Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 525

Since wall friction is to be accounted for, Coulomb’s theory is to be applied.

γ = 18 kN/m^3 and H = 12 m

Ka =

sin ( )

sin .sin( ) sin( ).sin( )

sin( ).sin( )

2

2

2

1

αφ

ααδ φδ φβ

αδ αβ

+

−+ +−

−+

L

N

M

M

O

Q

P

P

α = 90° and β = 0° in this case. φ = 30° and δ = 20°

∴ Ka =

cos

cos sin( ).sin

cos

2

2

1

φ

δ φδ φ

δ

+ +

L

N

M

M

O

Q

P

P

=

cos

cos sin .sin

cos

2

2

30

20 1^5030

20

°

°+ °°

°

L

N

M

M

O

Q

P

P

= 0.132

Kp =

sin ( )

sin .sin( ) sin( ).sin( )

sin( ).sin( )

2

2

2

1

αφ

ααδ φδ φβ

αδ αβ

−

+− ++

++

L

N

M

M

O

Q

P

P

Putting α = 90° and β = 0°,

Kp =

cos

cos

sin( ).sin

cos

2

2

2

1

φ

δ

φδ φ

δ

−

L +

N

M

M

O

Q

P

P

=

cos

cos sin .sin

cos

2

2

30

20 1^5030

20

°

°− °°

°

L

N

M

M

O

Q

P

P

= 2.713

Pa =

1

2

1

2

γHK^22 ..a=× × ×18 12 (^0132) = 171 kN/m
Pp =
1
2
1
2
γHK^22 ..p=× × ×18 12 2 713 = 3.516 kN/m.
Both Pa and Pp act at a height of (1/3)H or 4 m above the base of the wall and are
inclined at 20° above and below the horizontal, respectively.
Example 13.16: A retaining wall is battered away from the fill from bottom to top at an angle
of 15° with the vertical. Height of the wall is 6 m. The fill slopes upwards at an angle 15° away
from the rest of the wall. The friction angle is 30° and wall friction angle is 15°. Using Cou-
lomb’s wedge theory, determined the total active and passive thrusts on the wall, per lineal
metre assuming γ = 20 kN/m^3.
H = 6 m
β = 15°
α = 75° from Fig. 13.61