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Stability Calculation for Head wallConditions:

When Dam is empty

When dam is full.

Whe dam is overflowing.

Assumptions as per design :

NSL= 93.50

FTL= 94.00

MWL= 94.50

TBL= 95.00

Top width of head wall in m. tw = 0.60

D/S Slope in wall m = 0.80

U/S Slope in wall n = 0.00

Bottom width of Head wall in m. bw =tw+H*(m+n)= 1.00

Height of Head wall in m. H = 0.50

Head over crest in m. h =MWL-FTL 0.50

Water Head hw= FTL - NSL 0.50

Specific gravity of Dam material (RR Masonry) in Kg / cum sgm = 2300

Unit weight of water in Kg / cum w = 1000

Coefficient of Friction = 0.65

Coefficient of Uplift C = 0.50

Vertical Horizontal

Self weight W1 = tw x H x Sgm = 690.00 m H+tw/2 = 0.70

d/s slope W2 = 0.5 x m x H2

x Sgm = 230.00 2/3 mH = 0.27

u/s slope W3 = 0.5 x n x Hx

Sgm = 0.00 mH+tw+1/3 nH = 1.00

Weight of overflowing

water W4 = (tw + n.H) x h x w = 300.00 m H+(tw +nH)/2 = 0.70

Weight of water wedge W5 = 0.5 x n x hwx w 0.00 mH +tw +1/3 n hw = 1.00

Overflowing water force W6 = w x h x H = 250.00 H/2 = 0.25

Uplift pressure U = 1 / 2 x C x w x (hw+h) x bw -250.00 2/3 bw = 0.67

Water pressure PW = 1 / 2 x w x hw2

125.00 1/3 hw = 0.17

Total V = 970.00 375.00

Stability check:

Safety against overturning :

Factor of safety =

More than 1.50 Hence safe.

Safety against sliding:

Total Horizontal forces P = 375.00 Kg

Frictional forces = x V

= 630.5 Kg

3.02

Force DetailForce (Kg)

Lever Arm

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Sliding factor = Resisting forces V / Sliding forces P

= 1.68

Since V is greater than P, Hence structure is safe against sliding.

Safety against tension in masonry :

a2 + b2 + a x b

= 0.41 m

Eccentricity e = bw/2 - X

= 0.09 m

bw / 6 = 0.167 m

Since e is less than b/6, Hence structure is safe against tension at base.

Forces:

At toe Fmax = V / A (1 + 6e/b)

Vertical forces V = 970.00 Kg

Area of Base A = bw (for 1m length)

= 1.00 Sqm

Fmax = 1503.5 kg/ m2

= 0.15 kg/cm ( Compresion/ Tension)

At heel Fmin = V / A (1 - 6e/b)

Vertical forces V = 970.00 Kg

Area of Base A = bw (for 1m length)

= 1.00 Sqm

Fmin = 676.575 kg/ m2

= 0.07 kg/cm ( Compresion/ Tension)

Maximum permissible safe load on cement concrete is 200 Kg / cm2

(M 20 grade)

Maximum permissible safe load on cement concrete is 5 Kg / cm2,

Maximum permissible safe load on R R Masonry is 10 Kg / cm2

(compression)

Maximum permissible safe load on R R Masonry is 1 Kg / cm2

(Tension)

Hence structure is safe against crushing.

X =3 x (a + b)

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Runoff coefficient C = 0.50 (For weed, pasture & cultivated land having 5 - 10% slope in sandy loam soils)

Catchment area in Ha A = 11.3 (As per Survey sheet)

Maximum length of travel in Mt. L = 500 (As per Survey sheet)

Difference in elevation between most

remote point and outlet in Mt. H = 7.5 (As per Survey sheet)

K' = 5.914

Return period in years for Imax T = 25 Intencity - duration - return period

a = 0.1623 relationship for Nothern zone

b = 0.5

n = 1.1027

Assume length of weir crest in Mt. L = 7.5

Head over the crest in Mt. h = 0.5 (Assume)

Fetch length in Mt. Df = 65

Specific gravity of the dam material in Ton/cum. = 2.3 (For Stone masonary in cement mortar)

Height of head wall in Mt. H = 0.50

Design peak runoff rate in cumec

K = L3 / H = 4082.48

Time of concentration in Min. Tc or t = 0.01947 (K)0.77 = 11.743 Min.

= 0.196 Hours

Intensity of rainfall in mm / hr for T year recurrence interval I = K' *Ta / (t + b)n = 14.877 cm / hr

= 148.77 mm / hr

Estimated peak rate of runoff Q = C I A / 360 = 2.33 cumecs

Design peak rate of runoff through a

broad crested weir Q =2.1 x L x (h)3/2 = 5.57 cumecs

Since design peak rate of runoff is more than estimated peak rate of runoff hence design is safe

DESIGN OF CREST WEIRHead over the crest h=(Q / 2.1xL )2/3 = 0.280 Mt.

Or say 0.50 Mt.

Free board in meter F = 1.5 hw

Where wave height in meter is hw = 0.014 (Df)1/2

Hence F = 0.17 Mt.

Take minimum free board = 0.50 Mt.

Height of weir H' = h + F 1.00 Mt.

STRUCTURAL DESIGN

(I) HEAD WALL

Top width of head wall (/ H+H' )/3 0.408 Mt.Or say minimum TW as 0.60 Mt. As per check against sliding

Bottom width of head wall 0.8(H)+TW 1.00

Take BW 1.24 Mt. As per check against sliding

Bottom width of head wall concreting BW +0.30 = 1.54

(2) HEAD WALL EXTENSION

Length of head wall extension H+H' = 2.00 Mt.

But as per site condition (Left) = 2.00 Mt.Length of head wall extension (Right) = 2.00 Mt.

DESIGN OF BROAD CREST WEIR FOR TANK D, AT Central University

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Height of head wall extension 1.00

Or say 1.00 Mt.

Bottom width of head wall extension 0.75

0.75 Mt.

Top width of head wall extension 0.50 x H = 0.25

Or say 0.60 Mt.

(3) BASIN / APPRON

Width of the basin LB 0.75 x (H + H') + H = 1.63 Mt.

Or say 2.00 Mt.

Thickness of basin (Including concreting) = 0.60 Mt.

(4) SIDE WALL

Height of side wall

(At head wall joint up to toe of head wall) 1.50

Or say 1.50 Mt.

(At Toe wall of basin) 1.50 x H' = 0.50Or say 0.50 Mt.

Length of side wall LB+(BW of HW-TW of HW)/2 = 2.00 Mt.

Or say 2.00 Mt.

Bottom width of side wall 0.40(H+H') + 0.40 = 1

Or say 1.00 Mt.

(5) WING WALL

Length of wing wall up stream side 7.22

Length of wing wall down stream side provide 5.77 Mt.

Height of wing wall at end 0.50

Top width of side wall & wing wall = 0.60 Mt.

(6) TOE WALL

Top width of toe wall = 0.60 Mt.

Height of toe wall = 0.30 Mt.

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1.65

Fc

1.50 1

1.75

U

Assumptions as per design :

Top width of head wall in m. a = 0.85

Bottom width of head wall in m. b = 1.75

Height of Head wall in m. H = 1.50

Head over crest in m. h = 1.65

Specific gravity of Dam material in Kg / cum = 2300 ( For cement concrete structure)

Unit weight of water in Kg / cum w = 1000Coefficient of Friction = 0.65

Coefficient of Uplift C = 0.50

X1 = 1.33

W1 = a x H x = 2932.5 Kg

W2 = 1 / 2 x (b - a) x H x = 1552.5 Kg

Uplift pressure U = 1 / 2 x C x w x (H + h) x b = 1378.1 Kg

Water force Fa = w x h x H = 2475 Kg

Water force Fb = 1 / 2 x w x h = 1125 Kg

Water force Fc = w x a x h = 1402.5 Kg

1 . Safety against overturning

W1 x X1 + Fc x X1 + W2 x 2 / 3 x (b- a) = 6675.4 Kg

Fa x H/2 + Fb x H/3 + U x2 / 3 x b = 4026.6 Kg

STABITLITY CHECKS

0.85

Wieght / metre

length of dam

W1

W2

Fb

Fa

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Factor of safety =

Since factor of safety is more than 1.5; hence structure is safe against overturning

2 . Safety against Sliding

Total vertical forces V = W1 + W2 + Fc - U

= 4509.4 Kg

Total Horizontal forces P = Fa + Fb

= 3600 Kg

Frictional forces = x V

= 2931.1 Kg

Sliding factor = Resisting forces V / Sliding forces P

= 0.8142

Since V is greater than P, Hence structure is safe against sliding.

3 . Safety against Tension at the base (Eccetricity check)

a2 + b2 + a x b

= 0.676 m

Eccentricity e = b/2 - X

= 0.199 m

b / 6 = 0.2917 m

Since e is less than b/6, Hence structure is safe against tension at base.

4 . Safety against Compression (Crushing)

Max.m

compressive stress at baseFmax = V / A (1 + 6e/b)

Where, Vertical forces V = W1 + W2 + Fc - U

= 4509.4 Kg

Area of Base A = b (for 1m length)

= 1.75 Sqm

Fmax = 4335.2

Maximum permissible safe load on cement concrete is 44000 Kg / m2,

Hence structure is safe against crushing.

1.66

Position of resultantmeasured from Toe

X =3 x (a + b)