Design of a Gravity Dam with Siphon Spillway for the El Capitan Damsite Citation Beed, Carl Frederick (1925) Design of a Gravity Dam with Siphon Spillway for the El Capitan Damsite. Bachelor's thesis, California Institute of Technology. doi:10.7907/eg0d-h618. https://resolver.caltech.edu/CaltechTHESIS:07312024-152500531 Abstract No abstract. Item Type: Thesis (Bachelor's thesis) Subject Keywords: (Civil Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 June 1925 Record Number: CaltechTHESIS:07312024-152500531 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:07312024-152500531 DOI: 10.7907/eg0d-h618 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16603 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 01 Aug 2024 20:47 Last Modified: 01 Aug 2024 20:47 Thesis Files PDF (Thesis) - Final Version See Usage Policy. 4MB PDF (Plate 1. El Capitan Reservoir Plan, Dam Site no.2, San Diego County) - Supplemental Material See Usage Policy. 1MB PDF (Plate 2.Design of Maximum Gravity Section, Showing Siphon) - Supplemental Material See Usage Policy. 684kB PDF (Plate 3. Design of Siphon Spillway for El Capitan Dam) - Supplemental Material See Usage Policy. 532kB Repository Staff Only: item control page

".:'HE ~ESIGlI OF A ,J :RAVI~Y DAM ~ITH SIPHON SPitL~AY EL CAPITAN TAMSI~E by Carl 1<'. Beed Thesis ,Time 1~25 CALIFO~NIA INSTITUTE OF TI~CHNOLOGY Proceedings of the American Society of Civil -Sngineers, "Siphon Spi l lwa;rs" , vplume XLVII-no. 2 Paper by G.F'.Stickney, M.Am.Soc.C.E. T:iscussions in volume :X TNIII-No. 4 By ~harles F. Ruff F.d ward l'0e gmann · W. P . C re age r F . Ji'. ~unham Iarl R. Iennison Joel ;;.Justin H.B.Uuckleston Charles G.~arrach "The ""'esign and Test of a l'Eo del Siphon Sp illway" By Robert N. Allen. Thesis 1916 ~HEE~ CAPimAn nAM PROJECT ~he El Capitan Darn Site is located ab~ut thirty mil.es from San Diego, near Lakeside. In carrying out San Diego's water development program $4,500,000 was votea in November 1924 to construc t the first development of the El Capitan Dam on site muc1ber 2. ~he f1rst devel- opment was to be a dam 150 feet high, the com pleted dam is to be 200 feet high with a storage capacity of forty-three billion gallons or about 132,000 acre feet. ~here has been considerable discussion as to the relative merits of the El Capitan aamsite as compared with the Mission Valle y damsite which is located about se-venteen miles down the San Diego :?iver. These sites are shovm on the location map of plate III . The main disadvBntage of~the Mission Gorge sites is the large amount of valua ble farm l and .vhich wonld be f lood ed . Also the large surface area Rould cause considerable loss d L1.e to evaporat ion. since the loss is abont 68 inches per year. The F. l Capi.tan T'am, on the other hand,woalc1 be a deeper anc1 more narro w reservoir, and ,rnn1_c7. no t flooc1 so , mah fa rm land. Practicall~r t he only farm land which wi 11 have to be bonP:ht belongs to a small Indian reservation, abo,.1t 15 miles abov e th e c1amsite. :!:n general the l a nd ,vhiah rmst be bol1 p;ht ts l.not very va 1_nable. There are two El !Japi tan damsi tes, mi.mber 1 and numbe r 2. Co re d rillin g has reveale a the f a ct that site number 2 is more desireable. Th is can be seen from the results of th o Jore d ri ~l in g s hown on pl&te IV. The d ata for t he p robl em Ras obtained at the city engi n8er's office in the City Hall at San Diego. It consisted of the results of the core drilling at the two sites together with pr'.)files of the two locations. A cont our map of d amsi t e -/f2 was obtained, and a locution map 0f the differen t damsites on the San Diego River. This latter map shorrn the proposed ronte for the flume from El Capitan to the ,city of San Diego, emptyinp: into the UnivercitJr Hei?,°hts P. eservoir. This route is pro- p osed by Mr. Savag-e, who was hJrd rau 1 i c engineer for the city for a rnmber of years. S ince the proposed aam is to be 200 feet high it was c.ecided t .'.) desip,-n a dam of this height in order that comparisons might be made '.'fi th the design of the city enP:ineers. The ob.iect of this theois is simpl;v to c"l esip:n a d a m f or the ~1 Capit a n damsi.te wbich conditions,at a reasona ble cost. iiT0 1(nd best Emit t h e Although the initial ob_ject d id not inclucle the aestgn of a siphon s pillway, it later developed that this was the most suitable type, j_n the a 1.ithor' s estimation. This design was therefore incorp o rated in the problem and this was the most cliffic 11lt part clue to the ven_r small amount of wor'er ,1hich has been done on s i phon spi. l lway des i.gn. No a.esjgn showing placi.np.: of steel co 1.1 ld be fonnd, although I learned that old steel rails were used in the si phons at the Sweetwater ~eservo i r. In choostnp: the t:ype of dam to design, mnltiple arch, constant angle arch. a:>::'ched gravi t;:r, and straight gravity darns were considered. ':1he main a isadvantage of the r!lultipll~ arch dal'!l for this site is the e:xtreme height for which the dam must be designed. Since the advis- ability of a T.!l ,1.ltiple a:rJh dam over 100 feet hip:h is somewhat questionable, this ty pe was not used. ':1he question or a constant anp.:le arch dam was also considered but the e:xtrome length of the dam this type :ms11i.table. made This type would reqni re at least an anp.-le o f 100° for an economical section. r,,his would increase the length of the structure very considerably and wo t1ld. require probably as great an eYflend i t ;ue as a g ravity section and Nith less dependabili ty . ~he arched gravity was discarde d in favor of the st raigr1t p.:ravi ty for pract ic a 1 ly the sa-rie reusons as mentioned in th 8 prece d ing paragraph. It was thonght t hat the additional length of dam req ':iired to form the arch wo :1.ld offs·et an7 advantage gainea. through arch action. Also, the fact t },at the sic'ies of the canyon are not steep is against any ty pe of arch. since a very small amo :mt of slippinp: o:' the ar1h abatrients would be a very serious condition. A rravity section was therefore desiO'ned takir.rr into account the Nater press 1ire .vi thout the corisiderati □ n of npl i ft. The resultant aa s kent within the midctle thirc1 throughout. P'RET,IMINAF:V COTT8PYf,:,:Z.A."'IO:'TS OF A SIPHOIJ SPIT.,T,WAY A siphon s~illway was decided on for the following reasons: First. close rep:u.lati:m of the water seemed desireable due to the high value placed on water in this vicinity. Second, a weir spillway was out of the question due to the extreme length of crest required with a reasonable depth of flow over the weir. In order to pass a flow of 50,000 sedond feet over a weir with a depth of 4 feet it would require a length of 1880 feet. With a depth of 8 feet it would require a length of 663 feet. and with a depth of 10 feet a length of 475 feet. ':l'he length available for spill i.s limited to about 400 feet. Third, it was decided that a siphon spillway could be constracted considerably cheaper than a highpressure gate type, and that siphons ~vo 1ld be more dependable. The argument against siphon spi 1 lways i ·s.:; that very little is known of the stresses set up when siphonic acti:m takes pl.ace, especially if there is any tendency toward vibration within the siphon. However. due to the special type 0£' siphon used in the design very little vibration is to be expe~ted. if any at a ll. "'his desiP.,11 is different from other siphons in that • the water is allowed to l.eave the siphon without the usual upward bend at exit which would tend to xeflect badk i.nto the siphon any vibratory wave of water pressure. In , tbe ·design of the siphon an additional factor of safety was allowed to take care of any vibration which might occur, ana. as a factor of ignorance. PRIMING OF SIPHON The priming of a siphon occurs as soon as the siphon is sealed at the the top and at the bottom with a resulting rarification of the air within the tube. This rarification is caused by the water flowing through the siphon carrying with it bubbles of air from the inner chamber. This action is cumulative so that as soon as the pressure within is reduced.due to this rarification. more water begins to flow through vvhich carri.es Nith it additional air. This continues until the siphon is flowing full. mhe usual method of obtaining a seal at the bottom of the siphon is by means of a distinct upward bend just before exit. advantages. This type of seal has two dis- First. it tends to increase vibration in the siphon, as already r.ientionea: and second, in the gravity section of the dam as designed it would require consider~ble additional concrete. It alsn de- creases the efficiency of the siphon somewhat. Fo'r .c these reasons'- &-f f fe rent means of obtaining a seal .w ere us@d. PRIMING Or .SIPI-ION Fig/. Refering to fign.re 1. it can be seen that when the water flows with sufficient velocity over the lip of the siphon to strike the opposite side of the siphon wall, a seal of the lower end will be obtained. In this type of siphon a slightly greater head above the lip is required but this is of small consequence in comparison with its advantages. In computing the head required to accomplish this it is merely necessary to figure the head required on a weir to produce a velocity sufficient to get the water to the opposite side before the force of gravity gets the water to the bottom of the siphon. H = 1/2 gt 2 Time required for water to fall 30 feet t =Pf = Ex30 32.16 =1.87 seconds And averap.:e horizontal velocity '' V = 3.33 h 1/2 where h = head on weir Then and h = 1.26 feet It is estimated that the siphon will prime with a head between 1 and 1.26 feet. PRELIMINARY COMPUTATI1NS FOR SIPHON SPILtWAY The head acting in the siphon is taken from the lip of the siphon to the top of the siphon at discharge end. mhis is a conservative measurement as there will be a small head above the lip of the siphon. The efficiency for preliminary computations was taken as 6o% which is a safe assumption according to engineers who have written on the subject. A more accurate determination of the efficiency is made on the neyt few pages. The cross-section at the throat of each siphon is 4 by 6 feet. The discharge for each siphon is equal to Q = c A-J2gh x 24 ✓ 2x32. 2x32 = • 60 = 1640 sec.ft. per siphon Using 20 siphons the total available discharge capacity would be ~otal Q = 20 x 1640 = 32,800 sec. ft. Since the maximum flow recorded is 38,000 sec. feet 1.t was decided that a spill of at least 50,000 sec. feet should be provided for. The excess spill over the capacity of the siphons is to be taken care of by an ordinary weir type spillway. The length of weir required to take the remaining 17,200 sec. ft. assuming an 8 foot depth overflow. L -_ 17200 ~ = 236 feet 3. 33x8 37,.__, The losses which occur in a siphon are: T 2 Friction loss, h~ = ~ v 12000 v2 Entrance velocity loss. hv = - 2g Loss due to bends, hb = c -" , wh ere c is some constant 2g depending on the angle of b e n d . vcJ These losses were determined using a s a g Lli de Mr. Creager 's discussion of losses in siphons publishe d in the proceedings of the A.S.C. E . for Ap ril 1922. ~ eferri nf to Fig . I ~he losses from A t o Ba re: .2x:.v2 h.o = - ~ ... l2 0 •J 0 v2 hv = hb = 2g 1 = .00017 = . OI 55 vc' n Vt:_. " v-c, / s2g- = . 00194 V 2 The losses from B to Care: ,., ') hf = 9:xv2 12000 = . 0 0075 v2 hb = .9-- = ~0 Jl 39 2g ,.. from Loss to 1) are: V V2 , I 2 = 28-.Y._ = .00234 V 2 h.o ..... 1 2000 Losses from n to E are: h.o =15 J. v2 = .00125 12000 V 2 ,.., v i::, ht = .2 - - = .00311 v2 2g Total head = .03 9 0 v2 = 32 f t. Since the total head= .03~ v2 = 32 Therefore the velocity= 28.7 ft/sec. The theoretical velocity= ~2xgx32 = 45.4 ft/sec Therefore the efficiency= 28.7/4E.4 = 63.2 % ~aking the average section as 6.5 x 10 the discharge per siJ)hon, Q Total = . 632. x6f5 -.J 2g:x32 = 1860 sec. ft. Q = 20 x 1860 = 37,200 sec. ft. This fig:1re is probably more acc ·nate than the previous one. Since the maximum recorded flood recorded ts 38,000 sec. ft. it is possible that no weir spillway would be necessary. However, due to the short period for which records are available it is thonght that a weir spillway would be added to insure safety to the structure. The additional cost ~ould be quite n~gligi- ble in -eomparison vvith the total cost and the added insurance against flood to towns belon the strnct ine would :'ully w:a.rTant such constr,wtion. A glareing example of inadequate spillway capacity is found only about twenty -five miles from the Rl Capitan site. ·' This was the Sweetwater Reservoir which supplies the southerr. part of San Uiego with water. It was originally constructed with a spillway capacity of 1500 sec. ft. which was the maxim :1m flood recoreed at that time. It was necessary to enlarge this at three different times antil its present spillnay capacity is about 35,000 sec. ft. At this reservoir are lonated six siphons Nith a capacity of 12,000 sec. ft. IN S IPH0l'J In order to allow for any additional head which l"1ight come on the siphnns in time of maximum flood the stresses wi 11 be determined ass ,ming a flow of 2000 sec. ft. per siphon instead of 1890 sec. ft. The entrance velocity would then be v1 = 2000 = 16.7 ft/sed. 12:xlO The velocity at the throat 2000 V = = 33.4 ft/sec. 2 6xl0 The dynamic action of t "' e water dne to the first bend and acting horizontally on the front cantilever of the siphon Rx = gW ( V 1-~ - V.-Jt:., cos e ) where 9 is the angle throug-h Nhich the water is turned, taken as 60°. 2000:::{62. 4 ( 16.7 - 33.4xl/2 32.lfi = 0 force due to dynamic action The reason that tbis force is so small is dne to the fact that the water ~elocity is increased at the same time that it is turned. The only two forces acting on this front cantilever are the force due to water pressure and the force d ~e to atmospheric pressure. The reason that this latter force must be takin into account vacuum within the siphon. is due to the p artial For pur poses of computation the pressure within the siphon is taken as zero at the throat and uniformly varJri_ng down to the discharge. This distribution of pressure is borne ont approyimately by pressure tests in a s-:. phon which .vere made at the CTaliforni.a Institute of Technology in 1916 by Robert IT. Allen. Wi.th these assumptions the bonding moment acting on the front cantilever = f 2. 4x25 2 x25 + 2x3 = 162,500 + 14.7 x2fxl2 2 x25x2 / 3 2 441,000 = 603,500 ft.lbs. Considering the front of the siphon to act purely aA a cantilever the steel required 603 Aoo x 8 16000x 7 y 9 = 4.8 in2 per f)Ot The force acting per square foot on the face of the dam 12 feet below the lip of the siphon p = 62. 4 x 12 + -½}Yl4. 7xl44 = 749 + 1110 = 1859 lbs per ft 2 Considering this force to be taken into the 4 foot soldd sections betwee~ siphons the bending ~oment at tho chosen section is M= 1859xl4 2 xl2 = 655,000 in.lbs. l Then steel : required = 6.frf.....QQ_Q_ 16000x9xl2 x=-8..L = .43 in2 per ft 7 • The st eel c or.rputed above is vertical st ee 1 anc1 the latter is placed horizontal. Both are not necessary to the full amo:mt so about two thi rc1s of each wi 11 be used. The steel distribution is shown on Plate fil ~he upward reaction due to 15 0° bend is Ry =JL( Vl cos 0 g = 2000x62,4 - V2 -k 33.[ 32.16 = 243,000 lbs. .866 + 1 ) moment acting= 243,000x6xl2 = 1,75 0,000 in.lbs/ft. Steel required assuming about a 6 foot section A = s 1,750 ooox§ 16000~6xl2x7 = 1.74 1n2 At the 4 foot section the moment will be about 1/4 . , 1/4 x 1,750,0JO = .651 in2 And th .es t ee.1 requ1rea =-------~----16000:x 7 /8 x4xl2 These figures are total steel per siphon. Bending moment acting on the bac~ cantilever of siphon M~r = -1 4 ...1-x 25 ,, 2 A 8 Y. l2 2 x...2b_ 3 221.o_o_o__ = -~--~ - = = 221, OOJ ft. lbs per foot • 2 per ~oo p t . 2.63 1n 16000y 7 /8 Y.6 ~he shear in the concrete due to forces on the front cantilever near the top Yvhere shear is maxirnnrn l ,1. 7 x lQ 3.E x 2 V = = 21 lbs per 0. :. ~at Rl fleight above each siphon Y = 340 x l 'p,O x 14 = 715, ODD lbs. 1 Compressive stress in ~oncrete Hhen s iphon is not runnin~, Ti' n =715,000/ 24x4xl44 = 51.7 lbs per in 2 O. I . V iVr1en the siphon is running ful 1 this stress wi 11 be reduced. For the amount of steel used and th e placing consult Plate III Each siphon has two vent pipes located one foot above the lip of the siphon to prevent vibration. If this is not provided the siphon will be~in to flow b~fore there is sufficient head to keep it . running, ana the result is that the siphon Nill take in a gulp of air and then stop. r:'his is where the greatest a.anger from vibration oc~urs, and should be guarded against. The siphons are arranged as shown on plate I, there being ten siphons on each side ~ith a 200 foot weir spillway in the center. It was thoui:tht that this arrangement would tend toward gre ater stability in case of vibration in the siphons. ~very other siphon is lowered 6 inches so that five siphons will go into operation at the same time on either side of the dam. The total number of cubic yards of cqnctete .. re~uired is about E60,000. which is 4.25 cubic yards of concrete for each ucre foot of capa~ity. The cost of concrete at. the aamsite is $8 per cubic yard. This would mean a cost of $4,480,000 for the concrete alone. To this must be added the cost of the st•~l required for reinforcement. Al~o the cost ~f excavation wo~ld be ad- ditional and the cost of formwork for the siphons. The water to be taken .:'rom t 1-! e reservoir would be obtained by means of fma:r. valves located at elevations 590, 6::30, 670, and 710. From these valves , the . water . oould be run through a chlorinator, as is done at the Sweetwat er Darn,__ and then through the conduit to the city.  Plafe I N Cuyamaca WoferCa D1vertmg Dam ~~ • r, ~~ . - - - /~~~ V) ~/ ~i( /~cf>. . . v \) c:i 1verstfy Heigld.5,, , Reservo, r }, ~--, 0&>-.. /;,--'..__,,,... ,, • ,. (/) ~ ~ ~~ ~ - ~ Murray rreservo1r n {,,--' Q-';> ¥0 LOCATION 7 .5cale or Miles z 0 3 4 '/ \ \ .\\ "' • ""~ . \ ~ ~ "~ " ., I I I I CALIFORNIA . INSTITUTE OF TECHNOLOGY EL CAP/ TAN RESERVOIR PLAN - DAM SITE N0.2 . TOPOGRAPHY .SAN DIEGO Con four /nferva/:r /CJ rt Scale I"= 100 tf 0 t{)O ZOO /Vo-M-CoreOnllflolus 5howrn Thu.5 o COUNTY FROM SAN DIEGO CITY MAP <;:) ~ DAM DESIGNED BY CARL F. BEED TRACEO BY C.F:B . THESIS JUNE 1925  -----Elev. 760 b z w H 20 /0 60 12.5 .125 24 /{).52 /Z6 50 IZ.28 Zt4.5 /12..5 680 35 48 r l .397 . 526 /5.30 340.5 zoo .588 6130 61 + 2 18.96 312.5 612.5 .614 .1325 .631 .633 ELEV 740 720 700 fanR 640 74 +3 ZZ.90 509.5 720 620 87+3.5 Z6.95 97/ 600 101 +3.5 31.zo /262 800 580 560 115 + 4 35.65 10/2.5 .633 129+4.5 40.05 !598 /975 /250 450 540 /43 +5 44.40 2395 /512.5 .633 . 63Z. 5ZO 157+5.5 4B.80 2860 !800 .630 /7/ +6 53.20 3370 5780 3920 21 I Z.5 2450 .627 t 135 +6.5 500 480 RctdlU5 = 60 ff. .625 OE.5IGN OF MAXIMUM GRAVITY .SECTION .SHOWING SIPHON CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA CALIFORNIA DESIGNED <l TRACED BY C.F. BEED - JUNE 'cs GROUND LEVEL ,-------------'----j'---------t-'------------t---1500 -------------~------------'------------____.L_,___J480 :5cale /"=- io 1 0 zo' 40 1 Plafe JI  P!afe III OOWN-5TREAM VIEW .SECTION THROUGH 3/PHON UP-STREAM VIEW - - - - - - - - - ~ Elev 760 r-------,I I I I I I I ----- - -~ '-=-------,I I I I I I I I I I I I I I I I I I ,-------7 '<o i-------~L--.---------, I I I I I I I I I I I ---------1 t----- - --, I ~ i=------ -➔I I ------- I I I I I I I I I I I I I I ______ I I I .1 t---------4 r I I I I I I I I I }4''!/IBo r.5@6'' : I I ~--------' ~--------,I I I I I I r--------, I I I I I I JI I_________ .JI ,--------t 1-- - - - - - _J I I I I I I I I ,_______ I I I I I I .--- I I I I -------7 I Monzon fa .s fee I- I J{/j,@Z' ~ Is ,. I ., r I ,. I I I , ., J I • J I I Monzonfal ::,fee/ - JJ{¢@2' I I I I I I I I I I I I ._I _____ _ I I I I I I I I I I I I L-------.. I L ______ ..J I I I I I 1--------.J ' ',"'-, ', ~ -,~· ~ CALIFORNIA IN:5T!TUTE Or TECHNOLDGY '\ ~·,, '"'-, 5CALE t ''= 10 ff. o 10 1 DE:5/GN OF SIPHON 3P!LLWAY ·,. FOR EL CAPITAN DAM zo' DE.SIGNED AND TRACED BY CARL F BEED-JUNE 'Z5