Breast Wall

DESIGN OF BREAST WALL
a) Salient Levels
Retaining wall top level = 100.000 m
Ground Level = 98.500 m
Foundation slab bottom level = 98.000 m
Depth of foundation = 0.50 m
Cofficient of friction (µ) (For hard rock) = 0.80
b) Properties of backfill
Slope of backfill Vertical = 1

Horizontal = 4.0
2
Dry density of backfill soil γd = 20.00 kn/m
2
Saturated density of backfill soil γsat = 20.00 kn/m
2
Submersed density of backfill soil γsub = 10.00 kn/m
Angle of Internal friction φ = 30.00 degree 0.524
Angle of wall friction δ = 20.00 degree 0.349
Batter of wall with horizontal α= (90) = 90.000 degree 1.571
Inclination of Backfill with horizontal β = 14.04 degree 0.245
Active earth pressure Coefficient for active earth pressure By Coulomb's equation
Sin2(α+φ)
Ka =
Sin2α x Sin(α-δ) x [ 1+(Sin(φ+δ) x Sin(φ-β)/Sin(α-δ) x Sin(α+β))0.5]2
Coeff of active earth pressure Ka = 0.364

Ka cos d = 0.342
Ka sins d = 0.125
2
Safe bearing Capacity of soil SBC = 120.00 kn/m
2
Gross = 130.00 kn/m
c) Material Densities
3
Unit wt of rcc = 25.00 kn/m
3
Unit wt of stone masonry = 26.00 kn/m
3
Unit wt of water = 10.00 kn/m
Stability analysis under Normal case
H1 2242
H2
Foundation Slope
1 Vertical
5 Horizontal
Angle(w) = 11.62 deg.

= 0.203 radian
Cos(angle) = 0.980
Sin(angle) = 0.201
Foundation of wall is on slope

So all forces are broken in two direction; one parallel to foundation and another perpendicular to foundation
2
p1 = Ka cos(δ) x ɣd x q = 0.342 x 20 x 1.2 = 0.00 kn/m Surcharge pressure due to fill
2
p2 = Ka cos(δ) x ɣd x h1 = 0.342 x 20 x 2.242 = 15.34 kn/m Earth Pressure
H1 = 0.00 x 2.24 = 0.00 KN Surcharge pressure due to fill

H2 = 1/2 x 15.34 x 2.24 = 17.19 KN Earth Pressure
600
14.0
1500
1 2 H = 2000
150 GL
450
3
500
121
242
600 600
1200
Component Force (kn/m) Lever arm from toe (m) Moment

Resisting Overturning
1 2.24 x 0.6x x26 = 34.97 0.60 x 0.3 = 0.900 31.47
0.60 x 2.24x0.6 x26 = 17.49 0.60 x 0.67 = 0.400 6.99

0.15 x 0.5x0.5 x20 0.75 0.15/3 = 0.353 0.27
= 0.00 = 0.000 0.00
2 Vertical component of Ep 6.26 1.2 = 1.200 7.51
H1 0.00 x 2.24 = 0.00 = 1.121 0.00

H2 1/2 x 15.34 x 2.24 = 17.19 = 0.942 16.18
S Total Vertical force SV = 59.46 SH = 17.19 46.24 16.18
Check for Stabilty : Overturning (with backfill)
Resisting moment about toe MR = 46.24 Kn-m

Overtuning moment about toe Mo = 16.18 Kn-m
FOS against overturning MR / Mo = 2.86 > 2 Hence Safe
Check for Stabilty : Sliding (with backfill) µ = 0.80
Sliding force SH = 17.19 kn-m

Vertical load SV = 59.46 kn
Resisting force SR = µ xSV
= 47.57
FOS against sliding SR/SH = 2.77 > 1.5 Hence Safe
Check for Stabilty : Base Pressure (with backfill)
Location of resultant from toe Xo = (MR -Mo) / S V

= ( 46.24 - 16.18 ) / 59.46
= 0.505 m
Eccentricity of resultant e = B / 2 - Xo
= 1.200 / 2 - 0.51
= 0.095 m
Vertical load per meter basewidth P = 59.46 kn SV

Logitudianal moment at centerline base ML = 5.62 kn-m per meter base width
Length of base along traffic = 1.200 m
Plan area of base A = 1.200 m2 for 1 m width

Section modulus ZL = 0.24 m3 for 1 m width
Extreme stress at base = P/A +/- ML / ZL

= ( 59.46 / 1.20 ) +/- (5.62 / 0.24)
Maximum smax = 72.974 Kn/m2 < 130.00 kn/m
2
OK
Minimum smin = 26.130 Kn/m2 > 0 kn/m
2
OK
Check for stability without any fill
Stability checked for overturning and sliding about toe.

In this case heel side of wall will be toe
Component Force (kn/m) Lever arm from toe (m) Moment

Resisting Overturning
1 2.24 x 0.6x x26 = 34.97 0.60 x 0.3 = 0.900 31.47
2 0.60 x 2.24x0.6 x26 = 17.49 0.60 x 0.67
= 0.400
Component of load 1 and 2 perpendicular
to founding line =
(34.97 + 17.49) x 0.980 51.38
Load parallel to founding line for load sl no 1 =

34.971 x 0.201 = 7.04 = 1.121 7.90
Load parallel to founding line for load sl no 2 =

17.485 x 0.201 = 3.52 = 0.942 3.32
S Total Vertical force SV = 51.38 SH = 10.57 31.47 11.21
Check for Stabilty : Overturning (without backfill)
Resisting moment about toe MR = 31.47 Kn-m

Overtuning moment about toe Mo = 11.21 Kn-m
FOS against overturning MR / Mo = 2.81 > 2 Hence Safe
Check for Stabilty : Sliding (without backfill) µ = 0.80
Sliding force SH = 10.57 kn-m

Vertical load SV = 51.38 kn
Resisting force SR = µ xSV
= 41.10
FOS against sliding SR/SH = 3.89 > 1.5 Hence Safe

Breast Wall

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DESIGN OF BREAST WALL

Slope of backfill Vertical = 1

Coeff of active earth pressure Ka = 0.364

Stability analysis under Normal case

Angle(w) = 11.62 deg.

Foundation of wall is on slope

H1 = 0.00 x 2.24 = 0.00 KN Surcharge pressure due to fill

Component Force (kn/m) Lever arm from toe (m) Moment

1 2.24 x 0.6x x26 = 34.97 0.60 x 0.3 = 0.900 31.47

0.60 x 2.24x0.6 x26 = 17.49 0.60 x 0.67 = 0.400 6.99

H1 0.00 x 2.24 = 0.00 = 1.121 0.00

S Total Vertical force SV = 59.46 SH = 17.19 46.24 16.18

Check for Stabilty : Overturning (with backfill)

Resisting moment about toe MR = 46.24 Kn-m

Check for Stabilty : Sliding (with backfill) µ = 0.80

Sliding force SH = 17.19 kn-m

Check for Stabilty : Base Pressure (with backfill)

Location of resultant from toe Xo = (MR -Mo) / S V

Vertical load per meter basewidth P = 59.46 kn SV

Length of base along traffic = 1.200 m

Plan area of base A = 1.200 m2 for 1 m width

Extreme stress at base = P/A +/- ML / ZL

Check for stability without any fill

Stability checked for overturning and sliding about toe.

Component Force (kn/m) Lever arm from toe (m) Moment

Load parallel to founding line for load sl no 1 =

Load parallel to founding line for load sl no 2 =

S Total Vertical force SV = 51.38 SH = 10.57 31.47 11.21

Check for Stabilty : Overturning (without backfill)

Resisting moment about toe MR = 31.47 Kn-m

Check for Stabilty : Sliding (without backfill) µ = 0.80

Sliding force SH = 10.57 kn-m

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