Geotechnical Engineering

DHARM

798 GEOTECHNICAL ENGINEERING

∴σx ≤ pp

or mK

z

D

vF DZ K K zp a

HG

I

KJ

()(−> −θγ ).

At z = 0, the term

mK D z

D

vθ()− is a maximum.

∴ mKvθ ≤ γ(Kp – Ka)

or m

M

I

.( )≤−γKKpa

This condition should be satisfied. Also the maximum pressure at the base, pt, should

not exceed the allowable soil pressure. The minimum pressure, ph, should not be negative, so

as to avoid tension.

Ultimate Soil Resistance

The frictional force mobilised along the surface of rupture can be determined assuming the

surface to be cylindrical (Fig. 19.19). For circular wells, the surface of rupture is assumed to be

part of a sphere with its centre at the point of rotation and passing through the periphery of

the base.

If Wu is the total vertical load multiplied by a suitable load factor, the load per unit

width is Wu/B. It will be also equal to the upward pressure for a rectangular base.

Let us consider a small arc of length R.d. α at an angle α from the vertical axis.

∴ Vertical force on the element = R.d. α. cos α (Wu/B)

Normal force developed on the element

dFn =

W

B

FHG u..cosRdααIKJ

∴ Fn = 2 2

0

W

B

u..cos .Rdαα

θ

z

=

WR

B

u [sin.cos]θθθ+

H

h Scour level

B

D

O

R q rD

a da

dFn

Fig. 19.19 Ultimate soil resistance for a well (IRC)

whereθ = tan−

F

HG

I

KJ

1

2

B

nD

,