Geotechnical Engineering

DHARM

STRESS DISTRIBUTION IN SOIL 365

According to these equations the principal stresses for a given value of q depend solely
on the value of θ 0 ; hence for every point on a circle through c, d, and A [Fig. 10.9 (b)] the
principal stresses have the same intensity. It can also be shown that the principal stresses at
every point on the circle cd A pass through the points e and f respectively. These two points are
located at the intersection between the circle and the plane of symmetry of the loaded strip.
The special case when A lies on the plane of symmetry of the loaded strip is shown in
Fig. 10.9 (c). The vertical stress σz and the horizontal stress σx themselves will be the principal
stresses since τxz reduces to zero in view of (θ 2 + θ 1 ) being zero, in this case. Hence, substituting

θ 2 = +

θ 0

2

and q 1 = −

θ 0

2

in equations 10.25 and 10.27, we have:

σz = σ 1 =

q

π

(sin)θθ 00 + ...(Eq. 10.32)

σx = σ 3 =

q

π

(sin)θθ 00 − ...(Eq. 10.33)

The vertical stresses at different depths below the centre of a uniform load of intensity

q and width B are as follows:

Table 10.4 Vertical stress under centre of strip load

Depth z σz

0.1 B 0.997 q

0.2 B 0.977 q

0.50 B 0.818 q

B 0.550 q

2 B 0.306 q

5 B 0.126 q

10 B 0.064 q

A few typical pressure bulbs for this case of strip loading are shown in Fig. 10.10.

B=2b

Pressure

bulbs

q/unit area

sz/q=—^12

sz/q=—^14

Fig. 10.10 Pressure bulbs for strips load of infinite length (After Terzaghi, 1943)