RETAINING WALL

0 HEIGHT OF WALL 4.400 m

T2

H
EARTH FACE

GL

B2 T1 B1

D
B
HEEL TOE

DATA
BACK FILL Angle of slope of bank Ф(deg) to horizontal, (max Ф=θ) 0
Angle of repose θ (deg) = 30
Density of back fill (kN/m3) = 18
Density of saturated back fill (kN/m3) = 20.8
Surcharge Uniform Surcharge load (kN/m2) = 21.6
Base Soil Safe Bearing Capacity of Soil (kN/m2) = 100.00
Coefficient of base friction between soil and concrete 0.6

Wall Height of Wall, H (m) 4.400

Profile Depth of Water Table below GL, H1 (m) 5.400
Depth of soil above toe slab, H2 (m) 1.000
Wall thickness at top of base slab, T1 (m) 0.500
Wall thickness at top, T2 (m) 0.300
Base slab width, B (m) 4.000
Base slab toe dimension, B1 (m) 1.500
Base slab thickness, D1 (m) 0.500
Base Heel slab dimension, B2 (m) 2.000
Base Heel slab thickness, D2 (m) 0.500
Shear key depth, D3 (m) 0.000
Shear key thickness, T3 (m) 0.000
Material Concrete Grade, fck M 25
Data Steel Reinforcement Grade, fy (N/mm2) = 500
Concrete In base slab (mm) = 50
Cover In earth face of wall (mm) = 50
In front face of wall (mm) = 50
Active Coefficient of earth pressure 0.33
Passive Coefficient of earth pressure 3.00
Concrete density kN/m3 25
Water density kN/m3 10

Horizontal Pressures, Moments and Shears on Wall (Service Load Condn.)

Bending
Shear on(-
Depth of wall Horizontal Pressure on wall (kN/m2) Bending Moment Shear on Moment(-
surcharge)
Surcharge)

Surcharge Pr. on wall (kNm/m) wall (kN/m) on wall

from top (m) Soil Pressure Grd Water Pr wall (kN/m)
(kNm/m)
0.0 0.00 0 7.200 0.00 0.00 0.00 0.00
0.88 5.28 0 7.200 3.47 8.66 0.68 2.32
1.76 10.56 0 7.200 16.60 21.96 5.45 9.29
2.64 15.84 0 7.200 43.49 39.92 18.40 20.91
3.52 21.12 0 7.200 88.22 62.52 43.61 37.17
4.40 26.40 0 7.200 154.88 89.76 85.18 58.08
4.90 29.40 0 7.200 204.09 107.31 117.65 72.03

Value at max
depth neglecting
4.4 204.09 107.31 117.65 72.03
surcharge
pressure =
 Passive Resistance Considered
Passive pressure at top, (kN/m2) = 54.00
2
Passive pressure at bottom, (kN/m ) = 81.00
Depth of passive resistance (m) = 0.50
Passive Force (kN/m) = 33.75
Passive Moment about Toe (kNm/m) = -5.49

Vertical Loads per metre length (Service Load condition)

Load case Vertical load (kN) Lever arm to Toe (m) B.M. (kNm)
Wall (Rectangle) 33.000 1.850 61.050
Wall (Triangle) 11.000 1.633 17.967
Base Slab 50.000 2.000 100.000
Shear Key 0.000 2.000 0.000
Soil load over Toe Slab 18.000 0.750 13.500
Soil +sub-soil water(if any) over Heel Slab 158.400 3.000 475.200
Surcharge load 7.200 3.000 21.600
Maximum Total = 277.600 - 689.317
Total neglecting surcharge load = 270.400 - 667.717
Total for 0.9 x (wall+base+soil over toe) & no surcharge = 270.400 - 667.717
C.G. of vertical loads from Toe: Case: Total load = 689.317 /277.6 2.483 m
Case: Total neglecting surcharge load = 667.717 /270.4 2.469 m
Eccentricity= 0.483 < B/6 0.67 Hence OK
Moment on C.L. of Base:
Case: Total load = = 204.085+ (-5.493)+277.6 x ( 2 -2.483) 64.511 kNm
Case: Total neglecting surcharge load = = 117.649+ (-5.493)+270.4 x ( 2 -2.469) -14.66 kNm

Soil Pressure under Base Slab (Service Load Condition)

Safe Bearing capacity of soil= 100.00 kN/m2
Case: Total load including soil load over toe slab
Pressure at Toe = (277.6/ (4))+(64.511 x 6/ ( 4^2)) 93.59 kN/m2
Pressure at Heel = (277.6/ (4)) - (64.511 x 6/ ( 4^2)) 45.21 kN/m2
Case: Total including soil load over toe slab, but neglecting surcharge load: Soil Pressures O.K.
Pressure at Toe = (270.4/ (4))+(-14.662 x 6/ ( 4^2)) 62.10 kN/m2
Pressure at Heel = (270.4/ (4)) - (-14.662 x 6/ ( 4^2)) 73.10 kN/m2
Soil Pressures O.K.
SBC of soil is more than the design pressures, hence base width is O.K

Stability Calculations (Service Load Condition)

Case: Total load including soil load over toe slab & Surchrage
Over Turning Moment about Toe = 204.09 kNm
Resisting Moment = 689.317 kNm
Factor of safety against over turning = 3.38 > 1.5, Section O.K.

Horizontal Sliding Force = 107.31 kN

Resisting Force = 270.4 x 0.6 +33.75 195.99 kN

Factor of safety against sliding = 1.83 > 1.5, Section O.K.

Total for 0.9 x (wall+base+soil over toe) & no surcharge:

Over Turning Moment about Toe = 117.65 kNm
Resisting Moment = 667.717 kNm
Factor of safety against over turning = 5.676 > 1.5, Section O.K.

Horizontal Sliding Force = 72.03

Resisting Force = 270.4 x 0.6 +33.75 195.99
Factor of safety against sliding = 2.72 > 1.5 Section O.K.

Design of Wall by Limit State Method (Partial Safety Factor, γf = 1.5)

Ult. Eff. Depth (mm)

Depth of wall Sqrt(Mu*1000/3.33)
Bar ф (mm) Ast (mm2) Vertical Reinf't Horizontal Reinf't
Moment

from top (m) Mu, kNm Reqd. Provided Vertl. Horzl. Reqd. Provided Main Reinf't Distr Reinf't

(0.5 fck/fy)*(1-sqrt(1- Adopted Dia/Spacin Max

Ru= 3.33
(4.6*Mu/fck*bd*d))bd Max c/c Adopted c/c Dia/Spacing
c/c g c/c
12 dia
0 0.0 0 244.00 12 8 0 565 310 200 210 200 8 dia at200c/c
at200c/c
12 dia
0.88 5.2 40 227.60 12 8 63.649 565 310 200 210 200 8 dia at200c/c
at200c/c
12 dia
1.76 24.9 86 267.20 12 8 262.563 565 310 200 210 200 8 dia at200c/c
at200c/c
16 dia
2.64 65.2 140 304.80 16 8 613.587 1005 310 200 210 200 8 dia at200c/c
at200c/c
16 dia
3.52 132.3 199 442.00 16 8 857.231 1005 235 200 210 200 8 dia at200c/c
at200c/c
16 dia
4.4 232.3 264 442.00 16 8 1546.313 2011 130 100 210 200 8 dia at200c/c
at100c/c
Check for Shear in Wall by Limit State Method (Partial Safety Factor, γf = 1.5)

Depth of wall Ult. Shear Shear Stress 100 Ast Perm. Shear Stress Design Status

from top (m) Vu, kN τv, N/mm2 bd τc, N/mm2 of Wall

Beta τc, N/mm2
IF((0.8*25/(6.89*%st))<
0.85*Sqrt(0.8*25)*(Sqrt(1+5*B
0,1,
eta)-1)/(6*Beta)
(0.85*25/(6.89*%st)))

0.00 0.000 0.000 0.232 13.308 0.344 Section is OK

0.88 12.989 0.057 0.248 12.413 0.354 Section is OK
1.76 32.947 0.123 0.212 14.573 0.330 Section is OK
2.64 59.875 0.196 0.330 9.351 0.400 Section is OK
3.52 93.773 0.212 0.227 13.560 0.341 Section is OK
4.40 134.640 0.305 0.455 6.780 0.459 Section is OK

Design of Base Slab

Case: Total load including soil load over toe slab

Soil Pressure at P = 93.59 kN/m2
Soil Pressure at Q = 75.45 kN/m2
Soil Pressure at R = 69.40 kN/m2
Soil Pressure at S = 45.21 kN/m2

Designing the base slab by limit-state method, Partial load factor, γf = 1.5
Moment at Q = 1.5 x(75.45x 1.5^2/2 +18.142x1.5^2/3 -(18+1.5x0.5x25) x0.75 106.388 kNm
Moment at R = 1.5 x(45.208x 2^2/2 +24.192x2^2/6 -(158.4+7.2+2x0.5x25) x1 -126.084 kNm

Case: Total including soil load over toe slab, but neglecting surcharge load:

Soil Pressure at P = 62.102 kN/m2

Soil Pressure at Q = 66.23 kN/m2
Soil Pressure at R = 67.60 kN/m2
Soil Pressure at S = 73.098 kN/m2
Designing the base slab by limit-state method, Partial load factor, γf = 1.5
Moment at Q = 1.5 x(66.23x 1.5^2/2 +-4.12800000000001x1.5^2/3 -(18+1.5x0.5x25) x0.75 65.775
Moment at R = 1.5 x(73.098x 2^2/2 +-5.498x2^2/6 -(158.4+0+2x0.5x25) x1 -61.304

Areas of Reinforcement in Base Slab

Mu Eff. Depth(mm) Bar Ф (mm) Ast (mm2) Main steel Distribn.Steel
Location
(kNm) Reqd. Provided Main Distbn. Reqd. Provided Ф - Crs (mm) Ф - Crs (mm)
Spacing
Sqrt(Mu*1000/3.33) (0.5 fck/fy)*(1-sqrt(1-(4.6*Mu/fck*bd*d))bd Adopted c/c Dia/Spacing Reqd Adopted c/c Dia/Spacing
(0.12%)
Steel
Q 3.33 Steel req Req spacing, C/C
Provided
16 dia
Toe Slab 106.39 178.74 442 16 8 684.59 294 1005.31 200 210 200 8 dia at200c/c
at200c/c
16 dia
Heel Slab 126.08 194.58 442 16 8 815.45 247 1005.31 200 210 200 8 dia at200c/c
at200c/c

Check for Shear in Base Slab

Case: Total load including soil load over toe slab

Soil Pressure at P = 93.59 kN/m2
Soil Pressure at Q = 75.45 kN/m2
Soil Pressure at R = 69.40 kN/m2
Soil Pressure at S = 45.21 kN/m2
Ultimate Shear (Partial lad factor, γf = 1.5:
Shear at Q(@d/2) = 1.5 x (75.45x1.25+(93.592- 75.45 ) x 0.5 x 1.25-(1x 18x1.5+1.25 x 0.5x 25) 94.54 kN
Shear at R(@d/2) = 1.5 x (45.208x1.75+(69.4- 45.208 ) x 0.5 x 1.75-(4.4x 18x1.75+1.75 x 0.5x 25) 90.29 kN

Case: Total including soil load over toe slab, but neglecting surcharge load:
Soil Pressure at P = 62.10 kN/m2
Soil Pressure at Q = 66.23 kN/m2
Soil Pressure at R = 67.60 kN/m2
Soil Pressure at S = 73.10 kN/m2
Ultimate Shear (Partial lad factor, γf = 1.5:
Shear at Q = 1.5 x (66.23x1.25+(62.102- 66.23 ) x 0.5 x 1.25-(1x 18x1.25+1.25 x 0.5x 25) 63.12 kN
Shear at R = 1.5 x (73.098x1.75+(67.6- 73.098 ) x 0.5 x 1.75-(4.4x 18x1.75+1.75 x 0.5x 25) 56.05 kN

Check for Shear in Base Slab by Limit State Method (Partial Safety Factor, γf = 1.5)

Ult. Shear Shear Stress 100 Ast Perm. Shear Stress Design Status
Location
Vu-max, kN τv, N/mm2 bd τc, N/mm2 of Base
Toe Slab 94.539 0.214 0.455 0.459 Section is OK
Heel Slab 90.290 0.204 0.455 0.459 Section is OK