Civil Engineering Reference
In-Depth Information
where
m
∗
is the rate of increase of
G
∗
with depth). For example, suppose that the
variation of shear modulus with depth,
z
, is approximated as
G
=
10
+
4
z
MPa (
z
being the depth in m)
(4.76)
For a pile of diameter 0.6 m, with equivalent modulus
E
p
=
10
3
MPa, a first guess
for the critical pile length might be 6 m (that is 10 pile diameters). Taking Poisson's
ratio as 0.3, the characteristic modulus,
G
c
, is calculated as
×
30
G
c
=
(10
+
4
×
6
/
2)(1
+
3
×
0
.
3
/
4)
=
27
.
0 MPa
(4.77)
This gives a revised estimate of the critical pile length of
10
4
0)
2
/
7
L
c
=
0
.
6
×
(3
×
/
27
.
=
4
.
45 m
.
(4.78)
Further iteration yields final values of
L
c
=
6 MPa.
The concept of a characteristic shear modulus,
G
c
, and a critical pile length,
L
c
,
may be used to write expressions for the ground level deformation of the pile. Thus
the lateral deflection,
u
, and rotation,
4
.
63 m,
G
c
=
23
.
θ
, are given by
E
p
/
G
c
1
/
7
ρ
c
G
c
0
27
H
L
c
/
M
L
c
/
u
=
.
2
+
0
.
30
2
2
(4.79)
E
p
/
G
c
1
/
7
ρ
c
G
c
0
H
L
c
/
M
L
c
/
80
√
ρ
c
θ
=
.
30
2
2
+
0
.
2
3
These expressions have been derived by synthesizing a number of finite element analy-
ses (Randolph, 1981). The similarity with those obtained from the subgrade reaction
approach (equations (4.69)) is evident.
Generalized profiles of deflection and bending moment down the pile may be drawn
for piles subjected to shear force loading,
H
, or moment loading,
M
. These profiles
are shown in Figures 4.46 and 4.47. The maximum moment for a pile under a lateral
load of
H
, occurs at a depth between
L
c
/
3 (for soil
with stiffness proportional to depth). The value of the maximum moment may be
estimated as
4 (for homogeneous soil) and
L
c
/
M
max
=
(0
.
1
/ρ
c
)
HL
c
(4.80)
For piles within a group, the pile cap may prevent rotation of the head of the pile. For
such 'fixed-headed' piles, equations (4.79) may be used to find the fixing moment,
M
f
.
Setting
θ
=
0, the fixing moment is given by
0
ρ
c
)
1
/
2
HL
c
M
max
=−
.
/
1875
(
(4.81)
