Pile Design and Construction Practice, Fifth edition

6.3.9 Bending and buckling of partly embedded
single vertical piles

A partly embedded vertical pile may be required to carry a vertical load in addition to a
lateral load and a bending moment at its head. The stiffness factors Rand Tas calculated
from equations 6.11 and 6.12 have been used by Davisson and Robinson(6.24)to obtain the
equivalent length of a free-standing pile with a fixed base, from which the factor of safety
against failure due to buckling can be calculated using conventional structural design
methods.
A partly embedded pile carrying a vertical load P, a horizontal load H, and a moment M
at a height eabove the ground surface is shown in Figure 6.37a. The equivalent height Leof
the fixed-base pile is shown in Figure 6.37b.

Piles to resist uplift and lateral loading 351

00

0.2

rc =1

0.4

0.75

0.5

rc =1 0.75

0.5

rc 51

0.75

0.5

rc =1

0.75

0.5

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

Z/I

c

Z/I

c

Z/I

c

Z/I

c

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0.1

• 0.2 0.2 0.4 0.6 0.80 0.20 0.4 0.6 0.8^1

0.2 0.3 0.4 0.5 0.6

M/H 0 Ic

M/M 0

0 0.05 0.1 0.15 0.2

(a) (b)

(c) (d)

yroGc 1/7

H 0

Ep

Gc

yro^2 Gc 3/7

M 0

Ep

Gc

Figure 6.36Generalized curves giving deflected pile shape and bending moment profile for lateral force
and bending moment applied to pile head (after Randolph(6.23)) (a) Deflected pile shape for
lateral force loading (b) Bending moment profile for lateral force loading; (c) Deflected pile
shape for moment loading (d) Bending moment profile for moment loading.