Civil Engineering Reference
In-Depth Information
planned and loading levels arranged to give the minimum degree of extrapolation in
the analysis.
9.3 Dynamic testing of piles
The use of dynamic testing methods for estimating the ultimate capacity and integrity
of piles is now widespread. Assessment of pile capacity during driving has been under-
taken routinely by the use of empirical driving formulae such as those discussed in
section 4.1.4. There are many limitations to such formulae, particularly in respect
of uncertainties in the proportion of the available driving energy that is transmit-
ted to the pile. The accuracy of dynamic methods of estimating pile capacity has been
improved significantly using modern instrumentation and fast data acquisition systems
that allow measurement of the dynamic force and velocity waves in the pile during
driving. The data may be analyzed at different levels of sophistication, as described in
the following sections, to give estimates of the static pile capacity at time of driving.
Similar techniques, with lower energy input, may be used to assess the integrity of piles
(particularly cast-in-situ piles), as discussed in Chapter 8.
9.3.1 Wave equation analysis
The propagation of driving energy along a pile, allowing for interaction with the
surrounding soil, may be analyzed with sufficient accuracy using a 'one-dimensional'
idealization. In this idealization, only vertical (strictly speaking 'axial'), displacement
of the pile is considered, and the governing differential equation is
2
w
∂
2
w
∂
(
AE
)
p
∂
)
p
∂
=
(
A
ρ
−
f
(9.1)
z
2
t
2
or
∂
2
w
∂
c
2
∂
1
2
w
∂
f
(
AE
)
p
=
−
(9.2)
z
2
t
2
where
(
AE
)
p
is the cross-sectional stiffness of the pile.
(
A
ρ
)
p
is the mass per unit length of the pile.
=
√
E
c
is the wave propagation speed in the pile (
/ρ
).
w
is the vertical displacement of the pile.
z
is the distance down the pile.
t
is the time variable.
f
is the mobilized soil resistance per unit length of pile.
Historically, this equation has been implemented using finite difference or finite ele-
ment techniques, with the pile being modelled as a discrete assembly of mass points
interconnected by springs. This model, originating in the work of Smith (1960), forms
the basis of a range of computer programs for studying pile drivability.
