Geotechnical Engineering

(Jeff_L) #1
DHARM

STRESS DISTRIBUTION IN SOIL 369

B=2a q/unit area

0

a

2a

3a

4a

0.9 q
0.8 q
0.7 q
0.6 q
0.5 q
0.4 q
0.2 q

0.3 q

0.15 q

0.1 q
0.05 q

B=2a q/unit area

0

a

2a

3a

4a

0.2 q
0.275 q
0.3 q
0.275 q
0.25 q
0.225 q
0.2 q
0.125 q
0.10 q
0.075 q

0.05 q

(a) For vertical stress

(b) For shear stress

Fig. 10.13 Pressure bulbs for vertical and shear stress due to uniform
load on a circular area (After Jürgenson, 1934)

10.5.1 Uniform Load on An Annular Area (Ring Foundation)
This case may arise in the case of a foundation for hollow circular bins, silos, etc.
Let an annular area of a inner radius ai and outer radius ao be loaded uniformly at q per
unit area. (Fig. 10.14)


q

Inner circular
boundary

Outer
circular
boundary

Annular
area
loaded
uniformly

ai
ao

Fig. 10.14 Uniformly loaded annular area (Ring loading)
Applying the case of a uniformly loaded circular area just considered, the vertical stress
at a depth z directly beneath the centre of the ring, σz, may be written:

σz = q
a
z

q
a
z

oi

1

1

1

1

1

1

2 32 2 32


+F
HG

I
KJ

R
S

|
T|

U
V

|
W|

L


N


M M M M M M


O


Q


P P P P P P


−−

+F
HG

I
KJ

R
S

|
T|

U
V

|
W|

L


N


M M M M M M


O


Q


P P P P P P


//
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