Design of single piles - Piling Engineering - page 164

pile length falls below about 0 8 L c . Carter and Kulhawy (1988) have presented a

solution for essentially rigid piles in homogeneous soil (

.

ρ c = 1). For piles where

G c ) 1 / 2 , the ground level deflection and rotation are given by

L / d ≤ 0 . 05( E p /

L
d

− 1 / 3 L

d

− 7 / 8

32 H
dG c

16 M
d 2 G c

u = 0 . + 0 .

(4.86)

L
d

− 7 / 8 L

d

− 5 / 3

H
d 2 G c

25 M
d 3 G c

θ = . + .

0 16 0

With such short piles, the design will normally hinge on the possibility of the pile
failing by rigid body movement through the soil. Analysis of this type of behaviour
has been discussed in section 4.3. Further charts giving the response of short piles to
lateral loading may be found in Poulos and Davis (1980).

4.4.3 Cantilever idealization

The main shortcoming of the idealization of laterally loaded piles as cantilevers, fixed
at some depth below ground surface, has been the lack of consideration of the role
of the relative pile and soil stiffnesses in determining an appropriate depth of fixity.
Equations (4.79) may be rewritten in a form more familiar to engineers with a struc-
tural background, by substituting for G c in terms of E p and the critical length, L c
(see equation (4.73)) and then replacing E p by ( EI ) p / d 4 ( π / 64). In most cases, it will

be appropriate to take ρ c equal to 0.5, allowing for very low soil stiffness near the

ground surface, where the strain level in the soil is high. For this case, equations (4.79)
transform to

L c
2

3 L c

2

2

424 H
EI

472 M
EI

u = 0 . + 0 .

(4.87)

L c
2

2 L c

2

472 H
EI

887 M
EI

θ = 0 . + 0 .

These equations are similar to those that would be obtained from a cantilever ide-
alization of the pile, with a depth of fixity of L c /

2. In that case the three independent
coefficients on the right-hand sides would be 1/3, 1/2 and 1 respectively, instead of the
values of 0.424, 0.472 and 0.887. Thus the errors involved in estimating pile defor-
mations from a cantilever idealization will be small, providing the appropriate depth
of fixity of L c / 2 is adopted.

The cantilever idealization is not suitable for estimating the profile of induced bend-
ing moments. For example, in the simple case of a pile under force loading, H , only,
equation (4.80) gives a maximum bending moment of 0

. 2 HL c (taking ρ c = 0 . 5), occur-

ring at a depth of L c / 3. The cantilever approach would give a maximum bending

moment at the base of the cantilever (a depth of L c / 2) of magnitude 0 . 5 HL c .