Geotechnical Engineering

DHARM

378 GEOTECHNICAL ENGINEERING

B

q/unit area

L

1

2

1

2

szav

(B+z)

Fig. 10.21 Two is to one method

10.9 ILLUSTRATIVE EXAMPLES

Example 10.1: A concentrated load of 22.5 kN acts on the surface of a homogeneous soil mass
of large extent. Find the stress intensity at a depth of 15 meters and (i) directly under the load,
and (ii) at a horizontal distance of 7.5 metres. Use Boussinesq’s equations.

(S.V.U.—B.E., (R.R.)—Dec., 1970)

According to Boussinesq’s theory,

σz =

Q

zrz^2252

32

1

.

(/ )

[(/)]/

π

+

(i) Directly under the load:

r = 0. ∴ r/z = 0

z = 15 m Q = 22.5 kN

∴σz =

22 5

15 15

32

1052

. .(/ )
× ()+ /

π

= 47.75 kN/m^2.

(ii) At a horizontal distance of 7.5 metres:

r = 7.5 m z = 15 m

r/z = 7.5/15 = 0.5

∴ σz =

22 50

15 15

32

105252

.

.

(/ )

× [( +(. ) ]/

π

= 27.33 N/m^2.