TAIL WATER RATING CURVE 75.00
74.50
6.070
74.00
3.049
ELEVATION, (m.)
73.50
1.232
73.00
0.427
72.50
Column B
0.197
72.00 0
71.50
71.00
70.50 0
0.197
0.427
1.232
DISCHARGE, (cms)
3.049
6.070
PROJECT: PROPOSED DIVERSION DAM LOCATION : BRGY. Burabod, McArthur, Leyte
A.) DETERMINE THE DESIGN FLOOD DISCHARGE: METHOD 1. EMPERICAL FORMULA: Drainage Area: Discharge, Qrare = Discharge, Qocc =
780
150*A/sqrt(A+13) 85*A/sqrt(A+9)
TENTATIVE DESIGN, Q
sq. km.
=
4,154.79
=
2,360.34
=
3,257.57
METHOD 2. CORRELATION METHOD: Correlate this stream flow with the record published by National Water Resources Board, utilizing the annual peak flows for a gage watershed more or less similar watershed characteristics as with the damsite: Drainage Area of Gaging Station, Ag : Standard Deviation, Ds : Mean Flow, Q :
900.000 680.000 1,540.000
FOR RETURN PERIOD, Tr : No. of years Tr -1 = lnTr/Tr-1 = Reduced Variate, Y =
25 24 0.0408 3.196
50 49 0.0202 3.902
N:
25
sq.km. cu.m./sec. 100 99 0.0101 4.600
Other Reduced Variate Equation: Qr = (Y-C)Ds/a' - Q Where:
N 10 15 20 25
FROM CREAGER'S FORMULA: No. of years 25 50 100
a' 0.970 1.02 1.06 1.09 Where, A: Qr 3,199.56 3,639.12 4,073.90
;
C 0.500 0.513 0.524 0.53
a' C
= =
10 C Discharge,Q 106.65 2,978.63 121.30 3,387.84 135.80 3,792.60
1.092 0.531
DESIGN FLOOD DISCHARGE, Q =
3,525.08
CMS
B.) PLOT THE TAIL WATER RATING CURVE: Roughness Coeficient, n : Slope Gradient, S :
ELEV. 72.00 72.50 73.00 73.50 74.00 74.50 75.00 76.00
AREA (sq.m.) 0 3.98 7.86 17.68 35.48 54.98 74.48 113.48
0.2 0.03
WETTED HYDRAULIC PERIMETER RADIUS (m) R=A/P 0 0 9.20 0.433 15.80 0.497 24.50 0.722 35.90 0.988 38.20 1.439 38.2 1.950 38.2 2.971
R^2/3
S^1/2
VELOCITY (mps)
DISCHARGE (cms)
0 0.572 0.628 0.805 0.992 1.275 1.561 2.067
0 0.017 0.017 0.017 0.017 0.017 0.017 0.017
0 0.050 0.054 0.070 0.086 0.110 0.135 0.179
0 0.197 0.427 1.232 3.049 6.070 10.067 20.309
C.) DETERMINE THE REQUIRED LENGTH OF DIVERSION DAM: Based on the cross-section taken from the dam axis the approximate stable river width: 264.00 meters. The Maximum Flood Concentration, q: Actual:
q = Q/L
13.40
cms/m
L = Q/q
235.01
m
15.00
SAFE
Check : LACEY'S Minimum stable river width Pw = 2.67 sqrt Q Pw USE:
=
where:Q = 941.85 ft.
L = (L+Pw)/2 SAY:
124,435.39
287.15
m.
261.08 261.00
m m
cfs
cms/m
D.) DETERMINE THE AFFLUX ELEVATION: FOR HIGH STAGES: q :cms/s TW EL.: P : PARTICULARS
FORMULA
Afflux Elev. Ht. Of Afflux Elev., da Velocity of Approach, Va Head of Approach, ha Energy Elevation, He Ho
Assummed da = Afflux El. - Flr. Line Va = q/da ha = Va^2/2g He = Afflux Elev. + da Ho = Energy El-Dam Crest P/Ho From Fig. A-4 hd = Energy El.-TW El. hd + da hd/Ho hd + da/Ho From Fig. A-5 Cs = (100-Co')*Co/100 q = Cs/1.811*(Ho)^3/2
Free Flow Coef., Co hd
Coef. Of Decrease, Co Coefficient, Cs Discharge, q ANALYSIS
13.40 47.500 3.000
cms/m m. m.
1
2
48.100 8.100 1.654 0.139 48.239 5.239 0.573 3.820 0.739 8.839 0.141 1.687 0.160 3.209 21.250 Try Again
47.800 7.800 1.718 0.150 47.950 4.950 0.606 3.830 0.450 8.250 0.091 1.667 0.250 2.873 17.471 Try Again
Flr. Line : Dam Crest: P 3 47.650 7.650 1.752 0.156 47.806 4.806 0.624 3.835 0.306 7.956 0.064 1.655 0.390 2.339 13.611 Try Again
FOR LOW STAGES: 40.00 q : 43.00 TW El. 3.00 P: TRIALS 4 1 47.600 46.6 7.600 6.60 1.763 1.403 0.158 0.100 47.758 46.70 4.758 3.70 0.630 0.811 3.835 3.69 0.258 -0.80 7.858 5.80 0.054 -0.216 1.651 1.568 0.395 0.17 2.320 3.063 13.298 12.038 O.K. Try Again
E. HYDRAULIC JUMP ANALYSIS AND LENGTH OF DOWNSTREAM APRON: FOR HIGH STAGES: q :cms/m 13.40 TW El. : Ho = Afflux El.-Dam Crest 4.650 Flr. Line: P: 3.00 d2 :Sup. HE = Afflux El.-D/S Apron El. 7.650 V2 PARTICULARS
FORMULA
d1 V1 hv1 HE ANALYSIS:
Assumed q/d1 V1^2/2g hv1 + d1 Difference:
Jump Height
d2=-d1/2+sqrt(d1^2/4+2v1^2d1/9.81)
Froud Number APRON LENGTH
From Fig. A-8, F<4.5,C: RIPRAP LENGTH
d2 Theor./d2 Supplied V1/sqrt(g*d1) From A - 9 F<4.5, TYPE I , La: 2.5>F<4.5, TYPE II, La: F>4.5, TYPE III, La: 5.6 L = Cd2 LRa = 1.5(L-La) LRb = (0.65Ho/d2)^3/2*V2^2 LR = (LRa + LRb)/2 LR minimum Ht. Of Chute Blocks: Ht. Of Baffle Blocks: Ht. Of End Sill: FREE BOARD
47.50 40.00 7.50 1.79
m/s
2
3
FOR LOW STAGES: q: 9.26 HE : 6.400 P: 0.30 Ho : 2.25 TRIALS
1 1.500 8.933 4.068 5.56750 -2.08250 OK 4.247 OK
1.300 10.308 5.415 6.71532 -0.93468 OK 4.696 OK
4
1.250 10.720 5.857 7.10721 -0.54279 OK 4.823 OK
1
1.200 11.167 6.355 7.55548 -0.09452 OK 4.956 OK
0.900 10.288 5.395 6.295 -1.35529 OK 3.980 TRY
2.33
2.89
3.06
3.25
3.46
13.734 Next OK Lang
16.981 16.437 OK Lang
17.863 16.879 OK Lang
18.779 17.345 OK Lang
15.399 13.929 OK Lang
23.78 15.072 4.044 9.558 10.00
26.30 13.977 3.478 8.727 9.00
27.01 13.715 3.342 8.529 9.00
27.75 13.460 3.208 8.334 8.00
22.29 10.332 4.458 7.395 7.00
30 cm. 60 cm 30 cm. 1.64
40 to 60 cm. 40 to 60 cm. 40 to 60 cm. 80 to 120 cm. 80 to 120 cm. 80 to 120 cm. 30 to 40 cm. 30 to 40 cm. 30 to 40 cm. 1.64
40 to 60 cm. 80 to 120 cm. 30 to 40 cm.
PARTICULARS
FORMULA
Discharge
q : cub. ft/sec/ft
RIPRAP SIZE WT. OF RIPRAP RIPRAP THICKNESS GRAVEL BLANKET THICKNESS Note:
DEPTH OF SCOUR
f R Depth of Cut-off Wall
V2: fps From Fig. A-12(dia. In inch) 4/3*3.14*R^3*165: Lbs. 1.5*Stone dia.(2.54), mm RIPRAP THICKNESS/2, mm 40% of riprap layer should consist smaller sizes to fill voids From Fig. A - 13 Depth of Scour, ft.: Depth of Scour, m.: S = Riverbed Slope Q = cfs q^2 f = (1788S)^3/5*Q^1/10 R = 0.9(q^2/f)^1/3 Tail Water Depth,m. R - Tail Water Depth,m.
USE:
HIGH
LOW
144.163
99.61
5.860 6.30 12.501 240.03
4.05 2.5 0.781 95.25
120.02
25 7.62 0.20 123,414.68 20,782.84 109.94 1.57 7.50 0.12
47.63
19 5.79 0.20 85,278.25 9,923.11 105.96 1.25 6.10 -0.31
OW STAGES: 9.26 47.50 3.00 2 46.40 6.40 1.447 0.107 46.51 3.51 0.856 3.67 -0.99 5.41 -0.283 1.542 0.27 2.679 9.714 Try Again OK
3 46.250 6.25 1.481 0.112 46.36 3.36 0.892 3.67 -1.14 5.11 -0.339 1.521 0.27 2.679 9.119
4 46.2 6.20 1.493 0.114 46.31 3.31 0.905 3.67 -1.19 5.01 -0.358 1.513 0.01 3.633 12.102 Try Again
TW El. : Flr. Line : d2 :Sup. V2
47.50 40.00 7.5 1.23
m/s
2
3
4
0.890 10.404 5.517 6.407 -1.24337 OK 4.009 TRY
0.880 10.522 5.643 6.523 -1.12728 OK 4.038 TRY
0.870 10.643 5.773 6.643 -1.00682 OK 4.068 TRY
3.52
3.58
3.64
15.594 14.031 OK Lang
15.792 14.134 OK Lang
15.992 14.239 OK Lang
22.45 10.283 4.410 7.346 7.00
22.61 10.235 4.362 7.298 7.00
22.78 10.186 4.313 7.250 7.00
40 to 60 cm. 40 to 60 cm. 40 to 60 cm. Width & Space of Endsill (Dentated) 80 to 120 cm. 80 to 120 cm. 80 to 120 cm. Top Width of Sill 30 to 40 cm. 30 to 40 cm. 30 to 40 cm.
CREST SHAPE 0.000
-0.200
Y COORDINATE
-0.400
-0.600
Column F
-0.800
-1.000
-1.200 X COORDINATE
DETERMINE THICKNESS OF DOWNSTREAM APRON: POINT
LENGTH OF HEAD LOSS NET HEAD EFFECTIVE HEAD CREEP Lc, m
9 D E
8.187 8.853 9.520
HL = Lc/C Hw H-HL,m 2.416 2.612 2.809
h, ft.
-0.976 -1.172 -1.369
Y9 = 0.75Ho = YD = YE
1.44
-3.20 -3.85 -4.49
T9(150) = 4/3(62.5)(2.08 + T9) -266.70 -4.000
-1.220 TD(150) = 4/3(62.5)(1.87 + TD) TD(150 - 83.33) = TD =
-320.47 -4.807
-1.466 TE(150) = 4/3(62.6)(1.65 + TE) TE(150 - 83.33) = TE =
T9(150) = 4/3(62.5)(2.08+T9) TD(150) = 4/3(62.5)(1.87+TD) TE(150) = 4/3(62.5)(1.65+TE)
From Fig. A - 15, Type 10 Flow
SOLVING THE EQUATION:
T9(150 - 83.33) = T9 =
EQUATION
ft. m.
ft. m.
-374.24 -5.613
ft.
-1.711
m.
5)(2.08+T9) 5)(1.87+TD)
DETERMINATION FOR TENSILE REINFORCEMENT AT POINT 7 AT THE DAM SECTION DUE TO UPLIFT DURING NORMAL OPERATION POINT P7-8H P8-9V W5 W6
FORCES/WEIGHTS LEVER ARM MOMENT ABOUT PT. 7 (lbs.) (m) (lbs -m) 415.80 0.3 654.00 0.4 (218.03) 0.4 (775.20) 0.2 SUMMATION OF MOMENT:
124.74 261.60 (87.21) (155.04) 144.09 472.61 641,343.56
lbs. - m. lbs. - ft. n - mm.
IF THE OGEE SECTION BUILT UP OF RUBBLE MASONRY WITH CLASS B CONCRETE BINDER USING WORKING STRESS DESIGN: fs = n = j = k = fc' = fc = d = AREA =
15,000.00 12.00 0.84 0.47 2,500.00 1,125.00 0.495 19.482 Moment/fsjd 0.02 78.54 63.39 161.01
Try: 10 mm dia. SPACING = USE:
30
USING ULTIMATE STRESS DESIGN: psi.
psi. m. inches sq. inches sq. mm. inches cm. cm. o.c.
FOUNDATION REACTION: fa = (f toe + f Heel) = A = Moment/fsjd
3,478.12
=
2.04
SPACING = USE:
0.72 1.82 1.82
inches cm. cm.
fy = fc' = Pmin. = w = d^2 = d = AREA, As = SPACING, S = USE:
206.80 Mpa 17.24 Mpa 0.00677 0.08 484.62 22.01 mm. 149.03 sq. mm. 527.00 mm. 52.70 cm. 30.00
cm. o.c.
STABILITY ANALYSIS
POINT
LENGTH (ft.)
P0-1 V P1-2 H P2-2' V P3-4 H P4-5 V P5-6 H P6-7 V P7-8H P8-9V P10-11 V P11-12 V P11-12 H P12-13 V P12-13 H P13-0 V P13-0 H
1.64 3.28 1.64 1.31 3.61 1.97 4.92 1.97 2.62 0.98 1.92 1.48 4.1 1.41 0.82 0.07
PRES. (PSF) 359.16 483.60 563.75 464.66 -420.55 -268.50 -178.39 211.28 -249.24 438.29 364.29 -364.29 298.48 -298.48 305.86 -305.86 Sum (FV) Sum (FV)^ Sum (FH)
EXTERNAL FORCES (lbs.) 589.02 1,586.19 924.55 609.63 (1,517.34) (528.42) (877.69) 415.80 (654.00) 431.28 699.43 (537.68) 1,223.77 (420.98) 250.81 (20.06) 4,118.85 (3,049.03) 1,104.48
MOMENT ABOUT LEVER ARM TOE RIGHTING (m.) (m-lbs.) 2.550 0.500 4.800 0.400 2.850 0.300 1.550 0.300 0.400 0.150 0.550 0.850 1.254 0.725 0.125 1.580 Sum of MOMENT
OVERTURNING
1,502.01 793.10 4,437.84 243.85 4,324.42 158.52 1,360.42 124.74 261.60 64.69 384.68 457.03 1,534.61 305.21 31.35 31.70 8,907.65
7,108.12
UNIT WEIGHT OF CONCRETE SECTION WEIGHT AREA PER STRIP (sq.m.) (lbs.) W1 W2 W3 W4 W5 W6
0.660 0.560 0.276 0.888 0.135 0.480
1,065.90 904.40 446.14 1,433.31 218.03 775.20
SUM W
4,842.98
SUMMARY:
1615
LEVER ARM
lbs/sq.m/ft
(m)
MOMENT ABOUT THE TOE (lbs.-m)
2.850 2.550 2.175 1.425 0.600 0.400
3,037.82 2,306.22 970.36 2,042.47 130.82 310.08 SUM Mr
8,797.76
CASE I:
Summation of MOMENT:
10,597.29
Summation of FORCES VERTICAL:
5,912.80
Summation of FORCES HORIZONTAL:
1,104.48
MEAN, X = Summation of Moment/Summation of Vertical Forces e =B/2- Mean X
1.792 -0.092
FOUNDATON REACTIONS: f toe = Sum.Forces Vert./B(1+6e/b), (psf) f heel = Sum. Forces Hor./B(1-6e/B), (psf) FACTOR OF SAFETY OVERTURNING: FACTOR OF SAFETY SLIDING:
1455.918
SAFE
2022.202
UNSAFE
2.49 0.19
SAFE SAFE FOR GRAVEL & COARSE SAND
CASE II: DURING NORMAL OPERATION WITH SIESMIC FORCES: 1.) LATERAL FORCE DUE TO EARTHQUAKE 0.15W F = 0.15 W 726.45 Lbs. M toe = F(Lever Arm) = 762.77 Lbs.-m. 2.) LATERAL FORCE DUE TO HYDRODYNAMIC FORCE: From Fig. !-17: Fw = 0.583wH^2a/g Using: a = 0.15g Fw = 58.801 Lbs. M toe = 61.741 Lbs. - m. 3.) COMBINING THE COMPUTED FORCES: MOMENT Righting = VERTICAL FORCES = HORIZONTAL FORCES =
9,772.77 Lbs. - m. 5,912.80 Lbs. 1,889.73 Lbs.
THEREFORE: Mean X = Summation of Moment/Summation of Vert. Forces Mean X = 1.6528 m. OK, within middle third e = B/2- Mean X 0.047 FOUNDATION REACTION: f toe = Sum.Forces Vertical/B(1+6e/b), (psf) f heel = Sum. Forces Vertical/b(1-6e/b), (psf)
1883.865 Lbs. - m. 1594.255 Lbs. - m.
SAFE SAFE
FACTOR OF SAFETY, OVERTURNING =
2.23 SAFE
FACTOR OF SAFETY, SLIDING =
0.320 SAFE OF ROCK, JOINTING & LAMINATION
F.) DETERMINATION OF CREST SHAPE: Maximum Afflux Elev. Energy Elev. Dam Crest Elev.
98.25 98.42 96.50
Ho = Energy El.-Dam Crest El. ha = Energy El. - Afflux El. ha/Ho From Fig. A-3: Xc/Ho Yc/Ho To Simplify: Xc=Ho/4 Yc=Ho/8
1.92 0.17 0.089 0.46 0.17 0.48 0.24
Using: From Fig. A-24:
ASSIGN COORDINATES: X 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
y/Ho = -K(x/Ho)^n R1/Ho R1 R2/Ho R2
X/Ho 0.130 0.260 0.391 0.521 0.651 0.781 0.911 1.042
Where:
K n
0.51 1.84
0.48 0.922 0.20 0.38
(X/Ho)^n 0.024 0.084 0.178 0.302 0.454 0.635 0.843 1.078
Y -0.023 -0.083 -0.174 -0.295 -0.445 -0.622 -0.826 -1.055
G.) STABILITY ANALYSIS: Length of Creep from A to C =1.00 + 0.80 + 4/3 + 0.40 + 1.20 = Distance BC = sqrt((4)^2+(.8)^2) = 4.079
4.733 OK
Determine what type of foundation material the dam would be judged safe: Total Creep Length up to point F = 1.00 + 0.80 + 1.60 + 1.20 + 0.80 +(4.0 + 0.50 + 2.30 + 7.50)/3 = 10.167 Weighted Creep Ratio, C = 3.389 Safe for Boulders, Gravel & Sand Case I @ Maximum Flood Condition: Calculate the Pressure Head above OGEE CREST: Hd+da/Ho Dam Crest Height = 3.00 hd/Ho @ Point 10 = Dist. Fr. Crest/Ho 1.563
1.655 0.064
From Fig. A-15 Type 10 Flow: Y = C*Ho C,factor Crest Dist. @ Point 10 0.80 0.65 @ Point 11 0.75 0.65 @ Point 12 0.45 0.60 @ Point 13 0.65 0.20 @ Point 0 0.80 0.00 @ Point 1 0.90 0.24
Y 2.19 2.090 1.46 1.45 1.54 1.97
Calculate Hydrostatic Pressure on the Dam: Percolation Factor, C
=
Total Creep Length/Diff. In Water Level
3.773
POINT LENGTH OF CREEP,Lc(m) Available Head Loss Net Head Pressure Head Head (m) 0 1 2 2' 3 4 4' 5 6 7 8 9 10 11 12 13
3.133 3.533 5.933 6.267 6.867 7.320 7.920 8.187
1.54 1.97 2.75 2.75 2.95 3.35 3.35 3.35 2.75 2.75 3.35 3.35 2.19 2.090 1.46 1.45
Lc/c
0.830 0.936 1.572 1.661 1.820 1.940 2.099 2.170
h(m)=H-HL P=205h (psf) 1.536 1.968 2.750 2.750 2.120 2.414 1.778 1.689 0.930 0.810 1.251 1.180 2.186 2.090 1.464 1.448
314.88 403.44 563.75 563.75 434.53 494.80 364.41 346.30 190.71 166.08 256.48 241.99 448.13 428.45 300.12 296.84
