In carrying out the design, the following points should be considered:

= Total length of Pile = 15.00 m

- Excavation Depth = 3.5 m
- Wall Height = 3.5 m
- Depth of unplanned excavation = 0.50 m
- Design Wall Height = 4 m
- Surcharge (behind the wall) = 10 kN/m2
- Water Table = 1.5 m
- β = 0 0 Deg
Soil -1 Soil -2
- Φ = 30 27 Deg
- Wall friction angle δ = 20 16 Deg
- ϒ Bulk/moist = 15 16 kN/m3
- ϒsat = 17 19 kN/m3
- ϒwater = 9.8 9.8 kN/m3
- Ka 0.33 = 0.336 9.8 (Assume)
- KP 3 = 4.416

Partial factor on actions -Combination 1

- Permanent unfavourable action = 1.35
- Permanent favourable action = 1
- Variable Unfavourable conditions = 1.5
- Angle of Shear resistance = 1
- Weight denstiy = 1
Surcharge = 10 kN/m2

W.T. level 1.50 m

2
1

3
2.5 m
Excavation
level 4

d = 10.5
3' 4'
6
5
R
14.5
Passive Earth Pressure Retaining Wall Active Earth
Configuration Pressure
By considering the earth pressures shown in Figure and by taking moments about point C, the following values are obtained:

K
Sr. No. Area factor Level (m) Details ϒ/ q Force (KN) L.A. (M) Moment (KN.m)
A P
1 1.0 R 0 15 Surchage 0.34 10 48.72 7.25 353.22
2 0.5 T 0 1.5 Above W.T. 0.34 15 5.67 13.50 76.55
3 1.0 R 0 2.5 Below W.T. 0.34 7.2 9.07 11.75 106.60
3' 1.0 R 0 10.5 Below W.T. 0.34 7.2 63.50 5.25 333.40
4 0.5 T 0 3.5 Below W.T. 0.34 7.2 14.82 11.67 172.87
4' 1.0 R 0 10.5 Below W.T. 0.34 7.2 88.91 5.25 466.75
5 0.5 T 0 10.5 Below W.T. 0.34 7.2 133.36 3.50 466.75

6 0.5 T 0 10.5 Below W.T. 3.00 7.2 -1190.70 3.50 -4167.45

Balancing the moments then gives -2191

Giving: d = 10.5 m

Depth of Embedment
As noted above, the depth of embedment should be increased by 20%
In solving the problem, the actual depth of embedment is 2.5 + 10.5 = 13.0 m
i.e. actual required embedment = 15.6 m

Required Value
R is the force of R by the passive soil pressure on the back of the wall below
generated
point C, where the wall tends to rotate back into the soil.
For horizontal equilibrium:

Total passive Force = Total Active Force + R

So R = 826.65 KN
This force has to be generated on the back of the sheet piles by the extra 20%
length added above – i.e. between point C and a point 2.6 metres below this.
The situation is shown in Figure 3, where forces 8, 9 and 10 will be passive earth
pressures and 11 and 12 will be active pressures

Surcharge = 0 kN/m2

1 2
 W.T. level 1.50 m

1 2
5 Excavation
2.50 m
level

6 d = 10.50 3
7 4
R

8 9
12 11 2.60 10

17

Retaining Wall Active Earth

Passive Earth Pressure Configuration Pressure

K
Sr. No. Area factor Level (m) Details ϒ/ q Force (KN) L.A. (M) Moment (KN.m)
A P
8 1.0 R 0 2.6 Below W.T. 4.416 7.2 82.67 1.30 107.47
9 1.0 R 0 2.6 Below W.T. 4.416 7.2 1157.35 -1.73 -2006.07
10 0.5 T 0 2.6 Below W.T. 4.416 7.2 107.47 1.30 139.71

11 1.0 R 0 2.6 Below W.T. 0.3 7.2 0.00 0.87 0.00

12 0.5 T 0 2.6 Below W.T. 0.3 7.2 8.18 1.30 10.63

Note: In this case no reduction factor is applied to the passive earth pressures as owing to
where they are generated they are more reliable
R available = 1339.30 KN > 826.65 KN OK
In carrying out the design, the following points should be considered:
- Excavation Depth = 3 m
- Wall Height = 3 m
- Design Wall Height = 3.3 m
- Surcharge (behind the wall) = 10 kN/m2
ϒsat = 20 kN/m3
ϒ Bulk = 18 kN/m3
ϒwater = 9.8 kN/m3
Water Table = 4 m
Φ = 30
Ka = 0.33
KP = 3.00

Surcharge = 10 kN/m2

W.T. level 4.00 m

1 2
0.70 m
5 Excavation
level

6 d = 6.48 3
7 4
R
10

Retaining Wall Active Earth

Passive Earth Pressure Configuration Pressure
By considering the earth pressures shown in Figure and by taking moments about point C, the following values are obtained:

K
Sr. No. Area factor Level (m) Details ϒ/ q Force (KN) L.A. (M) Moment (KN.m)
A P
1 1.0 R 0 10 Surchage 0.333 10 34.95 5.24 183.18
2 0.5 T 0 4 Above W.T. 0.333 18 48.00 7.82 375.22
3 1.0 R 0 7 Above W.T. 0.333 18 146.32 3.50 512.10
4 0.5 T 0 7 Below W.T. 0.333 10.2 83.30 2.33 194.37
5 0.5 T 0 0.7 Above W.T. 3.0 18 -13.23 6.72 -88.87
6 1.0 R 0 7 Above W.T. 3.0 18 -264.60 3.50 -926.10
7 0.5 T 0 7 Below W.T. 3.0 10.2 -107.10 2.33 -249.90

Balancing the moments then gives 0.00

Giving: d = 6.5 m

Depth of Embedment
As noted above, the depth of embedment should be increased by 20%
In solving the problem, the actual depth of embedment is 0.7 + 6.5 = 7.2 m
i.e. actual required embedment = 8.6 m

Required Value
R is the force of R by the passive soil pressure on the back of the wall below
generated
point C, where the wall tends to rotate back into the soil.
For horizontal equilibrium:

Total passive Force = Total Active Force + R

So R = 72.37 KN
This force has to be generated on the back of the sheet piles by the extra 20%
length added above – i.e. between point C and a point 1.4 metres below this.
The situation is shown in Figure 3, where forces 8, 9 and 10 will be passive earth
pressures and 11 and 12 will be active pressures

Surcharge = 0 kN/m2

W.T. level 4.00 m

1 2
5 Excavation
0.70 m
level
 1 2
5 Excavation
level

6 d = 6.48 3
7 4
R

8 9

12 11 1.44 10

12

Retaining Wall Active Earth

Passive Earth Pressure Configuration Pressure

K
Sr. No. Area factor Level (m) Details ϒ/ q Force (KN) L.A. (M) Moment (KN.m)
A P
8 1.0 R 0 1.4 Below W.T. 3.000 10.2 43.96 0.72 31.58
9 1.0 R 0 1.4 Below W.T. 3.000 10.2 618.08 -0.96 -592.02
10 0.5 T 0 1.4 Below W.T. 3.000 10.2 31.58 0.72 22.69

11 1.0 R 0 1.4 Below W.T. 0.3 10.2 40.23 0.48 19.27

12 0.5 T 0 1.4 Below W.T. 0.3 10.2 3.51 0.72 2.52

Note: In this case no reduction factor is applied to the passive earth pressures as owing to
where they are generated they are more reliable
R available = 649.89 KN > 72.37 KN OK
Input Data :-
Dia. Of Pile = 0.75
H = 6.58 m
Dead Load of Pile = 0.44 x 6.58 x 25.00 x 1.35
= 98.14 kN

Socket length of Pile in Rock (Ls)

Max. Horizonatal Force at Top of Rock Socket H = 6.94 m

Maximum actual moment at top of Rock Socket M = 24.21 T.m
Diameter of pile Shaft D = 0.75 m
Permissible compressive strength in rock socket σ1 = 286.7 T (Should be min. of 30 & 0.33 Qc)
Under wind and seismic condition σ1 is taken 25% more. For Wind and Seismic Condition
σ1=1.25*σ1 = 358.3333 T
Uniaxial comp. strength of rocks in socket. Qc = 860.0 * t/m2 Min. of 30 Kg/cm2 or 0.33 Qc
Where, Qc = uniaxial comp. strength of rocks in
socket.

Qc = 300.00 t/m2 Or 286.67 t/m2

For Normal Conditions
Ls = 0.0646 + 0.8245
= 0.89 m
For Wind and Seismic condition
Ls = 0.0516 + 0.737
= 0.79 m
 Design Data
- Diameter of Pile = 750.0 mm
- Characteristic Compressive Str. Of Concrete fck = 35.0 Mpa
- Characteristic Yield Str. Of Steel fyk = 500.0 Mpa
- Partial Safety factor for Reinforcement gs = 1.15
- Design Yield Strength of Reinforcement fyd = 400.0 MPa
- Characteristic Yield Str. Of Stirrups fywk = 500.0 Mpa
- Modulus of elasticity of steel Es = 200000.0 N/mm2
- Modulus of elasticity of cocnrete Ecm = 32000.0 N/mm2
- Clear Cover c = 50.0 mm
- Gross cross section area of concrete Ac = 441786.5 mm
- Mean Value of Axial Tensile Strength of concretefctm = 0.259*fck^2/3
= 2.77 N/mm2

Design of Pile
- Provide Diameter of londitudinal bar = 25 0 mm
+
- Number of longitudinal bars = 12 0 no.
- Clear spacing provided between vertical bars = 148 > 100 mm Safe

- Diameter of lateral ties = 10 mm

- Spacing of lateral ties provided = 150 mm

Effective cover d' = 72.50 mm

Effective depth of Pile deff = 677.50 mm
Area of reinforcement provided Ast provd = 5890.49 mm2
Minimum area of reinforcement required Astmin = 0.4% of AG
[ IRC:112-2011, cl.no. 16.2.2 (4)] = 1767.15 mm2 OK

Percentage of steel provided pt % = 1.33

Effective cover to Depth Ratio d' / D = 0.10
Check for Flexural capacity

Maximum compression capacity of pile Puz [IRC 112:2011, cl.no. 8.3.2 (4)]

Where, Ac = 441786.47 mm2

fcd = 15.63 N/mm2 αcc = 0.67
Ay = 5890.49 mm2 ɣm = 1.5
fyd = 400.00 N/mm 2

Puz = 9262.79 kN

Minimum Axial load and Corresponding B.M.

V HL HT ML MT
KN KN KN KN.m KN.m
62.8 99 0 339.22 0

Minimum Axial Load on Pile Pmax = 62.80 kN

ML = 339.22 Kn.m

For, p/fck = 0.038 Mu/fck.D^3 = 0.062 (From SP 16)

P/fck.D^2 = 0.003

Mu = 915.47 KN.m
ML /Mu = 0.37 SAFE
Design of Pile Head

Width of Pile Head = 900 mm

Depth of Pile Head = 900 mm
Dia. Of Pile = 750 mm
Characteristic Compressive Strength fck = 35 Mpa
Characteristic Yield Str. Of Steel fyk = 500 Mpa

Check for Flexure in Transverse Direction

Width of 900 is considered in design
Moment at face of Pier MT = 0 kN-M
Assume Reinforcement Dia. = 20 + 0
Spacing = 195
deff Prov = 840
b = 900
Ast prov = 1571 mm2

xu / d = (0.87 fy Ast)
(0.36 fck b d)

xu / dprov. = 0.067
xu / dlim. = 0.46

Check = 1 Under-reinforced

Mu = 0.87 fy Ast d * (1 - (Ast fy) / (b d fck) )

= 556.93 kN-M Revise

Check for Minimum Reinforcement

Ast, min = 0.26*fctm*b*d/fy OR 0.0013*b*d

Ast, min = 1089.4 mm2 Or 982.8 mm2
= 1089.4 mm2 OK

Check for Minimum Surface Reinforcement

Act min = 0.01* cover * width

= 450 mm2 OK

Minimum Reinforcement at Top

Note:- There is no net tension at top in the pile cap due to sum of the reactions from the pile. Hence, minimum surface reinforcement is provided.
Provide 12 mm dia. at 195 mm c/c at top

Ast,Top = 565.49 mm2 Safe