Total dam Approximat Total weight corrected
Rise in width of weight of Approxim Weight of weight of U/S D/S corrected
height upto e width of above width of
S. No. h2 depth of top of dam above ate weight water in dam and extension extension weight of
top of strip bottom of bottom of bottom of
strip (h) strip 'n strip 'n' of strip 'n' strip 'n' water (Xn) (Xn') strip
'n' (H) strip 'n strip 'n' strip 'n'
1 90 100 10 4.52 10.97 69130.85 1859.03 0.00 69130.85 70989.88 70.62 1.88 64.22 9016.39
2 100 110 10 70.62 79.06 78147.24 17961.19 1782.77 79930.01 97891.20 78.30 1.27 6.41 17870.50
3 110 120 10 78.30 86.14 96017.74 19733.27 3121.21 99138.95 118872.22 88.73 1.40 9.03 20044.01
4 120 130 10 88.73 96.69 116061.75 22250.66 4727.81 120789.56 143040.22 99.39 1.39 9.27 22574.87
5 130 140 10 99.39 107.35 138636.61 24808.92 6466.31 145102.92 169911.84 110.41 1.42 9.59 25175.87
6 140 150 10 110.41 118.39 163812.49 27455.51 8384.19 172196.68 199652.19 121.75 1.45 9.89 27858.16
7 150 160 10 121.75 129.76 191670.64 30180.24 10482.47 202153.11 232333.36 133.41 1.48 10.18 30618.33
8 160 170 10 133.41 141.45 222288.98 32982.62 12771.75 235060.72 268043.34 145.38 1.51 10.47 33454.76
9 170 180 10 145.38 153.45 255743.74 35860.40 15259.98 271003.71 306864.11 157.66 1.54 10.74 36365.57
10 180 190 10 157.66 165.77 292109.31 38811.83 17955.15 310064.46 348876.29 170.24 1.57 11.01 39349.07
11 190 200 10 170.24 178.38 331458.38 41835.17 20864.82 352323.20 394158.36 183.12 1.61 11.27 42403.62
water on
U/S
1782.77
1338.44
1606.60
1738.50
1917.88
2098.28
2289.27
2488.23
2695.18
2909.67
3131.41
Total dam Width of
Depth of
height upto bottom
S.No. strip 'n' Xn Xn'
top of strip of strip 'n'
(yn)
'n' (Hn) (Bn)
1 90 60.95 0 0
2 100 10 68.53 1.53 9.79
3 110 10 78.34 1.53 9.79
4 120 10 88.71 1.53 9.79
5 130 10 99.38 1.53 9.79
6 140 10 110.39 1.53 9.79
7 150 10 121.73 1.53 9.79
8 160 10 133.40 1.53 9.79
9 170 10 145.37 1.53 9.79
10 180 10 157.66 1.53 9.79
11 190 10 170.24 1.53 9.79
12 200 10 183.11 1.53 9.79
16.82 107.74
Magnitude of force in KN
Moment
(KNm)
Designation Vertical Horizontal Resisting
S.no. Forces type Lever arm , m Remarks
if any Downward (+ve) and Towards upstream (+ve) and towards (+ve) and
upward (-ve) downstream (-ve) overturning (-
ve)
W1 0.00 4.52 0.00
1 Dam weight W2 357.00 3.52 1256.10
W3 117.91 1.68 197.98
∑V1 474.91 ∑M1 1454.0730517
P1 0.00 4.52 0
2 Weight of water P2 0.0 4.52 0.00
P3 0.00 0.00 0
∑V2 0.00 ∑M2 0
Horizontal P -240.35 2.33 -560.805
3
Hydrostatic force P' 0 0 0
∑H -240.35 ∑M3 -560.805
Reservior empty case: Reservior Full case:
Sum of Horizontal forces (∑H) 0 Sum of Horizontal forces (∑H) -240.35
Sum of vertical forces(∑V) 474.91 Sum of vertical forces(∑V) 474.91
Sum of resesting moments (∑MR) 1454.07305165251 Sum of resesting moments (∑MR) 1454.07305165251
Sum of overturning moments (∑MO) 0 Sum of overturning moments (∑MO) -560.805
Sum of moments (∑M) 1454.07305165251 Sum of moments (∑M) 893.268051652505
͞X 3.06 ͞X 1.88
e -0.80 e 0.38
e<0, Resultant lies towards heel e>0, Resultant lies towards toe
Pmax 217.109982 Ptoe NO TENSION Pmax 157.907464066 Ptoe NO TENSION
Pmin -6.90053593 Pheel IN TENSION Pmin 52.3019816792 Pheel NO TENSION
STRESSES AND STABILITY CHECK ABOVE GROUND LEVEL
Force magnitude, KN
Moment, KNm
Lever
S. No. Forces Designations Vertical Down Horizontal, U/S Resisting (+ve) and
arm
(+ve) and up (-ve) (+ve) and D/S (-ve) Overturning (-ve)
WI 0.00 4.52 0.00
WII 408.00 3.52 1435.54
WIII 117.91 1.68 197.98
1 Self weight
WIV 0.00 4.52 0.00
WV 0.00 2.26 0.00
WVI 0.00 0.00 0.00
∑V1 525.91 ∑M1 1633.52
PvI 0.00 0.00 0.00
PvII 0.00 0.00 0.00
Weight of
2 PvIII 0.00 0.00 0.00
water
PvIV 0.00 0.00 0.00
Pv' 43.24 0.98 42.35
∑V2 43.24 ∑M2 42.35
UI -48.90 2.35 -114.70
UII -27.80 4.02 -111.69
UIII -27.80 4.19 -116.33
∑V3 -104.49 ∑M3 -342.72
3 Uplift force
UI -103.55 1.76 -182.17
UII -31.64 2.35 -74.22
UIII -47.42 4.02 -190.54
UIV -17.99 4.19 -75.27
∑V4 -200.59 ∑M4 -522.19
Hydrostatic P -240.35 2.33333333333333 -560.81
4
force P' 44.145 1.00 44.15
∑H1 -196.20 ∑M5 -516.66
W'I 0.00 4.52 0.00
W'II 30.60 3.52 107.67
Vertical inertial W'III 8.84 1.68 14.85
5 force due to
earthquake W'IV 0.00 4.52 0.00
W'V 0.00 2.26 0.00
W'VI 0.00 0.00 0.00
∑V4 39.44 ∑M6 122.51
W''I 0.00 4.52 0.00
Horizontal W''II 61.20 3.52 215.33
inertial force W''III 17.69 1.68 29.70
6
due to W''IV 0.00 4.52 0.00
earthquake W''V 0.00 2.26 0.00
W''VI 0.00 0.00 0.00
∑H2 78.89 ∑M6 245.03
Pe 38.48 2.884 110.96
Hydrodynamic
7
force ∑H3 38.48 ∑M7 110.96
Remarks
uplift without drainage
normal uplift with drainage
h>H/2, so, q1 is angle made by
joining heel to top
STRESSES AND STABILITY ANALYSIS OF DAM
Force magnitude, KN
Moment, KNm Resisting
Vertical Horizontal, Lever
S. No. Forces Designations (+ve) and Overturning (-
Down (+ve) U/S (+ve) and arm
ve)
and up (-ve) D/S (-ve)
WI 0.00 4.52 0.00
WII 408.00 3.52 1435.54
WIII 117.91 1.68 197.98
WIV 0.00 4.52 0.00
1 Self weight
WV 0.00 2.26 0.00
WVI 0.00 0.00 0.00
WVII 7.34 4.62 33.91
WVIII 216.89 2.26 490.00
∑V1 750.14 ∑M1 2157.43
PvI 0.00 0.00 0.00
PvII 0.00 0.00 0.00
2 Weight of water PvIII 0.00 0.00 0.00
PvIV 0.00 0.00 0.00
Pv' 43.24 0.98 42.35
∑V2 43.24 ∑M2 42.35
UI -62.80 3.01 -189.16
UII 0.00 4.52 0.00
UIII 0.00 4.52 0.00
∑V3 -62.80 ∑M3 -189.16
3 Uplift force
UI -132.98 2.26 -300.43
UII -40.63 3.01 -122.40
UIII 0.00 4.52 0.00
UIV 0.00 4.52 0.00
∑V4 -173.61 ∑M4 -422.83
Hydrostatic P -240.35 2.33333333333333 -560.81
4
force P' 44.145 1.00 44.15
∑H1 -196.20 ∑M5 -516.66
W'I 0.00 4.52 0.00
W'II 30.60 3.52 107.67
Vertical inertial W'III 8.84 1.68 14.85
5 force due to
earthquake W'IV 0.00 4.52 0.00
W'V 0.00 2.26 0.00
W'VI 0.00 0.00 0.00
∑V4 39.44 ∑M6 122.51
W''I 0.00 4.52 0.00
Horizontal W''II 61.20 3.52 215.33
inertial force W''III 17.69 1.68 29.70
6
due to W''IV 0.00 4.52 0.00
earthquake W''V 0.00 2.26 0.00
W''VI 0.00 0.00 0.00
∑H2 78.89 ∑M6 245.03
Pe 37.83 2.884 109.11
Hydrodynamic
7
force ∑H3 37.83 ∑M7 109.11
Remarks
uplift without drainage
normal uplift with drainage
h>H/2, so, q1 is angle made by
joining heel to top
S.N. Desciption Values Unit
1 Height of retaining wall above ground level 5m
2 Density of soil 18 KN/m3
3 Angle of repose 30 degree
4 Safe bearing capacity of soil 200 KN/m2
5 coefficient of friction between soil and concrete 0.5
6 M30 30 N/mm2
7 Fe500 500 N/mm2
8 Unit weight of water 9.81 KN/m3
9 Water level 3.5 m
Dimensions of retaining wall
S.N. Desciption Values Unit
1 Minimum depth of foundation 1.23513125434 m
Provided depth of foundation 1.25 m
2 Overall depth of the wall (D) 6.25 m
3 Thickness of the base slab (t) 0.52083333333 m
Adopt thickness of base slab (t) 0.55 m
4 Height of the stem (h) 5.7 m
5 Width of base slab (b) 4.375 m
Adopt width of base slab (b) 4.5 m
6 Width of heel 2.25 m
7 thickness of stem at bottom(T) 0.52083333333 m
adopt thickness of stem at bottom(T) 0.55 m
8 thickness of stem at top(t') 0.275 m
adopt thickness of stem at top(t') 0.35 m
9 water level raise from the the toe 4.75
10 stem length with water level 4.2 m
Kp= 2.99931576013
Ka= 0.33340937733
Kw= 1
Active pressure due to water (Pa) 110.6690625 KN
Overturning moment (Mo) 175.226015625 KNm
FOS against overturning 2.95550469862 >1.5
eccentricity 0.5563354575 0.75
qmax 95.5964675926 <200KN/m2
qmin 14.1721990741 <200KN/m3
Resisting force(F) 123.48975
Sliding force(Pa) 110.6690625
FOS against sliding 1.11584707786 <1.5
Hence, provide a shear key.
Assume a shear key of 300mm*400m at a distance of 1.8m from toe.
h1 0.75 m
a 0.3 m
b 1.03899343662
Passive pressure on shear key 102.614217028
FOS against sliding 2.0430639053 >1.5
Design of Toe slab
Pressure due to self weight of toe slab 13.75 KN/m2
P3 64.8361883745 KN/m2
Thus net upward pressure varies from 81.846 KN/m2 to 51.086 KN/m2
Assume 16mm bar and clear cover of 75mm
dia of bar 16 mm
clear cover 75 mm
d 0.467 m
467 mm
Design shear force at deff from the face of stem
Vu 122.929473606 KN/m
Design bending moment at the face of stem
Mu 155.177916772
Ast 785 mm2
Spacing 256.129846917 mm
Provide 16mm bars @260mm C/C
Distribution steel 560.4 mm2
Spacing 140.149565203 mm
Provide distributors of 10mm at 145mm C/C
Development length 47dia
Ld 752 mm
Design of heel slab
Pressure due to soil 46.5975 KN/m2
Pressure due to self weight of heel slab 13.75 KN/m2
Total pressure 60.3475 KN/m2
P4 44.9324782922 KN/m2
Thus, net downward pressure varies from 15.415 KN/m2 to 46.175 KN/m2
dia of bar 16 mm
clear cover 75 mm
d 14.0891990741 m
467 mm
Moment at the face of the stem
Mu 136.390867318
Ast 688.3 mm2
Spacing 292.113801874
Provide 16mm bars @290mm C/C
Distribution steel 560.4
Spacing 140.149565203 mm
Provide distributors of 10mm at 145mm C/C
development length 1.3*Ld
977.6 mm
Design of vertical stem
Assume 16mm bar and clear cover of 50mm
dia of bar 16 mm
clear cover 50 mm
deff 0.484 m
Pa 86.5242 KN/m
Mu 181.70082 KNm
Ast 898.229 mm2
Spacing 223.842616782
Provide 16mm bars @225mm C/C
Curtailment of reinforcement
At h/2 (approx) 2.85 m
Asty 176.437839286 mm2
Hence curtail alternative bars at this section
Temperature and Shrinkage
minimum steel 3078 mm2
No of 10mm bars 39.1903131869
40
Provide 20mm on the inner face @ 177mm c/c
Provide 20mm on the exposed face @ 100mm c/c
Remarks unit weight of concrete
unit weight of soil
forces and moment acting on the wall
0.5235 rad no Notation Item
1 W1 Footing
2 W2 Rectangular portion of wall
3 W3 Traingular portion of wall
4 W4 Water on heel
5 W5 Soil in inclined slope
Remarks
(P/W)*((1-sin0)/(1+sin0))^2
D/12
D-t
0.7D
0.5*b
T/2
therefore, safe.
>B/6, Therefore safe
Therefore safe
Therefore safe
Unsafe
Therefore, safe.
1.7 m
81.84647
51.08619
0.016
0.075
A16 201.061929829747
A10 78.5398163397448
beyond the face of stem
15.41502
46.1753
2.25
0.016
0.075
beyond the rear face of stem
0.016
0.05
484
A20 201.061929829747
25 KN/m3
18 KN/m3
Force (KN) Distance from heel(m) Moment (KNm)
61.875 2.25 139.21875
39.9 2.425 96.7575
14.25 2.66666666666667 38
92.7045 1.125 104.2925625
38.25 3.65 139.6125
246.9795 517.8813125
mm2
mm2
mm2
