MINISTRY OF MINES, ENERGY AND WATER RESOURCES
ETHIOPIAN WATER RESOURCES AUTHORITY
LAND AND WATER STUDIES AGENCY
ADDIS ABABA
BlREIE DAM PROJECT DESIGN OF DIVERSION STRUCTUREMINISTRY OF MINES, ENERGY jiND ./ATER 1J3SOU CES
LAND AND V ATER STUDIES AGENCY
BItffiTE DAM PROJECT
DESIGN OF DIV SION STRUCTURE
by
BAITS AHMAD, UN ENG. BERING
AUGUST 1980
ADDIS ABABAABSTRACT
Birete Dam diversion structure design report covers the scheme proposed for diversion, leaving a gap for the first rainy season thus making it possible to have an economical size of diversion conduit. It eiso includes the hydraulic
and structural design of conduit and details the inlet and ' outlet structures.- ii -
TABLE OF CONTENTS
PAGE
ABSTRACT
TABLE OF CONTENTS ................................................................  11
1.     DESIGN CONSIDERATIONS ............................................... 1
2.   GAP........................................................................................... 2
3.   CONDUIT................................................................................. 3
a)   Hydraulie Design ...............................................................  3
b)   Structural Design ............................................................... 4
4.   INTAKE STRUCTURE ...........................................................  24
5.   OUTLET ................................................................................... 26
6.   ACKNOV'LEDGEIIENT .........................................................  27
7.   REFERENCES .........................................................................  27RTRETE dam project DESIGN OF DIVERSION STRUCTURE
1.       DESIGN CONSIDERATIONS
w#
The diversion of the river is planned in such a way that
the construction of the dam is facilitated and is completed
in the stipulated time* On the other hand it is kept in
view that the cost of the diversion remains low.
The construction of the diversion structure is scheduled
to be finished in the first dry season. In the second dry
season, it is suggested to continue cons traction of the dam
from both sides leaving a gap in the embankment in addition
to the diversion conduit. The dimensions of the gap are
decided by the following considerations:
(a) The gap should have an adequate capacity (area) to
pass safely a flood discharge having a return period of 25
years;
(b)         The bottom width should be such that the construction by machines is possible.
(c) Side slopes of gap should be such that a proper bond between tlje earlier and later construction is ensured. Side
slope
|4H is adopted. This side slope would also minimire
—-
the possibilities of damage to the slope during floods and
avoid cracking of the dam on account of differential settlement.
(d) Closing of the gap should be possible with the machines and labour available in a reasonably short time.
The gap would facilitate passing of the flood in the rainy season following the second dry season. In the third dry season the river is diverted through the conduit and the gap in the embankment is closed.2
Th® above sequence of construction on one hand would enable the construction of the embankment in the gap portion quick
enough to build up head of water sufficient for the diversion conduit tn pass at least a discharge having a return period
of five years during the dry season avoiding any eventuality
ef damage to the dam and on the other hand would make it possible to keep the size *f the conduit small thus affecting saving in
cast. Drawing No. SW101 shows the alignment of the conduit.
2.         GAP
During the construction ef the dam to pass flood discharge at the end of first dry season, the gap proposed to be left
in the embankment would have the following dimensions:
Discharge for once in 25 years frequency = -64 m^/sec. Bed slope ef the river at the dam axis is 1 in 160 metres
S « 1              = 0.00625
TW
Considering a depth of 1.5 metres in the gap
A = (22+10)-J-xl. 5 
P = 12.36 +10 
R = A =                     1.073
R’ =         1.048
v «  1 x 1.048 x (O.OO625)* 
577728
Q a 2.96 x 24 a 71 m /sec " O.K.
a 24.0 m2
= 22.36 m
»       2.96
m/sec
3• 3 -
Total earthwork and rockfill volume in the gap for
20,5 «n height,
Area      of      gap
Volume
A volume ef
3.         CONDUIT
«  2(20.5x4) *20 x | x 20.5
«  (1886x8) + (9l»3x7<.9)
«
3
say 90 000 m
f
90fH00 m^ ran be easily done in
«  1886 n2
88,5^8 •3
one dry season.
(a) Hydraulic Design
At      the      beginning      of      the      second      dry      season      the      river would be diverted through the conduit ana the gap closed.
Discharge for once in 5 years frequency » 
3
40 m /sec.
A circular conduit having  a  di meter of 2.00  m is adopted and the head of water required t. pass 40  nr/sec is checked.
Hydraulic mean Radius,
Velocity, V =                         40
3.141
R=A = da
F
R* = 0.63
= 12.73 m/sec
2 . 0.50
5"
Friction loss is calculated by Manning
V = 1 x R^ x
formula
1
0.014
S «= 0.08- 4 -
Length  of  conduit  ■  (20.5  x  1.8)   ♦   8   ♦   (20 Head loss due to friction =       85.9 x O.Oo
C -w o
Entrance lose ■ 0.10 V ■
5g 
Exit Iocs ■ 0.20 V  , 
2
0.1 (12^73/
19.6
0 .2 (12.73)2
—1576
85.9 «"
6.87 ■>
0.83 m
1.66 n
2< 
Total head required ■ 6.87*0.83+1.66
Likely bod level of conduit at exit
Centre of conduit at exit = 108.80 + 1.00
Level  of  water  on  the  upstream  to   pass  the discharge ■    109.80 ♦ 9.32 
Likely f « ydatinn level of the dam at the
deepest point 
Dam height to be achieved in the gap 119 12-107.50 «
Including  a  little  margin  the    height    to    be    ach-1      erred in the gap may be taken 
Volume of earth and rockfill,
•ap area for 12.5 ■ height =      2(12.5x4' >20 xyxl2.5 ■ Sloping length ■ (12.5x1.8) ♦ (12.5x2)
Horizontal length   ■ 85.9-47.5 
Volume of fill - (75® x U?.5) *.750,38.4)
say 
9-32 m
e 
108.80
> 
109.80
- 
119.12
s
■
=
=
■
Volume of fill Im   the gap upto  12.5   metres            height             is such that it ean be completed in  a reasonably  short           time,    therefore              the size of the conduit adopted  would suffice.
(b) Structural Design
(i) Lighter loaded portions
For structural thickness conduit, is divided into two,
the heaviest loaded fentral portion and the lighter loaded portion
of sides. Considering the lighter loaded pc f ms upto the fill
level of 120 .gp,
Assume a thickness of conduit, t = 0.30 m which is-r
~3- 5 -
Foundation         level         at         the         load         point         =         109-00-0.30 Top level of conduit = 108.70 ♦ 2.60
Height of fill over the conduit = 120.00-111.30
For-'e general condition oflaading, (when the conduit projects above the natural ground or the .ditch in which it is cast is wide nough not to influence loading) , The extreme cases to cater for
the initial and the long term effect of loading recommended in the Engineer Manual EM 1110-2-2902, Corps of Engineers, U.S.A., are
as below:
= 108.70
= 111.30
=
8.70 m
Case i)
0.5 * 
M **h
H
Case il)
JH
w
e
=
Vertical load of earth per m
2
P
e
a
=
Horizontal load of earth per m
2
=
Unit weight of soil
»h
=
Height of fill above horizontal
diameter of conduit
H
=
Height of fill above point
considered.
Since        the depth of
effect of concentrated
the fill on the conduit is 16.70  m
t
liTe load would be negligible.
the
For worst condition the fill on top of the conduit is considered saturated and the conduit empty.6
Case (i),
Vertical load,
=1
=1
«h
2
5 x 2150x8-70 
=
28,058 kg/m
A          uniform
vertical
react
on of the same intensity is
considered.
Horizontal             pressure, H at top of conduit
H at bottom of conduit
P fe
P at
e
top       of       conduit
=        0. ' X «
=        8.70 m
=        8.70 + 2.60 
= 0.5x2150x8.70 =
=     11.30        m
9,353        kg/m2
P       at       bottom       of       conduit
e
Loading         including         the         se shown in the Figure,
=        0.5x2150x11.00             = 12,1*8 f wight of circular conduit is
=      2,795 kg/m2
kg/m2
12,148 - 9,353r at bottom of conduit
0.5* x 2150 x 11.30 = 12,148kg/m'
Loading      including      the      self      weight      of      circular      conduit shown in tne Figure.                 ^’=12,148-9,353=2,i 95kg/m
1.499 kg/m
0.333 cr kg/m Unit weight
c=2400 kg/m'
+ sign convention is shown in the8
Moment, Thrust and Phear are calculated in the fallowing taking ceeffieiente from Engineering Monograph 14 - ” 3e88s Deformeter Sxrees Anaylsis of Single Barrel Cenduits " by U.S.B.R.
Coefficients
Values
Vert.
Lfud
Heriz,
Unif. 
Lead
Horiz.
Trlang.
Lead
Ta tai
Self
Load
Joeff.1
2
cw r
e
Coeff.2
2
xT
e
^oeff.0
Coef£/
3
x cr
1
e
3
4
1
1
2
3
4
5
6
7
a
9
10
11
12
13
*0.333
+0.239 +0,167
0
-0.167
-0,239
•0.333
-0.280 -0.167
0
*0,167
+0J289
*0.333
-O.J33
•0.289
-0.167
•
+0,167
+0.239
*0,333
+0,289
+6,167
•
•0,167
-0,280
-0.333
-0.147
-0.132
-0.087
-0.020
+0,057
+0.126
+0.165
*0.159-
+0.10C
+0.016
+0.083
-0,161
-0|190
+0.111
+0.097
+0.057
+0.001
-0.058
-0.103
-0.117
-0.095 -0.045
+0.015
+0.064
+0.088
+0.093
+9,343 +8,109 +4, 686
0
—4,686 -8,109 -9,343 -8,109 -4,686
0
+4,686 +8,109 +9,343
2
-3,115 -2,703 -1,562
0
+1,562 1+2,703 +3,115 +2,703 +1,562
0
-1,562 -2,703 -3,115
3
-411
-369
-243
- 56
+159
+352
+461
+444
+296
+ 45
-232
-450
-531
4
+266 +233 +137
+ 2
+139 -247
-28”
-228
-108
* 36 ♦i 54 +211 +223
kgm
+6,083 +5,270
+3,018
-        54
-3,104
-5,301
-6,048
-5,i90
-2,936
+ 81
+3,046
+5,”67
+5^920
——        - «9
Case Ci)
Coefficients
Values
4
Vert. 
Load
Horiz.
Unif. 
Load
leriz. Triang. Load
Total
Self
Load
Coeff.1
^e 1
Coeff.2
Per
Coeft.3
4
Coeff./ x ci?
1
2
3
4
1
2
3
4
kg
1
2
3
4
5
6
7
8
9
*10
11
12
13
0
+0.089
+0.333
+0.667
+1.000
+1.244
+1.333
+1.244 +1.000 +0.667 +0.333 +0.089
12
♦4.333 +1,244 +1,000 +0.667 +0.333 +0.089
0
+0.089
+0.333
+0.667
+1.000
+1,244
+1.333
+".395
+0.381 +0.336 +0.259
+0.156
+0.055
0
+0.035
+0.178
+0.408
+0.664
+0.863
.+0.939
+0.024
+0.049
+0.122
+9,233
+0.364
+0.498
+0.611
+0.817
+0.474
+0.264
+0.08(
-0.00( -0.02^
0
+2,497 +9,343
■8^715 +$,058
■64,904
■07,401 +34 904
■e^058 #1^715 +9,343 +2,497
0
+12,468 +11,635
+ 9,353 + 6,238 + 3,115
+ 832
0
+      832 + 1,115
+'6;?38
+ 9,353
+11,635
+12,468
+1,104     ■+ 58
+1,065      +118
+    939     +293
+    724     +559
+    436     +874
+    154     +1195
0           +1 466 +      98     +1481 +    498     +1138
+1,140      + 634 +1,856     +206 +2,412     - M +2,624     - 58
+13,630
+15,315
+19,928
+26,236
+32,483
+37,085
+38,867
+37,315
+32,809
+26,727
+20,758
+16,530
+15,034- 10
Case (i)
nI
I
N<v  Self
Coefficients
1
Heriz.   d ioriz. 
Values
------ r
♦    Unif. ■   Triang, 
Total
I;
Vert. I
11Load                                       Load
Coeff.1     Coeff.2
Coeff.3
Load [Load
l
xw r
ee
xP r
Coeff.4
xC r2
1
1
11
i
1
3
2 1
4
1
2
3
4
kg
1
1
2
3
4
5
6
7
3
9
10
11
12
13
0
+0.333
+0.577
+0.667
+0.577 +0.333
0
-0.333
-0.577
■*0,667
-0.577 -0.333
0
1
n00
-0.333    -0.102 |     +0.092
-0.577    -0.194      +0.165
—0.667 -0.259      +0.199
-0.577 -0.270 +0.183 -0.333 j -0.204 +0.109
0          -0.061      -0.024
+0.333   +0.129     -0.190
+0.577   +0.308     -0.301
+0.667 +0.408 -0.298 +0.577 +0.383 -0.196 +0.333 +0.231 -0.069
000
0
+9,343 +16,189 +18,715 +16,189
+ 9,343
0
- 9,343 -16,189 -18,715 -16,189
- 9,343
0
0
-3,115 -5,397 -6,238 -5,397
-3,115
0
+3,115 +5,397 +6,238 +5,397 +3,115
0
0
-285
-542
-724
-755
-570
-171
+361
+861
+1140
+1070
4- 646
0
0
+221
+396
+478
+439
+262
- 58
-456
-722
-715
-470
-166
0
0
+6,164 +10,646
+12,231
+10,476
+ 5,920
-       229 :
- 6,323
-10,653
-*2,052
-10,192
- 5,748
0- 11
Caae (ii)
Vertical load, wg
» 2150 x 2
A uni form vertical reactior of he parr- intensity is considered.
Horizontal pressure, P  =  H
v g/m2
eo
P* at top of conduit = 2150 x 3 "0 -> i8,705 kg/m2
P  at bottom of conduit = 215C r. 11.30 - 24,295 kg/m2
g
Pe » 24,295-18,705 = 5590 kg/m'
Coefficients      remain      the      same      as      the      previous      case, values    of    Be    B'.ing    moment,    Shear    ana    'hhwrt    for    case    (ii) loading are calculated below.
Na
I1 111
1
1
|
Values
Coeff.1 Coeff.2 Coeff,? ’ •'
•1 -■
2
x w  r  |
e
hl
:oeff. 4
r <r3
Total
1
•
12
3 ! 4 '
k
kgm
1I
1           +6,229            -6,229
2         +5,406            -5,406
3         +3,124             -3,124 00
I4
a                     -3,124        i +3,124
<D
B I 6 1 -5,406 +5,406
o
S I 7 -6,229 +6,229 I 8 -5,406 +5,406 I 9 -3,124 | +3,124
-822 +266
-738 j -233 -436  11 37
-112 2 +319 -139 -=-704 -2 47 -.922  ; •231 t839 1 -228 +593 -• 98
10            0                      0
11         +3,124         | -3,124
12         +5,406          1 -5,406
13 +6,229 -6,229
1 + 39 I
+ 36
'464 i + 54
-900
-1062 I-223
-556
-505
-349
-M0
+180
+457
+641
+661
+485
+125  |
▼310
-689
-83912 -
Valuec
No
Total
Coeff.1
x  rr  r
e
Coeff.2
xP  r
e
Coeff.3 Coeff.4
x 0 r2
1
2
3
4
kg
-p
g
1
1
2
3
4
5
6
7
8
9
10
11
12
13
J------
0
+ 1,665
+ 6,223
+12,476
+18,705
+23,269 +24,934 +23,269 +18,705 +12,476
+ 6,229 + 1,665
0
+24,934 +23,269 +18,705 +12,476
+6, 229
+ 1,665
0
+ 1,665
+ 6,229
+12,476
+18,705
+23,269 +24,934
+2,208 + 58 +2,130 + 118
+1,878          +    093
+1,448                 559
+    872         +    874
+ 308            ♦1 ,195
0            +1 ,466
+    196        +1 ,481
+ 995 +1 ,138 +2,281 -r 634
+3,712 206 +4,824 - 14 +5,249 - 58
+27,200
+27,182
+27,105
+26,959
+26,680
+26,437
+26,400
+26,611
+27,067
+27,867
+28,852
+29,744
+30,125Shear
Values
No
Total
Coeff.1 Coeff.2
x r
e
1
Zoeff.3
Coeff.4
x C r2
kg
1
2
3
4
5
6
7
8
9
10
11
12 |13
0
+    6,229 +10,793 +12,476 +10,793 + 6,229
0
-     6,229 -10,793 -12,476 -10,793 -   6,229
0
0
-   6,229 -10,793
-12,476 -10,793
-   6,229 0
+    6,229 +10,793 +12,476 +10,793 + 6,229
0
0
-      570 -1,035 -1,4’3 
-1,509 
-1,140
-     341
+    721
+1,722
+2,280 +2,141 +1,291
0
4
0
+221
+396
+478
+439
+262
- 58
-456
-722
-715
-470
-166
0
0
+    349
-     689
-      970
-1,070
-      878
-      283 +     265
+1,000
+1,565
+1,671
+1,125
0
Reinforcement required ia -,-orked out in the following Loading Case (i)
- At crown (Ser.D
Maximum +ve moment at crown (sm.l), M =» 6,083 kgm Thrust at crown (sec.i), N = 13,630 kgV. -
b s» 100cm
d => 26cm
d' » 4cm
d*<= 15-4 Horn
E - § + dW
■ 6°8^3k30~ + 11 “ 55.63cm ->
0.5563m
NE * 13,630 x 0.5563 = 7,58^ kgm ' z * 
Resisting moment, KF =» K
t d
t'
« 15.65 x 1°^q26-^~ “ 1C,579kgm
1
Since KJ  is more than NE, no compression reinforcement is needed.
Area of steel required for tension,
7.582x100               (1-0.374x26)
" 1406x0.87x26 
55-63
= 23.73 (1-0.408) -= 14.1 cm
- At springing (Sec.7)
Maximum -ve moment at Sec.7, M—6,048 kgm
,tension inside
Thrusr at seo.7 
, N = 38,867 kg
— ■- —
E 35^667° + 11 = 26,56cm = 0.2656m NE « 38,867x0.2656 => 10,323
KF -
Since KF is necessary.
Area
1O,579kgm
is
of
As
higher than NE, no compression reinforcment
r
steel require* "'or tension
“        323x1 °-—             (1-0.874x26) 1406x0.874x26                 5F3S—
« 32.31 (1-0.855) « 4,7 cm2 outside.
i tension                      <At , Invert (Sec.13)
Moment, M « 5,920kgm
Thrust, N ^15,034kg
E = g + d"
o  9920^x^100 * 15 „ 50.38cm                     = O.5O38m.
NE - 15,084 x 0.5038 = 7,574kgm
KF is higher than NE, no compression reinforcement is needed.
Tjfc'874x^ '
7.574x100 
(1 0.874x2,6)
23.71(1-0.451)
case(ii)
13.0cm2
, tension inside
Loading -At
Invert      (s«c.13)
Moment                M
9
839kgm
Thrust                   N 839x100
+  11
9
3O,125kg
13.79
E  30,125
NE = 30,125x0.1379 - 4,l54kgm
A » -------- 4154x1,00— (1-0.874x26)
B  1406x0.874x26                      13.?9
= 13.00 (1-1.648)
It shows that no structural steel is required. As the thrust is high, no tension is developed on the outside because of very little moment at invert in loading case(ii). Bhear.
Loading Case(i)
Max Shear => 12,231kg- 16 -
Shear Stress ■ —— «= 4.7kg/cm^
100x26
Allowable shear stress according to the code = 4.24kg/cm . Shear stress computed is slightly more. Since these portico'1
of conduit on the sides would be under the rockfill where the longterm differential settlement to induce loading cased) when the vertical load is multiplied by a factor of 1.5, nay not occur, little extra shear computed may be tolerated and no reimforcement may be provided.
2 - 17 -
(ii) Heavier loaded central portion of conduit.
Foundation of the conduit; 108.40
Top of
the
conduit:
108.40 * 2.80 = 111.20
So
H h =
128
- 111.20
3 16.80m
Case
(1)
we
“ 1.5 4r
Hh
Pe
“0.5 4
H
Case
(ii)
■ ■>-Hh
%
= /.H
Case ( i ) Vertical load
w  = 1.5 x 2150 x 16.80 » 54,180 kgf/m2
p
A uniform vertical reaction of is considered.
Horizontal pressure: P  = 0.5
g
H at top of conduit =• 16.80m
H at bottom of conduit =■ 16.80 * 2.80 “ 19.60m
the same     intensity J.H
P  et top of the conduit « 0.5
e
x 2150 
x          16.80 => 18,060 ;f/mZ
P
e
at   bottom   of   the   conduit=O.   5^215C~19.6O“21,   O^Ce^f/n2
P*  « 21070 - 18,060 => 3,010 kgf/m2
e
Case (ii) Vertical load:
we = 2150 x 16.80 = 36,120 kgf/mr
At top P  “ 2150 x 16.80 » 36,120 kgf/m2
e
At bottom *» PG a 2150 y* 19.60 = 42,140 kgf/n.~
P*  => 42,140 - 36,120 “ 6,020 kgf/m2
e
Looking at the analysis carried out fo~ lighter portions of the conduit, it is evident that the loading case (ii)
will not gover r. as such no computations been carried outw  - 54,180kg/m  T [_
e
2
I «
« 18,060kgf/jn-
I
Moment, Thrust and Shear are calculated in the follovTing taking the (linear interpolated) coefficients from Engineering monograph 14- "Beggs Deformeter Stress Analysis of Single Barrel Conduitfi" by U«S.B»R.- 19 -
Coefficients
V. lues
Vert,
Load
Horiz
Unif. 
Load
Horiz. Triang
Load
3
Self
Load
4
Coeff.1
___
Coeff 2 ♦P 0 • .  2
-
Coeff. 4
*c r^
1
1 0.354  -0.354 
2 0.307 -0.307 
3
4
5
6
7
8
0.178
0
0.178
0.307
0.354
0.307 -0.178
0 
+0.178 
+0.307 
+0.354
-0.176
0
+0.17
+0.30
+0.35
+0.30 +0.17
0
-0.17
-0.30
-0.35
-0.158  • +0.146 -0.141  +0.127 -0.093  +0.075
-0.020    +0..001
E   +0.0&     (£.076 
7   +0.135   -0.133 
4   +0.176   -0.146
7   +0.169   -0.115 6   +0.112   -0.052 
+0.C78  +0.023 
1    -0.086    +0.084
'     -0.168    +0.115
-0.198 +0
19,180 16,663
9,644
0
-9,644 --6,633
49,130
-16,633
-3,644
0
+9,644
■86,633 -8 9,180
-6,393! -5,544
-3,215
C
+3,215 +5,544 +6,393 +5,5 M +3,2 15
c
-3,215 +5,544
-6,5.9:
Coeff.3
3
-476
-424
-200
- 60
+187
+406
+530
+509
+337
+ 54
-259 {      -506
-596
Total
Kgm
+12,661 +10,970 + 6,329
58 -6,424 
+-1,002 
--2,607 
+10,856 
- 6,217 i
I
+350 +305 +■’80 +    2 -182 -319 +350 -276 -125 +  55 +202 +276 +290
;+        99
+   6,372 
+-0,859 
+12,4811
»- 20 -
Coefficients
Values
—1
Total
1
Vert, fe
Load r
oriz. ]
nif. 
oad
ioriz. < Triang. Load
5elf
Load
Ioeff.1
*W  r
eo
Coeff.2 ♦p r
e
Coeff.3
3
4
1
2
3
Coeff.4 ♦C r2
4
kg
*1
2
3
4 c
■3£
£
E-i 1
•
12
0  I1.417 0.095   1.322 0.354   1.063 0.709 | 0.709
> 1.06 3 [0.354 5  1.322 0.095
7      1.417        0
8  1.322         0.095
9 1.063  0.354
0 0.709  0.709
1    0.354    1.063
2 0.095   1.322
’3        0       1.417
0.415 0.401 *.354 0.272 0.164 0.057
0
0.038
0.191
0.437
0.709
0.922
1.002
0.044
0.077
0.171
0.313
0.482
0.652
0.797
0.802
0.613
0.338
0.103
-0.020 -0.044
0
5,147
19,180
38,414
57,593
71,626
76,773
71,626 57,593 38,414 19,180
5,147
0
25,591 23,875 19,198 12,805
6,393
1,716
0
1,716
6,393 12,805 19,198 23,875 25,591
’ "I
1,249 ' 1,207
1,066
819
494
172
0
114
575
1,315
2,134
2,775
3,016
106
185
410
751
1157
1565
1913
1925
1471
811
247
-48
-106
26,946 30,41411
39,854 52,789 65,637 75,079 78,686 75,381
66,032
|53,345
40,7591
31,749 28,501Coefficients
Values
Vert |>
loriz. Horiz. 
Inif. Triang. 
1              I1uoad |Load
Coeff.1
*W  r
e
Coeff.2 ( *P  r
e
oeff.3 *Pe r
3oeff.4
2
r
Total
1
2
3
Self
’ joad
4
1
2
3
4
kg
0
2 0.354
3 0.614
4 0.709 ' 5 O.614
6  0.354
7         0
8  -0.354
9 -0.614
10  -0.709
-0.614 1 2 -0.354
13         0
0
-0.354
-0.614
-0.709
-0.614 -0.354
0
+0.354
+0.614
+0.700
+0.614 +0.354
0
0
-0a107
-0.204
-0.272
-0.282
-0.212
-0.061
+0.141
+0.331
+0.436
+0.409 +0.247
0
0
0.117
0.208
0.251
0.228 0.130
-0.044
-0.261
-0.405
-0.400 -0.266 -0.097
0
0
19,179
33,267
38,414
33,267 19,179
0
-19,179
-33,267
-38,414
-33,267 -19,179
0
0
- 6,393 -11,089 -12,805 -11,039
- 6,393
0
+ 6,393 +11,089 +12,805 +11,089
+ 6,393
0
0
- 322
- 614
- 819
- 849
- 638
- 184
+ 424
+ 996
+1312 +1231 + 743
0
0
+281 +499 +602 +547 +312
-106
-626
-972
-960
-638
-233
0
0
12,745
22,063
25,392
21,876
12,478
- 290 -12,988
-22,154
-25,257
-21,585
-12,276
0
Reinforcement:
Thrust
d ® 38cm
d' a 4 cm
d"«          - 4 » 17cm Maximum moment at crown: (Sec.1)
M = 12,661 kgfm/m N = 26,946 Icgf/m- 22 -
E = fl x 100 ♦ 17 = 64.0cm
So NE => 17,242 togm/m
Resisting moment kF = 15.65 * 100 ~r
100
which is more than NE, so no compression steel will be needed.
Area of tension steel for the combined effect: a NE
B°
2
 22,599kgni/m
17.242 
1406x0.874x0.38
. 17.76 cm2/m- -0 25 1 27 
(1
 0.874x38
(at inside)
- At springing (Sea.7)
M * 12,607 kgf/m
Thrust: N = 78,686 kgf/m
E o 12x607 | 1Q0 + 1? = 33<Ocm
78,686 ”
= 0.330m
So: NE a 25,98<kgfm/ni           , which is more than TjF , so compression steel will be needed.
Area of tension steel:
NE
r .j.d
a
j.d =» 0.87-. H ,8 = 33.2cm             , which ie more than E , so no tension steel will be needed.
Area of compression Bteel:                   = NE - k7 cd= 489.5kgf/cm^
:                              284-22>599} _ ig,20 cm^/m
So a’
489.5 x 0.38
0 25      27
Shear:
Maximum shear to be taken by the concrete:
S = 38x100x4.2k = 16,112 kgf/m
So    in    sections    3,4    and    5    and    9,10,11    shear    reinforemer.t will be necessary.
Take    U-formed    stirrups    around    the    main    reinforcement    at distances of 20cm.
. SB11
in which: S_ =» part of the shear taken by the shear
reinforcement
=■ 25,392 - 16,112 « 9,280 kgf/m (See 4)
t = distance of stirrups
9^280^0             = 3.47cni2/m
A s " 1,40.6 X 38
Because    per    m’    there    will    be    bars,    the    erea    per    bar will be : ’’TOC x 3,47 ° 0.94cm2 , provided 0 16.- 24 -
4.          INTAKE STRUCTURE
Intake is provided with a stop log slot and upstreem of the stop log slot, the entrance is give^. a bell mouth shepe with an elliptical cuiy3.
Equation for the elliptical curue is adopted recommended by U.S.B.R.
Where D = diameter of conduit «■ 2.00m Therefor*equation of ellipse becomes
The coordinates of ellipse artcalculated below.
X
y
0
0.20
0.40
0.60
0.80
1 1.00
0.30''
0.29
0.27
0.24
0.18
°i
Dimension of the slot and intake walla are shown in the figure on the next pagfi.- 25 -
I
. 1
I
Elliptical bellmouth
Drawing No. D.S. BhowB the details of reinforcement5.         OUTLET
Outlet is provided with a diverging charnel 1'in?
for a length of 6 metres increasing the bed width of chennel to 6 metres at the end. The side walls are flared out ending in a side slope of 1 :1  This trtructures in
e
necessary to direct the diverted flor; away from the toe of dam during construction.
Details of reinforcement
are shown in drawing No D.S.1026.    ACKNOWLEDGEMENT
The help of Mr. Simon de Haan is acknowledged with 
thanks for computing structural part of cna portion of the
conduit.
7.   REFERENCES
A)  Design of small Dams
by United States Bureau of Reclamation, Denver, Colorado, U.S.A.
B)   Design of concrete structures by Winter, Urguhart, 
O’Rourke, Nilson, McGraw Hill Book Company.
C)  Engineering Manual EM1110-2-2902- "Conduits Culverts and Pipes" by the Department of the Army, Office of the
Chief of Engineers, Washington D.C., U.S.A.
D)  Engineering Monograph No.14 - " Beggs Deformeter Stress Analysis of Single Barrel Conduits" by United States Bureau of Reclamation, Denver, Colorado, U.S.A.Date Due
AUTHOR
TITLE
CALL NO.
(
I
EDITION
VOLUME
CAcc NO....................

Summery

Birete Dam Project - Design Summary

Birete Dam Project - Design of Diversion Structure

Project Overview

The document presents the design of the diversion structure for the Birete Dam project in Ethiopia, prepared by the Ethiopian Water Resources Authority in August 1980. The design includes hydraulic and structural components for river diversion during dam construction.

Key Design Features

Construction Sequence: Three-phase approach using both a temporary gap in the embankment and a permanent diversion conduit
Gap Design: Temporary opening left in embankment to pass 25-year flood events (64 m³/sec)
Conduit Design: 2.00m diameter circular conduit to handle 5-year flood events (40 m³/sec)
Hydraulic Calculations: Detailed flow capacity analysis for both gap and conduit
Structural Design: Reinforced concrete conduit with thickness varying from 0.30m to 0.42m

Main Components

1. Gap in Embankment

Parameter	Value
Design Flood	25-year return period (64 m³/sec)
Dimensions	Bottom width: 10m, Side slopes: 1:4 (H:V)
Flow Depth	1.5m
Earthwork Volume	Approx. 90,000 m³

2. Diversion Conduit

Parameter	Value
Type	Circular reinforced concrete
Diameter	2.00m
Design Flood	5-year return period (40 m³/sec)
Velocity	12.73 m/sec
Length	85.9m
Structural Thickness	0.30m (lighter loaded portions) to 0.42m (heavier loaded portions)

3. Intake Structure

Bell-mouth entrance with elliptical curve
Equation: x²/1 + y²/(0.30)² = 1
Includes stop log slot for flow control

4. Outlet Structure

Diverging channel with 1:8 slope
6m length expanding to 6m bed width
Side walls flared to 1:1 slope

Structural Analysis Highlights

The document includes detailed structural analysis for both lighter and heavier loaded portions of the conduit:

Two loading cases considered (Case i and Case ii) with different earth pressure distributions
Moment, thrust, and shear calculations at 13 sections around the conduit circumference
Reinforcement requirements calculated for each critical section
Shear reinforcement provided where concrete capacity is exceeded

References

Design of Small Dams - USBR
Design of Concrete Structures - Winter et al.
Engineering Manual EM1110-2-2902 - US Army Corps of Engineers
Engineering Monograph No.14 - USBR