Geotechnical Engineering

DHARM

774 GEOTECHNICAL ENGINEERING

Ht. of centre of buoyancy, B, above the base

AB=

545

2

.

= 2.725 m

AG is given as 4.200 m

∴ BG = 4.200 – 2.725 = 1.475 m

BM(M being the Metacentre) =

I

V

=

1

12

18 9^1

882 35

×××^3

.

= 1.240 m

∴ AM=+AB BM = 2.725 + 1.240 = 3.965 m

AG being 4.200 m, M is below G, and the metacentric height MG is negative (the nu-
merical value of MG is 0.235 m). The caisson is, therefore, unstable.

The caisson can be made stable by filling it with, say, sand ballast (Assume γsand = 22
kN/m^3 ).

Let us try a thickness of 0.5 m of sand.

The height of the new centre of gravity, G′, above the base

AG′ =

9000 4 2 9 18 0 5 22 0 25

9000 9 18 0 5 22

×+××××

+× × ×

...

(.)

m

= 3.55 m

9m

10 m

G

A

4.2 m

Fig. 19.9 Stability of box caisson (Ex. 19.3)

New depth of immersion, d′ =

()

.

9000 1782

10 2 9 18

+

×× = 6.525 m

(^) AB′=6 525
2

. m = 3.263 m

BM I V′′= = × × ×

××

/(/)

.

112 18 9

1

9 18 6 525

(^3) m = 1.035 m
AM′=AB′+ ′ ′B M = 3.263 + 1.035 = 4.298 m
Since AM′>AG′, M′ is above G′( ...MG′′=4 298 3 550 0 748 m)− =. Since M′ is above G′,
the metacentric height M′G′ being positive, the caisson is stable.