Geotechnical Engineering

DHARM

526 GEOTECHNICAL ENGINEERING

φ = 30°

δ = 15°

γ = 20 kN/m^2

15°

6m

Wall

a= 75°

b= 15°

Fig. 13.61 Battered wall with inclined surcharge (Ex. 13.15)

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

=

sin

sin .sin sin .sin

sin .sin

2

2

2

105

75 60 1^4515

60 90

°

°°+

°°

°°

L

N

M

M

O

Q

P

P

= 0.542

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

=

sin

sin .sin sin .sin

sin .sin

.

2

2

2

45

75 90 1^4545

90 90

° 6 247

°°− °°

°°

L

N

M

O

Q

P

=

Total active thrust, Pa, per lineal metre of the wall

=

1

2

1

2

γHK^22 ..a=×××20 6 0 542 = 195 kN

Total passive resistance, Pp, per lineal metre of the wall

=

1

2

1

2

γHK^22 ..p=×××20 6 6 247 = 2,249 kN

Example 13.17: A vertical retaining wall 10 m high supports a cohesionless fill with γ = 18
kN/m^3. The upper surface of the fill rises from the crest of the wall at an angle of 20° with
the horizontal. Assuming φ = 30° and δ = 20°, determine the total active earth pressure using
the analytical approach of Coulomb. (S.V.U.—U.Tech. (Part-time)—Sep., 1982)