Example 17: Vibratory Hammer Analysis Page 1 of 2
GRLWEAP Standard Examples
Example 17: Vibratory Hammer Analysis
The echo print of the input data and the numerical output from the Wave Equation
Analysis is contained in the Example 17 Output file both for English and SI Units.
Although it was attempted to limit differences between this example and the
corresponding one of earlier GRLWEAP versions, differences may be noted. Please note
that descriptions of basic input features of GRLWEAP have been included in earlier
examples and may not be repeated here.
17.1 General Remarks
Vibratory pile driving analysis has not yet matured to the point where it is as
reliable as impact pile driving analysis. Not many correlation tests between
static capacity and soil resistance during vibratory pile driving exist. For that
reason, GRLWEAP still uses the basic wave equation approach with some
modifications, consisting of higher damping factors for shaft damping in
cohesive soils, Smith viscous damping, and higher shaft quakes in cohesive
soils. One of the difficulties of vibratory pile driving analysis is the assessment
of the soil resistance during driving. Even though the general agreement is
that sandy soils lose their shaft strength during vibratory pile driving,
experience with GRLWEAP to date has shown that the analysis is not very
sensitive to the magnitude of lost shaft resistance. On the other hand, the
end bearing seems to control the speed and refusal of pile penetration.
The vibratory hammer model has been explained in theBackground Report.
Actually, the model is very simple. Two masses are connected by a very soft
spring that practically isolates the upper mass from the vibrations of the
lower one. The lower mass is acted upon by a sinusoidal force which is a
function of frequency and eccentric mass. This force can be reduced by an
efficiency value.
The following example demonstrates the analysis of a 99 ft (30.2 m) long
double sheet pile (2 PS 31 with a combined cross sectional area of 29.9
square inches or 193 cm2) using an ICE 815 vibratory pile driver. The sheet
piles form a circular cofferdam. In order to maintain the alignment of the
sheets, it is necessary to drive the piles at most 3 ft (.9 m) at a time and
then to move on to the next double sheet. Unfortunately, relatively early
refusal is encountered which is in part attributed to a high interlock friction.
The refusal situation may also be explained by the fact that the soil, a soft
and then firm clay, exhibits strong set-up during driving interruptions whose
rather long duration is governed by the time required to drive sheets around
the whole cofferdam.
The ICE 815 has a maximum frequency of 26.6 Hz and an eccentric moment
of 0.37 kip-ft (50.7 kg-m). In theHammer Data File for the Vibratory
Hammer, the eccentric moment is represented by an eccentric weight of 1.84
kip (8.188 kN) with an eccentric radius of 0.2 ft (0.06096 m). The maximum
power that can be supplied by the power unit is 375 kW. In the field, the
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Example 17: Vibratory Hammer Analysis Page 2 of 2
hammer was only run at a frequency of 22.5 Hz, thus the default value is
replaced with 22.5 Hz for this example. An "efficiency" of 0.7 is used in the
analysis to match measurements with analysis results. It is assumed that the
clamp has a weight of 2 kips (8.9 kN). The clamp is rigidly connected to and
adds weight to the oscillator weight.
For the soil resistance, it is estimated that toe resistance includes some
interlock friction concentrated near the bottom of the sheets. This explains
the relatively high end bearing of 30%, where 70% shaft resistance is used
as an input value. The shaft resistance is distributed triangularly, considering
the increasing strength of the clay with depth. CAPWAP results from impact
records, obtained immediately after vibratory driving had stopped, indicated
damping factors of 0.35 s/ft (1.15 s/m) and 0.2 s/ft (.66 s/m) for shaft and
toe, respectively. These factors (for impact driving relatively high) are used in
the vibratory analysis together with quakes of 0.2 inches (5 mm).
Impact records were taken and evaluated after vibratory driving reached an
unacceptably high penetration time of 280 s/ft (1600 s/m). The impact
records indicated a "bearing capacity" of 160 kips (712 kN) and since only a
short time elapsed between vibratory and impact driving, it may be assumed
that no substantial soil set-up occurred before impact driving started. For the
160 kips (712 kN) resistance level, the vibratory analysis yields an acceptable
penetration time. However, an increase of capacity of 20% or a decrease of
the shaft resistance percentage from 70 to 60% would produce refusal
conditions. Measured compressive and tensile stresses are 6.45 and 5 ksi (45
and 35 MPa), respectively, which compare well with the calculated values at
the 160 kip (712 kN) resistance level.
Please note that the general recommendation for damping and quake factors
is a doubling of those used for impact driven piles combined with the
assumption of Smith viscous damping. In the present case, this would have
produced refusal at the indicated capacity. The reason is primarily a very high
CAPWAP-calculated shaft damping factor obtained from impact records. Had
twice the standard values been used (0.4 and 0.3 s/ft for shaft and toe or 1.3
and 1.0 s/m, respectively, the penetration speed predication would have been
more reasonable.
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