain size appears to be persistent a real advantage for predicting roughness & transport during floods: a low flow measurement of bed composition may suffice (unless dunes develop) Increasing transport grain size balances change in grain mobility to produce a constant bed surface A SBTM needed to model transients

41 (III) Sediment Transport in Alluvial Channel Design reconnaissance, planning, and design phases 41

42 Connecting sediment supply to the design problem 1. Reconnaissance phase: What is the trajectory of the stream? How has it responded to changes in water and sediment supply over the years? {Henderson relation mixed size seds} 2. Develop flood series, specify flood frequency Q bf. {Select Q bf for flood frequency specified to maintain riparian ecosystem & prevent vegetation encroachment} 3. Estimate sediment supply 4. Planning phase: What slope S is needed to carry the sediment supply with the available flow? {How does S vary with Q s and width b?} 5. Develop flow duration curve 6. Design phase: Evaluate trial designs. Will the sediment supply be routed through the reach over the flow duration curve? {Build 1 d hydraulic model for trial design. Calculate cumulative transport over flow duration curve at each section; evaluate sediment continuity.}

43 R e c o n n a i s s a n c e Lane/Borland Stable Channel Balance (USBR ) Sediment Supply Transport Capacity This defines the controls for an alluvial channel

44 R e c o n n a i s s a n c e Einstein-Brown depth-slope continuity Chezy 3 q* ( *) RS qur U RS or b or for two cases 3 3/2 qb q R S 3/2 D q The Lane Balance, quantified almost 40 yrs ago by Henderson (1966, Open Channel Flow) ( RS) D q R 3/2 q S b 2 2 q S D 3/2 q D b q 3/4 3/4 2 qb2 2 1 S D q S q D q 1 b1 1 2 S Pay attention to this slide What if q b increases and D decreases? Lane s balance is indeterminate.

45 Surface based transport model can be used in both forward & inverse forms Forward: predict transport rate & grain size as function of and bed surface grain size Inverse: predict and bed surface grain size as function of transport rate & grain size Don t try this with a subsurface based model! We can use an inverse transport model to forecast, or design, a steady state channel that will transport a specified sediment supply rate and grain size with the available flow (!)

46 Presenting. isurf 1. State Diagram I transport v. discharge, lines of constant slope 2. State Diagram II transport v. slope, lines of constant discharge 3. Channel Stability Diagram Inverse Model: predict and bed surface grain size as fn(transport rate & grain size) Specify discharge and basic channel geometry and solve for slope (& depth)

47 R e c o n n a i s s a n c e Stream State Diagrams "Given": qq,, p,,, g t i s "Find": Uh,,, SFn,, q q * t * w q t ( s1) gd q w ( s1) gd i 3/2 s 3/2 s F p i i : Surface grain size : Transport grain size Conservation Relations Water Mass q Uh Momentum ghs Constitutive Relations Roughness relation n f( F i ) Sediment transport isbtm gives, Fi Flow resistance S 2/3 U h n We are working per unit width The isbtm routine calculates bed shear stress and bed surface grain size for a specified transport rate and transport grain size. Each transport rate and grain size and, therefore, shear stress and bed surface grain size, can be produced by different combinations of unit discharge q and slope S. The state diagrams present families of curves giving either transport rate and water discharge for specified values of S, or transport rate and S for specified values of water discharge.

48 R e c o n n a i s s a n c e Slope Sediment Transport Rate per unit width qt (kg/m/s) Less armored More armored Lines of constant slope Water Discharge per unit width q W (m 2 /s) Low flow High slope Lines of constant unit water discharge Low slope S=0.001 S=0.002 S=0.005 S=0.01 S=0.02 S=0.05 G1=25.07,G2=25.07 G1=16.85,G2=16.85 G1=2.79,G2=2.79 qw=0.10 m^2/s qw=0.32 qw=1.0 qw=3.2 qw=10.0 G1=25.07,G2=25.07 G1=16.85,G2=16.85 High flow G1=2.79,G2=2.79 More armored Less armored Sediment transport Rate per unit width q T (kg/m/s)

49 P l a n n i n g How big the channel? Given Water discharge and sediment supply Find channel slope, depth & width (& velocity & shear) We have enough general relations to solve for all but one of these unknown variables If we specify channel width, we can solve for the rest of the variables What slope is needed to transport the supplied sediment with the available water?

50 P l a n n i n g For a specified supply of water and sediment, what is the slope needed to transport the supplied sediment with the available flow? Hydraulic Design of Stream Restoration Projects September 2001 RR Copeland, DN McComas, CR Thorne, PJ Soar, MM Jonas, JB Fripp

51 Sometimes, sediment supply does not matter Sometimes, it does Bankfull with (m) Alberta Britain I Idaho Colorado R Britain II Maryland Tuscany Bankfull Discharge (cms)

52 So, there must be a boundary between cases where sediment supply matters or not Threshold Bed & banks immobile Easier to model & design Bed & banks must only be strong enough Extend Threshold definition to include small sediment supply rates requiring a slope negligibly larger than the zero supply case Alluvial Active transport Harder to design Requires a balance between transport capacity & sediment supply Focus on cases in which slope is sensitive to supply Nothing new under the sun see SCS in the 30s

53 Why we can neglect small sediment supply rates 1. Small sediment supply rates many storms (and many decades) req d to produce significant aggradation and degradation. 2. Small sediment supply rates channel morphology and slope required to transport the supplied sediment can be negligibly larger than that of a threshold channel.

54 So, what is a SMALL sediment supply rate? That sounds dangerously like a real question, so first, lets deal with real sediments, which contain a mixture of sizes But for mixed size sediment, there are complications Grain size of bed grain size of transport Bed is sorted spatially and vertically Transport is a function of the changing population of grains on the bed surface

55 isurf Channel Stability Diagram what slope is needed to transport a specified sediment supply of specified size distribution with a specified discharge? h b m 1 Find velocity, boundary stress, depth, slope, and bed surface grain size from continuity, momentum, flow resistance, and the Wilcock Crowe Surface Based Mixed Size Sediment Transport Model

56 P l a n n i n g % Finer Slope 0 Discharge 1 = 17.0 Discharge 2 = Channel Width (m) Case 1 Transport Case 2 Transport Case 1 Bed Surface Case 2 Bed Surface b = 14.0 m As a bonus, you find out how armored the bed becomes! Slope Case 1 Slope Case 2 Depth Case 1 Depth Case Grain Size (mm) Slope Channel Stability Diagram Sed Supply 1 = 954 kg/hr Sed Supply 2 = 95 kg/hr Case Depth (m) Case 2 Your sediment supply Discharge 1 = 17.0 cms Discharge 2 = 17.0 cms And get a measure of where you are relative to the threshold/alluvial channel boundary! b = 14.0 m ,000 10, ,000 1,000,000 Sediment Supply Rate (kg/hr)

57 Is an accurate sediment supply estimate needed? If your sediment supply is safely below the boundary between low slope and high slope, channel slope is relatively insensitive to sediment supply you are less likely to accumulate sediment given an error in estimating sediment supply Q = 70.8 cms b = 19.0 m Threshold Design Approach Slope Your sediment supply Just make the channel strong enough to stand up to high flows threshold ,000 10, ,000 1,000,000 Sediment Supply Rate (kg/hr)

58 Design steps incorporating sediment supply 1. Reconnaissance phase: What is the trajectory of the stream? How has it responded to changes in water and sediment supply qb over the years? isurf State Diagrams b 2. Develop flood series, specify flood frequency Design Q. {Select Q bf for flood frequency specified to maintain riparian ecosystem & prevent vegetation encroachment} 3. Estimate sediment supply 4. Planning phase: What slope S will transport the sediment supply with the available Q bf? Calculate (b, S) combination {S and valley slope determine sinuosity} Check if alluvial v. threshold channel 5. Develop flow duration curve 6. Design phase: Evaluate trial designs. Will the sediment supply be routed through the reach over the flow duration curve? {Build 1 d hydraulic model for trial design. Calculate cumulative transport over flow duration curve at each section; evaluate sediment continuity.} 7. Bottlenecks or blowouts? Adjust for sediment continuity Slope Discharge 1 = 15.0 Discharge 2 = / S D q S q D q Slope Case 1 Slope Case 2 Depth Case 1 Depth Case Channel Width (m) Slope Case 1 Case 2 Your sediment supply Discharge 1 = 15.0 cms Discharge 2 = 25.0 cms b = 11.0 m Sed Supply 1 = 954 kg/hr Sed Supply 2 = 2862 kg/hr ,000 10, ,000 1,000,000 Sediment Supply Rate (kg/hr) Depth (m)

59 D e s i g n Some Design Detail Step-backwater model gives S(Q), U(Q) at each section 3/2 n Grain stress: ' D 1/4 3/2 ' 17 SD65 U Calculate transport over the flow dur. curve at each section Adjust x/s transport for lateral variation in Query potential bottlenecks, blowouts transport < capacity? flow model reliable? erosion/deposition desirable? Adjust channel dimensions & shape to match supply, within tolerance level & design objectives. Transport (Mtons) Q = 1600 cfs n o Cum Qb * lateral correction (skn) Section Use transport modeling to: i. Evaluate design, esp. Qs from section to section ii. Determine if more accurate transport modeling is needed

60 (IV) Alluvial Channel Design Example 60

61 (6.7 m) Design (70.8 m 3 /s) 1. Supply reach Estimate sediment transport rate 2. Design reach Given discharge and sediment supply rate and grain size, calculate slope needed to transport supplied sediment at a specified channel width

62 1. Find stress in upstream supply channel NEH-654 Chapter 9 Example 2, p. 39 Given geometry of a trapezoid channel w/ specified bed material and side roughness, find boundary and grain stresses Q cms S D mm D84 22 mm m 1.6 nd ns 0.07 Enter information only in green cells!! No cutting and pasting! No inserting or deleting rows! F M w B F Bo 6.71 nc h 2.97 B 16.2 A 34.0 R 1.90 U 2.08 o 46.6 ' 21.1 u*' m composite n m m m^2 m m/s Pa total Pa Grain m/s Grain T w Bo nc h B A R U boundary stress stress ft ft ft ft^2 ft ft/s stress as a shear velocity

63 2. Find transport rate in upstream supply channel SBTM - calculate transport rate and transport grain size from specified shear velocity and bed surface grain size RULES, CONVENTIONS, AND UNITS 1. Cells for input data are highlighted in GREEN, cells for output data are ORANGE 2. Grain-diameters must be in millimeters (mm) 3. Cumulative percentiles, not fractions, are used 4. Cumulative grain-size distribution percentiles must span from 0 to 100 % 5. Shear velocity must be in meters-per-second (m/s) 6. The 0 and 100 % must be EXACTLY 0 and 100 INSTRUCTIONS 1. In table below, enter grain size and cumulative % in order of decreasing grain size 2. Enter your bed shear velocity 3. Check input for errors, press Enter, and then click once on the Run SBTM button Parameter Value Description Units u* 1.45E-01 Bed shear velocity m/s qt 8.17E-04 Total transport rate m 2 /s D (mm) Surface CDF GSD (% Finer) Transport CDF GSD (% Finer)

64 3. Enter transport rate and grain size from upstream supply channel as input to the channel stability code Parameter Value Description Units Q Case 1 water discharge m 3 /s Q T Case 1 sediment supply rate m 3 /s Q Case 2 water discharge m 3 /s Q T Case 2 sediment supply rate m 3 /s b min 3.00 Minimum bottom width m b max Maximum bottom width m D (mm) Case 1 Transport Grain Case 2 Transport Grain Size Size (% Finer) (% Finer)

65 isurf (Wilcock&Crowe) solution including case with 3x sediment supply Discharge 1 = 70.8 cms Discharge 2 = 70.8 cms Slope Case 1 Slope Case 2 NRCS Sed Supply 1 = kg/hr Sed Supply 2 = kg/hr Slope Potential Aggradation Channel Width (m) S v Potential Degradation

66 For this design problem, slope is very sensitive to sediment supply rate (because it is large) Q = 70.8 cms b = 19.0 m Slope Your sediment supply ,000 10, ,000 1,000,000 Sediment Supply Rate (kg/hr) isurf design module provides this plot of slope vs. sediment supply rate

67 A simple example of all three channel types Pay attention to the next four slides! 3 Q 100 m /s D D n mm 128 mm 10% % 1 2 mh Bo h mh 3 3 Q 100 m /s {160 m /s} Q s 20 t/hr {60 t/hr} Supply D mm (0.5 mm mm) * c %

68 Failure in a threshold channel = grain entrainment Slope Depth Slope Channel Depth (m) Bottom Width (m) mh Bo h mh 3 Q 100 m /s D D n mm 128 mm 10% % * c %

69 Mobile channel design = match transport capacity to sediment supply 1 2 mh Bo h mh 3 3 Q Q s 100 m /s {160 m /s} 20 t/hr {60 t/hr} Supply D mm (0.5 mm mm)

70 Over capacity Threshold: combine threshold and alluvial Slope Threshold Slope Alluvial 100/20 Alluvial 160/ Bottom Width (m) Q 100 m /s D D 64 mm 128 mm 10% n % 1 2 mh Bo h mh 3 3 Q 100 m /s {160 m /s} Qs 20 t/hr {60 t/hr} Supply D50 13 mm (0.5 mm mm) * c %

71 Bottom Line: specify a width, a channel and its bed material, and a water & sediment supply Critical Shields Number gives threshold channel slope Transport Model gives alluvial channel slope Range of widths gives indication of adjustments with respect to bed material transport Threshold Channel Alluvial Balance Slope Bottom Width (m)

72 Threshold Channel Alluvial Balance Slope Bottom Width (m) Threshold Channel Alluvial Balance Slope Evacuate Accumulate Bottom Width (m)

73 But the watershed, and the water and sediment supply may also be changing aka moving the goalposts Discharge Rate of Sediment Supply Grain Size of Sediment Supply Threshold Channel Alluvial Balance Slope Bottom Width (m) Arrows indicate response to an INCREASE in each driving variable

74 (V) Channel Design Strategy 74

75 Strategy (i) Determine if the sediment supply is a big number or a little number (a) if big, invest in more accurate estimate of sediment supply be prepared for a dynamic channel reserve riparian corridor and let the stream go or plan to trap and remove sediment (b) if little, design a threshold channel (ii) Estimate uncertainty and account for the consequences esp. potential for aggradation, degradation Q = 70.8 cms b = 19.0 m Slope Your sediment supply ,000 10, ,000 1,000,000 Sediment Supply Rate (kg/hr)

76 OR, Make your channel (i) steep enough: transport capacity exceeds supply and (ii) strong enough: bed material immobile an overcapacity threshold channel Design Basis: Channel Type Topography & Bed Material Flow Competence Threshold Channel Competence & Capacity Overcapacity Threshold Transport Capacity Alluvial Channel Static Static Dynamic Pipe like channels: an increasingly common & safe design option, may provide acceptable aesthetics. Does not provide anything like native structure & function

77 Assess magnitude of sediment supply small Threshold channel design large Alluvial channel design Use risk assessment and P(failure) to guide design Overcapacity channel design Invest in improved sediment estimate Allow for dynamic stream

78 Sediment Transport in Channel Design Environmental Drivers Objective sediment & nutrients property & infrastructure biological recovery aesthetics, recreation penance What needs fixing? Nothing Stormwater control Introduced species Channel change Disturbance Internal or external? Estimate flood frequency Design threshold channel Estimate sediment supply & flow duration Design alluvial channel Channel Design Sediment Objectives Is Sediment Supply Large or Small? External Internal Fence out the cows! Remove the concrete! Template approach can work Design Threshold AND Alluvial Channel Alluvial, Threshold, or Overcapacity Threshold Channel?

79 We can go beyond equilibrium channel design by Specifying desired channel behavior and incorporating sediment transport with uncertainty, Which allows calculation of risk of undesirable behavior while accommodating typical channel dimensions Specified equilibrium dimensions Channel Design Specified channel behavior Account for uncertainty & risk Accommodate typical dimensions

80 isurf does Provo 2016

81 PRRP OFFICE

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83 Transport Observations by BioWest Inc mm 1000 > 16 mm White Bridge River RD Midway Casperville River RD Midway Casperville Transport Rate (tons/day) Does not include transport samples <1g for the 2-16mm size class Transport Rate (tons/day) Does not include transport samples <200g for the >16mm size class No meaasured transport in this size range at White Bridge Discharge (cfs) Discharge (cfs)

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86 isurf Channel Stability Diagram for 1200 cfs and 1800 cfs flows CHANNEL STABILITY DIAGRAM FOR GRAVEL-BED RIVERS - INPUT WORKSHEET For the input entered below, here are max and min values of RULES, CONVENTIONS, AND UNITS water discharge per unit width 1. Cells for input data are highlighted in GREEN Maximum q Minimum q 2. Grain-diameters must be in millimeters (mm) 4.25 m^2/s 0.68 m^2/s Case 1 3. Cumulative percentiles, not fractions, are used 6.38 m^2/s 1.02 m^2/s Case 2 4. Cumulative grain-size distribution percentiles must span from 0 to 100 % 5. The 0 and 100 % must be EXACTLY 0 and 100 For the input entered below, here are max and min values of INSTRUCTIONS sediment transport rate per unit width 1. In first table below, enter water discharge and sediment supply rate in units of m 3 /s Maximum qs Minimum qs and the minimum and maximum channel widths to be evaluated 0.00 kg/m/s 0.00 kg/m/s Case 1 2. In second table below, enter grain size and cumulative % in order of decreasing grain size 0.48 kg/m/s 0.08 kg/m/s Case 2 3. In cells to right, enter side slope angle z and side slope roughness ns 4. Check input for errors and then click once on the Run STAB button this cell intentionally left blank 5. Results appear on Worksheet "STAB OUTPUT" Parameter Value Description Units Parameter Value Description Units Q 1 34 Case 1 water discharge m 3 /s z 1 side slope z:1 H:V 0 Q T Case 1 sediment supply rate m 3 /s ns 0.08 side slope roughness #&%@$ Q 2 51 Case 2 water discharge m 3 /s 100 Input transport size distributions Q T Case 2 sediment supply rate m 3 /s GSD1 80 b min 8.00 Minimum bottom width m GSD2 60 b max Maximum bottom width m D (mm) Case 1 Transport Grain Case 2 Transport Grain Size Size (% Finer) (% Finer) Grain Size (mm) Statistic FIRST Transport GSD SECOND Transport GSD Units D min mm D max mm D mm D g mm g /-units F s % % Finer Reset Run STAB h Reset: inserts some harmless data and cleans up output cells b z

87 isurf Channel Stability Diagram for 1200 cfs and 1800 cfs flows Channel Stability chart developed using inverse calculation of the Wilcock & Crowe (2003) transport relation. z 1 side slope z:1 H:V ns 0.08 side slope 1. CHANNEL STABILITY DIAGRAM 2. THRESHOLD CHECK - SLOPE AS FN(SEDIMENT SUPPLY RATE) AT MEAN WI Slope Armor Ratio Dsm/Dtm Discharge 1 = 34.0 cms Discharge 2 = 51.0 cms Slope Case 1 Slope Case 2 Depth Case 1 Depth Case 2 Sed Supply 2 = kg/hr Channel Width (m) Armor Case 1 Armor Case 2 Froude # Case 1 Froude # Case 2 Sed Supply 1 = 38 kg/hr Channel Width (m) Depth (m) Froude Number Slope Case 1 Case 2 Your sediment supply Discharge 1 = 34.0 cms Discharge 2 = 51.0 cms b = 29.0 m ,000 10, ,000 1 Sediment Supply Rate (kg/hr) At b=29.0m U=1.6m/s qt=0.000kg/m/s 3. GRAIN-SIZE DISTRIBUTIONS At b=29.0m U=2.3m/s qt=0.133kg/m/s % Finer Case 1 Transport Case 2 Transport Case 1 Bed Surface Case 2 Bed Surface b = 29.0 m Grain Size (mm)

88 (VI) Overtime Threshold & Alluvial Channel Design from the guys who invented it 88

89 Some useful readings 89

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93 Fortier and Scobey (1926) Increased Bank Velocity in Bends Vss R log Vavg W Vss: depth-averaged velocity at 20% slope length from toe Vavg: X/S average velocity R : bend hydraulic radius W : channel top width

94 1. Calculate total stress (use RAS if flow non-uniform) 2. Calculate grain stress ' using 3/2 n ' D 0 and nd 0.013D n for D in mm 3. Choose critical Shields Number 4. Compare ' and c 1/6

95 Step 1 Determine design bed material gradation/channel boundary. Step 2 Determine preliminary width. Step 3 Estimate critical shear stress/velocity. Step 4 Determine flow resistance (Manning s n). Step 5 Calculate depth and slope. Step 6 Determine planform. Step 7 Assess for failure and sediment impact.

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98 (6.7 m) Design (70.8 m 3 /s) 1. Supply reach Estimate sediment transport rate 2. Design reach Given discharge and sediment supply rate and grain size, calculate slope needed to transport supplied sediment at a specified channel width

99 NRCS (Brownlie, SAM) solution NRCS Slope S v Channel Width (m)