13. LATERAL EARTH PRESSURE
Stability Criteria
2.5 Stability of Rigid Walls
Failures of the rigid gravity wall may occur
due to any of the followings:
Overturning failure
Sliding failure
Bearing capacity failure
In designing the structures at least the first three of the
design criteria must be analysed and satisfied.
14. LATERAL EARTH PRESSURE
Stability Criteria
The stability of the retaining wall should be checked against :
(i) FOS against overturning (recommended FOS = 2.0)
Resisting moment
FOS =
Disturbing moment
(ii) FOS against sliding (recommended FOS = 2.0)
RV tan δ + (0.5 - 0.7) Pp + cw B
FOS =
RH
15. LATERAL EARTH PRESSURE
Stability Analysis
The stability of the retaining wall should
be checked against :
2.3.1 FOS against overturning
(recommended FOS =
2.0)
Resisting moment
FOS =
Disturbing moment ∑V
Ph
Pp
.. overturning about A
A
16. LATERAL EARTH PRESSURE
Stability Criteria
2.3.2 FOS against sliding
(recommended FOS = 2.0)
RV tan δ + (0.5 - 0.7) Pp + cw B
FOS =
RH
∑V
Ph
Pp
Friction & wall base adhesion
17. LATERAL EARTH PRESSURE
Stability Criteria
2.3.3 For base pressure (to be compared against the
bearing capacity of the founding soil. Recommended
FOS = 3.0)
RV 6e
qb = 1 +
B B
Now, Lever arm of base resultant
∑ Moment
x=
RV
B
Thus eccentricity e = - x
2
19. LATERAL EARTH PRESSURE
Stability Analysis
Worked example :
Figure below shows the cross-section of a reinforced concrete
retaining structure. The retained soil behind the structure and
the soil in front of it are cohesionless and has the following
properties:
SOIL 1 : φu = 35o, γd = 17 kN/m3,
SOIL 2 : φu = 30o, δ = 25o , γd = 18 kN/m3,
γsat = 20 kN/m3
The unit weight of concrete is 24 kN/m3. Taking into account the
passive resistance in front of the wall, determine a minimum value
for the width of the wall to satisfy the following design criteria:
Factor of safety against overturning > 2.5
Factor of safety against sliding > 1.5
Maximum base pressure should not exceed 150 kPa
20. LATERAL EARTH PRESSURE
Stability Analysis
THE PROBLEM 30 kN/m2
0.5 m
SOIL 1
2.0 m
4.0 m GWT
SOIL 2
2.9 m
SOIL 2
0.6 m
4.5 m
2.0 m
21. LATERAL EARTH PRESSURE
Stability Analysis
30 kN/m2
THE SOLUTION
0.5 m
SOIL 1
W1 2.0 m P1 P3
W3 GWT
4.0 m
SOIL 2
W41
2.9 m
W2 P2 P4
SOIL 2
PP P5 P6
0.6 m
4.5 m
2.0 m
22. LATERAL EARTH PRESSURE
Stability Analysis
Determination of the Earth Pressure Coefficients
1 − sin φ 1 - sin 35 o
K a1 = = = 0.271
1 + sin φ 1 + sin 35 o
1 − sin φ 1 - sin 30
o
K a2 = = = 0.333
1 + sin φ 1 + sin 30 o
1 + sin φ 1 + sin 30 o
K p2 = = = 3.00
1 − sin φ 1 − sin 30 o
24. LATERAL EARTH PRESSURE
Stability Analysis
To check for stability of the retaining wall
(i) FOS against overturning > 2.5
Resisting moment 1288.55
FOS = = = 3.83 > 2.5, thus it is OK
Disturbing moment 336.50
(ii) FOS against sliding > 1.5
RV tan δ + 0.5 Pp 452.9 tan 25 o + 0.5 x 60.75
FOS = = = 1.34 < 1.5
RH 180.94
Thus it is not OK
25. LATERAL EARTH PRESSURE
Stability Analysis
(iii) For base pressure
RV 6e
qb = 1 +
B B
Now, Lever arm of base resultant
∑ Moment 1288.55 - 336.5
x= = = 2.10
RV 452.9
B
Thus eccentricity e = - x = 2.25 - 2.10 = 0.15
2
452.9 6 x 0.15
Therefore qb = 1 +
4.5 4.5
26. LATERAL EARTH PRESSURE
Stability Analysis
qb = 120.8 and 80.5 kPa
Since maximum base pressure is less than the bearing pressure of
the soil, the foundation is stable against base pressure failure.
DISTRIBUTION OF BASE PRESSURE
80.5 kPa
120.8 kPa
In conclusion the retaining wall is not safe against sliding. To
overcome this the width of the base may be increased or a
key constructed at the toe.
