LOAD RESISTANCE FACTOR DESIGN (LRFD) FOR DRIVEN PILES BASED ON
DYNAMIC METHODS WITH ASSESSMENT OF SKIN AND TIP RESISTANCE
FROM PDA SIGNALS
By
ARIEL PEREZ PEREZ
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING
UNIVERSITY OF FLORIDA
1998
Copyright 1998
by
Ariel Perez
To my parents
ACKNOWLEDGMENTS
Above all, I would like to thank all the geotechnical engineering staff. With their
knowledge, teaching skills, experience, and professionalism, they have provided me with
an excellent level of education. I wish to express my sincere appreciation and gratitude to
the chairman of my supervisory committee, Dr. Michael C. McVay, for providing me
with the opportunity to conduct this research and for his generous assistance and guidance
throughout the course of this study. Grateful acknowledgment is also made to Dr. Frank
C. Townsend for serving as committee member and sharing with me his extensive
experience in the geotechnical field. Special thanks are given to Dr. Fernando E.
Fagundo. Besides being a committee member, Dr. Fagundo has offered me his support
and friendship from our first meeting before arriving to Gainesville. Lastly, I would like
to acknowledge Dr. Limin Zhang, for his continuing guidance and encouragement in the
preparation of this manuscript. Without his work, this project would not have been
accomplished.
I wish to thank all my friends here in Gainesville, especially Alvin Gutierrez,
Beatriz Camacho, Elzys Boscan, Nereida Padr6n and Gabriel Alcaraz. Their friendship
has provided me with life experiences I could not have gained elsewhere.
I am deeply grateful to Paul Bullock and Tanel Esin from Schmertmann &
Crapps, Inc. for their assistance in providing useful load test data appearing in this thesis.
The help from Dr. Ching L. Kuo from PSI, Inc. is also gratefully appreciated. Dr. Ching
Kuo was always willing to help by providing any requested information or by sharing his
vast experience in the deep foundation field. The funding of this research by the Florida
Department of Transportation is also acknowledged and appreciated.
TABLE OF CONTENTS
page
A C K N O W L E D G M E N T S .................................................................................................. iv
A B S T R A C T ............................................................................ ............... ix
CHAPTERS
1 IN T R O D U C T IO N ............................... .................. ....................................................
2 REVIEW OF FLORIDA PILE DRIVING PRACTICE............... ........ ................... 4
C u rren t F lo rid a P practice ................................................................................................ 4
B hearing R equirem ents ............................................................... ..... ................... 4
B low count criteria ................. ............................ ... ...... ... .......... 5
P practical refusal ................................. .................. ..............5
Setchecks and pile redrive........................................ ............................ 5
Pile heave .......................................... 6
Piles w ith insufficient bearing................................................ .............. 6
M methods to D term ine Pile Capacity.................................. ......................... 6
W ave equation ...................................... 7
B hearing form ulas ........................................ ........................ .. ............ 9
D ynam ic load tests ...................................... ...................................... 9
Static load tests ...................... ............. ... .............. 9
Evaluation of Florida Practice Changes ............................... ...... ................ 10
B hearing R equirem ents ............................................................. ..... ................... 10
M methods to D term ine Pile Capacity................................ ......................... 11
3 PILE CAPACITY ASSESSMENT USING STATIC AND DYNAMIC
METHODS ........................................................ 14
D avisson's C capacity ................................................. ....... .. .......... 14
D ynam ic M ethods R eview ....................................................................... 16
M om entum C conservation .................................................. .......... .............. 16
ENR ................ ..... ......... .. ................................ 16
Modified Engineering News Record formula ............................................... 17
F D O T ........................................ 18
G ates m ethod ............................ .... ................ 19
Combined Wave Mechanics and Energy Conservation................................... 19
Sakai et al. Japanese energy m ethod .............. ............................. ....... ....... 19
P aik ow sky 's m eth o d ........................................................................................ 2 0
Wave Mechanics .............................. ............ .. 21
vi
P D A m eth o d ....................................................................... 2 1
C A P W A P program .......................................................................................... 2 5
4 UNIVERSITY OF FLORIDA PILE DATABASE .............................................. 27
G general Inform ation and H istory....................................................... ... ................. 27
P IL E U F In form action ................................................................................................... 2 9
G e n e ra l ............................................................................. 2 9
Soil Classification .. ................. ........................ ................ 29
D driving Inform action ...................................... .............................. ............ .. 30
Dynamic Data (CAPWAP and PDA) .......................................... ............. 31
L oad Test R results .................. ............................. ....... .. ........ .... 31
SPT94 Capacity....................................................... 32
G gathering N ew Inform ation ........................................................................................ 32
Additional Required Information ............................... ............................ 33
C riteria for N ew E ntries ........................................................................................ 33
5 A SD A N D LRFD CON CEPTS......................................................... ... ................. 34
Allowable Stress Design (ASD) M ethod .......................................... ..... ......... 34
Load Resistance Factor Design (LRFD) Method ................................................... 35
Advantages of LRFD Over A SD ................................................. ....... ....... 36
Lim station of LRFD .................. .............................. ....... .. ........ .. 36
Calibration of LRFD .............................. ............ .. 37
E engineering Judgem ent ....................................................................... 37
Fitting A SD to LRFD .................................................................... ..... 37
Reliability Calibration ............................................... ...... .. .......... 39
Statistical data .. ........................................... ......... 39
Probability density function ........................................ ......... .............. 41
LRFD com ponents .................... ................. ...................... .............. 42
6 LRFD DATA PRESENTATION AND ANALYSIS ............................................ 51
Data Reduction......................................... ............ 51
LRFD A analysis of R esults...................................................................... ................. 56
Effect of Bridge Span Length and Probability of Failure.................................. 57
Level of Conservatism and Accuracy Indicators ............................................. 60
/ R R atio ...................................................................... ......... 63
M ethods com prison .......................................................... .............. 64
EOD versus BOR ................ ............................. ..... .. ........ .. .... ....... 64
Evaluation of cases with capacity smaller or larger than 1779 kN .............. 64
R ecom m ended Safety Factors ...................................................... ..... ....... .. 65
A SD D esign E valuation ........................ ........................... ...................................... 68
7 SKIN AND TIP STATIC CAPACITY ASSESSMENT OF DRIVEN PILES........... 69
M ethod 1 ................................................ ......................... 70
Method 2 (Suggested) .......................... ..... .... ........ 72
Description and Main Assumptions ................................................................. 72
Case Damping Coefficient, Jo, versus Tip to Skin Ratio................................... 75
Sensitivity Analysis of Case Damping Coefficient, J ....................................... 77
Static and Dynamic Load Test Data................................................................... 78
Automating the Suggested M ethod ............................................... ................. 79
R results and A analysis ............ .............. ........................ .... ....... ........... ... 81
Presentation of R results ........................................................... .... .. .......... .. 81
Analysis of Total Capacity Predictions .............. ........................................... 86
Analysis of Skin and Tip Capacity Predictions................... ................................ 87
Sensitivity of Jc and Pile R esistance............................................ ... ................. 91
8 CONCLUSIONS AND RECOMMENDATIONS ............................................... 94
LRFD Calibration for Eight Dynamic Methods................................................ 94
Conclusions ........................ ...................... 94
Recom m endations ......... .............. ...... .......... .. ................................ .. 95
Suggested Method to Determine Pile Capacity...................................... ......... ........ 96
C conclusions .......................................... ........ ........ ......... . 96
R ecom m endations ................................................. .. .......... .. 98
APPENDICES
A LRFD ANALYSIS RESULTS CAPWAP PROCEDURE ...................................... 99
B LRFD ANALYSIS RESULTS PDA METHOD................................................ 104
C LRFD ANALYSIS RESULTS PAIKOWSKY'S ENERGY METHOD .............. 109
D LRFD ANALYSIS RESULTS SAKAIET AL (JAPANESE) METHOD............ 114
E LRFD ANALYSIS RESULTS FDOT METHOD ................................................. 119
F LRFD ANALYSIS RESULTS ENGINEERING NEWS RECORD (ENR).......... 128
G LRFD ANALYSIS RESULTS MODIFIED ENR........................ ................. 137
H LRFD ANALYSIS RESULTS GATES FORMULA............................................ 146
I FORCE AND VELOCITY TRACES FROM PDA SIGNAL .................................. 155
J OUTPUT FILE FOR SUGGESTED METHOD & GRL PROCEDURE
(F O R T R A N ) ..................................................... 179
LIST O F R EFEREN CE S ................................................... ................................. 185
BIOGRAPHICAL SKETCH........................................ 187
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering
LOAD RESISTANCE FACTOR DESIGN (LRFD) FOR DRIVEN PILES BASED ON
DYNAMIC METHODS WITH ASSESSMENT OF SKIN AND TIP RESISTANCE
FROM PDA SIGNALS
By
Ariel Perez Perez
December, 1998
Chairman: Dr. Michael C. McVay
Major Department: Civil Engineering
Eight dynamic methods to estimate the static capacity of driven piles were
evaluated based on a Florida database and Load Resistance Factor Design (LRFD). The
dynamic methods investigated were four stress wave approaches (CAPWAP, PDA,
Paikowsky Energy, and Sakai Energy) and four driving formulas (ENR, modified ENR,
FDOT, and Gates). In the case of the older driving formulas, the database was broken
into both small (i.e. Davisson capacity less than 1779 kN) and large (Davisson capacity
larger than 1779 kN) capacity piles. It was demonstrated that the modern methods based
on wave mechanics, such as CAPWAP, PDA, and Paikowsky's energy method, are more
accurate than the old driving formulas. The utilizable measured Davisson capacity,
defined as 0/4R (ratio of resistance / mean capacity), shows that the new dynamic
methods are more cost effective to meet a reliability index in comparison with the old
methods based on momentum conservation. In addition, the Gates formula, when used
separately for Davisson capacity larger than 1779 kN or less than 1779 kN, may have
comparable accuracy with the modern methods.
A suggested empirical method is presented to calculate the total, skin, and tip
static resistance of driven piles. This method has proved to be equally or more accurate
than the most widely used method (i.e. PDA, and CAPWAP). Additional features of the
suggested method include determining the total, skin, and tip static capacities as the piles
are being driven, saving construction time, therefore, saving construction costs.
CHAPTER 1
INTRODUCTION
Dynamic testing has been a tool for estimating pile capacities and hammer
suitability since 1888 when the first driving formula, i.e. the Engineering News formula,
was published. From then to the early seventies, many driving formulas were proposed
and adopted into codes, all derived on the principles of impulsemomentum conservation.
In the sixties, pioneer research investigated predicting both stresses and pile capacities
based on wave mechanics. The results were the creation of programs such as, WEAP
(GRL, 1993), PDA (Pile Dynamics Inc., 1992), and CAPWAP (GRL, 1996). Recently,
energy approaches based on both wave mechanics and energy conservation have been
developed to determine the pile capacity.
Since the implementation of the PDA and CAPWAP about fifteen years ago, it is
unknown the accuracy of these methods in comparison with the older driving formulas.
Moreover, it is unknown how the newer energy equations compare to the past and present
methods for Florida soil conditions.
Recently, the American Association of State Highway and Transportation
Officials (AASHTO) has moved from the Allowable Stress Design (ASD) to the Load
Resistance Factor Design (LRFD) analysis. The latter method employs resistance factor,
6, based on reliability indexes. However, in order to determine the accurate resistance
factors, the LRFD requires a database to assess the probability of failure of a given
method.
Based on the University of Florida pile database and AASHTO's recommended
reliability index, and live to dead load ratios, the resistance factors (LRFD) and
equivalent safety factors (ASD) were developed for a number of dynamic pile capacity
methods. These parameters served as a tool to evaluate the accuracy and level of
prediction of the dynamic methods studied. The dynamic methods investigated were four
stress wave approaches (CAPWAP, PDA, Paikowsky Energy, and Sakai Energy) and four
driving formulas (ENR, modified ENR, FDOT, and Gates). In the case of the older
driving formulas, the database was broken into both small (i.e. Davisson capacity less
than 1779 kN) and large (Davisson capacity larger than 1779 kN) capacity piles.
Since 1994, the Florida Department of Transportation specifications recommend
the use of Wave Equations to determine the suitability of the driving system and to
estimate the pile capacity. It is also recommended the use of dynamic and/or static load
tests to verify the estimated capacity. For the dynamic procedures, FDOT recommends
the use of PDA or CAPWAP only. The capability of CAPWAP to estimate the skin and
tip capacity in addition to the distribution of damping through the pile have created a
level of confidence in the pile industry over the PDA whose result consists only of the
total static capacity. However, the CAPWAP program needs highly trained people to run
it, and involves a series of iterations. The latter creates delays in the pile driving
operations and increase in foundation costs.
A suggested empirical method is presented to calculate the total, skin, and tip
static resistance of driven piles using the PDA Case solution. This method has proved to
be equally or more accurate than the most widely used methods (i.e. PDA, CAPWAP). In
addition, the suggested method allows the users to determine the pile capacities instantly
as the piles are driven, saving construction time. Because all the calculations for the
suggested method are performed automatically, a technician with a high level of expertise
is not required.
CHAPTER 2
REVIEW OF FLORIDA PILE DRIVING PRACTICE
In this chapter, the pile driving practice in Florida will be presented. Because the
Florida Department of Transportation (FDOT) uses a large percentage of driven piles
versus the private industry, the information presented herein is based on their
recommendations. It is the author's intention to present the current driving practice
together with a discussion of the most relevant changes throughout the years. This
discussion is focused on aspects such as bearing requirements, and methods to determine
pile capacity.
Current Florida Practice
The information presented is in relation to the current Florida practice, which was
obtained from the FDOT Standard Specifications for Road and Bridge Construction of
1999. For more details, the reader is referred to the latest FDOT specifications.
Bearing Requirements
As a general criterion the engineer in charge of the driving process may accept a
driven pile if it has achieved the minimum penetration, the blow count has a tendency to
increase and the minimum bearing capacity is obtained for 600 mm of consecutive
driving. The engineer may also accept a driven pile if the minimum penetration was
reached and the driving has achieved practical refusal in firm strata. Aspects such as
practical refusal and others driving criteria will be discussed in detail in the following
sections.
Blow count criteria
Using the Wave Equation Analysis for Piles (WEAP) the engineer can determine
the number of blows per specific penetration to reach a design pile capacity. The blow
count has to be averaged for every 250 mm of pile penetration or through the last 10 to 20
blows of the hammer. It should be noted that the driving equipment must be selected in
order to provide the required resistance at a blow count ranging from 30 blows per 250
mm to 98 blows per 250 mm.
Practical refusal
Practical refusal is defined as a blow count of 20 blows per 25 mm for 50 mm of
driving. The FDOT specifications recommend that driving ceases after driving to
practical refusal conditions for 250 mm. If the required penetration can not be achieved
by driving without exceeding practical refusal, other alternates should be considered such
as jetting or Preformed Pile Holes.
Setchecks and pile redrive
Setchecks. Set checks are performed in the event that the Contractor has driven
the pile up to the point that the pile top elevation is within 250 mm of the cutoff
elevation and the pile has not reached the required resistance. Prior to a set check, the
driving process is interrupted for 15 minutes. Then, the engineer is provided with a level
or other suitable equipment to determine elevation in such a way that the pile penetration
during the setchecks could be determine in a very accurate manner. If the initial set
check results are not satisfactory, additional setchecks could be performed. The pile is
then accepted if the pile has achieved the minimum required pile bearing.
Pile redrive. Pile redrive consists of redriving the pile after 72 hours from
original driving. The pile redrive is considered when time effect is important in the pile
capacity. Other considerations include the pile heave.
Pile heave
Pile heave is defined as the upward movement of a pile from its originally driven
elevation. In occasions, driving a pile can cause excessive heave and/or lateral
displacement of the ground. The previously driven pile should be monitored, and in the
event of pile heave (6 mm or more), all piles must be redriven unless the engineer has
determined that the heave is not detrimental to the pile capacity.
Piles with insufficient bearing
In the event that the pile top has reached the cutoff elevation without achieving
the required bearing resistance, the FDOT specifications recommends:
1. Splice the pile and continue driving.
2. Extract the pile and drive a pile of greater length.
3. Drive additional piles until reducing the adjusted required bearing per pile to
the bearing capacity of the piles already driven.
Methods to Determine Pile Capacity
The FDOT Specifications recommend the use of Wave Equation to determine pile
capacity for all structures or projects. The use of static load tests or dynamic load tests, or
both, is recommended to verify the capacity estimated from Wave Equation predictions.
Nevertheless, the prediction by the Wave Equation (blow count criteria) could be adjusted
to match the resistance determined from the static or dynamic load tests, or both.
Wave equation
The FDOT Specifications recommends to use the WEAP program to predict the
pile capacity. This program allows the engineer to evaluate other aspects of the driving
process. In the following paragraphs, a description of these aspects will be presented.
Evaluation of driving system. Evaluate the suitability of the driving system
(including hammer, follower, capblock and pile cushions. The driving system must be
capable of driving the pile to a resistance of 3.0 times the design load, plus the scour and
down drag resistance or the ultimate resistance, whichever is higher.
Determine pile driving resistance. The pile driving resistance, in blows per 250
mm or blows per 25 mm could be determined. The required driving resistance is defined
as the design load multiplied by the appropriate factor of safety plus the scour and down
drag resistance or the ultimate bearing capacity, whichever is higher.
Evaluate pile driving stresses. The engineer must evaluate the driving system to
avoid overstressing the pile at any moment during the driving. If the Wave Equation
analyses show that the hammer will overstress the pile, the driving system has to be
rejected. The FDOT Specifications 4555.11.2 presents the allowable stresses for piles
made out of concrete, steel and timber. Equation 21, 22, and 23 give the maximum
allowable tensile and compression stresses for prestressed concrete piles.
The allowable compressive stress is,
sC = 0.7fc 0.75fpc
(21)
For piles length less than 15 meters the allowable tensile stress is given by
sa = 0.54(fY +1.05fp, (22)
And for piles length greater than 15 meters
spt = 0.27(f + 1.05fp (23)
where Sapc Maximum Allowable Pile Compressive Stress, MPa
Sapt Maximum Allowable Pile Tensile Stress, MPa
fcl Specified Minimum Compressive Strength of
Concrete, MPa.
fpc Effective Prestresses at Time of Driving.
For steel piles the maximum allowable compression and tensile stresses are equal
to ninety percent (90 %) of the yield strength (0.9 fy) of the steel. While for timber piles
the maximum allowable pile compression and tensile stresses are 25 MPa for Southern
Pine and Pacific Coast Douglas Fir and 0.9 of the ultimate parallel to the grain strength
for piles of other wood.
Bearing formulas
The FDOT under specification 4555.11.3 recommends the following bearing
formula for temporary timber piles driven with power hammers:
167E
R =1 (24)
s+2.54
where R Safe Bearing Value, in Kilonewtons.
s The Average Penetration per Blow, in Millimeters.
E Energy per Blow of Hammer, in Kilojoules.
The latter specification also clearly states that this formula should not be used to
determine pile capacity of any other pile type. No other bearing formula is suggested in
the specifications for concrete or steel piles.
Dynamic load tests
Dynamic load testing consists of predicting pile capacity from blows of the
hammers during drive and/or redrive of an instrumented pile. Chapter 3 includes more
details of how the dynamic load test is performed (see PDA and CAPWAP sections).
Static load tests
Static load testing consists of applying a static load to the pile to determine its
capacity. The FDOT recommends the Modified Quick Test. For more details about the
static load test, the reader is referred to the FDOT specification 4552.2.1. Some general
information about this test, and the procedure to obtain the pile capacity are explained in
Chapter 3.
Evaluation of Florida Practice Changes
In the following sections the most relevant changes in the Florida practice (i.e.
bearing requirements and proposed methods to determine pile capacity) for approximately
the last 10 years are discussed. For this purpose, the actual practice will serve as a
reference for any comparison. To facilitate the comparison process, only the changed
criteria will be discussed. The latter does not mean that the aspects not mentioned within
this document did not vary (i.e. only the topics related to this thesis will be investigated).
Because the largest change in FDOT specifications related to pile foundation were found
in the 1994 version versus 1991 version specifications, the discussion will be based on
these two references. To simplify the comparison, the FDOT specifications of 1991 and
prior to 1991 will be called "old specifications" and any other specification after 1991
will be called the "new specifications."
Bearing Requirements
In general, there was a great change in the FDOT specifications of 1994 in
comparison to the older FDOT specifications. In the old specifications the piles were
allowed to be driven to grade. Even if the practical resistance had not been reached at
that point, the engineer was able to drive the pile below grade and build up. After driving
12 inches (0.305 m) below grade, a setcheck could be performed after 12 hour of initial
driving. The latter criterion differs from the new practice in the elevation at which the
setcheck is recommended. The new practice recommends the setcheck to be performed
at approximately 10 inches above the cutoff elevation.
Another important difference is related to the bearing formulas. In the old
specifications, the FDOT recommend the use of bearing formulas to determine the pile
bearing capacity for piles made out of timber, concrete, composite concretesteel and
steel. Then, from 1994 to date the specifications limited the use of bearing formulas to
timber piles driven with power hammers only.
Methods to Determine Pile Capacity
It was noted that in the old specifications there was not any requirement for using
Wave Equation programs to determine the pile capacity. The same observation applies to
the use of dynamic testing as a method to determine the pile capacity. Prior to 1994, the
FDOT recommended the use of static load test to determine the pile capacity of any pile
that did not reach the required resistance at the end of drive or as directed by the engineer.
The new specifications recommend the use of Pile Driving Analyzer (PDA), the Wave
Equation Analysis for Pile (WEAP), and the static load test separately or in a combination
of each, as recommended by the engineer (the safety factor for design depends upon the
number and kind of test performed).
The other difference is in the criterion for determining the pile capacity from the
static load test. In the old specifications, the failure criterion is given by either or both
conditions shown below:
1. One and onehalf times the yield load settlement develops. The yield load is
defined as that load beyond which the total additional settlement exceeds 0.03
inch per ton, for the last increment applied.
2. The total permanent settlement of the top of the pile is greater than 14 of an
inch.
The new specifications present two criteria to determine the static pile capacity.
Those criteria are as follows:
1. Davisson for shafts with diameter up to 600 mm, the load that causes a shaft
top deflection equal to the calculated elastic compression, plus 4 mm, plus
/120 of the shaft diameter in millimeters.
2. FHWA for shafts with diameter larger than 600 mm, the load that causes a
shaft top deflection equal to the calculated elastic compression, plus 1/30 of the
shaft diameter.
The changes in criteria for selecting the failure load reflect, first, an increase in the
use of larger piles in the construction field, and second, the FDOT recognizes that for
larger piles (diameter larger than 600 mm) the capacity according to Davisson's criterion
is conservative.
As a general observation, the FDOT has abandoned the old methods to determine
the bearing capacity of piles (i.e. bearing formulas, based on momentum conservation).
At the same time, the FDOT has adopted other prediction methods such as Wave
Equation, PDA, and CAPWAP, which are based on piles dynamic and wave propagation
through the pile, to estimate the static pile capacity. Other old methods such as Gates,
ENR, and Modified ENR are not considered as alternates in estimating the pile capacity,
neither are the relatively new methods such as Paikowsky's method and Sakai et. al.
method.
13
It was proposed by the FDOT to investigate the new FDOT specifications in
relation to the old methods based on momentum conservation (i.e. FDOT, Gates, ENR,
Modified ENR). Another important consideration was to evaluate the old methods for
large capacity piles, which are used today, separately from small capacity piles (i.e. piles
with capacity up to 2000 kN approximately). The latter reflects the magnitude of design
loads for which piles were designed in the past in comparison to the present practice.
CHAPTER 3
PILE CAPACITY ASSESSMENT USING STATIC AND DYNAMIC METHODS
The Florida Department of Transportation (FDOT) under contract No. BB349
required UF to evaluate the older empirical methods for determining pile capacity and
compare them to the modern instrumented methods. In addition, it was required to obtain
the resistance factor for each method (Load Resistance Factor Design LRFD). In order
to perform the latter, the Davisson's capacity served as the measured capacity for each
pile. In the following sections, a brief description of the Davisson criterion together with
the description of the empirical methods investigated will be presented.
Davisson's Capacity
The Davisson method (Davisson, 1972) is one of many methods developed to
determine the pile capacity based on a static load test results. Davisson defined the pile
capacity as the load corresponding to the movement which exceeds the elastic
compression of the pile by a value of 4mm (0.15 inches) plus a factor equal to the
diameter of the pile in millimeter divided by 120. Figure 31 presents the load
displacement curve resulting from a static load test. From this curve, the Davisson's pile
capacity can be obtained. The steps to obtain the Davisson's capacity are as follow:
DAVISSON'S METHOD
MOVEMENT (INCHES)
Figure 31. Construction of Davisson's Pile Capacity
1. Plot a line with slope representing the elastic deformation of the pile
(Slope m):
m =
where A
E
L
Crosssectional Area of the Pile
Elastic Modulus of the Pile Material
Pile Length
2. Draw a line parallel to the elastic deformation line with an intercept, x, on the
settlement (movement) axis given as
(31)
x=4.0+ (32)
120
where D Diameter of Pile in millimeters
x horizontal displacement of elastic deformation line
in millimeters
3. The Davisson's capacity (point D on Figure 31) is defined as the intersection
point between the loadsettlement curve and the elastic deformation line.
Dynamic Methods Review
Eight methods were considered in this study, which are subdivided in three
categories: momentum conservation, combined wave mechanics with energy
conservation, and wave mechanics alone. The methods are the Engineering News Record
(ENR), Modified ENR, FDOT, Gates, Paikowsky, Sakai (Japanese), Pile Driving
Analyzer (PDA) and the Case Pile Wave Analysis Program (CAPWAP). In the following
sections, a brief description of each method is presented.
Momentum Conservation
ENR
One of the older formulas developed to estimate the driven pile capacity was the
formula published in the Engineering News Record (ENR) (Coduto after Wellington,
1994). It has since become known as the Engineering News Record formula:
Wh
P = (33)
F(s+0.1)
where Pa Allowable Pile Load
Wr Hammer Ram Weight
h Hammer Stroke (the distance the hammer falls)
F Factor of Safety
s Pile Set (penetration) per Blow in Inches
Wellington (1888) recommended using a Safety Factor of 6.0.
Modified Engineering News Record formula
In 1961, the Michigan Highway Department (Housel, 1966) performed a series of
pile driving tests with the objective of evaluating the accuracy of the ENR formula. After
evaluating 88 piles, the investigators found that the ENR formula overpredicted the pile
capacities by a factor of 2 to 6. The findings mean that piles designed with a SF of 6 will
have a real factor of safety of 1 and 3. Based on their results, the Michigan Highway
Department developed the Modified Engineering News Formula:
0.0025E(W, +e2W) (3
a (s+0.1)(W,+Wp)
Pa Allowable Pile Load (kips)
where
E Rated Hammer Energy Per Blow (ftlb)
Wp Weight of Pile plus Driving Appurtenances (lb)
Wr Weight of Hammer Ram (lb)
s Pile Set (in/blow)
e Coefficient of Restitution
FDOT
The Florida Department of Transportation under specification 4553.3 (1991)
recommends the following bearing formula (FDOT, 1991).
2E
R = (35)
S+0.1+0.01P
where R Safe Bearing Value in Tons
P Weight of Pile as Driven, in Tons
S Average Penetration per Blow, in Inches
E Energy per Blow of Hammer, in FootTons
The last formula was used for concrete piles, composite concretesteel piles and
steel piles. The bearing capacity obtained using the latter FDOT approach either
coincided or exceed the design capacity (suggested FS = 1.0).
Gates method
The method was the results of a research performed by Marvin Gates, J.M (1957).
The basic assumption is that the resistance is directly proportional to the squared root of
the net hammer energy. This relationship is presented by
S= aeE,(b logs) (36)
where Pu Static Pile Resistance
eh Hammer Efficiency (0.85 used for all Cases)
Eh Hammer Energy
a, b 27 and 1.0 Respectively (English units)
s Point Permanent Penetration per Blow Set
A suggested safety factor equal 3.0 is recommended.
Combined Wave Mechanics and Energy Conservation
Sakai et al. Japanese energy method
Sakai's pile driving formula was developed based on stresswave theory.
According to Sakai, this consideration introduced two advantages, it is theoretically
accurate as well as easy to use (Sakai et al., 1996). For a blow by an elastic hammer
Sakai et al. recommend
S J 2, 1 ) (37)
LP 2MH ma
where A Pile Cross Sectional Area
E Young's Modulus of Pile Material
Lp Length of the Pile
Mp Mass of the Pile
Dmax Maximum Penetration of Pile per Blow
s Permanent Set
Paikowsky's method
The Paikowsky method or "Energy Approach" is a simplified energy approach
formulation for the prediction of pile resistance based on the dynamic measurements
recorded during driving. The basic assumption of the method is an elastoplastic load
displacement pilesoil reaction. The Paikowsky method uses as input parameters the
maximum calculated transferred energy and maximum pile displacement from the
measured data together with the field blow count. Equation 38 presents the solution for
the dynamic pile capacity R, (Paikowsky, 1994).
R = m (38)
Set+ max
2
where R, Dynamic Pile Capacity
Em Maximum Energy Entering the Pile
Dmax Maximum Pile Top Pile Movement
Set Point permanent penetration per blow
The static pile resistance P, can be obtained by
P= K R (39)
where Ksp 'Static Pile' Correlation Factor Accounting for all Dynamic
Energy Looses.
For easy driving of piles with small area ratios, Paikowsky recommends a value of
Ksp smaller than 1.0, while for hard driving cases with large area ratios, the recommended
Ksp value must be larger than 1.0. A value of Ksp equals 1 was used in our calculations.
Wave Mechanics
PDA method
In the 1960's a new method to determine the pile capacity was developed at the
Case Institute of Technology in Cleveland, Ohio. This new method called Pile Driving
Analyzer (PDA) is based on electronic measurements of the stress waves occurring in the
pile while driving. Some advantages of dynamic pile testing are (GRL, 1996):
1. Bearing Capacity The bearing capacity can be found at the time of testing.
For the prediction of a pile's long term bearing capacity, measurements can be
taken during restriking (Beginning of Restrike BOR)
2. Dynamic Pile Stresses While the pile is driving the stresses within the pile
can be monitored. This avoids any possibility of pile damage due to
compression or tension stresses. Bending stresses caused by asymmetry of the
hammer impact can be also monitored.
3. Pile Integrity To detect any existing damage within the pile
4. Hammer Performance The performance of the hammer is monitored for
productivity and construction control purpose.
The PDA is considered as field equipment for measuring the forces and
accelerations in a pile during driving. The methodology is standardized and is described
in ASTM standard D4945.
The equipment includes three components (Coduto, 1994):
1. A pair of strain transducers mounted near the top of the pile on each side.
2. A pair of accelerometers mounted near the top of the pile.
3. A pile driving analyzer (PDA)
The main purpose of the PDA is to compute the static resistance of the pile using
the Case method as it is driven. To perform the latter, the dynamic capacity has to be
separated from the static capacity by mean of a damping value Jc, or Case damping value.
In the following paragraph a summary of the basic equations used by PDA is presented.
The pile wave speed, c, can be determined prior to pile installation while the pile
is still on the ground. The accelerometers are installed and the pile is hit with a hammer.
Knowing the pile length and the wave travel time, the wave speed can be calculated using
Equation 310.
(310)
where
Length of the Pile
Time Required for the Pulse to Travel Twice the Pile
Length
The dynamic modulus of the pile material, E, is presented in Equation 311. The
mass density of the pile material is represented by p and the wave speed c.
E= pc2 (311
Equation 312 presents the impedance, Z, of a pile as a function of the dynamic
modulus, E, the wave speed, c, and the pile crosssectional area, A.
EA
Z= (312
c
)
)
The force within the pile can be obtained from the strain transducers and knowing
the elastic modulus of the pile material and crosssectional area, according to Equation 3
13.
P= EA
(313)
The velocity is obtained from the integration of the acceleration signal acquired by
the accelerometers. It should be noted that the force and velocity used in the PDA
calculation is the result from the average of the two strain transducers and the two
accelerometers. The velocity is then converted to force units by multiplying by the pile's
impedance (Z). The result of the force and velocity are then plotted in a graph versus
time for a given blow. Figure 32 shows an example of the force and velocity traces for a
given hammer blow.
2500
2000
SForce
1500 .. .... Velocity
Z 1000
LL 500
0.01 0.02 0.0o 0_ 4 ,50 )6
500
1000
Time (s)
Figure 32. Typical Force and Velocity Traces from PDA
The main equation used by PDA to determine the static capacity of piles was
derived assuming that the pile is linearly elastic and has constant cross section properties
along the length. This equation is based on the force and velocity records at a time T1 and
at a time T2 equal to T1 plus 2L/c, and the Case damping constant. Equation 314
presents the PDA equation for determining the static pile capacity. The reader is referred
to the PDA manual for detailed information and more thorough derivation.
RSP= (1J) 1Z z + Jc) 2 (314)
2 2
where RSP Total Static Capacity
Jo Case Damping Constant
P1,P2 Force at Time T1 and T2 Respectively
V1,V2 Velocities at Time T1 and T2 Respectively
Z Impedance
CAPWAP program
The Case Pile Wave Analysis Program (CAPWAP) is a computer program that
combines the wave equation's pile and soil model with the Case method of forces and
velocities from PDA. The CAPWAP solution includes the static total resistance, skin
friction and toe bearing of the pile, in addition to the soil resistance distribution, damping
factors, and soil stiffness. The program calculates acceleration, velocities, displacements,
waves up, waves down and forces at all points along the pile.
The procedure used by CAPWAP includes inputting the force trace obtained from
PDA and adjust the soils parameters until the velocity trace obtained from PDA can be
recreated. It should be noticed that the opposite procedure (i.e. input velocity trace and
generate the force trace) can also be performed. When the match obtained is
26
unsatisfactory, it is necessary to modify the soil parameters, until reaching a satisfactory
match results. The process of running CAPWAP is considered an iterative one.
CHAPTER 4
UNIVERSITY OF FLORIDA PILE DATABASE
General Information and History
The University of Florida in conjunction with the Florida Department of
Transportation (FDOT) has developed a database on driven piles inside and outside the
state of Florida. This database, called PILEUF, is the result of many years of research to
predict pile capacity from static and dynamic means.
Originally, the database was on a Lotus 123 spreadsheet format. However, the
database information was transferred to a Microsoft Excel format for this research. By
doing the latter, the automatic tasks (macros) or links from Lotus 123 were eliminated.
Also, new pile information was obtained from the original geotechnical reports, as well as
new cases studied.
Currently, there are 242 piles in the database. Out of these 242 piles, 198 are
concrete piles (both square and round), 21 are steel pipe piles, and 9 are HPiles. Table 4
1 summarizes the number of piles, classification and diameter for the Florida cases while
Table 42 summarizes the same information for the Non Florida cases.
The Florida State total includes 175 piles obtained from 60 sites and represents
218 cases. The difference between the number of piles and cases is due to the multiple
attempts to determine the same pile's capacity. The NonFlorida total from Table 42
represents 22 sites. In this occasion the number of cases are equal to the number of piles.
Table 41. Classification of Florida Driven Piles
Pile Number of Piles
Diameter Squared Pipe SubTotal
(inches) Concrete Piles
10 4 3 7
12 14 2 16
14 26 8 34
18 34 0 34
20 12 0 12
24 44 0 44
30 26 0 26
36 2 0 2
SubTotal 162 13 175
Table 42. Classification ofNonFlorida Driven Piles
Pile Number of Piles
Diameter Squared Round Pipe HPiles SubTotal
(inches) Concrete Concrete Piles
10 3 0 1 6 10
10.75 2 0 0 0 2
12 15 2 0 1 18
12.75 3 0 0 0 3
14 2 0 3 2 7
16 5 0 0 0 5
18 2 0 0 0 2
24 2 0 0 0 2
59.06 0 0 4 0 4
SubTotal 34 2 8 9 53
It should be noted that for the NonFlorida information in Table 42 the total
number of piles does not include 14 piles with unspecified diameter.
The following sections describe briefly the information gathered in the database
PILEUF to date.
PILEUF Information
General
Each pile record contains general description of the site location, together with pier or
bent number (if available). Four pile types were selected to describe the piles within the
database based on shape and materials. The four categories were:
1. Square concrete pile
2. Round concrete pile
3. Pipe pile
4. Hpile
The geometry of the piles was described by the pile width, total length, embedded
length, and cross sectional area. In addition, the dates when the piles were driven and
tested were recorded.
Soil Classification
The soil information includes the soil stratigraphy (description and properties)
with insitu tests such as SPT, CPT, etc. Nine soil types were used to allow consideration
of several combinations of cohesive and noncohesive soil. The nine soil categories were
presented according to the following numbering:
1. Plastic clay
2. Siltsandclay, silts and marls
3. Clean sand
4. Limestone, very shelly sands
5. Clayey sand
6. Sandy Clay
7. Silty clay
8. Rocks
9. Sandy gravel, tills
The original database combined the side and tip soil number to form a twodigit
code, in which the first digit is the side soil type and the second digit is the tip soil type.
Driving Information
The driving information includes the driving system type, hammer and pile weight
and manufacturer's rated energy together with the efficiency of the hammer. Additional
information includes the dynamic modulus, wave speed and the pile impedance. If the
impedance was not available from CAPWAP or other results, it was calculated as EA/c.
The average set for EOD and BOR was taken as the inverse of the blow counts as near as
possible to the blow used in PDA or CAPWAP analysis, although it may represent an
average of the last foot of driving in some cases, if inchbyinch information was not
available. A record of the depth of penetration and blows per foot (calculated for
penetration intervals less than one foot) facilitated the determination of set, knowing the
tip depth at the time of the blow.
Dynamic Data (CAPWAP and PDA)
The CAPWAP and PDA results were sometimes available only for EOD or BOR.
Furthermore, not all CAPWAP analyses have complete PDA results available or vice
versa. Having both results was not a requirement during the construction of the database.
The PDA results include date, RMX (maximum Case Static Resistance calculated
during the blow analysis) or other PDA calculated capacity as listed in the source report.
The database also presents the PDA Case damping used for calculating the Total Static
Resistance.
CAPWAP results include date, tip and friction capacities, total capacity, and Case
and Smith damping factors for side and tip, where the Case damping factors were
calculated from the Smith damping factors. The latter was performed by dividing the
Smith damping value by the impedance and multiplying the result by the side or tip
resistance.
Load Test Results
PILEUF contains load test information, measured at the top of the piles. It
includes the load in tons and settlements in inches at failure for a given criterion. The
failure criteria presented in the database are:
1. Davisson
2. FullerHoy
3. DeBeer
4. FDOT
The database also includes the maximum load in tons from the static load test, in
addition to the date at which the load test was performed.
SPT94 Capacity
SPT94 (most recent version SPT97) is a pile capacity prediction program. It is
based on the Research Bulletin 121 (RB121), "Guidelines for use in the Soils
Investigation and Design of Foundations for Bridge Structures in the State of Florida",
prepared by Schmertmann in 1967, and the research report "Design of Steel Pipe and H
piles" prepared by Dr. Michael McVay et al in 1994. The method calculates pile capacity
based on N values obtained from the Standard Penetration Test. SPT94 is capable of
evaluating round and square concrete piles, Hpiles, and steel pipe piles (open or close
end). It calculates an Estimated Davisson capacity by summing the Ultimate Side
Friction and 1/3 of the Ultimate End Bearing (Mobilized End Bearing) capacity of the
pile.
SPT94 predictions presented in PILEUF include the Ultimate Side Friction,
Ultimate Tip Capacity, Mobilized Tip Capacity, Ultimate Total Capacity, and Davisson's
Capacity.
Other related information presented in the database is the input data for SPT94
program. It includes the layering and the soil properties (i.e. unit weight and SPT blow
count).
Gathering New Information
During the course of evaluating the eight dynamic method (See Chapter 3), some
extra information was necessary. In order to acquire it, it was required to restudy the
geotechnical reports from which the original information was obtained. Some of these
parameters are presented in the next sections.
Additional Required Information
Two parameters that were not found in the PILEUF database were the maximum
displacement and the maximum energy transfer to the pile. They were essential to obtain
the Paikowsky and Sakai capacities (See Chapter 3). Both, the maximum energy transfer
to the pile and the maximum displacement were obtained from the CAPWAP output
printout in the geotechnical reports.
Criteria for New Entries
As a general criterion, new entries in the database should be within the State of
Florida. Pile cases from outside the State of Florida were not considered in this study.
Because the evaluation of the dynamic methods was performed in correlation to the
Davisson capacity, new entries in the database should have the load test carried to the
point in which Davisson capacity could be determined. Other information required will
depend of the methods to be evaluated. The more information obtained for a particular
record, the more dynamic methods there are to be evaluated in relation to the Davisson
capacity.
CHAPTER 5
ASD AND LRFD CONCEPTS
Over the years, multiple design procedures have been developed which provide
satisfactory margins of safety. Safety in design is obtained when the material properties
exceed the demand put on them by any load or loads combination. Another way to
describe the same principle is that the resistance of the structure must exceed the effect of
the loads, i.e.:
Resistance 2 Effect of Loads (51)
When a specific loading condition reaches its limit, failure occurs. Two general
states of interest to engineers are Strength and Service Limit. Strength Limit State
involves the total or partial collapse of the structure (i.e. bearing capacity failure, sliding,
and overall instability). On the other hand, Service Limit State only affects the function
of the structure under regular service loading conditions (i.e. excessive settlement and/or
lateral deflection, structural deterioration, etc).
Allowable Stress Design (ASD) Method
In geotechnical engineering, the ASD has been the primary method used in U.S.A.
ASD procedures are different for Service Limit and Strength Limit States. For the
Strength Limit State, safety is obtained in the foundation elements by restricting the
ultimate loads to values less than the ultimate resistance divided by a factor of safety,
(FS):
R
,> ,_Q' (52)
FS
where Rn Nominal Resistance
XQi Load Effect (Dead, Live and Environmental Loads)
FS Factor of Safety
For the Service Limit State, the deformations (i.e. settlements) are calculated
using the unfactored loads, and the values obtained are compared to the allowable
deformation for that structure.
Load Resistance Factor Design (LRFD) Method
The LRFD specifications as approved by AASHTO in 1994 recommend the use of
load(s) factors to account for uncertainty in the load(s) and a resistance(s) factor to
account for the uncertainty in the material resistance(s). This safety criterion can be
written as
OR,, = r y, Q, (53)
e) Statistically Based Resistance Factor
where
Rn Nominal Resistance
11 Load Modifier to Account for Effects of Ductility,
Redundancy and Operational Importance
yi Statistically Based Load Factor
Qi Load effect
Even though the LRFD method differs from the accustomed ASD procedure, it
has been widely approved by the geotechnical engineers. Some of the advantages and
disadvantages of the LRFD method over the ASD method are presented next (Withiam et
al., 1997).
Advantages of LRFD Over ASD
1. Account for variability in both resistance and load.
2. Achieves relatively uniform levels of safety based on the strength of soil and
rock for different limit states, foundation types, and design methods.
3. Provide more consistent levels of safety in the superstructure and substructure
when the same probabilities of failure are employed.
4. Using load and resistance factors provided in the code, no complex
probability and statistical analysis is required.
Limitation of LRFD
1. Implementation requires a change in design procedures for engineers
accustomed to ASD.
2. Resistance factors vary with design methods and are not constants.
3. The most rigorous method for developing and adjusting resistance factors to
meet individual situations requires availability of statistical data and
probabilistic design algorithms.
Calibration of LRFD
Calibration is defined as the process of assigning values to resistance factors and
load factors, which are indispensable for the LRFD approach. This process can be
performed by use of engineering judgement, fitting to other codes (e.g. ASD method), use
of reliability theory, or a combination of them. In the following sections these approaches
will be discussed.
Engineering Judgement
The calibration of a code using engineering judgement requires experience. Such
experience is usually obtained through years of engineering practice. Sometimes, using
such an approach results in certain level of conservatism with little validation. Also
under varying conditions where no experience exists both excessive conservatism or ever
unconservatism may develop.
Fitting ASD to LRFD
Fitting ASD to LRFD includes using parameters from LRFD (i.e. resistance
factor) that result in equivalent physical dimensions of a substructure or superstructure as
by ASD. It does not provide a better or more uniform margin of safety. In order to
calibrate the ASD method, the first step is to rewrite equations 52 and 53 as
R
SQD+QL
FS
kRn YLQL + YDQD
(54)
(55)
It should be noted that the loads only include dead and live loads. Environmental
loads (i.e. wind, earthquake, etc) were not taken into consideration for the derivation of
the ASD fitting equation. Solving both equations for Rn we obtain
R 2 FS(QD+ QL )
R >YLQL + YDQD)
e jk
(56)
(57)
Setting Equation 56 equal to Equation 57 and solving for 6
SYLQL +YD D
FS(Q, +Q QD
(58)
Dividing both the numerator and the denominator of Equation 58 by QL
QD
YD + YL
= QL
(59)
Equation 59 is the resulting calibration equation for ASD fitting to the LRFD or
vice versa. For deep foundation design, the values of yD and YL recommended by LRFD
Highway Bridges Design Specifications (AASHTO, 1994) are 1.25 and 1.75 respectively.
The QD/QL definition and values will be presented in more detail in latter sections.
Calibration by fitting is recommended when there is insufficient statistical data to
perform a more sophisticated calibration by optimization. When statistical data is
available it is recommended to make use of reliability theory.
Reliability Calibration
Statistical data
In order to perform a reliability calibration for deep foundations (obtain resistance
factor, 0), such as piles and drilled shafts, the designer must have available statistical data
for the method of interest. This statistical data must include real or measured capacities
and the estimated or nominal capacities of the shafts. Next, the bias is defined as
=& (510)
where kRi Bias Factor
Rm Measured Resistance
Rn Predicted (nominal) Resistance
The biases for all history cases using the same design procedure are subsequently
determined for the database and the values of mean, standard deviation and coefficient of
variance are then found. Equations 511, 512 and 513 are used for this purpose
(Withiam et al., 1997).
R = (511)
N
R (512)
NI
COVR = (513)
where tR Average Resistance Bias Factor
N Number of Cases
CYR Resistance Standard Deviation
COVR Resistance Coefficient of Variance
For calibrations of the methods that predict driven pile capacity, the values of the
measured resistance (Rm) were obtained from insitu load test employing the Davisson's
capacity. The nominal resistances (Rn) were obtained from the various dynamic
equations under study (Chapter 3).
Probability density function
For the LRFD design, the probability of failure to occur for a given load and
resistance distribution is of fundamental importance. The latter is calculated with the
"probability density function" which is defined as the probability that X occurs in the
interval x to x + dx asf,(x)dx (see Figure 51). The total area under the curvef,(x) must
be equal to unity because a probability of 1 includes all possible outcomes.
x x+dx x
Figure 51. Lognormal Probability Density Function
Based on the distribution of the resistance data, a lognormal probability
distribution was recommended for the resistance data by the AASHTO Specification. A
normal function was used to represent the observed distribution of load data. Equation 5
14 presents the lognormal probability density equation.
e
s, 1< I(nx80
2^x 2^
(514)
In Equation 514 the values of 0 and are the lognormal mean and lognormal
standard deviation respectively,
=2 In 1+ 1 (515)
S=ln 1 2 (516)
2
Where OR and kR are the standard deviation and the mean of the resistance as
defined in prior sections.
LRFD components
Probability of failure. The LRFD approach defines the probability of failure of a
structure based on the load and resistance distribution curves. Figures 52 shows the
probability density functions for normally distributed load and resistance. The shaded
area represents the region of failure where the resistance is smaller than the loads. For the
load and resistance curves, the margin of safety can be defined in terms of the probability
of survival as
p, = P(R > Q)
(517)
fQ(q)
I Q
SRELIABILITY R Q R
BOUNDARY
Figure 52. Probability Density Functions for Normally Distributed Load and Resistance
And the probability of failure, pf may be represented as
Pf = 1 p, = P(R < Q) (518)
where the right hand of Equation 518 represents the probability, P, that R is less than Q.
It should be noted that the probability of failure can not be calculated directly
from the shaded area in Figure 52. That area represents a mixture of areas from the load
and resistance distribution curves that have different ratios of standard deviation to mean
values. To evaluate the probability of failure, a single combined probability density curve
function of the resistance and load may developed based on a normal distribution, i.e.
g(R,Q)= RQ (519)
If a lognormal distribution is used the limit state function g(R,Q) can be written as
g(R, Q) = n(R) ln(Q) = ln(R/Q) (520)
For both Equation 519 and 520 the limit state is reached when R=Q and failure
will occurs when g(R,Q)<0.
Reliability index. The reliability index is a simple method of expressing the
probability of failure using function g(R, Q) (Eq. 520). The frequency distribution of
g(R,Q) would look similar to the curve shown in Figure 53.
f(g) 0
FAILURE REGION
AREA = Pf
0 g= n(JRQ) g= n(RIQ)
Figure 53. Definition of Reliability Index, 3 for lognormal Distributions of R and Q
Evident from the curve is that if the standard deviation is small or the mean value
is located further to the right, the probability of failure will be smaller. The reliability
index 3, is defined as the number of standard deviations, g, between the mean value, g
(average), and the origin, or:
f g (521)
If the resistance, R, and load, Q, are both lognormally distributed random
variables and are statistically independent, it can be shown that the mean values of g(R,
Q)is
g= InL (522)
Q 1+COVR
and its standard deviation is
= ln[(1+COV2 X1 +COV2) (523)
Substituting Equations 522 and 523 into Equation 521, the relationship for the
reliability index, 3, can be expressed as
In [R/Q (1 + COV2 )/( + CO2 )
P = (524)
ln [(+CO X )(1+COV )
Equation 524 is very convenient because it depends only on statistical data and
not on the distribution of the combined function g(R, Q). A very precise definition of
probability of failure, pf, is in terms of reliability index, Fu(3) (Withiam et al. 1997).
=1F (,) (525)
Standard Normal Probability Density Distribution
045
040
0 35
0 30
S0.25
0 020
015
010
0 05
0.00
4 3 2 1 0 1 2 3 4
Reliability Index, 0
Figure 54. Reliability Definition Based on Standard Normal Probability Density
Function
In the latter equation, F,(x) is the standard normal cumulative distribution
function.
F~(f3>iJ 1 e 1p 2V
p3 2ir 2 }
(526)
A graphical representation of Equation 526 is presented in Figure 54. The
shaded area in Figure 54 represents the probability of failure, pf, to achieve a target
reliability index, 3T.
47
Another commonly accepted relationship between the reliability index, 3, and the
probability of failure, pf, has been developed by Rosenblueth and Esteva (1972) using the
relationship for values between 2 and 6.
1 OE+00
1 OE01
1 OE02
1 OE03
1 OE04
1 OE05
1 OE06
1 OE07
1 OE08
1 OE09
1 OE10
Reliability Index, J, vs. Probability of Failure, pf
(Comparison of Methods)
S.. p= 460 exp (4.33)
Esteva et al. (1972)
True value
Withiam et al. (1997)
0 1 2 3 4 5 6 7
Reliability index,1
Figure 55. Comparison of Esteva and Withiam Methods to Obtain Reliability Index, P.
Pf = 460exp(4.33)
(527)
Figure 55 presents a comparison of the results for both, the Rosenblueth and
Esteva method and the Withiam method, to determine the reliability index, P. It can be
observed that Rosenblueth and Esteva approximation method will yield good values of
probability of failure for values of reliability index between 2.0 and 6.0 as recommended
by the author of the method.
Resistance factor, 0. Once the reliability index, 3, a resistance factor, 0, may be
calculated. Assuming lognormal distributions of load and resistance in Eq. 55
substituted into Eq. 524 gives the follow resistance equation
Q I+COV2o +COV2
Q, 1+ COV2
0= RQ n O +CO +CO )]) (528)
<(';LQL +D LQL) exp f, ln[(++ CO+VQD +C )]
where Resistance Factor
kR Resistance Bias Factor
COVR Resistance Coefficient of Variance
PT Target Reliability Index
kQD, kQL Bias (Dead and Live Load)
QD/QL Dead to Live Load Ratio
The dead to live load ratio (QD/QL) in Eq. 528 varies with the bridge span. For
any bridge the live load is obtain by a standard procedure, while the dead load is based
upon the size of the structure. In other words, for the majority of bridges the live loads
are mostly constant while the dead loads vary. The dead to live load ratio has been
correlated to the span of the bridges by the following representation (Hansell and Viest,
1971):
QD QL = (+IM)(0.0132L)
(529)
where QD/QL Dead to Live Load Ratio
IM Dynamic Load Allowance Factor (equal 0.33)
L Span Length (feet)
Table 51 presents typical values of bridges span and the corresponding dead to
live load ratios.
Table 51. Values of QD/QL Based on Bridge Span Length
Span Length, L Dynamic Load QD/QL
(m) Allowance, IM
9 0.33 0.52
18 0.33 1.06
27 0.33 1.58
36 0.33 2.12
45 0.33 2.64
60 0.33 3.53
O/R definition and importance. The axial design capacity of a pile may be
represented as
(530)
PDesign = OR,
However, from Eq. 510, we know the nominal resistance may be expressed in
terms of measured value as
Rn= m (531)
LR,
Substituting Equation 531 into Equation 530 the PDesign becomes
PDegn Rm (532)
Equation 532 gives the design capacity of a shaft for a specific site. If the bias
kRi is replaced by the bias factor kR, (which represents the average of the bias), then the
design capacity is directly related to measured resistance (i.e. Davisson's capacity) and the
LRFD fitting parameters 4, and ). The 0//R ratio then represent the percentage of
Davisson capacity is allowed for design for a given probability of failure. Obviously the
higher the ratio fewer piles required and the better the method.
CHAPTER 6
LRFD DATA PRESENTATION AND ANALYSIS
Data Reduction
Prior to determine the LRFD for each dynamic method, a simple statistical
analysis was performed. For all the dynamic methods, graphs of measured capacity
(Davisson Capacity) related to the estimated capacity at End of Drive (EOD) and
Beginning of Restrike (BOR) were constructed. The number of cases for each method
was determined based on the availability of parameters needed to obtain the estimated
capacity for the corresponding method. The statistic and some of the LRFD results
(tables & graphs) from each method are contained within separated Appendices (i.e.
Appendix A for all CAPWAP Procedure results, Appendix B for all PDA results,
Appendix C for Paikowsky's Energy Method results, etc...)
Figures 61 and 62 present the plots for the PDA at BOR. Figure 61 presents a
simple graph of PDA BOR capacity versus Davisson Capacity. A line with slope equal
45 degrees has been drawn to facilitate the comparison between the two methods of
determining pile capacity. A regression line with the corresponding equation and R2 is
shown in the plot. This latter graph is ideal to visually determine how scattered the
predictions are for each method. The second graph (Figure 62, PDA at BOR) presents
the ratio of measured to predicted capacity on the vertical axis and the measured
8000
7000 y = 0.9966x
R2= 0.4851
*
6000 
5000 
4000 4 _
3000 
2000 **
1000 
0
0 2000 4000 6000
Davisson Capacity (kN)
Figure 61. Davisson Capacity vs. PDA BOR Capacity
8000
2.5
Cases=42
c 2.0 _
2. Mean=1.036
o Standard Dev.=0.32
0. 1.5 
* *
S1.0
(0
5 0.5
0.0
0 1000 2000 3000 4000 5000 6000 7000
Davisson Capacity (kN)
Figure 62. Measured Over Predicted Capacity for PDA at BOR
Davisson capacity on the horizontal axis. On each graph, the number of cases for each
dynamic method, the mean (or bias factor, kR), and standard deviation, OR, and the ratio
of measured to predicted capacity is presented.
Appendices A throughout H present the resulting plots for all the methods
studied, while Tables 67 and 68 summarize the number of cases, mean and standard
deviation.
In addition to the mean and standard deviation, a lognormal probability density
function was computed for each method. To assess the latter, Equations 514 to 516
were used. Figures 63 and 64 present a summary of the lognormal probability density
functions for the eight dynamic methods at EOD and BOR respectively. The lognormal
probability density function is used for a resistance distribution of a single pile. However,
if it is used for the ratio of measured to predicted capacity, it is a good indicator of how
good the method is to reach a desired capacity. For example, by inspection it can be
observed that dynamic methods such as ENR and Modified ENR have a very small mean
and standard deviation in comparison to the rest of the methods. On the other hand, the
Energy (Paikowsky) method has an excellent mean but with a larger standard deviation.
Figure 64 presents the same analysis for BOR cases, where the same observations can be
obtained. At an early stage of this research, it was noted that the old methods (i.e. Gates,
FDOT, ENR, and Modified ENR) gave good estimates of the Davisson capacity for piles
with Davisson capacity less than 200 tons (1779 kN). This finding is clearly justified
because the range of pile capacity in the past did not exceed 1779 kN for driven piles,
primarily because of limitation of construction equipment.
3.50
3.00
2.50
2
2.00
1.50
, \ 5
I.UU T
1 2 3 4 5 6
Davisson Capacity / EOD Capacity
0.
0.50
0.00
0
Figure 63. Log Normal Probability Distribution at EOD
0
c
C3
LL
0
L.
 1 ENR Cases=77 mean=0.30 std. dev=0.16
2 Modified ENR Cases=61 mean=0.45 std. dev=0.27
3 FDOT Cases=72 mean=2.38 std. dev=1.34
4 Gates Cases=74 mean=1.74 std. dev=0.79
 5 Energy Cases=27 mean=1.11 std. dev=0.37
6 CAPWAP Cases=44 mean=1.60 std. dev=0.56
 7 PDA Cases=48 mean=1.34 std. dev=0.44
8 Japanese Energy Cases=21 mean=1.50 std. dev=1.26
6
3
4.00
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
8
Davisson Capacity / BOR Capacity
Figure 64. Log Normal Probability Distribution at BOR
7
I A
1
2
5
>7
 1 ENR cases=71 mean=0.24 std dev=0.16
2 Modified ENR cases=63 mean=0.36 std dev=0.25
 3 FDOT cases=63 mean=2.57 std dev=1.29
 4 Gates cases=71 mean=1.89 std dev=0.72
5 Energy cases=72 mean=0.84 std dev=0.30
6 CAPWAP cases=79 mean=1.26 std dev.=0.44
 7 PDA cases=42 mean=1.04 std dev=0.32
 8 Japanese Energy cases=52 mean=1.46 std dev=0.78
It was then decided to study the old methods under three circumstances, first, for piles
with Davisson capacity less than 1779 kN, second, for pile with capacity larger than 1779
kN, and finally for the all cases.
Based solely on the statistical analysis and the lognormal probability distribution,
the assessment of the eight dynamic methods to determine pile capacity could not be
successfully completed (i.e. no criterion). The LRFD resistance factor was then
recommended to assess the performance of each method. In the next section, a
description of the LRFD results is presented.
LRFD Analysis of Results
In order to obtain the resistance factor, 0, two approaches were considered. The
first approach consists of fitting ASD to LRFD, by use of Equation 59. For this
approach, the 0 factor depends on the safety factor (ASD) and the ratio of dead load to
live load for a given bridge. The second approach used was Reliability Calibration (See
Chapter 5) in which the 0 factor was determined based on the covariance of the measured
to predicted (k, bias), the reliability index, 3, and the ratio of dead load to live load.
In order to perform the LRFD analysis, the statistical result calculated earlier
became extremely useful. For example, the bias factor (kR) and standard deviation (oR)
of the bias were used in addition to the covariance of the resistance (COVR). These
parameters were employed with AASHTO's load statistics (see Chapter 5) and the failure
probabilities also recommended by AASHTO to obtain the resistance factor, 4.
Additional attention was paid to the target reliability index, 3T. For this study, the
reliability index was calculated using the Withiam method instead of the Rosenblueth and
Esteva method which is the method recommended by AASHTO in their procedure (See
Chapter 5). The values recommended in the Withiam method yield an exact reliability
index, while the values obtained using the Rosenblueth and Esteva result in an
approximate quantity. Thus, the probability of failure, pf, was back calculated from the
AASHTO recommended reliability indexes.
Table 61 all through Table 66 show typical output results for each LRFD
analysis performed. Tables 61 to 63 present the results for PDA at EOD, while tables 6
4 to 66 present the commensurate for PDA at BOR.
Tables 61 and 64 summarize the resistance factors, ), evaluated for four
different failure probabilities (i.e. reliability indexes) and eight bridge span lengths based
on LRFD calibration of the method. Tables 62 and 65 show the equivalent ASD safety
factors based on the resistance factors calculated using the LRFD calibration method for
the same bridge span lengths and failure probabilities. Finally, Tables 63 and 66 present
the resistance factor, reliability index and probability of failure that correspond to the
actual safety factor that have been used in current ASD procedures. Appendices A
throughout H present in detail the LRFD analysis results for each dynamic method
studied.
Effect of Bridge Span Length and Probability of Failure
The bridge span lengths evaluated in this study range from 9.0 to 60.0 meters,
each length corresponding to a recommended (AASHTO) dead to live load ratio. After
observing the results for the PDA, EOD and/or BOR it is evident that the bridge span
length has negligible effect on the resistance factor, ), or the corresponding safety factor.
Table 61. ( Values Evaluated for PDA (EOD)
Span length Failure Probability pf / Reliability Index PT
(m) QD/QL 2.50E02 6.22E03 1.22E03 1.79E04
1.96 2.5 3.03 3.57
9 0.52 0.856 0.694 0.565 0.458
15 1.00 0.821 0.666 0.542 0.439
18 1.06 0.818 0.663 0.540 0.437
27 1.58 0.796 0.645 0.525 0.426
36 2.12 0.781 0.633 0.515 0.418
45 2.64 0.770 0.625 0.508 0.412
50 3.00 0.765 0.620 0.505 0.409
60 3.53 0.758 0.615 0.500 0.405
Table 62. ASD Design Safety Factor Values Evaluated for PDA (EOD)
Span length Failure Probability pf / Reliability Index pT
(m) QD/QL 2.50E02 6.22E03 1.22E03 1.79E04
1.96 2.5 3.03 3.57
9 0.52 1.845 2.276 2.796 3.449
15 1.00 1.827 2.253 2.769 3.415
18 1.06 1.825 2.251 2.766 3.412
27 1.58 1.814 2.237 2.749 3.391
36 2.12 1.806 2.228 2.738 3.377
45 2.64 1.801 2.221 2.730 3.367
50 3.00 1.798 2.218 2.725 3.362
60 3.53 1.795 2.214 2.720 3.356
Table 63. 0 Factors for Safety Factor
2.50 PDA (EOD)
Span length
(m) QD/QL PT Pf
9 0.52 0.632 2.742 0.0035
15 1.00 0.600 2.767 0.0031
18 1.06 0.597 2.770 0.0031
27 1.58 0.578 2.786 0.0029
36 2.12 0.564 2.797 0.0028
45 2.64 0.555 2.804 0.0027
50 3.00 0.550 2.808 0.0026
60 3.53 0.544 2.813 0.0026
Table 64. ( Values Evaluated for PDA (BOR)
Span length Failure Probability pr / Reliability Index PT
(m) QD/QL 2.50E02 6.22E03 1.22E03 1.79E04
1.96 2.50 3.03 3.57
9 0.52 0.682 0.557 0.457 0.373
15 1.00 0.654 0.534 0.438 0.358
18 1.06 0.652 0.532 0.436 0.356
27 1.58 0.634 0.518 0.425 0.347
36 2.12 0.622 0.508 0.417 0.340
45 2.64 0.614 0.501 0.411 0.336
50 3.00 0.609 0.498 0.408 0.333
60 3.53 0.604 0.493 0.404 0.330
Table 65. ASD Design Safety Factor Values Evaluated for PDA (BOR)
Span length Failure Probability pf / Reliability Index pT
(m) QD/QL 2.50E02 6.22E03 1.22E03 1.79E04
1.96 2.50 3.03 3.57
9 0.52 2.316 2.835 3.458 4.234
15 1.00 2.293 2.807 3.424 4.192
18 1.06 2.291 2.805 3.421 4.188
27 1.58 2.277 2.787 3.400 4.163
36 2.12 2.267 2.776 3.386 4.145
45 2.64 2.260 2.768 3.376 4.133
50 3.00 2.257 2.763 3.370 4.127
60 3.53 2.253 2.758 3.364 4.119
Table 66. ( Factors for Safety Factor
2.50 PDA (BOR)
Span length
(m) QD/QL 0 Pf
9 0.52 0.632 2.164 0.0418
15 1.00 0.600 2.191 0.0373
18 1.06 0.597 2.193 0.0369
27 1.58 0.578 2.210 0.0344
36 2.12 0.564 2.221 0.0328
45 2.64 0.555 2.229 0.0317
50 3.00 0.550 2.233 0.0311
60 3.53 0.544 2.238 0.0304
At a target reliability index of 2.5 for both EOD and BOR, the 0 factor decreases only
6.8% and the safety factor decreases only 1.6% when the span length increased from 15.0
meters to 50.0 meters. The latter phenomenon was observed throughout all the methods
evaluated. Thus, for practical purposes the rest of LRFD analysis results are summarized
for a 27 meters bridge span length.
In terms of the probability of failure, pf, the increase in probability of failure was
directly related to a decrease in reliability index, 3, and a diminishment in the resistance
factor, 4. This effect could be easily understood, because lowering the probability of
failure for a given structure should be accompanied by a reduction of the resistance factor,
which means, penalizing the structure resistance and producing a more conservative
design. Different to the effect of the bridge span length, the reliability index has a big
influence in the resistance factor 4, and the equivalent safety factor. The relation of
0 factor and reliability index, 3, is inversely proportional and linear. For piles AASHTO
recommends a reliability index, 3, of 2.0 to 2.5.
Level of Conservatism and Accuracy Indicators
Similar analyses as those presented in Tables 61 to 66 were performed for each
of the eight dynamic methods, as well as breaking the old methods in terms of Davisson
capacity less than 1779 kN and larger than 1779 kN. A summary of the results is
presented in Tables 67 and 68 for EOD and BOR respectively.
The results show that the higher the bias factor 4R, for a given method the higher
the resulting resistance factor will be. For example, for CAPWAP at BOR the mean is
equal to 1.260 and 0 is equal to 0.58 (for 3 = 2.50) while FDOT method shows a mean
Table 67. Load and Resistance Factor Design (LRFD) of Driven Piles Using Dynamic Methods at EOD
Prediction Method Number Mean, XR Standard COVR Pf=0.62% (pT=2.50) Pf=2.50% (PT=1.96)
of cases (Dav/Pred) Deviation FS /X1R 0 FS /XR1
CAPWAP 44 1.597 0.559 0.350 0.733 1.970 0.459 0.912 1.584 0.571
PDA 48 1.344 0.443 0.329 0.645 2.237 0.480 0.796 1.814 0.592
Paikowsky Energy 27 1.110 0.372 0.335 0.527 2.740 0.475 0.651 2.216 0.587
Sakai et al Energy 21 1.504 1.256 0.835 0.231 6.254 0.153 0.348 4.150 0.231
FDOT (overall) 72 2.381 1.341 0.563 0.669 2.160 0.281 0.909 1.588 0.382
FDOT (<1779 kN) 34 1.490 0.782 0.525 0.457 3.161 0.307 0.611 2.362 0.410
FDOT (>1779 kN) 38 3.158 1.248 0.395 1.307 1.104 0.414 1.658 0.871 0.525
ENR (overall) 77 0.299 0.159 0.532 0.090 16.024 0.301 0.121 11.935 0.405
ENR (<1779 kN) 34 0.250 0.129 0.515 0.078 18.395 0.314 0.105 13.801 0.419
ENR (>1779 kN) 43 0.338 0.171 0.507 0.108 13.388 0.319 0.143 10.074 0.424
Modified ENR (overall) 61 0.446 0.267 0.599 0.115 12.533 0.258 0.159 9.086 0.357
Modified ENR (<1779 kN) 25 0.325 0.222 0.683 0.069 20.818 0.214 0.099 14.604 0.305
Modified ENR (>1779 kN) 36 0.530 0.321 0.606 0.135 10.720 0.254 0.186 7.749 0.352
Gates (overall) 74 1.742 0.787 0.452 0.633 2.280 0.363 0.822 1.756 0.472
Gates (<1779 kN) 32 1.071 0.351 0.328 0.515 2.802 0.481 0.635 2.272 0.593
Gates (>1779 kN) 42 2.254 0.717 0.318 1.109 1.302 0.492 1.361 1.061 0.604
Table 68. Load Resistance Factor Design (LRFD) of Driven Piles Using Dynamic Methods at BOR
Prediction Method Number Mean, XR Standard COVR Pf=0.62% (pT=2.50) Pf=2.50% (PT=1.96)
of cases (Dav/Pred) Deviation FS 3/XR 0 FS /XR1
CAPWAP 79 1.260 0.438 0.347 0.581 2.485 0.461 0.722 1.999 0.573
PDA 42 1.036 0.322 0.311 0.518 2.787 0.500 0.634 2.277 0.612
Paikowsky Energy 72 0.836 0.301 0.360 0.374 3.857 0.448 0.468 3.086 0.560
Sakai et al Energy 52 1.457 0.784 0.538 0.433 3.334 0.297 0.583 2.477 0.400
FDOT (overall) 63 2.574 1.293 0.502 0.832 1.735 0.323 1.103 1.309 0.429
FDOT (<1779 kN) 8 1.355 0.380 0.280 0.724 1.995 0.534 0.875 1.650 0.646
FDOT (>1779 kN) 55 2.751 1.284 0.467 0.966 1.495 0.351 1.262 1.144 0.459
ENR (overall) 71 0.235 0.160 0.681 0.050 28.597 0.215 0.072 20.080 0.306
ENR (<1779 kN) 9 0.186 0.057 0.306 0.094 15.348 0.505 0.115 12.562 0.617
ENR (>1779 kN) 62 0.242 0.169 0.698 0.050 28.841 0.207 0.072 20.120 0.296
Modified ENR (overall) 63 0.363 0.246 0.676 0.079 18.314 0.217 0.112 12.881 0.308
Modified ENR (<1779 kN) 8 0.277 0.062 0.224 0.166 8.704 0.598 0.196 7.356 0.708
Modified ENR (>1779 kN) 55 0.376 0.260 0.692 0.079 18.321 0.210 0.113 12.810 0.300
Gates (overall) 71 1.886 0.715 0.379 0.810 1.783 0.429 1.020 1.416 0.541
Gates (<1779 kN) 9 1.067 0.201 0.189 0.681 2.121 0.638 0.796 1.815 0.746
Gates (>1779 kN) 62 2.005 0.684 0.341 0.938 1.540 0.468 1.162 1.242 0.580
and resistance factor of 2.574 and 0.97 respectively for the same reliability index. This
effect could be explained in terms of the bias factors meaning. As defined in the
preceding chapters, the bias factor is the ratio of measured to predicted capacity. Then, a
large bias factor means a very conservative method and the result is a higher resistance
factor.
Although the resistance factor is a good qualitative method to determine the
degree of conservatism or unconservatism, it does not indicate the accuracy of the
method. The combination of both, mean and standard deviation through the COVR (i.e.
ratio of standard deviation to the mean or bias) has proved to be a good indicator of the
accuracy of the methods. Under this criterion, the new methods such as PDA,
Paikowsky, and CAPWAP have the best accuracy, while ENR and modified ENR have
the worst accuracy.
)/XR Ratio
The efficiency or performance of the dynamic methods can be evaluated by the
ratio of 0/4R, indicating the percentage of the measured Davisson capacity that can be
utilized for design to reach a predefined structure reliability. It must be remembered that
the average bias factor XR is an average of each pile bias, therefore, 4/XR ratio is an
"approximated" percentage of the measured Davisson capacity. The latter consideration
makes the 4/XR ratio remarkably valuable from an economic point of view. The higher
the O/XR ratio the more cost effective the method is.
Methods comparison
From Table 67 (LRFD Results for Dynamic Methods at EOD) it can be observed
that for the reliability index, 3 = 2.50, the 0//R values for the new methods such as
CAPWAP (0/4R=0.459), PDA (4/kR=0.480), and Paikowsky (4/kR=0.475) are by far the
highest in the table. In the other hand, the lowest 0//R are represented by the old driving
formulas, given by FDOT (4/kR=0.281), ENR (0/4R=0.301), Modified ENR
(0/,R=0.258), and the Sakai et al. (4/RR=0.153) method. The same trend is observed for a
reliability index of 1.96.
In Table 68 (LRFD Results for Dynamic Methods at BOR) the prior observations
are valid, in terms of the trend that was observed for the EOD results. Only one
exception was observed in relation to the Gates method whose 4/XR ratio was equal to
0.541 and compares favorable with the new driving methods.
EOD versus BOR
In general, the 0/R ratio tends to be a little higher at BOR. This effect is easily
explained by the value of 4R, which at BOR decreases due to an increase in capacity
prediction from the dynamic methods. This effect can be attributed to pile freezing on the
pile or dissipation of pore water pressure that are created during the driving of the pile.
Evaluation of cases with capacity smaller or larger than 1779 kN
After separating the cases with capacity larger than 1779 kN from the cases with
capacity smaller than 1779 kN for the old methods, all the statistical and LRFD analysis
was performed for each driving equation method. The results are summarized in Tables
67 and 68. For Gates and FDOT methods, the bias for cases with capacity smaller than
1779 kN tended to be close to unity in comparison to the overall bias which tended to be
a higher value. This results agree with the observations on the measured versus predicted
capacity plots. For ENR and Modified ENR a decrease in bias was observed, but because
these two methods are very unconservative, the bias for cases with capacity smaller than
1779 kN tends to be even more unconservative.
In terms of 4/0R, as a general observation, the piles with capacity larger than 1779
kN have larger values than the overall cases, and the piles with capacity smaller than
1779 kN have smaller values than the overall cases. Therefore, the equivalent ASD
factor of safety decreases for cases with capacity larger than 1779 kN. An example of
this pattern is shown with the Modified ENR at EOD (3 = 1.96), which safety factors
decrease from 14.6 for pile with capacity smaller than 1779 kN to 7.75 for piles with
capacity larger than 1779 kN. For a reliability index, 3, equals 2.5 the decrease in safety
factor is also by a half.
Recommended Safety Factors
The factor of Safety shown on Tables 67 and 68 were calculated using Equation
59. This procedure makes the FS depend only on the resistance factor, 4, and the bridge
span length. The values of FS obtained for EOD and BOR are summarized on Table 69,
together with the recommended FS. All values were calculated using a 27 meters bridge
span length. The recommended FS are the average of the FS found for probabilities of
failure of 0.62 % and 2.50 % respectively.
From Table 69 it can be observed that ENR and Modified ENR methods use
higher safety factor than the actual recommended safety factor (FS=6.0). Factor of Safety
are as high as 28.60 for a probability of failure of 0.62 percentage for ENR at BOR. This
results show that ENR and Modified ENR are very unconservative method (i.e.
overestimate the pile capacity).
Table 69. Recommended Safety Factors for Dynamic Methods
FS at FS at FS at FS at Recommended FS
Prediction Method pf=0.62% pf=2.50% pf=0.62% pf=2.50%
BOR BOR EOD EOD EOD BOR
CAPWAP 2.48 2.00 1.97 1.58 1.80 2.25
PDA 2.79 2.28 2.24 1.81 2.00 2.50
Paikowsky Energy 3.86 3.09 2.74 2.22 2.50 3.50
FDOT (overall) 1.74 1.31 2.16 1.59 1.90 1.50
FDOT (<1779 kN) 2.00 1.65 3.16 2.36 2.75 1.80
FDOT (>1779 kN) 1.49 1.14 1.10 0.87 1.00 1.30
ENR (overall) 28.60 20.08 16.02 11.93 14.00 24.00
ENR (<1779 kN) 15.35 12.56 18.40 13.80 16.00 14.00
ENR (>1779 kN) 28.84 20.12 13.39 10.07 12.00 24.00
Modified ENR (overall) 18.31 12.88 12.53 9.09 11.00 16.50
Modified ENR (<1779 kN) 8.70 7.36 20.82 14.60 17.70 8.00
Modified ENR (>1779 kN) 18.32 12.81 10.72 7.75 9.20 16.50
Gates (overall) 1.78 1.42 2.28 1.76 2.00 1.60
Gates (<1779 kN) 2.12 1.81 2.80 2.27 2.50 2.00
Gates (>1779 kN) 1.54 1.24 1.30 1.06 1.20 1.40
The FDOT method recommends a safety factor equals 1, but according to the database, a
higher safety factor must be used during design. It is recommended a FS of 1.50 for BOR
and 1.90 for EOD. Other methods such as CAPWAP, PDA, and Gates should use a
lower FS.
For the Paikowsky's Energy method, it is recommended to modify only the safety
factor at BOR from 2.50 to 3.50, while at EOD the actual safety factor of 2.50 is
appropriated.
Table 610. Summary of Results for Fitting the ASD to the LRFD
Prediction Method ASD LRFD Equiv. ASD Design (EOD) ASD Design (BOR)
FS 4/XR p Pf (%) 4/XR p Pf (%)
CAPWAP 2.5 0.578 0.362 3.089 0.100 0.458 2.515 0.596
PDA 2.5 0.578 0.430 2.786 0.267 0.557 2.210 1.357
Paikowsky Energy 2.5 0.578 0.520 2.267 1.171 0.691 1.449 7.374
Sakai et al Energy 2.5 0.578 0.384 1.293 9.810 0.396 1.976 2.411
FDOT (overall) 1.0 1.444 0.606 1.146 12.600 0.561 1.445 7.430
FDOT (<1779 kN) 1.0 1.444 0.969 0.369 35.630 1.065 0.536 29.620
FDOT (>1779 kN) 1.0 1.444 0.457 2.274 1.150 0.525 1.688 4.575
ENR (overall) 6.0 0.241 0.805 0.700 24.210 1.024 0.115 45.440
ENR (<1779 kN) 6.0 0.241 0.963 0.395 34.660 1.293 0.032 51.300
ENR (>1779 kN) 6.0 0.241 0.713 0.976 16.470 0.994 0.146 44.220
Modified ENR (overall) 6.0 0.241 0.540 1.263 10.340 0.662 0.788 21.550
Modified ENR (<1779 kN) 6.0 0.241 0.741 0.605 27.280 0.868 1.306 9.586
Modified ENR (>1779 kN) 6.0 0.241 0.454 1.534 6.258 0.640 0.815 20.770
Gates (overall) 3.0 0.481 0.276 3.067 0.108 0.255 3.718 0.010
Gates (<1779 kN) 3.0 0.481 0.450 2.676 0.363 0.451 3.703 0.010
Gates (>1779 kN) 3.0 0.481 0.214 4.694 0.0001 0.240 4.177 0.0015
ASD Design Evaluation
Because Equation 59 relates LRFD to ASD in terms only of the bridge span
length, and load factors, all methods that use the same safety factor will have the same
load resistance factor, 0. These are not the same findings obtained for the reliability
index, 3, which depends on the COVR and 4R. Table 610 presents the LRFD equivalent
load resistance factor, 0, the 0/R ratio, reliability index, 3, and the corresponding
probability of failure, pf (percent) for the actual ASD procedure.
Using as a reference value the AASHTO's recommended probability of failure for
single piles (i.e. 0.62 % for 3 = 2.50 and 2.50% for 3 = 1.96), a comparison of the
probability of failures for each method could be performed. First, the ENR and Modified
ENR procedures show extremely high probability of failures, which reflect the level of
unconservatism as discussed in preceding sections. On the other hand, Gates method
shows a probability of failure as low as 0.010 percent, typical of a very conservative
method. Other methods such as CAPWAP, PDA, and Sakai show relative good
agreement to the recommended probability of failure from AASHTO.
CHAPTER 7
SKIN AND TIP STATIC CAPACITY ASSESSMENT OF DRIVEN PILES
As discussed in the previous chapter, the PDA Case method was found to be as
accurate as the other dynamic methods such as Paikowsky and CAPWAP procedures.
This trend was observed for driven piles at both, EOD and BOR.
The PDA Case method results depend on the estimated damping coefficient, J,.
The recommended values for Jo vary according to the soil type near the tip of the pile. On
the other hand, CAPWAP selects the Coefficient of Damping and the pile resistance in
such a way that the force trace can be reproduced from the velocity trace. The latter
permit CAPWAP to estimate the skin resistance distribution and the tip resistance for any
given pile. The estimate of the skin and tip capacity in addition to the distribution of
damping and skin friction along the pile from CAPWAP have resulted in its use (scour
areas, etc.) versus the PDA, in which only the total static capacity is obtained. However,
CAPWAP is a multivariable program that requires iterations (i.e. time consuming) and a
significant level of expertise by the technician who use it.
In the next sections, two methods to determine the skin and the tip static capacity
from the PDA traces are presented. The results will be compared to the Davisson's
capacity determined by the static load test.
Method 1
In this method, the GRL procedure to determine the total dynamic skin capacity is
used as starting point. The GRL procedure (Likins et. al., 1988) makes use of the pile top
measurements of force and velocity histories during a hammer blow as recorded by the
PDA. Figure 71 illustrates this procedure.
? I r:C
Force
Velocity
Time (s)
Figure 71. GRL procedure to determine the total skin capacity of a driven pile.
To obtain the total dynamic skin friction, the rise time must be determined. The
rise time is defined as the time between initial rise and the peak. This rise time is used to
determine point "b" which is one rise time earlier than time "a".
At time "a", the separation between force and velocity (Fa Z*Va) represents the
total pile skin friction above that point on the pile. The point "a" was moved back one
rise time from 2 L/c to exclude any reflections from the pile tip of the initial input wave.
The assumption of this method is that the skin friction of the bottom one rise length is the
same as the one additional rise time length above. Based on that assumption, the skin
resistance is the separation of force and velocity at point "a" added to the increase in
resistance from point "b" to point "a" as stated below.
SFT = (F ZV)+ [(FZV (Fb ZVb )] (71)
Once the estimate of dynamic skin friction is determined using the GRL
procedure, as described above, the static tip and skin capacity were calculated according
to the following methodology (Method 1). First, the total dynamic capacity, RTL, is
determined using the Case solution for dynamic capacity (Equation 314 for Jc equals 0).
Then, knowing the total dynamic capacity and the GRL estimate of skin dynamic
capacity, the dynamic tip capacity, TT, could be computed.
TT = RTL SFT (72)
where TT Dynamic Tip Capacity
RTL Total Dynamic Capacity
SFT GRL Estimate of Dynamic Skin Capacity
Then, the total tip to skin capacity ratio, T/S, may be determined
TT
T/S TT (73)
SFT
The static skin and tip resistance can be calculated assuming the tip to skin ratio
for the dynamic capacity equals to the tip to skin ratio for the static capacity. It is then
necessary to define the total static capacity in order to calculate the skin and tip static
capacity. For this purpose, the PDA Rmax obtained from the driving records was used.
Method 2 (Suggested)
Description and Main Assumptions
For this method, the tip/skin ratio is obtained directly from the force and velocity
traces of the PDA. Figure 72 presents an example of a PDA force and velocity traces.
This method differs from method 1 in the procedure to obtain the tip to skin ratio. Instead
of determining the dynamic skin resistance (GRL procedure) by extrapolating the skin
resistance from the rise time before the tip reflection, the method considers the skin
capacity prior the tip reflection and the tip reflection itself.
For driven piles, when the hammer suddenly hits the pile, a compression wave is
produced. This compression wave travels at a constant speed through the pile, reaches
the tip, and, depending on the resistance of the pile tip, reflects back as a tension or a
compression wave. Before the compression wave reaches the pile tip, a series of
compression waves are reflected back to the top due to the skin resistance of the pile. By
measuring the Force and Velocity (and velocity multiplied by impedance) at the pile top,
the skin resistance can be calculated as the force minus the velocity (twice the wave up).
This principle only applies before any reflection from the tip arrives.
73
6000
2L/c
5000
4000
Force
Velocity
3000 P V
( 2000
L.
1000
0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04, 0.045 0. 5
1000
2000
Time (s)
Figure 72. Typical Force, Velocity and Double Wave up Traces from PDA.
In order to determine the time at which the pile tip reflection arrives to the pile
top, the rise time must be considered. The rise time accounts for how fast the tip
reflection is developed and it will depend on how fast the hammer transmits the energy to
the pile top. The larger the rise time, the more difficult to have an estimate of the skin
capacity of the pile. Knowing the rise time allows us to determine the skin resistance at a
distance "x" from the top of the pile as
RT
x = L (74)
2c
where
Length of Pile Below Gages
Wave Speed
Rise Time
Under this consideration all the skin capacity near the tip of the pile (length equals
RT/2c) can not be calculated. Figure 73 shows the plot of force minus velocity for the
same PDA signal presented in Figure 72 (i.e. double wave up). After that point in time
(point "b") the reflection from the tip begins to arrive.
2500
b
2000
1500 
500 
NRT
0
2 Uc
500
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
Time (s)
Figure 73. Procedure to Determine Tip to Skin Ratio for the Suggested Method
0.05
From point "b" to a time equals 2L/c from the force peak (point "c"), both skin
and tip reflections interact creating an abrupt change in the force up trace. The decrease
in the force up trace shown in Figure 73 corresponds to the increase in velocity and
decrease in the force at time 2L/c (see Figure 72). This condition is attributed to piles
with small tip capacity, and piles that, although they possess large tip capacity, the energy
imparted by the hammer is too large to mobilize the tip capacity.
The proposed method makes use of the two concepts mentioned to determine the
tip to skin ratio. The basic assumption of this method is that the tip/skin ratio is equal to
the decrease in the wave up trace from point "b" (time 2L/c minus rise time) to point "c"
(time 2L/c from maximum force) divided by the net increase in the wave up trace from
point "a" to point "b". The mathematical expression for the proposed method is
Tip (F,ZVJ(F z)]
(75)
m [(Fb )(F Z )] (75)
The use of wave up at point "a" is to account for any error in the instrumentation
readings. Because a decrease in the wave up is needed to obtain a tip to skin ratio, the
hammer must be able to mobilize the whole pile capacity.
Case Damping Coefficient, Jc, versus Tip to Skin Ratio
In the process of finding a method to obtain the Case damping coefficient, Jc,
directly from the PDA signal, the relation between the tip to skin ratio and the Jc value
was studied. To do the latter, the measured Davisson's capacity was substituted as RSP
in Equation 314, and the Jc coefficient was then determined. Subsequently, this damping
value was plotted versus the suggested tip to skin ratio. The results are presented in
Figure 74.
Two observations can be made from Figure 74. First, for tip to skin ratios
smaller than 1.0, the Jc is on the order of 0.4 to 0.6, and there is a tendency for Jc to
decrease as the tip to skin ratio is increased. Second, the values of Case damping are
scattered. It is believed that there are two reasons for the latter: 1) the hammer may or
may not impart enough energy to mobilize the static pile capacity; and 2) PDA capacity
predictions assumes pile damping occurs at pile toe which may not always be true.
However, as part of this study a sensitivity analysis was performed on the influence of Jc
on the static pile capacity (see next section). An important finding of this study is that a
30% variation in Jc results in only a 10 % variation in static pile capacity.
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0 2.0 4.0 6.0 8.0 10.0
Suggested Tip / Skin Ratio
Figure 74. Suggested Tip to Skin Ratio versus Case Damping Coefficient
Suggested Regression Curve
Jc = 0.09744 In (Tip/Skin) + 0.2686
*
* *
Figure 74 shows the regression curve for the Jc. This curve is significant,
because it allows us to obtain a Case damping coefficient, Jc, directly from the PDA
traces, without taking into consideration the soil type in which the pile is embedded. The
suggested equation to correlate tip to skin ratio to Jc is
J =0.097441n Ti +0.2686 (76)
Because the latter equation was obtained from a comparison with the Davisson's
capacity at BOR, it is only recommended for estimating the pile capacity from dynamic
tests performed at BOR.
Sensitivity Analysis of Case Damping Coefficient, Jc
In order to measure how sensitive the Case method resistance (RSP) solution is to
the variation of Jo, the coefficient of variance was used. The following steps were
followed to obtain a relation between the coefficient of variance for the resistance and the
coefficient of variance for J,. Using the Case method solution for the pile resistance, R,
the average (bars for average) resistance based on the average value of J.is given as
R= 1 [JXF, + ZV)+ (+ (JXF2 ZV2)] (77)
2
If the standard deviation of the resistance is defined in terms of the standard
deviation of the Case damping, we obtain
oR = J [ (F + ZV)+(F Z )] (78)
2 r
Then the covariance of the resistance can be written as follow:
COV _R a J[(F +ZVI)+(F2ZV2)] (79)
R 1([J, F,+ZVI)+ +JX F2 ZV2,)
If we define the constant r in terms of the force and velocity at time T1 and time
T2 (T1 plus 2L/c), then
(F1 ZVI )
(2Z2) (710)
S(F,+Zv)
Next divide the numerator and denominator of Equation 710 by the average J,
and making the appropriate substitutions for r1 we obtain
COV =COVR 1+ 1+ (711)
1 2 11
Equation 711 allows us to determine the variance in the Jo for a given percent of
variance in the resistance, or viceversa.
Static and Dynamic Load Test Data
The criteria for selecting a load test pile for this study includes the Davisson's failure load
from a static load test, and the PDA force and velocity traces. For the dynamic load test,
the selected blow was chosen as close to the static load test date as possible (i.e. neglect
freeze). For all the cases, the dynamic load test closer to the static load test was
performed after the load test (i.e. the static capacity was compared to the Beginning of
Restrike). Other requirements include having a measured skin capacity by mean of a pull
out static load test or Osterberg load cell test. For each pile, it was required to know both
geometric and driving parameters, such as, wave speed, pile length below the gages,
crosssectional area, and material modulus. Based on the latter requirements, 18 test pile
were considered. Table 71 summarizes general information of each load test pile. The
pile population represents 9 sites and 3 diameters, while the range of depths of the piles
below the gages varies from 9.15 to 34.45 meters. Only one test pile is from a location
outside the State of Florida.
Automating the Suggested Method
A Fortran program was developed in order to simplify the calculation process.
This program is able to read directly from the PDA record the force and velocity signal
and perform the data reduction. The input parameters for this program are the length of
the pile below the gages, the wave speed, the material modulus, the crosssectional area,
and the datasampling interval.
The output file contains a general description of the pile itself and the driving
information entered previously. In addition, it presents in a tabular form the time
increment, velocity, force, velocity times impedance, displacement, and double wave up
(P ZV). The latter information can be easily plotted to obtain the PDA traces.
Appendix I contains the PDA traces (force, velocity, double force up, and displacement)
for the signals studied. At the end of the output file, the results from the suggested
Table 71. Geometric and Driving Information of Load Test Piles
File Site Pile Shaft Shaft Wave Material CrossSec. Data Sampling
Name Location Location Length Diameter Speed Modulus Area Increment
(m) (m) (m/s) (kN/m2) (m2) (s)
Pascagoula, Mississippi
Vilano Bridge
Escambria Bridge
Buckman Bridge
Buckman Bridge
Buckman Bridge
Buckman Bridge
Acosta Bridge
Acosta Bridge
Acosta Bridge
Vilano West Bridge
Vilano East Bridge
Buckman Bridge
Seebreze Bridge
Aucilla Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Test Site 4
Test Site 1
Bent 5 / Pile 27
Test Site 13
Test Site 19
Test Site 24
Test Site 29
Pier F6 / Pile 44
Pier G13 / Pile 95
Pier H2 / Pile 26
STA. 142+74
STA. 183+47
STA. 362+90
STA. 353+15
STA. 494+47
Pier FSB3 / Pile 2
Pier 5 / Pile x
Pier 11 / Pile 38
Pier 23 / Pile 13
Pier 29 / Pile 7
Pier 35 / Pile 7
Pier 41 / Pile x
FSB 26 / Pile 3
34.45
29.88
26.83
33.84
32.74
30.98
29.27
19.21
17.68
10.64
19.05
10.98
9.15
25.91
20.43
24.36
18.63
29.76
29.27
29.00
27.16
24.09
19.82
0.61
0.61
0.61
0.76
0.76
0.76
0.76
0.61
0.61
0.61
0.46
0.46
0.46
0.46
0.46
0.61
0.76
0.76
0.76
0.76
0.76
0.76
0.61
4325.0
3929.9
4425.0
3935.7
3993.9
3937.1
3984.2
3872.0
4325.0
4116.2
4186.6
3730.2
3900.6
3926.6
3993.8
4172.7
4329.3
4643.0
4520.8
4208.8
4292.1
4412.0
4283.2
44905380
37684870
47005420
37184330
38292260
37211220
39470520
35989530
39470519
40656360
42075920
33402750
36523850
37011970
38291580
41796700
43612000
51750160
49062030
42524060
44224220
46728270
44041520
0.37
0.37
0.37
0.48
0.48
0.48
0.48
0.37
0.37
0.37
0.21
0.21
0.21
0.21
0.21
0.37
0.42
0.42
0.42
0.42
0.42
0.42
0.37
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0002
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
TS41
TS1B102
B5RS2
TS13A1A
TS19FRCB
TS24ALTA
TS29RC
F658A
G1337
H227B
VLWA61 D
VLE32C
BKM30J
BZ83N
AUC63K
B176F
PR5R2
B897R2
B1489R2
B1794R2
PR35FIN
B2376F2
B2763F
method and the GRL procedure are presented. In addition, the important time records
such as the time of maximum force, T1, and time T2 (T1 + 2L/c), rise time, etc, are also
presented. Appendix J presents an example of the Fortran output. Only the first five
pages and the last page of the output are included.
Results and Analysis
In the following sections, the results from the suggested method will be presented
in addition to the results of other methodologies such as method 1, PDA, and the
CAPWAP procedure. The reader is referred to Appendix I for the plots of force, velocity,
double wave up, and displacement traces for each case studied. In order to evaluate the
accuracy of the methods studied, a series of comparison of total static capacity have been
performed in relation to the static load capacity. In addition, the predicted skin capacity
of the piles was evaluated for piles with performed pullout tests or Osterberg tests in
which skin failure occurred.
Presentation of Results
Table 72 summarizes the results for the suggested method and the load tests. The
tip to skin ratio is presented together with the recommended Case damping coefficient, J,.
Based on these two parameters and using the PDA Case solution, the total capacity was
computed.
The load test results include the Davisson's capacity for all compression tests and
the skin capacity for piles with a performed tensile load test or an Osterberg test with skin
failure. Table 73 presents the estimated capacities using Method 1 and CAPWAP.
Table 72. Suggested Method Results and Static Load Test Results
File Suggested Method Static Capacities Load Test Results (kN)
Name Location Tip/Skin Jc Total Skin Tip Type of Davisson
Ratio (kN) (kN) (kN) Test Total Skin Tip
Pascagoula, Mississippi
Vilano Bridge
Escambria Bridge
Buckman Bridge
Buckman Bridge
Buckman Bridge
Buckman Bridge
Acosta Bridge
Acosta Bridge
Acosta Bridge
Vilano West Bridge
Vilano East Bridge
Buckman Bridge
Seebreze Bridge
Aucilla Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
Choctawhatche Bridge
0.33
0.29
0.24
0.27
0.19
0.34
0.16
0.32
0.26
0.10
0.12
0.26
0.05
0.27
0.15
0.29
0.10
0.38
0.24
0.45
0.35
0.14
0.25
5069.7
4140.9
3256.3
5456.4
5279.6
6599.9
4797.8
4096.2
3990.6
3530.5
1403.8
2722.7
1561.5
3244.8
2419.9
3349.8
3722.9
6618.2
4734.1
3196.9
5013.0
4355.2
3547.6
3261.9
2270.8
1389.9
2772.2
1671.2
4455.8
1207.0
2589.1
1948.9
543.1
246.5
1325.2
153.4
1629.5
558.4
1822.7
570.2
4986.3
1997.2
2752.9
3440.3
942.9
1633.8
1807.8
1870.1
1866.4
2684.2
3608.3
2144.1
3590.8
1507.1
2041.7
2987.3
1157.4
1397.5
1408.1
1615.3
1861.4
1527.1
3152.7
1631.9
2736.9
444.0
1572.7
3412.3
1913.8
Osterb.(T&T)
Static (C&T)
Static (C)
Static (C&T)
Static (C&T)
Static (C&T)
Static (C&T)
Static (C)
Static (C)
Static (C)
Osterberg
Osterberg
Osterberg
Osterberg
Osterberg
Static (C)
Static (C)
Static (C)
Static (C)
Static (C)
Static (C)
Static (C)
Static (C)
3282.6
4919.5
3780.8
4092.2
4376.8
4892.8
4519.2
3451.6
4964.0
2570.9
n/a
n/a
n/a
n/a
n/a
2215.1
5444.4
6360.6
2846.7
4074.4
6485.2
6253.9
4270.1
1316.6
2775.6
n/a
1601.3
1396.7
2490.9
1734.7
n/a
n/a
n/a
382.5
1150.3
120.1
1470.5
938.5
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
1966.0
2143.9
n/a
2490.9
2980.2
2401.9
2784.4
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
TS41
TS1B102
B5RS2
TS13A1A
TS19FRCB
TS24ALTA
TS29RC
F658A
G1337
H227B
VLWA61 D
VLE32C
BKM30J
BZ83N
AUC63K
B176F
PR5R2
B897R2
B1489R2
B1794R2
PR35FIN
B2376F2
B2763F
0.57
0.8
1.34
0.97
2.16
0.48
2.98
0.58
1.05
5.50
4.70
1.06
9.18
0.99
3.33
0.84
5.53
0.33
1.37
0.16
0.46
3.62
1.17
Table 73. CAPWAP, and Method 1 Results
File Method 1 CAPWAP Static Results
Name Location Tip/Skin Total (PDA) Skin Tip Tip/Skin Total Skin Tip
Ratio (kN) (kN) (kN) Ratio (kN) (kN) (kN)
TS41 Pascagoula, Mississippi 1.6 4581.4 1785.4 2796.0 2.6 4518.3 1265.9 3252.4
TS1B102 Vilano Bridge 0.1 3433.9 3116.0 317.8 0.3 3915.1 2930.8 984.3
B5RS2 Escambria Bridge 1.1 2526.5 1217.6 1308.9 0.6 2610.1 1623.1 987.0
TS13A1A Buckman Bridge 0.9 4803.8 2468.6 2335.3 1.1 4007.6 1950.0 2057.6
TS19FRCB Buckman Bridge 1.9 5640.1 1947.5 3692.5 2.1 6510.1 2087.9 4422.2
TS24ALTA Buckman Bridge 9.0 6636.4 661.8 5974.6 0.5 6240.5 4123.7 2116.8
TS29RC Buckman Bridge 3.1 5239.7 1276.1 3963.6 3.6 5115.2 1123.6 3991.6
F658A Acosta Bridge 0.3 3771.9 2926.2 845.7 0.1 3474.8 3052.7 422.1
G1337 Acosta Bridge 1.1 5177.5 2457.7 2719.8 1.2 4826.1 2224.0 2602.1
H227B Acosta Bridge 3.2 3967.6 948.1 3019.6 5.2 4091.3 658.3 3433.0 oo
VLWA61D Vilano West Bridge 1.5 1080.9 430.1 650.8 0.9 916.3 494.6 421.7
VLE32C Vilano East Bridge 0.8 2570.9 1395.0 1176.0 0.9 2691.0 1400.7 1290.4
BKM30J Buckman Bridge 1.5 1961.6 772.6 1189.0 1.2 1939.3 881.6 1057.7
BZ83N Seebreze Bridge 0.2 2628.8 2183.4 445.4 0.3 2361.9 1774.8 587.1
AUC63K Aucilla Bridge 4.6 1757.0 313.4 1443.6 0.7 1823.7 1045.3 778.4
B176F Choctawhatche Bridge 0.0 3220.4 3233.3 12.9 0.2 2231.6 1907.3 324.3
PR5R2 Choctawhatche Bridge 8.7 3255.9 334.7 2921.2 6.0 2596.3 371.0 2225.3
B897R2 Choctawhatche Bridge 1.4 4554.8 1863.6 2691.1 0.2 3621.6 3033.1 588.5
B1489R2 Choctawhatche Bridge 0.5 3131.4 2029.4 1102.0 0.1 1975.4 1802.3 173.0
B1794R2 Choctawhatche Bridge 0.0 3700.7 3780.1 79.4 0.0 3452.5 3288.9 163.7
PR35FIN Choctawhatche Bridge 0.3 4661.5 3650.4 1011.1 0.3 4045.0 3231.9 813.1
B2376F2 Choctawhatche Bridge 7.9 4448.0 645.7 5093.7 3.8 2155.9 453.7 1702.2
B2763F Choctawhatche Bridge 0.8 2673.2 1452.1 1221.2 3.6 2503.3 542.2 1961.1
8000
7000
6000
5000
4000
3000
2000
0 1000 2000 3000 4000 5000 6000 7000 8000
Davisson Capacity (kN)
Figure 75. Davisson Capacity vs. Suggested Method Capacity
0 1000 2000 3000 4000 5000 6000 7000 8000
Davisson Capacity (kN)
Figure 76. Davisson Capacity vs. CAPWAP Capacity
Number of Cases = 18
Mean = 1.00
Std. Dev. = 0.29
COV = 0.29
8000
7000
6000
z
5000
U
0.
S3000
U
4
2000
1000
0
8000
7000
6000
S5000
S 4000
W, 3000
200 Number of Cases = 18
Mean = 1.09
Std. Dev. = 0.35
1000 COV = 0.32
0
0 1000 2000 3000 4000 5000 6000 7000 8000
Davisson Capacity (kN)
Figure 77. Davisson Capacity vs. PDA Rmax Capacity (used in Method 1)
The total dynamic capacity was obtained using the Case solution for time T1 located at
the maximum force entering the pile. Then, the tip and the tip to skin ratio were calculated
using Equations 72 and 73. With this tip to skin ratio and the PDA Rmax the static skin and
tip capacity for the Method 1 were calculated.
A series of figures show the results from the three methods studied, i.e. CAPWAP,
Method 1 (using PDA Rmax), and the suggested method in comparison with the measured
capacity. Figure 75 shows the Davisson's capacity versus the estimated capacity by the
suggested method. The CAPWAP estimated capacity versus the Davisson's capacity is
presented in Figure 76, and the same relation for the PDA estimated capacity is presented in
Figure 77.
Analysis of Total Capacity Predictions
For the total capacity analysis, only 18 cases out of 23 cases were used. The bias factor kR,
the standard deviation, a, and the coefficient of variance, COVR, were calculated
(see bias factor, standard deviation, and coefficient of variance definition on Chapter 5).
Table 74 presents the findings for the three methods studied.
Table 74. Comparison of Mean, Standard Deviation, and COVR.
Method Mean, XR Std. Dev. o COVR
Suggested 1.00 0.29 0.29
Method
CAPWAP 1.28 0.58 0.45
Method 1 1.09 0.35 0.32
It should be noted that although the number of cases studied are only 18, the mean,
standard deviation, and coefficient of variance for CAPWAP and PDA show good agreement
with the database. According to the database, for PDA capacity at BOR the mean, standard
deviation, and COV are 1.04, 0.32 and 0.31 respectively. For CAPWAP at BOR the mean is
1.26, the standard deviation is 0.44, and the COVR is 0.35.
From Table 74, it can be observed that the best method to estimate the Davisson's
capacity is the suggested method with a mean value of 1.0 (it is important to remember that
the suggested method was calibrated to have a mean value of 1.00). The PDA underestimated
the Davisson's capacity by 9 percent, while the CAPWAP procedure underestimated the
Davisson's capacity by 26 percent at BOR.
In Chapter 6, it has been explained how the coefficient of variance could be a useful
tool to measure the accuracy of a dynamic method. Making use of this criterion, the suggested
method (COVR equals 0.29) can be considered the most accurate of the three methods
followed by the PDA (COVR equals 0.32). The CAPWAP procedure was the less accurate of
the three methods (COVR equals 0.45).
Analysis of Skin and Tip Capacity Predictions
The number of cases to evaluate the skin and tip predictions is much smaller than the
number of cases used for total capacity prediction. For the skin prediction, the total number of
cases is 10, while for the tip prediction the number of cases drops to only six. The reason for
this decrease in number of cases is the limited number of tensile test and Osterberg tests.
From the six Osterberg tests, one test failed at the tip and five failed at the skin). The tensile
tests are very helpful to determine the skin capacity. With the skin capacity calculated, and
knowing the total static capacity the tip capacity can be calculated.
Table 75. Statistical Analysis for Skin and Tip Predictions
Method Skin Capacity Prediction (10 Cases) Tip Capacity Prediction (6 Cases)
Mean, XR Std. Dev. o COVR Mean, XR Std. Dev. o COVR
Suggested 1.04 0.40 0.39 0.96 0.16 0.17
Method
CAPWAP 0.80 0.35 0.43 1.08 0.59 0.55
Method 1 1.29 1.15 0.89 1.94 2.47 1.27
5000
4500
4000
C 3500
c 3000
2500
2000
o b Number of Cases= 10
1500 
1500 Mean = 1.04
I* Std. Dev. = 0.40
S1000 COV = 0.39
500
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Davisson Skin Capacity (kN)
Figure 78. Davisson Capacity vs. Suggested Method Capacity (Skin Capacity)
5000
4500
4000
z 3500
' 3000
o 2500
S2000 
(L Number of Cases = 10
1500 Mean = 0.80
0 Std. Dev. = 0.35
0 1000 COV = 0.43
500 
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Davisson Skin Capacity (kN)
Figure 79. Davisson Capacity vs. CAPWAP Capacity (Skin Capacity)
89
5000
4500
4000
3500
3000
., 2500
0 Number of Cases = 10
V Mean = 1.29
1500 Std. Dev. = 1.15
z 1500
SCOV = 0.89
1000
500
0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Davisson Skin Capacity (kN)
Figure 710. Davisson Capacity vs. Method 1 Skin Capacity
6000
 5000
z
S4000
C,
.E
* 3000
"0
2000
20 Number of Cases = 6
SStd. Dev. = 0.16
S1000 COV= 0.17
0
0 1000 2000 3000 4000 5000 6000
Davisson Tip Capacity (kN)
Figure 711. Davisson Capacity vs. Suggested Method (Tip Capacity)
90
6000
5000
. 4000
.5
U
. 3000
CL Number of Cases = 6
2000 Mean = 1.08
2 00 Std. Dev. = 0.59
0 COV= 0.55
1000 *
0
0 1000 2000 3000 4000 5000 6000
Davisson Tip Capacity (kN)
Figure 712. Davisson Capacity vs. CAPWAP Capacity (Tip Capacity)
6000 
5000
z
, 4000
o
a 3000
"o Number of Cases = 6
 2000 Mean = 1.94
Std. Dev. = 2.47
COV = 1.27
1000
0
0 1000 2000 3000 4000 5000 6000
Davisson Tip Capacity (kN)
Figure 713. Davisson Capacity vs. Method 1 Capacity (Tip Capacity)
