Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 519

Total passive resistance per metre run of the wall

Pp =

1

2

1

2

γHK^22 .(p=× × 20 7 2.).×2 488 = 1289.8 kN

The pressure is considered to act parallel to the surface of the backfill soil and the
distribution is triangular for both cases. This resultant thrust thus acts at a height of (1/3) H or
2.4 m above the base at 9° to horizontal, as shown in Fig. 13.55.

Example 13.7: The Rankine formula of active earth pressure for a vertical wall and a level fill
is much better known than the general form and sometimes it is used even when it does not
apply. Determine the percentage error introduced by assuming a level fill when the angle of
surcharge actually equals 20°. Assume a friction angle of 35° and the wall vertical. Comment
of the use of the erroneous result. (S.V.U.—B.E. (R.R.)—Nov., 1974)

φ = 35°

Active pressure coefficient of Rankine for inclined surcharge:

Kai = cos.

cos cos cos

cos cos cos

β

ββφ

ββφ

−−

+−

F

H

G

G

I

K

J

J

22

22

when β = 0° for horizontal surface of the backfill,

Ka =

1

1

−

+

sin

sin

φ

φ

Kai for β = 20° and φ = 35° is given by

Kai = cos

cos cos cos

cos cos cos

20

20 20 35

20 20 35

22

° 22

°− °− °

°+ °− °

F

H

G

G

I

K

J

J = 0.322

Ka for β = 0° and φ = 35° is given by

Ka =

135

135

0 271

−°

+°

=

sin

sin

.

Percentage error in the computed active thrust by assuming a level fill when it is actu-

ally inclined at 20° to horizontal

=

0 322 0 271

0 322

.. 100

.

F −

HG

I

KJ

× = 15.84

The thrust is understimated by assuming a level fill, obviously.

Example 13.8: A retaining wall 9 m high retains a cohesionless soil, with an angle of internal

friction 33°. The surface is level with the top of the wall. The unit weight of the top 3 m of the

fill is 21 kN/m^3 and that of the rest is 27 kN/m^3. Find the magnitude and point of application of

the resultant active thrust.

It is assumed that φ = 33° for both the strata of the backfill.