Pile Capacity Based on Dynamic
Methods & Wave Equation
Bigman Hutapea-Prodi Teknik Sipil,FTSL-ITB
Sebagian besar materi diambil dari materi
kursus singkat oleh Peter J. BosscherUniversity of Wisconsin-Madison
Presentation Overview
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Dynamic Formulas
Dynamic Analysis Using Wave
Equation
Dynamic Pile Testing and Analysis
Dynamic Formulas
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To predict static load capacity based on the
foundation’s response to dynamic loads
This technique probably harkens back to when
people first began driving piles
Based upon pile set (per blow) information obtained
during driving
Engineers tried to base on energy concepts equating
hammer kinetic energy to resistance of pile
penetration (difficult and easy to drive)
ENR proposed by Wellington in 1893
Dynamic Formulas
Wh  Rsb
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Basic Equation:
where:
W = ram weight
h = ram stroke
R = soil resistance
sb = pile set per blow (diperoleh di
lapangan)
Due to simplicity, widely used
Variations exist which consider pile weight,
Do They Work?
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From pioneer foundation engineer,
Lazarus White (1936):
“I read some of the papers last night
where some of these pile driving
formulas were derived, and the result
was that my sleep was very much
disturbed”.
ASCE Committee on Pile Foundations,
1941
Karl Terzaghi’s Response
“In spite of their obvious deficiencies and their unreliability, the pile formulas
still enjoy a great popularity among practicing engineers, because the use
of these formulas reduces the design of pile foundations to a very simple
procedure. The price one pays for this artificial simplification is very high.
In some cases the factor of safety of foundations designed on the basis of
the results obtained by means of pile formulas is excessive and in other
cases significant settlements have been experienced. On account of
their inherent defects all the existing pile formulas are utterly misleading
as to the influence of vital conditions, such as the ratio between the
weight of the pile and the hammer, on the result of the pile driving
operations. In order to obtain reliable information concerning the effect of
the impact of the hammer on the penetration of the piles it is necessary to
take into consideration the vibrations which are produced by the impact.”
(Terzaghi, 1943)
Why are dynamic formulae
inaccurate?
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Improper modeling of:
– driving system
• kinetic energy is not full picture
• ram, anvil, helmet, cushion(s) all have effect
– soil
• does not resist with constant force
• rapid soil resistance different than static
– pile
• not rigid but rather flexible
• pile length has effect
Dynamic Formulae Summary
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Except where well supported empirical
correlations under a given set of
physical and geological conditions are
available, dynamic formulas should
not be used. This is especially true of
the ENR formula.
Alternative Methods
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Wave Equation Analysis Programs
(WEAP)
Dynamic Testing and Analysis Tools
(Pile Driving Analyzers [PDA])
Further improvements with CAPWAP
Dynamic Analysis Using Wave
Equation
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Involves the mathematical modeling of
all elements in pile driving: hammer,
cushions, helmet, pile, and soil.
Developed by E.A.L. Smith (1960)
Software:
– TTI (1976) in public domain
– WEAP (1976, 1986) in public domain
– GRLWEAP (continued updates) commercial
Wave Propagation in Piles
Idealized Model of Pile/Soil
The Wave Equation
Provides two important items:
– a guide in the selection of properly sized driving equipment
and piling to ensure the pile can be driven to the final grade
without exceeding allowable driving stresses; and
– a penetration rate (minimum number of blows per inch of
penetration) for impact hammers to determine when the pile
has been driven sufficiently to develop the required capacity.
From WEAP
6
5
Capacity/Pile Area (ksi)
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4
3
2
1
0
0
5
10
15
Number of blows/inch (N)
20
25
Hasil Analisis Sebelum Pemancangan
FADWAVE
Result
forSet
Pre-Installation
Hubungan
Ru Terhadap
Final
Untuk Energi Analysis
Yang Bervariasi
With Various Rated Energy
8000
7500
7000
6500
6000
5500
Ru (kN)
5000
Energy = 50
Energy = 60
Energy = 70
Energy = 80
Energy = 90
4500
4000
3500
3000
2500
2000
Various Final Set of Ru = 4895 kN, From 70 - 165 blows/ft
1500
1000
500
0
0
25
50
75
100
125
150
175
200
225
250
275
Final Set (blows/ft)
300
325
350
375
400
425
450
475
500
Benefits of WEAP during Design
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Can design pile section for driveability
to the required depth and/or capacity
Can select pile material properties
based on probable driving stresses
Can justify new depths, design loads,
and/or different number of piles
Benefits of WEAP during
Construction
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Construction engineers can use for:
– hammer approval and cushion design
– to select an economical combination of
driving equipment to minimize installation
cost
Proper Use of WEAP
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Note: the wave equation does not determine
the capacity of the pile based on soil boring
data.
It calculates driving resistance for an
assumed ult. capacity or calculates capacity
based on field observed driving resistances.
Therefore, precede WEAP w/ static analysis
Be prepared for pile setup (EOD vs BOR)
Dynamic Pile Testing and
Analysis (PDAs)
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Based on measurements of strain and
acceleration taken near the pile head as a
pile is driven or restruck with a pile driving
hammer
Can be used to evaluate the performance of
the pile driving system, calculate pile
installation stresses, determine pile integrity,
and estimate static pile capacity
Pile Driving Analyzer
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Strain transducer: strain data, combined with the
modulus of elasticity and cross-sectional area of the
pile gives the axial force in the pile
Accelerometers: the acceleration data, double
integrated with time produces the pile displacement
during the hammer blow.
Pile Driving Analyzer (PDA)
Uji PDA
Uji PDA
Pile Driving Analyzers
Other measurements are sometimes made
such as the ram velocity (with radar or the
time between two impacts of the ram).
 This information is plugged into a closed form
solution (based on an assumption of ideal
plastic soil behavior and ideal elastic and
uniform piling) called the Case Method.
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The Case Method
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Given the measured pile top force F(t) and the pile top
velocity v(t), the total soil resistance is:
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 
1
Z
R(t )   F (t1 )  F (t 2   v (t1 )  v (t 2 )
2
2
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where
Z = EA/c = pile impedance
t2 = time = t1 + 2L/c
L = pile length below the gauges
c = (E/)0.5 = speed of the stress wave
E = elastic modulus of the pile
 = pile mass density
A = pile cross sectional area

The Case Method
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The total soil resistance consists of a dynamic
and a static component.
Rt   Rs t   Rd t 
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The static component is the desired pile bearing
capacity.
The dynamic component may be computed from
a soil damping factor, J, and a pile toe velocity,
vt(t), which is calculated for the pile toe. The
equation used is:
Rd (t )  J F (t )  Z  v(t )  R(t )
Suggested Damping (J) Factors
Soil Type at Pile Toe
Damping Range
Clean Sand
0.10 to 0.15
Silty Sand, Sand Silt
0.15 to 0.25
Silt
0.25 to 0.40
Silty Clay, Clayey Silt
0.40 to 0.70
Clay
0.70 or higher
Pile Driving Analyzer Limits
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Calculates pile stress at gage location
but maximum stress may occur
elsewhere (eg: end bearing pile)
Judgement required to distinguish
between low displacement piles or piles
with large shaft resistance versus piles
with large toe resistances.
CAPWAP provides more information
CAPWAP: Case Pile Wave
Analysis Program
 combines
the wave equation model with
Case Method measurements
 uses single-blow record from EOD or
BOR
 method iteratively determines several
unknowns by signal matching
 determines stresses along the pile
Benefits/Losses of PDAs
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Provides record of pile installation (QC)
Fairly quick and painless (except $$$)
Can reduce amount of static pile testing
Hard driving (>10 blows/inch) can yield lower
bound capacities
Estimate of static pile capacity at time of
testing (i.e.:may not include soil setup).
Piles which do not form soil plug may indicate
lower capacity dynamically versus actual
static capacity