Geotechnical Engineering

DHARM

518 GEOTECHNICAL ENGINEERING

Total active thrust per lineal metre of wall,

Pa = Area of pressure distribution diagram =

1

2

KH KqH^2

aaγ+

=

1

2

××+×= +59 9 6 3 23 8 6 3 188 7 149 9.. .... = 338.6 kN

The height of its point of application above the base may be obtained by taking mo-

ments:

z =

188 7^1

3

6 3 149 9^1

2

63

338 6

....

.

F ×× + ××

HG

I

KJ

m = 2.56 m

Example 13.6: A vertical wall with a smooth face is 7.2 m high and retains soil with a uniform
surcharge angle of 9°. If the angle of internal friction of soil is 27°, compute the active earth
pressure and passive earth resistance assuming γ = 20 kN/m^3

H = 7.2 m β = 9°

φ = 27° γ = 20 kN/m^3

2.4 m

7.2 m PorPap

Wall

9°

b=9°

Fig. 13.55 Retaining wall with inclined surcharge

and pressure distribution (Ex. 13.6)

According to Rankine’s theory,

Ka = cos

cos cos cos

cos cos cos

β

ββφ

ββφ

−−

+−

F

H

G

G

I

K

J

J

22

22

= cos

cos cos cos

cos cos cos

9

9927

9927

22

22

°

°− °− °

°+ °− °

F

H

G

G

I

K

J

J

= 0.988 × 0.397 = 0.392

Kp = cos

cos cos cos

cos cos cos

.

.

β

ββφ

ββφ

+−

−−

F

H

G

G

I

K

J

J

=×

22

22

0 988^1

0 397 = 2.488

Total active thrust per metre run of the wall

Pa =

1

2

1

2

γHK^22 .(a=× × 20 7 2.).×0 392 = 203.2 kN