Geotechnical Engineering

DHARM

386 GEOTECHNICAL ENGINEERING

Area IV: m = 0.5/1 = 0.5; n = 1/1 = 1

IσIV=

1

4

205105 1 1

05 1 1 05 1

05 1 2

05 1 1

205105 1 1

05 1 1 05 1

22

22 22

22

22

1

22

π^2222

×× ++

+++ ×

++

++

+

×× ++

++− ×

L

N

M

M

O

Q

P

P

.. −

..

.

.

.

tan

..

..

= 0.1202

∴ σz = 360(0.2434 – 0.1372 – 0.2024 + 0.1202)

= 8.64 kN/m^2.

Example 10.10: A ring foundation is of 3.60 m external diameter and 2.40 m internal diam-
eter. It transmits a uniform pressure of 135 kN/m^2. Calculate the vertical stress at a depth of
1.80 m directly beneath the centre of the loaded area.

With the notation of Fig. 10.14,

ai = 2.40/2 = 1.20 m

ao = 3.60/2 = 1.80 m

z = 1.80 m

q = 135 kN/m^2

σz = q. KBC

where K
a
z

a

z

B

io

C=

+F

HG

I

KJ

R

S

|

T|

U

V

|

W|

−

+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

1

1

1

1

2 32 // 2 32

=

+F

HG

I

KJ

R

S

|

T|

U

V

|

W|

−

+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

1

1 120

180

1

1 180

180

.^232232

//

= 0.222

∴ σz = 135 × 0.222 ≈ 30 kN/m^2.

Summary of Main Points

1. When the surface of a soil mass is level and its unit weight constant with depth, the vertical
   geostatic stress increases linearly with depth, the constant of proportionality being the unit
   weight itself.


2. The Boussinesq solution for point load is the most popular and is applicable to a homogeneous,
   isotropic and elastic semi-infinite medium, which obeys Hooke’s law within the range of stresses
   considered.


3. The Westergaard solution is applicable to sedimentary soil deposits with negligible lateral strain.


4. The stress isobar or pressure bulb concept is very useful in geotechnical engineering practice,
   especially in the determination of the soil mass contributing to the settlement of a structure.