Example 5: Pile Segment and Damping Input Page 1 of 4
GRLWEAP Standard Examples
Example 5: Pile Segment and Damping Input
The echo print of the input data and the numerical output from the Wave Equation Analysis is
contained in the Example 5 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, small
input and output differences were unavoidable. Please also note that descriptions of basic input
features may have been included in earlier examples and may not be repeated here.
5.1 Situation
A timber pile has to be driven through a soil of stratified clay and sand to a dense gravel
layer. The timber pile has a length of 36 ft, 2 inches (11.03 m). Its cross sectional area
varies from 128.7 (830.13) at the top to 56.2 inch2(362.58 cm2) at the bottom. For the
timber, an elastic modulus of 2000 ksi (13,789 MPa) and specific weight of 51 lb/ft3 (8.01
kN/m3) was assumed. The pile will be driven by a Link-Belt 440 hammer.
A soil investigation resulted in the following data: At a depth of 25 ft, 8 inches (7.83 m)
the pile point will penetrate into gravel where it should achieve an ultimate bearing
capacity of 150 kips (667 kN) of which 90% will act at the toe. The Smith shaft damping
factors are 0.05 s/ft (0.16 s/m) in the gravel layers and 0.20 s/ft (0.66 m/s) in the clay
layers. Different from normal recommendations, experience indicated a toe damping
factor of 0.05 s/ft (0.16 s/m).
5.2 Problem
The hammer should be run at a limited energy of 14.4 kip-ft (19.6 kJ) to avoid pile
damage. To what blow count must the pile be driven to insure the 75 ton [150 kip (670
kN)] ultimate bearing capacity and what would be the bounce chamber pressure (gauge)
corresponding to this energy level?
5.3 Solution
A single average shaft damping or quake value is used in a layered soil with little loss of
accuracy. For the purpose of demonstration only, the element lengths, masses and
stiffness are also calculated and entered for this non-uniform pile. Yet, it is still necessary
to input a pile profile for the calculation of pile stresses. This calculation is simplified using
as an area the profile value preceding the segment top. Thus, a detailed profile helps in
calculation of accurate stresses:
Click Options/Job Information and enter the necessary project description and file
name.
Find and click on Hammer ID No.83.
Click on Pile material Timber.
Enter and/or correct the pile information for the pile top (see also table below).
Click on Area of Hammer Cushion and then press F3. Click OK for Manufacturer's
recommended driving system. Click Linkbelt, LB440, Timber, pile size PS 10 (255) -14
(355), cushion material CM, 20% Al per 80% Micarta, Check All, OK.
Choose Non Uniform Pile from the Pile Option drop-down box and enter the following
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Example 5: Pile Segment and Damping Input Page 2 of 4
pile profile (perimeter and strength data are not needed for this analysis):
Depth (below pile top) X-Area E. Modulus. Spec. Wt.
ft in2 ksi lbs/ft3
0 128.67 2000 51
0.17 128.67 2000 51
7.00 112.65 2000 51
14.00 97.33 2000 51
21.00 83.13 2000 51
28.00 70.04 2000 51
36.17 56.2 2000 51
To enter the pile segment properties, click Options/Pile Parameters/Pile Segment
Option, and input the Number of Segments. PDI recommends that the number of pile
segments equals the pile length in meters. In other words, pile segments should have
lengths of approximately 1 m or 3.3 ft. In our example, we are choosing 12 segments for
the 37 ft long pile. Next choose from one of the three input options for pile segments:
l Equal segment length, automatic determination of stiffness and weight - this is the
normal GRLWEAP input mode which requires practically no calculation effort by the
user.
l User defined segment length, automatic determination of stiffness and weight -
this option allows the user to match the segment boundaries to the pile profile
thereby avoiding the averaging of segment properties over a sharp change of pile
cross section or material.
l User defined segment length, stiffness and weight - this option requires the most
preparation by the user. In our example, this option will be chosen for the purpose
of demonstration only; actually, the automatic (normal) option is sufficient to
solve this problem with very good accuracy.
The table of Segment Length, Segment Stiffness and Segment Weight now has to
be filled in. In our example, all segments are given the same length of approximately 3 ft.
Note that the individual segment lengths do not need to add up to the exact pile length;
the input values will be treated as relative segment length and will be normalized by
GRLWEAP. Segment weights and stiffness values are calculated from density, elastic
modulus, cross sectional area, and length values and entered in the input table.
Segment Number Segment Length Segment Stiffness Segment Weight
ft kips/inch kips
1 3.167 6582.0 0.141
2 3.000 6557.0 0.126
3 3.000 6167.0 0.118
4 3.000 5800.0 0.111
5 3.000 5445.0 0.104
6 3.000 5100.0 0.098
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Example 5: Pile Segment and Damping Input Page 3 of 4
7 3.000 4764.0 0.091
8 3.000 4440.0 0.085
9 3.000 4128.0 0.079
10 3.000 3823.0 0.073
11 3.000 3534.0 0.068
12 3.000 3257.0 0.065
As an example, let us calculate the properties of the first segment. Its area at the top is
128.7 in2. Interpolating we find that the area at the segment's bottom is 121.8 in2. The
average area is 125.2 in2 (over the top 3.17 ft). The weight of the first segment is
(125.2)(0.051)(3.17)/144 = 0.141 kips. The stiffness of the first segment is (125.2)
(2000)/(12)(3.167) = 6582 kips/inch. Note that for each segment an average area, an
elastic modulus of 2000 ksi (13,789 MPa), and a specific weight of 51 lb/ft3 (8.01 kN/m3)
was used.
Since it is intended to run the hammer at a limited energy, a hammer override value for
the stroke must be input. For closed end diesels, this stroke is an equivalent value. The
LB 440 has a ram weight of 4 kips (17.8 kN). Thus, for a potential ram energy of 14.44
kip-ft (19.6 kJ) the stroke should be set to 14.44/4 = 3.61 ft (19.6/17.8 = 1.10 m),
which can be done right below the Hammer List. To maintain the stroke and therefore the
fixed potential energy, the proper stroke option has to be chosen in the
Options/General Options/Stroke. This allows for selection of how the stroke is to be
used in the analysis (it may be used as a starting value or as a fixed value.) In the
present case we want to maintain a fixed stroke value and therefore choose the option
Convergence of pressure with fixed stroke.
In this example, soil parameters will be entered through the individual soil segment input
as follows:
l Click on the Resistance Distribution Option drop-down box and choose
Detailed Resistance Distr. A window opens that shows uniform ultimate
resistance values for all 12 segments (note that individual quake values can only
be entered if Detailed Resistance Distr. is activated).
l Modify the static resistance distribution as desired. These numbers may be actual
ultimate resistance values or only relative numbers. They will be recalculated
according to the Shaft Resistance Percentage and Ultimate Capacity input on the
main input screen. Click OK.
l Click Options/Soil Parameters/Soil Segment Damping/Quake. A window
opens that shows default values for shaft damping and quake values. For the
current example, the soil segment values are shown in the figure below.
The finished input should look as in the table below:
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Example 5: Pile Segment and Damping Input Page 4 of 4
5.4 Discussion of Results
The relatively complicated input should be checked by comparing the input data tables
shown above with the pile model table on the second page of the output. The summary
output shows that a blow count of 76 bl/ft (241 bl/m) would be required to drive the pile
to a 150 kip (667 kN) ultimate capacity if the hammer runs at 15.1 psi (104 kPa) bounce
chamber pressure. The transferred energy in the pile is then 4.7 kip-ft (6.4 kJ) and the
hammer should run at a speed of 92 bl/min. Note that the hammer was kept at a
relatively low energy setting (a specified equivalent stroke of 3.63 ft or 1.1 m). In fact,
the program had to reduce the file specified combustion pressure for the 150 kip capacity
to maintain this low stroke. At such an energy level, the atomized fuel injection LB 440
does not impact and the blow count becomes extremely sensitive to small changes in
hammer performance. Stresses are highest in the bottom segment where they reach 2.59
ksi (18MPa).
As mentioned earlier, stresses in this mode of input are calculated based on the areas in
the pile profile. In the present case these values were not sufficiently closely spaced for
good accuracy and more accurate results would be obtained with the standard pile input.
It is always recommended to check the program's stress calculations for non-uniform
piles by dividing the force maxima of the program's extrema table outputs with the
appropriate pile cross sectional areas. If one uses the maximum toe force (162 kips or
723 kN) of the extrema table in the numerical output for the 150 kip capacity and divides
it by the cross sectional area at the very bottom (56.2 inch2or 363 cm2), one finds a
maximum toe stress of 2.88 ksi or 19.9 MPa. This is a relatively high stress. Higher blow
counts and therefore capacities could easily lead to pile toe damage.
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