Civil Engineering Reference
In-Depth Information
4.3.2.1 Plasticity solution
Randolph and Houlsby (1984) describe an analytical solution for the flow of soil
around a cylindrical object. The solution was originally considered exact, within the
confines of the rigid plastic model of the soil, although subsequently it was discovered
that the best upper bound lies slightly above the lower bound. The solution allows for
limiting friction,
f
s
, at the pile-soil interface which is less than or equal to the shear
strength of the soil. Defining
sin
−
1
(
f
s
/
=
c
u
), the lower bound for the limiting bearing
factor,
N
pl
, is given by
4 cos
π
−
4
√
2
sin
π
−
4
P
u
N
pl
=
c
u
d
=
π
+
2
+
+
(4.65)
The variation of the limiting pressure with friction ratio
f
s
/
c
u
is shown in Figure 4.40.
The value of
N
pl
varies from9.14 for a perfectly smooth pile, up to 11.94 for a perfectly
rough pile, with a mean value of about 10.5.
Figure 4.41 shows the failure mechanism for the case of
f
s
/
c
u
=
0
.
5.
12
11.5
Upper bound
11
Lower bound
10.5
10
9.5
9
0
0.2
0.4
0.6
0.8
1
Interface friction ratio,
f
s
/
c
u
Figure 4.40
Variation of limiting lateral resistance with interface friction ratio (Randolph and
Houlsby, 1984).
Figure 4.41
Flow mechanism for soil around laterally loaded pile.
