Geotechnical Engineering

DHARM

LATERAL EARTH PRESSURE AND STABILITY OF RETAINING WALLS 485

f

B y

d

y

Pa

(+)fd

y

N

A

C

Rupture plane

L

x

G

x

D Ground line

yad=( – )

b

a

H

f-line

n

F

K y-line

E

M

Fig. 13.28 Poncelet graphical construction for active thrust
BC is the required rupture surface. The criterion may be checked as follows:
Since ∆ABC = ∆BCG, and BC is their common base, their altitudes on BC must be equal;
or AN sin ∠ANB = NG sin ∠GNC that is to say AN = NG, since ∠ANB = ∠GNC. (N is intersec-
tion of AG and BC). Thus, if AN and NG are measured and found to be equal, the construction
is correct.

The active thrust Pa is given by

Pa =

1

2

γψx^2 .sin , where CG = LG = x

= γ.(∆CGL)

=

1

2

γ..,xn where n = CM, the altitude on the LG.

(Incidentally, with the notation of Fig. 13.27 (a), it may be easily understood that W =

1

2

γ...xn in view of Eq. 13.43).

Validity of the Method

The validity of Poncelet construction may be easily demonstrated.

c^2 = BG^2 = BF^2 = BE^2 + EF^2

But EF^2 = BE. ED, from the properties of a circle.

∴ c^2 = BE^2 + BE. ED

= BE (BE + ED)