0 1 2 3 4 5 671.00

71.50

72.00

72.50

73.00

73.50

74.00

74.50

0

0.197156242964486

0.426909896576956

1.23184767998935

3.04864613788368

6.06964022069263

TAIL WATER RATING CURVE

Rating Curve

DISCHARGE, (cms)

EL

EV

AT

ION

, (m

.)

PROJECT: PROPOSED DIVERSION DAMLOCATION : BRGY. Burabod, McArthur, Leyte

A.) DETERMINE THE DESIGN FLOOD DISCHARGE:

METHOD 1. EMPERICAL FORMULA:

Drainage Area: 780 sq. km.

Discharge, Qrare = 150*A/sqrt(A+13) = 4,154.79

Discharge, Qocc = 85*A/sqrt(A+9) = 2,360.34

TENTATIVE DESIGN, Q = 3,257.57

METHOD 2. CORRELATION METHOD:

Correlate this stream flow with the record published by National WaterResources Board, utilizing the annual peak flows for a gage watershed more or lesssimilar watershed characteristics as with the damsite:

Drainage Area of Gaging Station, Ag : 900.000 sq.km.Standard Deviation, Ds : 680.000 Mean Flow, Q : 1,540.000 cu.m./sec.

FOR RETURN PERIOD, Tr : No. of years 25 50 100 Tr -1 = 24 49 99lnTr/Tr-1 = 0.0408 0.0202 0.0101

Reduced Variate, Y = 3.196 3.902 4.600

Other Reduced Variate Equation:

Qr = (Y-C)Ds/a' - Q ; N : 25

Where: N a' C10 0.970 0.500 a' = 1.09215 1.021 0.513 C = 0.53120 1.063 0.52425 1.092 0.531

FROM CREAGER'S FORMULA: Where, A: 10

No. of years Qr C Discharge,Q25 3,199.56 106.65 2,978.63 50 3,639.12 121.30 3,387.84

100 4,073.90 135.80 3,792.60

DESIGN FLOOD DISCHARGE, Q = 3,525.08 CMS

B.) PLOT THE TAIL WATER RATING CURVE:

Roughness Coeficient, n : 0.2Slope Gradient, S : 0.03

ELEV.WETTED HYDRAULIC VELOCITY DISCHARGE

AREA PERIMETER RADIUS R^2/3 S^1/2 (mps) (cms)(sq.m.) (m) R=A/P

72.00 0 0 0 0 0 0 072.50 3.98 9.20 0.433 0.572 0.017 0.050 0.19773.00 7.86 15.80 0.497 0.628 0.017 0.054 0.42773.50 17.68 24.50 0.722 0.805 0.017 0.070 1.23274.00 35.48 35.90 0.988 0.992 0.017 0.086 3.04974.50 54.98 38.20 1.439 1.275 0.017 0.110 6.07075.00 74.48 38.2 1.950 1.561 0.017 0.135 10.06776.00 113.48 38.2 2.971 2.067 0.017 0.179 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: 15.00

Actual: q = Q/L 13.40 cms/m SAFE

L = Q/q 235.01 m

Check : LACEY'S Minimum stable river width

Pw = 2.67 sqrt Q where:Q = 124,435.39 cfs

Pw = 941.85 ft. 287.15 m.

USE: L = (L+Pw)/2 261.08 mSAY: 261.00 m

cms/m

D.) DETERMINE THE AFFLUX ELEVATION:

FOR HIGH STAGES: FOR LOW STAGES:q :cms/s 13.40 cms/m Flr. Line : 40.00 q :

TW EL.: 47.500 m. Dam Crest: 43.00 TW El.P : 3.000 m. P 3.00 P :

PARTICULARS FORMULATRIALS

1 2 3 4 1Afflux Elev. Assummed 48.100 47.800 47.650 47.600 46.6

Ht. Of Afflux Elev., da da = Afflux El. - Flr. Line 8.100 7.800 7.650 7.600 6.60Velocity of Approach, Va Va = q/da 1.654 1.718 1.752 1.763 1.403

Head of Approach, ha ha = Va^2/2g 0.139 0.150 0.156 0.158 0.100Energy Elevation, He He = Afflux Elev. + da 48.239 47.950 47.806 47.758 46.70

Ho Ho = Energy El-Dam Crest 5.239 4.950 4.806 4.758 3.70P/Ho 0.573 0.606 0.624 0.630 0.811

Free Flow Coef., Co From Fig. A-4 3.820 3.830 3.835 3.835 3.69hd hd = Energy El.-TW El. 0.739 0.450 0.306 0.258 -0.80

hd + da 8.839 8.250 7.956 7.858 5.80hd/Ho 0.141 0.091 0.064 0.054 -0.216

hd + da/Ho 1.687 1.667 1.655 1.651 1.568Coef. Of Decrease, Co From Fig. A-5 0.160 0.250 0.390 0.395 0.17

Coefficient, Cs Cs = (100-Co')*Co/100 3.209 2.873 2.339 2.320 3.063Discharge, q q = Cs/1.811*(Ho)^3/2 21.250 17.471 13.611 13.298 12.038ANALYSIS Try Again Try Again Try Again O.K. Try Again

E. HYDRAULIC JUMP ANALYSIS AND LENGTH OF DOWNSTREAM APRON: FOR HIGH STAGES: FOR LOW STAGES:

q :cms/m 13.40 TW El. : 47.50 q: 9.26Ho = Afflux El.-Dam Crest 4.650 Flr. Line: 40.00 HE : 6.400

P : 3.00 d2 :Sup. 7.50 P : 0.30HE = Afflux El.-D/S Apron El. 7.650 V2 1.79 m/s Ho : 2.249

PARTICULARS FORMULATRIALS

1 2 3 4 1d1 Assumed 1.500 1.300 1.250 1.200 0.900V1 q/d1 8.933 10.308 10.720 11.167 10.288hv1 V1^2/2g 4.068 5.415 5.857 6.355 5.395HE hv1 + d1 5.56750 6.71532 7.10721 7.55548 6.295

ANALYSIS: Difference: -2.08250 -0.93468 -0.54279 -0.09452 -1.35529OK OK OK OK OK

Jump Height d2=-d1/2+sqrt(d1^2/4+2v1^2d1/9.81) 4.247 4.696 4.823 4.956 3.980

d2 Theor./d2 Supplied OK OK OK OK TRYFroud Number V1/sqrt(g*d1) 2.33 2.89 3.06 3.25 3.46

From A - 9APRON LENGTH F<4.5, TYPE I , La: 13.734 16.981 17.863 18.779 15.399

2.5>F<4.5, TYPE II, La: Next 16.437 16.879 17.345 13.929F>4.5, TYPE III, La: OK Lang OK Lang OK Lang OK Lang OK Lang

From Fig. A-8, F<4.5,C: 5.6L = Cd2 23.78 26.30 27.01 27.75 22.29

RIPRAP LENGTH LRa = 1.5(L-La) 15.072 13.977 13.715 13.460 10.332LRb = (0.65Ho/d2)^3/2*V2^2 4.044 3.478 3.342 3.208 4.458

LR = (LRa + LRb)/2 9.558 8.727 8.529 8.334 7.395LR minimum 10.00 9.00 9.00 8.00 7.00

Ht. Of Chute Blocks: 30 cm. 40 to 60 cm. 40 to 60 cm. 40 to 60 cm. 40 to 60 cm.Ht. Of Baffle Blocks: 60 cm 80 to 120 cm. 80 to 120 cm. 80 to 120 cm. 80 to 120 cm.

Ht. Of End Sill: 30 cm. 30 to 40 cm. 30 to 40 cm. 30 to 40 cm. 30 to 40 cm.

FREE BOARD 1.64 1.64

PARTICULARS FORMULA HIGH LOW

Discharge q : cub. ft/sec/ft 144.163 99.61

V2: fps 5.860 4.05 RIPRAP SIZE From Fig. A-12(dia. In inch) 6.30 2.5

WT. OF RIPRAP 4/3*3.14*R^3*165: Lbs. 12.501 0.781RIPRAP THICKNESS 1.5*Stone dia.(2.54), mm 240.03 95.25GRAVEL BLANKET

RIPRAP THICKNESS/2, mm 120.015 47.625THICKNESS

Note: 40% of riprap layer shouldconsist smaller sizes to fill

voidsFrom Fig. A - 13

DEPTH OF SCOUR Depth of Scour, ft.: 25 19Depth of Scour, m.: 7.62 5.79 S = Riverbed Slope 0.20 0.20

Q = cfs 123,414.68 85,278.25 q^2 20,782.84 9,923.11

f f = (1788S)^3/5*Q^1/10 109.94 105.96R R = 0.9(q^2/f)^1/3 1.57 1.25

Tail Water Depth,m. 7.50 6.10Depth of Cut-off Wall R - Tail Water Depth,m. 0.12 -0.31

USE:

FOR LOW STAGES:9.26

47.503.00

TRIALS2 3 4

46.40 46.250 46.26.40 6.25 6.20

1.447 1.481 1.4930.107 0.112 0.11446.51 46.36 46.31

3.51 3.36 3.310.856 0.892 0.905

3.67 3.67 3.67-0.99 -1.14 -1.195.41 5.11 5.01

-0.283 -0.339 -0.3581.542 1.521 1.513

0.27 0.27 0.01 2.679 2.679 3.6339.714 9.119 12.102

Try Again OK Try Again

TW El. : 47.50Flr. Line : 40.00d2 :Sup. 7.5

V2 1.23 m/s

TRIALS2 3 4

0.890 0.880 0.87010.404 10.522 10.643

5.517 5.643 5.7736.407 6.523 6.643

-1.24337 -1.12728 -1.00682OK OK OK

4.009 4.038 4.068

TRY TRY TRY3.52 3.58 3.64

15.594 15.792 15.99214.031 14.134 14.239

OK Lang OK Lang OK Lang

22.45 22.61 22.7810.283 10.235 10.186

4.410 4.362 4.3137.346 7.298 7.250

7.00 7.00 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 Sill30 to 40 cm. 30 to 40 cm. 30 to 40 cm.

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

CREST SHAPE

CREST SHAPE

X COORDINATE

Y C

OO

RD

INA

TE

DETERMINE THICKNESS OF DOWNSTREAM APRON:

POINT LENGTH OF HEAD LOSSNET HEADEFFECTIVE HEAD EQUATION

CREEP Lc, m HL = Lc/C Hw H-HL,m h, ft.

9 8.187 2.416 -0.976 -3.20 T9(150) = 4/3(62.5)(2.08+T9)

D 8.853 2.612 -1.172 -3.85 TD(150) = 4/3(62.5)(1.87+TD)

E 9.520 2.809 -1.369 -4.49 TE(150) = 4/3(62.5)(1.65+TE)

Y9 = 0.75Ho = YD = YE 1.44 From Fig. A - 15, Type 10 Flow

SOLVING THE EQUATION:

T9(150) = 4/3(62.5)(2.08 + T9)

T9(150 - 83.33) = -266.70

T9 = -4.000 ft.

-1.220 m.

TD(150) = 4/3(62.5)(1.87 + TD)

TD(150 - 83.33) = -320.47

TD = -4.807 ft.

-1.466 m.

TE(150) = 4/3(62.6)(1.65 + TE)

TE(150 - 83.33) = -374.24

TE = -5.613 ft.

-1.711 m.

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)

DETERMINATION FOR TENSILE REINFORCEMENT AT POINT 7 AT THE

DAM SECTION DUE TO UPLIFT DURING NORMAL OPERATION

POINT

P7-8H 415.80 0.3 124.74

P8-9V 654.00 0.4 261.60

W5 (218.03) 0.4 (87.21)

W6 (775.20) 0.2 (155.04)

SUMMATION OF MOMENT: 144.09 lbs. - m.

472.61 lbs. - ft.

641,343.56 n - mm.

IF THE OGEE SECTION BUILT UP OF RUBBLE MASONRY WITH

CLASS B CONCRETE BINDER

USING WORKING STRESS DESIGN: USING ULTIMATE STRESS DESIGN:

fs = 15,000.00 psi. fy = 206.80 Mpa

n = 12.00 fc' = 17.24 Mpa

j = 0.84 Pmin. = 0.00677

k = 0.47 w = 0.0812064965

fc' = 2,500.00 d^2 = 484.62

fc = 1,125.00 psi. d = 22.01 mm.

d = 0.495 m. AREA, As = 149.03 sq. mm.

19.482 inches SPACING, S = 527.00 mm.

AREA = Moment/fsjd 52.70 cm.

0.02 sq. inches USE: 30.00 cm. o.c.

Try: 10 mm dia 78.54 sq. mm.

SPACING = 63.39 inches

161.01 cm.

USE: 30 cm. o.c.

FOUNDATION REACTION:

fa = (f toe + f Heel) = 3,478.12

A = Moment/fsjd = 2.04

SPACING = 0.72 inches

1.82 cm.

USE: 1.82 cm.

FORCES/WEIGHTS (lbs.)

LEVER ARM (m)

MOMENT ABOUT PT. 7 (lbs -m)

STABILITY ANALYSIS

POINT OVERTURNING

P0-1 V 1.64 359.16 589.02 2.550 1,502.01

P1-2 H 3.28 483.60 1,586.19 0.500 793.10

P2-2' V 1.64 563.75 924.55 4.800 4,437.84

P3-4 H 1.312 464.66 609.63 0.400 243.85

P4-5 V 3.608 -420.55 (1,517.34) 2.850 4,324.42

P5-6 H 1.968 -268.50 (528.42) 0.300 158.52

P6-7 V 4.92 -178.39 (877.69) 1.550 1,360.42

P7-8H 1.968 211.28 415.80 0.300 124.74

P8-9V 2.624 -249.24 (654.00) 0.400 261.60

P10-11 V 0.984 438.29 431.28 0.150 64.69

P11-12 V 1.92 364.29 699.43 0.550 384.68

P11-12 H 1.476 -364.29 (537.68) 0.850 457.03

P12-13 V 4.1 298.48 1,223.77 1.254 1,534.61

P12-13 H 1.4104 -298.48 (420.98) 0.725 305.21

P13-0 V 0.82 305.86 250.81 0.125 31.35

P13-0 H 0.0656 -305.86 (20.06) 1.580 31.70

Sum (FV) 4,118.85 Sum of

Sum (FV)^ (3,049.03) MOMENT 8,907.65 7,108.12

Sum (FH) 1,104.48

LENGTH (ft.)

PRES. (PSF)

EXTERNAL FORCES (lbs.)

LEVER ARM (m.)

MOMENT ABOUT TOE RIGHTING

(m-lbs.)

UNIT WEIGHT OF CONCRETE 1615 lbs/sq.m/ft

SECTION WEIGHT LEVER ARM MOMENT ABOUTAREA PER STRIP THE TOE

(sq.m.) (lbs.) (m) (lbs.-m)

W1 0.660 1,065.90 2.850 3,037.82

W2 0.560 904.40 2.550 2,306.22

W3 0.276 446.14 2.175 970.36

W4 0.888 1,433.31 1.425 2,042.47

W5 0.135 218.03 0.600 130.82

W6 0.480 775.20 0.400 310.08

SUM W 4,842.98 SUM Mr 8,797.76

SUMMARY: 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 1.792

e =B/2- Mean X -0.092

FOUNDATON REACTIONS:

f toe = Sum.Forces Vert./B(1+6e/b), (psf) 1455.918 SAFE

f heel = Sum. Forces Hor./B(1-6e/B), (psf) 2022.202 UNSAFE

FACTOR OF SAFETY OVERTURNING: 2.49 SAFE

FACTOR OF SAFETY SLIDING: 0.19 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 = 9,772.77 Lbs. - m.

VERTICAL FORCES = 5,912.80 Lbs.

HORIZONTAL FORCES = 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) 1883.865 Lbs. - m. SAFE

f heel = Sum. Forces Vertical/b(1-6e/b), (psf) 1594.255 Lbs. - m. 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. 98.25Energy Elev. 98.42Dam Crest Elev. 96.50

Ho = Energy El.-Dam Crest El. 1.92ha = Energy El. - Afflux El. 0.17

ha/Ho 0.089From Fig. A-3: Xc/Ho 0.455

Yc/Ho 0.169To Simplify: Xc=Ho/4 0.48

Yc=Ho/8 0.24

Using: y/Ho = -K(x/Ho)^n Where: K 0.51n 1.838

From Fig. A-24: R1/Ho 0.48R1 0.922

R2/Ho 0.20R2 0.384

ASSIGN COORDINATES:X X/Ho (X/Ho)^n Y

0.25 0.130 0.024 -0.0230.50 0.260 0.084 -0.0830.75 0.391 0.178 -0.1741.00 0.521 0.302 -0.2951.25 0.651 0.454 -0.4451.50 0.781 0.635 -0.6221.75 0.911 0.843 -0.8262.00 1.042 1.078 -1.055

G.) STABILITY ANALYSIS:

Length of Creep from A to C 1.00 + 0.80 + 4/3 + 0.40 + 1.20 = 4.733Distance BC = sqrt((4)^2+(.8)^2) = 4.079 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 1.655 Dam Crest Height = 3.00 hd/Ho 0.064 @ Point 10 = Dist. Fr. Crest 1.562

From Fig. A-15 Type 10 Flow: Y = C*Ho C,factor Crest Dist. Y

@ Point 10 0.80 0.65 2.186 @ Point 11 0.75 0.65 2.090 @ Point 12 0.45 0.60 1.464 @ Point 13 0.65 0.20 1.448 @ Point 0 0.80 0.00 1.536 @ Point 1 0.90 0.24 1.968

Calculate Hydrostatic Pressure on the Dam:

Percolation Factor, C = Total Creep Length/Diff. In Water Level 3.773

POINTLENGTH OF CREEP,Lc(m)AvailableHead Loss Net HeadPressure Head

Head (m) Lc/c h(m)=H-HLP=205h (psf)

0 1.536 1.536 314.881 1.968 1.968 403.442 2.75 2.750 563.752' 2.75 2.750 563.753 3.133 2.95 0.830 2.120 434.534 3.533 3.35 0.936 2.414 494.804' 5.933 3.35 1.572 1.778 364.415 6.267 3.35 1.661 1.689 346.306 6.867 2.75 1.820 0.930 190.717 7.320 2.75 1.940 0.810 166.088 7.920 3.35 2.099 1.251 256.489 8.187 3.35 2.170 1.180 241.99

10 2.186 2.186 448.1311 2.090 2.090 428.4512 1.464 1.464 300.1213 1.448 1.448 296.84