Geotechnical Engineering

DHARM

CAISSONS AND WELL FOUNDATIONS 791

=

1

2

γ′DK()()pa−K D− 2 D 1 ...(Eq. 19.28)

(Note: For convenience, the height to F is also taken as D 1 nearly)

Taking moments about the base,

q′maxH 1 =

1

23

1

2

2

3

2 1

2

γγ′−−′−DK K

D

DK K

D

()()()pa pa

Substituting for q′max from Eq. 19.27,

1

2

γ′DK()().pa−K D− 2 D H 11 =^1

23

1

2

2

3

γγ′−−′−DK K^2 D DK KD^12

()()()p a p a

or (D – 2D 1 )H 1 =

D^2 D 12

3

2

3

−

or D 12 – 3D 1 H 1 + (1.5DH 1 – 0.5D^2 ) = 0 ...(Eq. 19.29)

Solving for D 1 ,

2 D 1 = 3323 HHDHD 11 ±−−()^2 ( 1 ) ...(Eq. 19.30)

or D 1 =

1

2

L 3923 HHDHD 11 ±− −^21

NM

O

QP

()

The positive sign yields a value for D 1 greater than D, which is ridiculous.

Hence, rejecting the positive sign,

D 1 =

1

2

L 3923 HHDHD 11 −− −^21

NM

O

QP

() ...(19.31)

Substituting this value in Eq. 19.28, q′max can be computed. For Kp and Ka, Rankine
values can be used. (It is interesting to note that Kp and Ka do not appear in the Eqs. 19.30
and 19.31).

In this simplified analysis, the moments due to side friction and base reaction are ne-
glected; the error is on the safe side, since this results in the under estimating of the stabilising
forces.

Heavy Wells

Wells are in general, heavy compared to bulkheads, with low ratios of length to lateral dimen-
sion. A heavy well is expected to rotate about its base, as observed in model experiments by
several investigators; the force per unit length may be obtained by taking moments about the
base (Fig. 19.16).

q′maxH 1 = (1/2)γ′ (Kp – Ka)D^2 ×

D 1

3

or q′max = (1/6)γ′(Kp – Ka)

D

H

3

1

...(Eq. 19.32)

Effect of Surcharge

The effect of surcharge due to the weight of soil above the scour line can be considered in
the analysis. The soil below the maximum scour line is subjected to a surcharge Z of the
unscoured soil (Fig. 19.17). The height Z may be taken as half the normal depth of scour
in case it is not possible to ascertain it by actual measurement.