Geotechnical Engineering

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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