DHARM

536 GEOTECHNICAL ENGINEERING

This acts at 1.33 m above the base, at an angle of 20° with the horizontal.

Pah = Pai cos β = 66.24 cos 20° = 62.25 kN/m

Pav = Pai sin β = 66.24 sin 20° = 22.66 kN/m

W 1 , wt of the rectangular portion of the wall = 1 × 4 × 24 = 96 kN

W 2 , wt of the triangular portion of the wall =

1

2

××× (^2424) = 96 kN
W 1 acts at 0.50 m and W 2 at 1.67 m from the vertical face.
ΣV = W 1 + W 2 + Pav = 96 + 96 + 22.66 = 214.66 kN
The distance of the point where the resultant strikes the base from the heel,
x =
Σ
Σ
M
V

×+×+ ×

(.. ..)
96 0 50 96 1 67 62 25 1 33
214 66
1 357 m
e =
b x
2
−=1 500 1 357 0143.. .m− =
σmax, at the heel =
ΣV
b
e
b
1 6 214 66
3
1 6 0143
3
F +
HG
I
KJ
=+F ×
HG
I
KJ
= 92 kN/m^2
σmin, at the toe =
ΣV
b
e
b
1
6 214 66
3
1
6 0143
3
F −
HG
I
KJ
=−
F ×
HG
I
KJ
= 51 kN/m^2
These are intensities of normal pressures at the base.
Check for sliding:
Factor of safety against sliding, ηs =
μ.N
T

0 45 214 66
162 25
×
= 1.55
This is O.K.
Check for overturning:
Factor of safety against overturning, η 0

Restoring moment about the toe
Overturning moment about the toe

(96 2.5 + 96 1.33 + 22.66 3)
62.25 1.33
×× ×
×
= 5.25
This is excellent.

Summary of Main Points

1. The property of soil by virtue of which it exerts lateral pressure influences the design of earth-
   retaining structures, the most common of them being a retaining wall.