Geotechnical Engineering

DHARM

488 GEOTECHNICAL ENGINEERING

Special Cases

(1) β is nearly equal to φ:
A special case of Poncelet’s (Rebhann’s) construction arises when β is nearly equal to φ
so that φ-line and the backfill surface meet at a large distance from the wall and hence cannot
be accommodated on the drawing. The following procedure may be adopted in such a case, as
illustrated in Fig. 13.30.

y

E 1

A 1

H

A

a

B y

f

G 1

Repture surface

C

n

x

L

M

G

D 1

f-line

x

y-line

K

b

Ground line

F 1

Fig. 13.30 Special case of Poncelet construction when β ≈ φ
(i) Represent the backface of the wall AB and the backfill surface through A.
(ii) Draw the φ-line through B inclined at φ with the horizontal.
(iii) Draw the ψ-line BK through B inclined at ψ with the φ-line.
(iv) Choose a convenient point D, on the φ-line, and draw the semi-circle on BD 1 as the
diameter.

(v) Draw D 1 A 1 parallel to the backfill surface to meet the wall in A 1.

(vi) Through A 1 draw A 1 E 1 parallel to the ψ-line to meet the φ-line in E 1.

(vii) Erect a perpendicular E 1 F 1 to the φ-line at E 1 to meet the semi-circle in F 1.

(viii) With B as centre and BF 1 as radius, draw an arc F 1 G 1 to meet the φ-line in G 1.

(ix) Through A draw AG parallel to A 1 G 1 to meet the φ-line in G.

(x) Through G draw a line parallel to the ψ-line to meet the backfill surface in C.

(xi) Join GC and with G as centre and GC as radius, draw an arc to meet the φ-line in L.

(xii) Join CL and drop CM perpendicular to GL.