Civil Engineering Reference
In-Depth Information
Any viscous enhancement of the static resistance is modelled by taking the limiting
dynamic resistance as
T
max
1
v
0
)
β
T
d
=
+
α
(
v
/
(9.18)
where
v
0
=
v
is the
relative
velocity between the pile and the soil. It is
more correct to use the relative velocity in this equation, rather than the absolute pile
velocity, since the main viscous effects will be confined to the zone of high shear strain
rate immediately adjacent to the pile. Typical values for the viscous parameters may
be taken as
1m/s and
β
=
0
.
2 (following Gibson and Coyle (1968) and Litkouhi and Poskitt
(1980)) and
α
in the range 0 for dry sand, up to 1 or possibly higher for clay coils.
9.3.1.2 Dynamic soil model at pile base
Suitable models for the dynamic response at the pile base have been discussed in detail
by Deeks and Randolph (1995), building on the analogue model first proposed by
Lysmer and Richart (1966). The basic model is very similar to that in Figure 9.30(b),
but with the addition of a lumped mass at the pile node. For undrained conditions
(
5), as appropriate for pile driving, the stiffness, damping and mass parameters
are given by (Deeks and Randolph, 1995)
ν
=
0
.
2
Gd
1
K
=
(9.19)
−
ν
85
d
2
1
0
.
G
V
s
C
=
(9.20)
−
ν
16
d
3
m
=
0
.
ρ
s
(9.21)
ρ
s
is the density of the soil beneath the pile tip.
In practice, the lumped mass makes little difference, as it represents only 60% of
the volume of a hemisphere (of diameter,
d
) of soil at the pile tip. Comparing the
magnitudes of the stiffness and inertial dashpot terms for the pile shaft and base, it
may be seen that the relative contribution from the dashpot at the pile base is only
about 40% of that along the shaft. However, this still represents a significant increase
in stiffness relative to static loading.
Further discussion and comparison of the original Smith formulations for dynamic
pile-soil interaction, and those described above, may be found in Randolph (2000),
where application to open-ended driven piles is also considered.
where
9.3.2 Dynamic stress wave data
Wave equation analysis, as described in the previous section, is used in determining the
drivability of piles, using commercially available software such as the WEAP family
(Goble and Rausche, 1976, 1986; Rausche
et al
., 1988). However, a potentially more
significant application lies in the interpretation of dynamic stress wave data measured
during pile driving. The data form the basis of a dynamic pile test, which may obviate
the need for more costly static loading tests.
