Geotechnical Engineering

DHARM

380 GEOTECHNICAL ENGINEERING

By symmetry the stress σz at 0 at 4 m depth is four times that caused by one load.

∴σz =

4 800

44

32

1122252

×

× +

. (/ )
[(/ )]/

π

= 71.44 kN/m^2
Example 10.4: A line load of 100 kN/metre run extends to a long distance. Determine the
intensity of vertical stress at a point, 2 m below the surface and (i) directly under the line load,
and (ii) at a distance of 2 m perpendicular to the line. Use Boussinesq’s theory.

q′ = 100 kN/m

z = 2 m

σz = (/).

(/)

[(/)]

qz

xz

′

+

2

1 22

π

(i) Referring to Fig. 10.23 at point A 1 ,

x = 0

∴σz = (/) (/)qz×=× 2

100

2

2

π

π

kN/m^2 = 31.83 kN/m^2

2m

2m

A 1 A 2

q = 100 kN/m¢

Fig. 10.23 Line load (Ex. 10.4)

(ii) x = 2 m at point A 2 ,

x/z = 1

∴ σz =

q

z

′.(/)2

4

π

=

q

z

′. 1

2 π

=

100

2

1

2

.

π