Tr25 Design of Open Channel
Tr25 Design of Open Channel
Tr25 Design of Open Channel
Fad or ozzy _Joe"y [seen leszry [ese"y [voy losz-y lose» [ore-y [ene [ oc-y | Wapim rosy iweay = P 6 ‘O0S"2t [ocor2t | 916-et [Ory el [vac ol [O16 G1 [9B GT [OTL 0 | ye "ez [Sed "se [009797 [WIA eUvamveds Oris -O 8 | S279 —[ste"9 [ashd e9e"s —209"9 [1279 —leser9 —Jose~z [c16°L —[629"8 | 000"6 —| WPF Woss04 STPHRAC™O Seg [sted [esy9 [ceo [Z1L-L [ect 6 eee 11 jooy-er | £ev-st [000 ct [009 ZT ‘OLres [oe "ts —[ 097s —Jor-7s Joe "19 [88-79 _]09°ZL —[SZ'8S [OF GOT [05-OTL [Or-IT Ze" ners [rs Te ep y" [rorya fee ere ere EssO[yns"O [8150 [vey [erro [ste -O_[ese-O [961-0 [es -O_ [91 SETS Ser-0eey 0 toy 0 est 09620 B1e"0 [ORT "0 6L0-0[sE0"0[ 600" UTE s= my Ve] 097"0]oz9"0| ev7"0 | n6e"0|9ze70 [oreo | 7ST"0 _|980°0 [8t0"0 [010° HEY toad = sh VT [oreo fers Clore ose so feet ols ojo to fers olor t [sor OL ws oo eer rr 30 Kay20T 9A © pus 13201 ¥ 03 ‘pd: O°8T APTA mo320q ‘woFaFeUEII 8FqI UT pentoauy 200 sF Yadop 18979729 s"puooes 30d 3003 93 sxenbs OL°25 Pex” ‘3993 O22"y WIdep ‘2005 S°Z1 30 GIPTA B YITA ‘TouUUGD pouTT s3ez0009 od 3903 $L°Z Jo Kay20Ton w pur 3003 exenbs Oy'yIT vere ‘T1z sedoTe epT $'4°D HE JO eBzvyDezp ¥ WITH ‘ToUUNGD Naz¥e Ue wos; UOF;eUEZ, TOTET UP WEzeOG 2907 Of "9 uadep51-7 FIGURE 5.I-I TYPICAL TRANSITION TO RECTANGULAR FLUME a7. . , sts jasoayaaae paar peas al eazs [Sane se [sae (ease 3 srs0| | ier Zw 4 570 -| Mele Such ele ting | 5700. yee’ f* seso1 | — = 5 ya au i ee ga ay 3 aagag ¢é Sena 2 oS 4 waree suerace prome S| a tty i] ] ax] ee] Top of Bonk + buztso® TiVORAULIE PROPERTIES.) =Canal- S:000024 920.018) ve27s 2314.5) -Hlume: $-0.0009 v5.98 Top of Lining 0.014 | esas | Tagg a3 4 a 3) aqua Section aT ¢ SECTION AA SecTion BBE10°O stenbe a xy ‘suoyatpucs peztsop 943 375 suopae2e UssAI0q “23 Jo soUeISTP & punos sen ay BuFII0Td AT x ey [eee [eer eee [stor [ee or [ett BupETT Fo WapyA dove oT gent lect [ety _|so"s |tes [eto eed Hx sodors opps = as" a B62 oot jose [eee [doy [ety H_SUyerT 30° a oT Tort] weet WPT ST TT sedors PFS ST STATE “SR = SPEIO OT 766 "66 [Tt OOT|SOT“OOT] ZIT “OOT] 6L0-0OT] 00" OOT 6990189 -Cot | Fas sav"eor] 6s" A V=go col Ae1a SN ET _[e6n00" [szoo* [yet00" sys zt [0zZ00"_| ¥ST00™ | 7ZTOO™ G ssexeny) 7 = TY TT = [890007 |e v0007 | e000" [8zO00™ | #7 WOT TeAzUREdOTS VOFIFAgeTex OT fog"e — |evre [es*e |99°e apm “AV/V =P 6 oat [96-1 [ee-mt _[zs~sT GELS) = WPM seeTeAy 6€ foors (peansven) ¢ SOL Zs -OT ESTEE Ls0 9 jet ve_[ te ce. cats s gee [129 jose 7 je90°T_[005"0 [tee “O joet “o e jeze-0 [600 |161-0 [000 z 96°0 [sv"0 [to Joso0 J or0-0 [00-o v 3 s z © 1 2 Te uoqaas ‘yeuurys yazve 02 woaz 3993 QZ 20.9 “Is aw SF Yadep TwOFATIO OTT etdmexe s7q2 UT ‘Te9F329 ur 192Ve28 edots w oa AjdxHYs YeoIq PINoYs IF IUFOd sTyI Ie ‘yadop TeOTATI Jo IUTOd ‘243 03 dn [2942739 9y2 URYI seoq odoTs F oney pIMoYs woII0q oY] UOFIFsURI] w YONs UT “ToUUEYD peuTT erezdu0D 943 UF TeOFIFIO UEYI sso] pur TouUEYD YIIPD oyI UT TPOzITI oy2 Uey2 reqex8 sf yIdep 042 o[duexe sFy OT spuoses rod 3297 O°St 30 KayD0Ta4 w pur a003 azenbs yE-ET Pore ‘2907 gS°z HIdep 3907 LT°S JO YAPFA BYAFA ToUUEYD poUTT |30z909 aeqnSae3202 e 03 puoces zed 3203 $*¢ JO AIFOOToA v pur 3eaz axenbs 11°26 Pare *T:Z/I-1 sedors opye ‘2e03 go" yadep $2903 O°OL WapFA wor20q ‘*s*d°D 0OZ JO SBIEYDSTP v YAFA TouURYD YIAVe UY Wosy UoFI;sueIT IoTUT Ue UBzSeqSele NOILISNWYL L3INI WOldAL 2-1's aunold 2 av NolLoas Fi EL 160.165 Sig or08 |! FLEL 00.7 F121 100078 FLEL 99.188 Megeede | | Nowoas wae | | -soiseswose Sinavaen 58) fo bp7 | NWid J7VH5.1-13 Z0°0 stenbo uy ‘euozatpuos pextssp 9y3 AFF suoTIEIs UssnIeq “33 ¢ JO SoUBISTP w avya PUNO; sua ay SuzIz0Id Aq on's sos or's zeny 09" Bupuzy Jo yaptA dor s* = us: st 00:2 Suit ore sste o9'e Wx sedos prs = as* - Hs"| LT 04:2 SLz ore ssie ore a= 8upuyT 30 ay8zeu | 91 or ov oT ot o'r sedols PFS | ST sry'tor | 9ez"tor | vtg*oor | szz"oot 00°001 P- "tg ‘s'h= epexp | ot 669°COT 919°EOT | PvE COT $£0°COT 00°EoT FyZ-"s'm V+ corm “Ta ssh | ET 690" sso" 070" 120" = 343] at 410" 9sto" | s8to o1zo" G eBezeay) ¢ = 3a] TT ‘y700" 700° | 400° 900° 2200" adoys vora2434 = 3441 OT 00°€ 0L'% 0072 92°1 00°1 yapre moazeq 318H = a S‘| 6 | Sz's £0's es 1? 00"? wapra doa 318d = 1 5*| 8 | sere eek es°9 a's 00° PHY = WapTA ofexany | 7 sz'z eee est sere 00°€ perms p| 9 £s°81 covet | zsor werst | 00st Adds eay| ¢ LL°01 wm | wet 60°ET €£°E1 zp = Al 9 008°T oze't | o8z'z 079°2 092 ay 7 - 90% = Aa) € 096°0 08 °0 0870 ozt"o oso e7s"uV= “UT | Zz 892°0 790 | BE"0 960°0 ss'm up ost sta | 1 $ 7 € z Te = oarT WoPTeS ‘seFazo0qa6 YBTY 205 AapooTeA UF eueyD uate kqprdex se8ueqo pesy Aapooqon aya 3ey3 puyM UT 0204 eq ptnoys 3} ‘saand eovzang aya aBuey> 03 La SF 37 wo730q pur apys e432 SufuoTrz0doad UF JI “opts youe 203 OI 03 1 anoqe wey z07B0A3 SBrenFp ION P[NOYs UOTIFSULIa Oya “POATOAUT soFIFOT OA YBFY 943 02 ang syeozayaoqns Buzoq syzdep yI0q ‘puoses 0d 3995 L/"O1 JO A3FOOTEA w pue a9—z oxEnbs US*et eae ‘1 02 1 sodots apts ‘3993 Gz" Yadep ‘3993 00°9 YaPFA oII0q ‘TeuUPYD peuTT 92030U0> xYI0UN 07 puoses 30d 3903 ¢"C1 Jo AIFOOTAA B pue ao0s sxENbs OO'ST Pere ‘T 03 1 sado[s epys ‘3003 00°F Yadep ‘3905 00°C ‘yapFa mo330q *s°3°D 00Z FO eBseqSEP w YIFA TeUUEYD PsUFT oyeX0U0D w WoIy UOFITsUEIa JoTINO Ue USTseq5.115 FIGURE 5.1-3 TYPICAL OUTLET TRANSITION Ser z Hyorauiic Properties "oor 3.900847 -a.012 se. Boys B P80 ViI077 see hy rhaoo"S117 FIGURE 5-4 TYPICAL INLET TRANSITION TO PIPE LINE Viv 20s KEL ay Ingeneral, the specif energy of flow at inter grelte setions of the ‘pansion must be compu iy Formula 7 Velcihee Oho campus fram crons Scétionsl arede token nor- ‘tol fo the bottom rather hon verkical sections. The compotations for the WS fine are.im giveroh by fio (orrorsimiler oo fhe method of com- puting flow in hon promote chutes ~~! A SECTION AT ¢ This hype of tronsition is used where its necessary fo develoe the roximum or near monimum capaci of the pipe line 1! the fone end of the transition or where ‘normal flow in tne pie fine 1s of partial death bal rot enought heaa’ can Be used of the iransilion te develop full Sorta! velacriy far the pipe In the later case, the trans ‘hsp may be acl bo deliver the water fo the enlrance of the peat full Somefer and allowing the wafer to occtiseate fire pipe th general, the length of this type of transition i creche by cose oP condtiucrihvid, the ope of he Eittom can ‘hol be made foo sleep [fenough hoc is ovoilable 10 deljver the water fo the pe St about mit dlameter or less, ie franaition nay be warped fo a U-shaped section af the pipe en ‘rice rather than the full round section SECTION AA SECTION 6B SECTION DD SECTION EE5.1-19 Less Important Transitions This type of design is used when head is not at a premium. The elevation of the water surface at each end is known, No attempt is made to trace out the water surface curve at intermediate points. The sides are straight lines and can be made vertical when going from an earth channel to a rectangular or circular section and vice versa, If the side slopes of the two sections are different, they should be gradually warped to meet the end conditions. The bottom should be laid in tangent to the grade at each end. In the absence of more specific knowledge the length of the transi- tion should be such that a straight line joining the flow line at the two ends of the transition will make an angle of about 12 1/2° with the axis of the structure. Neglecting friction the losses can be taken as 0.15 q h, for inlet, and 0.25 4 hy for outlet transitions. In transitioning from an earth channel to a lined channel with a velocity greater than the critical, the earth channel should be contracted at the entrance to the transition sufficient to develop critical depth, and not develop scouring velocities above. The bottom of the transition should drop rapidly from the entrance and connect tangent to the grade on the channel below. The procedure in designing such a transition is: 1. Compute the length. 2. Compute the change in water surface from: WS, equals 1.15 4 hy (inlets) W.S, equals 0.754 h, (outlets) (neglecting ordinary friction loss) To illustrate this procedure let it be required to design a transi- tion from an earth channel carrying 100 second feet, bottom width 12.6 feet, depth of water 2.1 feet, total depth 2.6 feet, side slopes 1-1/2 to 1 and an average velocity of 3.0 feet per second to a conerete lined channel with a bottom width of 3.0 feet, depth of water 1.72 feet, total depth 2.0 feet, side slopes 1-1/2 to 1 and an average velocity of 10.43 feet per second.541-20 ‘The normal depth in the concrete channel of 1.72 feet is less than the critical, therefore it is necessary to develop a velocity greater than the critical. The earth channel should be contracted to develop critical depth, without an excess drawdown effect in the earth channel above. In the earth channel under consideration it is necessary to contract the bottom to a width of 8.5 feet, the side slopes being 1-1/2 to 1. dy equals 1.44 feet Vo equals 6.5 feet per second 1, Length of transition 2.33 x cot 12-1/2° equals 2.33 x 4.51 equals 10.5 feet say 10.0 ft. 2. WS. equals 1.15 (aby) equals 1.15 (1.035) equals 1.19 feet (See Fig. 5.1-5)SeLe21 FIGURE 5.1-5 TyercAL TRANSITION WITH STRAIGHT SIDES Li-----| i T1260" 18.90" Edge W.5. Plan Showing Bottom & Lines at W.S. 1 Top of bank i” Top_of lining| ws Ls" 172" Side Elevation Showing Bottom & Approx. WS. roe -— bso Lsesf— es — Section A-A Section B-B 144!APPENDIX IT TO CHAPTER 5 MOMENTUM METHOD OF DETERMINING BRIDGE PIER LOSS * Flov past an obstruction has been divided into three types which follow roughly "Class A and BY flow as defined by Yarnell, and "Class G" Flow as indicated by Yarnell and defined herein. The definitions as given by Koch and Carstanjen for the three flow conditions follow: "Glass A" flow is defined as a flow condition whereby critical flow within the constricted bridge section is insufficient to produce the momentum required downstream. It is apparent that for this type of flow, the bridge section is not a "control point" and, therefore, the upstream water depth is controlled by the downstream water depth plus the total losses incurred in passing the bridge section. "Glass B" flow is defined as a flow condition whereby critical flow within the constricted bridge section produces or exceeds the momentum required downstream. When this condition exists, the up- stream water depth is independent of the downstream water depth, being controlled directly by the critical momentum required within the constricted bridge section and the entrance losses. 2G" A special form of "Class BY flow occurs when the upstrean water is flowing at a subcritical depth and containing sufficient momentum to overcome the entrance losses and produce a super critical velocity within the constricted bridge section. The drawing on the following page, entitled "Bridge Pier Losses by the Momentum Method" shows the water surface profiles and momentum curves for the three classes of flow. Momentum, as referred to above, is defined as total momentum or the total of static and kinetic momentum, and may be written as m+ Qu az where m= total static pressure of the water at a given section in pounds Q= discharge in cubic feet per second g = acceleration of gravity in feet per second per second A = channel cross-sectional area in square feet. * Data derived from "Report of Engineering Aspects, Flood of March 1938, Los Angeles, California," - Appendix I, Theoretical and Observed Bridge Pier Losses - U. S. Engineer's Office, Los Angeles, California, - May 1949 and from "Approximate Method Determines Bridge Pier Loss," by G. M. Allen, Jr., in March 1953, Civil Engineering.542-2 ‘The unit weight of water (w) should appear in each term, but since it would cancel in the final equations, it has been assumed equal to unity, dimensions being pounds per cubic foot. Based on experiments under all conditions of open channel flow where the channel was constricted by short flat surfaces perpend~ fcular to flow, such as bridge pier, Koch and Carstanjen found that 2 the total kinetic loss was equal to 40% where Ag is the area of AyeAL the obstruction on the upstream surface and Ay is the water area in the upstream unobstructed channel. For circular nose piers, Koch and Carstanjen show thac 2/3 of 0%) should be used. Te ts GyeAD apparent that the static pressure mg against the upstream obstructed area is not effective downstream, whereas the static pressure against the downstream obstructed area is effective domnstrean. Therefore, if we let the subscripts 1, 2, and 3 represent condi~ tions upstream, within and downstream of the constricted section, respectively, we may write the general monentun relationship as follows: ‘Total upstream momentum minus the momentum loss at entrance must equal the total momentum within the constricted section, or 2 2 © ms ©, oe AL hy 2 2 moot gat LADD = mt A ‘Total momentum within the constricted section plus static pressure on the downstream obstructed area must equal the total momentum in the downstream channel, or5.263 PIER 135 A) ALon| ‘= WATER DEPTH) 2 ae (CLASS A). i We 5-7 CLASS C FLOW czas = m= %(CLASY C)) = as Fe ae a ea a “MOMENTUM LONGITUDINAL PROFILE MOMENTUM CURVES GENERAL MOMENTUM EQUATION: Mt fg As > shay: my) Fi, T ee i \ Pagacee wed) de . BL. .- |e >s NOTATIONS : ‘LI sMomentum curves upstream, inside ond f & downstream of bridge respectively ; 0, te, shaver depthg wpathatin, aide Ghd i H ‘connsireom oF bridge.respectively. 7 “% dear Gite depth mithin artye Ms Bar0GE PIER __# ewannes_™ San Critical cep 7 i Inaige Spore moment in unebstrected channel : } imps State moment of bridge ier : Retyedroe of unobstructed channel in ay fb Bpttirea oF bridge pier in iF Ge Discharge inc. J" Grevitevione! constont GS catenin unabetructed channaly —______1 IGURE 5.2-/ BRIDGE PIER LOSSES BY THE PLAN MOMENTUM METHOD542-5 The general momentum equation follows: 2 2 @ @ ¢ my amg ty y= Ag) em te my mg AL aA, wy The above equations cannot be solved as presented, and it is necessary that a simpler method be used. The total sum of momentum and hydro- static pressure for each section (Fig. 5.2-3) for equal depths of flow past each section should first be determined. Using equal depths, Apo Ay = Ay = Ay = Ay (OF Ay = Ay) and N= My = = = My Cor My =). Also, for equal depths, the sum of momentum and hydrostatic pressure for each section I, II, and III is: pen, ny eet 1 x ¢ =u -4)+—o 17 %o* em aD 2 g & MIE =M, - M+ =m - mye as ay where, for equal depths, A, = A, The values for equations I, II, and II are determined for various depths, both subcritical and supercritical. A curve for each section is plotted using the depth as the ordinate and the values from col- ums I, II, and III as the abscissa (see Fig. 5.2-4). A vertical line passed through the three curves gives a graphic solution of the equations, as it gives, for equal momentum, the corresponding depths of flow. This vertical line must intersect a minimum of five depth values, and preferably six. Drwg. No. 7-N-Eng. 248, page 3, shows the depth of flow and its indicated class. If only one value’{s inter- sected on curve II, the flow is critical at Section II. Values of "d" on the lower portions of Curves I and III are used for supercritical flow, and on the upper portions for subcritical flow.522-6 Backwater computations will determine either a flow depth at Section I or III, depending upon type of flow conditions, and the curves give a direct solution, as the vertical line must pass through the known depth on Curve I or III, and must also pass through Curve II. If this vertical line does not pass through Curve II, it is possible that the momentum of the given depth is not great enough for the flow to pass the obstruction, and a change in the computed depth must be made. The flow would then be critical at Section II, as the critical depth is the depth at which the momentum and pressure is the minimum. Example Given a trapizoidal channel, base~width 16 feet, side-slopes 1-3/4:1 and capacity Q = 5000 c.f.s. Fig. 5.2~i Cross-section of channel showing center bridge pier.5.267 Fig. 5-2-3, Longitudinal section along centerline of channel indicates three locations: I - immediately upstream, II ~ Under bridge, III - Inmediately downstream. Compute M, - M, by solving for the distance F from the water surface to the center of gravity of the trapezoidal section where y= (E+ 20}. (= top width and b = base width) and multiplying 7 by the area A, or Qi, = FA). The F distance for the obstruction, which ts of rectangular area A, is $5 this miltiplied by A), will give M,. Quantities for the remaining columns can be easily computed by use of the formulas given on pages 5.2-2 and 5.2-5 and in the column head~ ings in Table 5.2-1. Momentum values given in colums I, II, and III, Table 5.2-1, are shown plotted on the graph, Fig. 5.2~4, giving curves I, II, and III. From a point on Curve I, which represents the upstream depth d,, draw a vertical line through Curves II and III which will give the depth values for the sections under the bridge and immediately down- stream, For the example given, refer to the curves on Fig. 5.24. For an upstream depth of 8.0 feet; the depth under the bridge is 9.3 feet and the depth immediately downstream is 8.7 feet. As the flow upstream is at subcritical depth, d, is less than d. and "Class G" flow applies (see Fig. 5.2-1).1 It is shown in Table 5.2-1 that the bridge section includes an 18-inch wide pier. As debris piles up on the center pier its net522-8 effect is to widen the center pier increasing Ay and My. The effect of such debris accumulations can be estimated by computing flow conditions for the wider pier that would result when debris had accumulated. In critical cases the effect of debris lodging against piers can be minimized by constructing a 2:1 incline on the upstream edge of the piers, This causes debris to rise toward the surface and widen only a portion of the pier height. It should be noted, however, that the top eight (8) feet are normally considered to be affected by such debris so an inclined leading edge on piers in shallow streams would not be too effective. ‘The momentum method of computing the approximate change of water surface is not dependent upon coefficients "K" as are necessary in the formulas derived by Nagler, Weisbach, Rehbock and others (see USDA Technical Bulletin No. 429, "Pile Trestles as Channel Obstructions" and USDA Technical Bulletin No. 442, "Bridge Piers as Channel Obstructions"). A check computation for the raise in water surface due to the bridge obstruction was made using the Nagler formula. The co- efficient K varies from .87 to .94 with the channel contraction approximately five percent. The difference in water surface elevation between the depth in the unobstructed channel ard the depth caused by the obstruction was from 0.7 to 0.8 foot. Dif~ ference in depths indicated by the Momentum Method was greater, shown by the curves to be 1.3 feet, and is on the conservative side. The water surface profile, above and below bridges, can be com- puted by the standard step method, as described in a report "Technical Memorandum - Water Surface Computation in Open Channels" by R, F. Wong, Los Angeles District Corps of Engi-~ neers, and also given in King's Handbook of Hydraulics.5.269 é Tom | ese | onsT Cele | SLee | OeLe | ORL a Ea a dese | sele | €ese | etee Ra a | 9eee | est | ott | Stee gum | 960% | alent | ese Ca €66n | a0 ots9 | 6189 | eo | T9e9 ‘Rese | zat eros | Ofte H+ Olas lesa] o ur 0 1 0 =fS.2-11 200" WMANaKON 2 e oe oe 99 20 9s +6 os. 9 2p st oe 200148 190Un I (a) Hte30 aa woeusd) Kelopoww) Teuuovd 38/9. Ine : > uwwug v0 Jag 2008 81 " BAYNO H1d30_ Y3VM -25 3uNdi4 2CHAPTER 6 ~ STABILITY DESIGN Introduction... ee eee Stability Design... sve ee eee Essentially Rigid Boundaries beeen Figure 6-1 -- Channel Evaluation Procedural Guide Mobile Boundaries 0 oe ee eee ee Procedure for Determining Sediment Concentration... . . Allowable Velocity Approach... ee ee eee General... +s | Figure 6-2 -- Allowable Velocities for Unprotected Earth Channels. ee ee eee ee es Procedures- Allowable Velocity Approach... . ~~ Examples of Allowable Velocity Approach . - Example 6-100 eee tee eee eee Example 6-206 eee eee eee Example 6-306 06sec eee eee Example 6-4 5... 06s eee Tractive Stress Approach so. se ee ee beeeee General eee Coarse Grained Discrete Particle Soils . . Actual Tractive Stress... - 1/1 eee Figure 6-3 -- Hydraulics: Channel Stability; Actual Maximum Tractive Stress t,, on Bed of Straight Trapezoidal Channels.» Ys. Figure 6-4 -- Hydraulics: Channel Stability; Actual Maximum Tractive Stress t,, on Sides of Straight Trapezoidal Channels». Ss... se 6-2 6-3 6-3 6-3 63 6-10 + 6-12 6-12 6-12 6-12 + 6-14Figure 6-5 -- Hydraulics: Channel Stability; Actual 2 on Bed and Sides Maximum Tractive Forces, t,, and t., of Trapezoidal Channels witfiin a Clfved Reach»... + + Figure 6-6 -- Hydraulics: Channel Stability; st» on Bed and Sides Maximum Tractive Stress, th and t of Trapezoidal Channels in Seraight Reaches Innediately Downstrean from Curved Reaches «ee ee ee ee Allowable Tractive Stress 6 - ee eee eee Fine Grained Soils...) eee ee ee eee ee Actual Tractive Stress. ee ee eee Actual Figure 6-7 -— Hydraulics: Channel Stability; Angle of Repose, $g, for Non-Cohesive Materials Figure 6-8 -- Hydraulics: Channel Stability; Limiting Tractive Force t,, for sides of Trapezoidal Channels Having Non-Cohes{¥e Materials... .. ++ - Figure 6-9 -- Graphic Solution of Equation 6-10... - Figure 6-10 -- Graphic Solution of Equation 6-10 . . . Figure 6-11 -- Values of v and 9 for Various Water Temperatures... 1. +++ Figure 6-12 -- Applied Maximum Tractive Stresses, +, On Sides of Straight Trapezoidal Channels... . - Figure 6-13 ~~ Applied Naxinun Tractive Stresses, tps on Bed of Straight Trapezoidal Channels... 1. ++ + Figure 6-14 -- Allowable Tractive Stresses Non-Cohesive Soils, Djg< 0.25" se eee eee ee eee eee Allowable Tractive Stress... +++ - Procedures ~ Tractive Stress Approach Examples of Tractive Stress Approach . Example 6-5. 0-0 eee eee Example 6-6... eee eee eee Formation of Bed Armor in Coarse Material Page 6-16 6-17 6-18 + 6-18 6-18 + 6-19 6-20 + 6-22 + 6-23 + 6-24 + 6-25 6-25 6-26 6-27 6-27 6-28 6-28 6-29 6-30Tractive Power Approach... 1+ ee eee ee eee Figure 6-15 -- Unconfined Compressive Strength and Tractive Power as Related to Channel Stability . . . Procedures - Tractive Power Approach»... .- Example 6-7 2... 22. dooguudG The Modified Regime Approach... 4-22... 45 Procedures ~ Modified Regime Approach... .. ~ Example 6-8... eee ee eee ee eee Channel Stability With Respect to Sediment Transport Application of Bedload Transport Equations . . . Sediment Transport in Sand Bed Streams Not in Equilibrium Figure 6-16 -- Relationship Between Mean Velocity and Sediment Transport on and Near Stream Bed Figure 6-17 -- Relation of Mean Velocity to Product of Slope Hydraulic Radius and Unit Weight of Example 6-9)... eee see Table 6-1 -- Mean Velocity Computations ~ Two Channel Sections... . ++. ess Table 6-2 -- Calculation of "n" adjusted for to 1 side slopes (riprapped).... 1... Figure 6-18 -- Reservoir Release Hydrograph Principal Spillway... see epee eee Water . Figure 6-19 -- Velocity-Area Curve... Figure 6-20 -- Velocity-Discharge Curve... Table 6-3 -- Bedload Sediment Transport . . . Example 6-10. 2. ee eee ee ee eee Figure 6-21 -- Discharge-Bedload Sediment Transport 6-32 6-33 6-33 6-35 6-37 6-38 6-40 6-40 6-41 6-42 6-43 64h 6-46 6-47 6-48 6-49, 6-50 6-52 + 6-53 6-54Page Figure 6-22 -- Synthetic Storm Hydrograph. ... 4... 6-55 Figure 6-23 -- Velocity-Area Curve 6... 14 es. 6°56 Figure 6-24 -- Velocity-Discharge Curve... . 1... 6-57 Table 6-4 -- Mean Velocity Computations ~ Three Channel Sections «se ee ee eee et ee ee O58 Slope (Bank) Stability Analysis... .......0. Fes 659 General ee ee 6559 Table 6-5 -- Bedload Sediment Transport - Three Stream Sections... eee ee ee 660 Figure 6-25 -- Discharge-Bedload Sediment Transport . . . 6-61 Types of Slides and Methods of Analysis ...... 2... . 6-62 Boundary Conditions and Parameters Affecting Slope Stability ee ee ee ee ee ws O64 Factors of Safety Against Sliding ... 1... 1. 14s ss 6-68 Paping ss eee ee er ee ee ee ee OBB Stabilizing Measures ©. ee ee ee 669 General 2 ee ee ee eae + 6-69 Bank Protection «6. ee ee ee ee ee O69 Channel Linings 2... ee ee ee OO Grade Control Structures... ee ee ee ee OTB Other Structures... ee ee + 6082 General oe ee OBZ Channel Crossings... . ~~ Boodoedodoooo dbo CT Channel Junction Structures ©... ee ee ee ee 682 Side Inlet Structures... ee ee OB Water Level Control Structures ©... 1 ee ee ee 684Design Features Related to Maintenance... . ++. ++ Added Depth or Capacity for Deposition ..... Relationship of Side Slopes to Maintenance Methods Berms . . . Maintenance Roadways». +e eee ee eee ee Epo i ee Entrance of Side Surface Water to Channel... - « Seeding... ee ee ee ee ee Pilot Channels Glossary of Symbols References « Page 6-84 6-84 6-85 6-85 6-85 6-85 6-85 = 6-86 6-86 6-87 6-90CHAPTER 6. STABILITY EVALUATION AND DESIGN Introduction The analysis of earth channels with acceptable limits of stability is of primary importance to Soil Conservation Service activities. The evalua~ tion or design of any water conveyance system that includes earth channels requires knowledge of the relationships between flowing water and the earth materials forming the boundary of the channel, as well as an understanding of the expected stream response when structures, lining, vegetation, or other features are imposed. These relationships may be the controlling factors in determining channel alignment, grade, dimensioning of cross section and selection of design features to assure the operational require~ ments of the system. ‘The methods included herein to evaluate channel stability against the flow forces are for bare earth. When evaluations indicate the ability of the soil is insufficient to resist or tolerate the forces applied by the flow under consideration it may be necessary to consider that the channel has mobile boundaries. The magnitude of the channel instability needs to be determined in order to evaluate whether or not vegetative practices and/or structural measures are needed. Where such practices or measures are required, methods of analysis that appropriately evaluate the strean's response should be used. Figure 6-1 provides general guidance in selecting evaluation procedures that apply to various site conditions. All terms used in this chapter are defined in the glossary on page 6-87. Stability Evaluation Methods presently used by the SCS in the evaluation of the stability of earth channels are based on the following fundamental physical concepts. 1. Essentially rigid boundaries. Stability is attained when the inter action between flow and the material forming the channel boundary is such that the soil boundary effectively resists the erosive efforts of the flow. Where properly evaluated and designed the bed and banks in this class of channels remains essentially unchanged during all stages of flow. ‘The principles of hydraulics based on rigid boundaries are applicable in analyzing such channels. ‘The procedures described in this chapter that are based on this definition of stability are: a, Allowable velocity approach. b. Tractive stress approach. ¢. Tractive power approach.