A COMPARISON OF DYNAMIC PILE DRIVING FORMULAS WITH THE WAVE EQUATION

by

Lee L. Lowery, Jr.

Assistant Research Engineer

James R. Finley, Jr.

Research Assistant

and

T. J. Hirsch

Research Engineer

Research Report 33-12

Piling Behavior

Research Study No. 2-5-62-33

Sponsored by

The Texas Highway Department

in cooperation with the

U.S. Department of Transportation, Federal Highway Administration Bureau of Public Roads

August 1968

TEXAS TRANSPORTATION INSTITUTE Texas A&M University College Station, Texas

FOREWORD The information contained in this report was developed on research study

2-5-62-33 entitled "Piling Behavior" which is a cooperative research study spon­sored jointly by the Texas Highway Department and the U. S. Department of Trans­portation, Federal Highway Administration, Bureau of Public Roads.

The broad objective of the research described in this report is to establish whether the resistance to penetration predicted by any of the commonly used pile driving formulas agrees with that found by the wave equation, and if so, to deter­mine which piles, driving hammers, and soil resistances provide agreement.

The use of the wave equation to determine the range of accuracy for various pile driving formulas would enable them to be used with far greater confidence than is presently the case.

The opinions, findings, and conclusions expressed in this publication are those of the authors and not necessarily those of the Bureau of Public Roads.

ii

TABLE OF CONTENTS Page

LIST OF FIGURES _________________________________________________________________________________________________________________________________________________________________ _iv

LIST OF TABLES _____________________________________________________________________________________________________________________________________________________________________ _iv

INTRODUCTION _________________________________________________________________________________________________________________________________________________________________________ l

PROBLEMS INVESTIGATED ___________________________________________________________________________________________________________________________________________________ l

PILE DRIVING FORMULAS USED IN THE INVESTIGATION __ --··-·--------------------------------------------------------------------------- 3

CORRELATION PROCEDURE------------------------------------------------------------------------------------------------------------------------------------------------- 5 DISCUSSION OF RESULTS ____________________________________________________ ------------------------------------------------------------------------------------------------- 5 CONCLUSIONS ___________________________________________________________________________________________________________________________________________________________________________ 6

REFERENCES ______________________________________________________________________________________________________________________________________________________________________________ l5

APPENDIX ___________________________________________________________________________________________________________________________________________________________________________________ l6

iii

LIST OF FIGURES ~re &~

l. Pile Driving Assembly of Vulcan No. 1 and Vulcan 80C hammers-Steel Pile __________________________________________________ 1 2. Pile Driving Assembly of Vulcan No. 1 and Vulcan 80C Hammers-Concrete Pile __________________________________________ 2 3. Driving Assembly of the Delmag D-22 Hammer-Steel Pile _________________________________________________________________________________ 2 4. Driving Assembly of the Delmag D-22 Hammer-Concrete Pile __________________________________________________________________________ 3 5. The Engineering News Formula Vs the Wave Equation-Vulcan No. 1 Hammer__ _________________________________________ 6 6. The Engineering News Formula Vs the Wave Equation-Vulcan 80C Hammer ______________________________________________ 7 7. The Engineering News Formula Vs the Wave Equation-Delmag D-22 Hammer__ ____________________________________________ 7 8. The Michigan Engineering News Formula Vs the Wave Equation-Vulcan No. 1 Hammer__ ______________________ 7 9. The Michigan Engineering News Formula Vs the Wave Equation-Vulcan 80C Hammer_ ___________________________ 7

10. The Michigan Engineering News Formula Vs the Wave Equation-Delmag D-22 Hammer _________________________ 8 11. The Eytelwein Formula V s the Wave Equation-Vulcan No. 1 Hammer__ ________________________________________________________ 8 12. The Eytelwein Formula Vs the Wave Equation-Vulcan 80C Hammer__ ___________________________________________________________ 8 13. The Eytelwein Formula Vs the Wave Equation-Delmag D-22 Hammer__ ________________________________________________________ 8 14. The Navy-McKay Formula Vs the Wave Equation-Vulcan No. 1 Hammer__ _________________________________________________ 9 15. The Navy-McKay Formula Vs the Wave Equation-Vulcan 80C Hammer__ ______________________________________________________ 9 16. The Navy-McKay Formula Vs the Wave Equation-Delmag D-22 Hammer _____________________________________________________ 9 17. The Hiley Formula Vs the Wave Equation-Vulcan No. l Hammer _________________________________________________________________ 9 18. The Hiley Formula Vs the Wave Equation-Vulcan 80C Hammer__ __________________________________________________________________ lO

19. The Hiley Formula Vs the Wave Equation-Delmag D-22 Hammer ------------------------------------------------------------10 20. The Terzaghi Formula Vs the Wave Equation:-Vulcan No. 1 Hammer __________________________________________________________ 10

21. The Terzaghi Formula V s the Wave Equation-Vulcan 80C HammeL--------------·--------------------------------------------10 22. The Terzaghi Formula Vs the Wave Equation---'Delmag D-22 Hammer __________________________________________________________ ll 23. The Redtenbacher Formula Vs the Wave Equation-Vulcan No. 1 Hammer ____________________________________________________ ll 24. The Redtenbacher Formula Vs the Wave Equation-Vulcan 80C Hammer _______________________________________________________ ll 25. The Redtenbacher Formula Vs the Wave Equation-Delmag D-22 Hammer__ __________________________________________________ ll 26. The Pacific Coast Formula Vs the Wave Equation-Vulcan No. 1 Hammer__ _________________________________________________ 12

27. The Pacific Coast Formula Vs the Wave Equation-Vulcan 80C Hammer-----------------------"--------------------------------12 28. The Pacific Coast Formula Vs the Wave Equation-Delmag D-22 Hammer__ _____ --------------------------------------------12 29. The Canadian Building Code Formula Vs the Wave Equation-Vulcan No. 1 Hammer__ ______________________________ 12 30. The Canadian Building Code Formula Vs the Wave Equation-Vulcan 80C Hammer__ __________________________________ 13 31. The Canadian Building Code Formula Vs the Wave Equation-Delmag D-22 Hammer _________________________________ 13 32. The Rankine Formula Vs the Wave Equation-Vulcan No. 1 Hammer__ ___________________________________________________________ 13

33. The Rankine Formula Vs the Wave Equation-Vulcan 80C HammeL---------------------------------------·----·-··-----···--·---13 34. The Rankine Formula Vs the Wave Equation-Delmag D-22 Hammer__ ___________________________________________________________ 14 35. The Gates Formula Vs the Wave Equation-Vulcan No. 1 Hammer__ ________________________________________________________________ 14 36. The Gates Formula Vs the Wave Equation-Vulcan 80C Hammer _____________________________________________________________________ 14 37. The Gates Formula Vs the Wave Equation-Delmag D-22 Hammer ________________________________________________________________ 14

Table

l. 2. 3. 4.

LIST OF TABLES Page

Hammer Properties-------------------------------------------------------------------------------------------------·--·------------------------------------------------- 2 Summary of Hammers and Soil Parameters Used in the Study ________________________________________________________________________ 3

Summary of Piles Analyzed·------------------------------------------------------------------------------------------------------------------------------------- 3 Pile Driving Formulas Used in This Investigation. ________________________________________________________________________________________________ 4

Appendix

A.l. Permanent Set of Pile Per Blow Predicted by the Wave Equation-Concrete Piles ______________________________________ 16

A.2. Permanent Set of Pile Per Blow Predicted by the Wave Equation-Steel Piles-------------------·--------·---------------16

iv

Introduction The use of the wave equation to investigate the

dynamic behavior of piling during driving has become more and more popular1• 2 during the past several years. Widespread interest in the method had its beginning in 1960 when E. A. L. Smith3 used a numerical solution to investigate the effects of such factors as ram weight, ram velocity, cushion and pile properties, and the dy­namic behavior of soil during driving. Since then, vast quantities of data have been amassed in experimentation to determine more accurate values for the input varia­bles required,4• 5 • 6• 7 • 8 and a multitude of full-scale pile tests have been correlated with the wave equation.9• 10• 11

These correlation studies have proven that the wave equation is more accurate than other methods and can he used with reasonable confidence. Because of this, the method is becoming widely used and recommended in the literature by foundation experts.1

However, as noted by Chellis,12 a wave equation analysis required the use of a high speed digital com­puter; before an engineer could utilize the method, he had to develop a relatively complex computer program which was both time consuming and expensive. There-

fore, even though the wave equation might be far more accurate, the simplicity of the dynamic pile driving formulas made their use attractive, especially for field use.

For this reason, Chellis and others13 suggested that the wave equation should be used to determine if there might exist ranges of application through which simpli­fied dynamic formulas were reasonably accurate. He suggested that, "if it can be determined that the Hiley or Engineering News Formula results are safe and that ultimate driving resistances are in reasonable agreement with wave equation results in any general range of con­ditions, then such formulas might permissibly be used within such limits. This might enable such simple for­mulas to be quickly applied in the office or field, thus avoiding the necessity of access to a computer in order to be sure of obtaining sufficiently reliable and eco­nomic results."

This report presents the results of such a study, and demonstrates that it is indeed possible to find ranges of agreement between the wave equation and certain pile driving formulas.

Problems Investigated The dynamic behavior of a pile during driving is

extremely complex, and involves a multitude of variables including the type of hammer, driving accessories, type of cushion, dimensions and properties of the pile, as well as the Jilroperties of the supporting soil medium. Since it was obviously impossible to compare the pile driving for­mulas with the wave equation for every possible com­bination of variables, the study was limited to the fol­lowing:

l. Hammers and pile driving assemblies. Three pile driving hammers were studied: the Vulcan No. 1, Vulcan 80C, and Delmag D-22. The hammer properties and operating char&cteristics listed in Table 1 were deter­mined from previous research conducted by the authors and published through the Texas Transportation Insti­tute.14 Typical hammer assemblies for the Vulcan No. 1 and Vulcan 80C, driving steel, and concrete piles, are illustrated in Figures 1 and 2, respectively. The Delmag D-22 was chosen as a typical diesel hammer, and typical driving assemblies used to drive steel and concrete piles are illustrated in Figures 3 and 4, respectively.

2. Pile material. Two. pile materials, steel and concrete, were used in this study. A modulu" of elas­ticity of 30 x 106 psi was assumed for steel, and 5 x 106

psi for concrete. 3. Pile length. To determine the limits of accuracy

of the pile driving formulas for various pile lengths, piles having lengths of 30, 60, 100, and 140 ft. were analyzed.

4. Cross-sectional areas of pile. Three typical cross-sectional areas were used in the study for each type of pile; the steel piles had cross-sectional areas of 10, 20, and 30 sq. in., whereas the concrete piles had cross-sectional areas of 150, 275, and 400 sq. in.

5. Magnitude of soil resistance. To maintain a reasonable number of problems for analysis, only two soil resistances for each pile were analyzed. The first resistance represented moderate driving (a low

VULCAN #I OR SOC HAMMER

CFfr-~-CAI

1

UNIFORM 1 SIDE SOIL 1 RESISTANCE

STEEL PILE

POINT SOl L RESISTANCE

Figure 1. Pile driving assembly of Vulcan No. 1 and Vulcan BOG hammers-steel pile.

PAGE ONE

TABLE 1. HAMMER PROPERTIES

Hammer Ram Anvil Helmet Hammer Rated Actual Cap block Cushion Coeffi-Weight Weight Weight Effi- Energy Energy Stiffness Stiffness Explosive cient of

(lbs) (lbs) (lbs) ciency Output Output Force Resti-(ft lbs) (ft lbs) (kips/in.) (kips/in.) (kips) tution

Vulcan No. 1 5,000 none 1,000 0.75 15,000 11,250 1,080 2,000 0 0.8 Vulcan SOC 8,000 none 1,000 0.85 24,800 21,500 1,080 2,000 0 0.8 Delmag D-22 4,850 1,576 1,200 1.00 39,700 29,100* 23,800 2,000 158.7 0.8

*Actual energy output of diesel hammer was determined by method presented in Ref. 8, E = Wh (efficiency) where W = ram weight and h = actual ram stroke (6ft in this case).

number of blows per foot) for the particular hammer, while the second was intended to simulate relatively hard driving. For the Vulcan No. 1, soil resistances of 50 and 200 kips were used. For the Vulcan SOC and Del­mag D-22 hammers, soil resistances of 100 and 400 kips were used.

6. Soil resistance distribution. For each of the previously mentioned cases, two distributions of soil resistance were studied. These distributions were as follows: (a.) all soil resistance at the point of the pile (no side friction), and (b.) all soil resistance uniform­ly distributed along the side of the pile (no point re, sistance).

7. Other factors. Other factors known to affect the behavior of piling during driving were determined

VULCAN #I OR soc HAMMER

a~z=:;::~~~;::Lz::q::~r~-- CAPBLOCK

r.::::IZ:.::::~c::..?:;~%~/J:J"'•>-. -- CUSHION

UNIFORM SIDE SOIL RESISTANCE

j CONCRETE

1 PILE

1 1~

1

1 1

......

'------.--....1

POINT SOIL RESISTANCE

Figure 2. Pile driving assembly of Vulcan No. 1 and Vulcan SOC hammers-concrete pile.

PAGE TWO

from experimental information published previously by the authors,14 and were held constant. These included such factors as hammer efficiency, cushion stiffness, coefficient of restitution, and others. These factors are listed in Table l.

Scope of the Investigation

Although this study was obviously small with re­spect to the number of variations possible, the results should give some indication as to the relative accuracy of the commonly used pile-driving formulas and demon­strate at least one method by which considerable useful data can be developed by future studies.

DELMAG D-22 DIESEL HAMMER

~ ANVIL ~

~~TI 1 STEEL

PILE

1 UNIFORM SIDE SOIL RESISTANCE 1

POINT SOIL RESISTANCE

CAP BLOCK

Figure 3. Driving assembly of the Delmag D-22 ham­mer-steel pile.

UNIFORM SIDE SOIL RESISTANCE

DEL MAG D- 22 DIESEL HAMMER

1 CONCRETE PILE

1 1~

1

1'---r----1

POINT SOIL RESISTANCE

CAPBLOCK

Figure 4. Driving assembly of the Delmag D-22 ham­mer-concrete pile.

Even though only two or three changes were made in each significant variable, this study required the solu­timi of 288 problems by the wave equation and by each of the 11 pile-driving formulas. It is therefore obvious that a complete study encompassing every type of ham­mer, pile, and soil would be relatively expensive and difficult.

Tables 2 and 3 summarize the variables used in this study.

TABLE 2. SUMMARY OF HAMMERS AND SOIL PARAMETERS USED IN THE STUDY

Hammer Type Soil Resistance Soil Distribution Case (kips) RUw

Vulcan #1 50

200

Vulcan SOC- 100

400

Delmag D-22 100

400

Point only Side only Point only Side only Point only Side only Point only Side only Point only Side only Point orily Side only

A B c D E F G H I J K L

*Each pile listed in Table 3 was solved.

TABLE 3.

Pile Material

Steel

Concrete

SUMMARY OF PILES ANALYZED

Pile Area Pile Length (in!) (ft.)

30 10 60

100 140 30

20 60 100 140

30 30 60

100 140

30 150 60

100 140 30

275 60 100 140 30

400 60 100 140

Number

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pile Driving Formulas Used In This Investigation Because of the vast amount of information previ­

ously published concerning the derivation, use, and prac­tical application of both the wave equation3 and the pile driving formulas17 used in this investigation, background material will not be presented here. For those inter­ested in the history and prior research which has been done on the wave equation, the references presented at the end of this report should be helpful.

The dynamic pile driving formulas are not presented in their most commonly used form, but rather have been modified to assure that the units are consistent, and to omit the factor of safety normally incorporated in the formula (if one exists). This permits a direct compari­son between the ultimate resistance to penetration at the time of driving predicted by the wave equation and that given by the driving formula.

In this study, eleven different dynamic pile-driving

formulas were used to predict the capacities of 288 steel and concrete piles of varying lengths and cross sectional areas. These formulas are presented in Table 4.

As was expected in the work, it was sometimes difficult to determine the constants to be used in the formula, since the values recommended in the literature varied widely. It should be noted that the authors did not intend to use the constants they considered the most accurate, but rather those equations and cop_stants most commonly used in the field.

The authors understand that many who read this report may feel that better results might have been obtained had some different form of the equations been used, or perhaps different constants applied. For this reason, the results of the wave equation analysis are tabulated in the Appendix.

PAGE THREE

This information should enable the reader to com­pare the results predicted by the use of other constants or pile driving formulas with that given by the wave equation.

TABLE 4. PILE DRIVING FORMULAS USED IN THIS INVESTIGATION .

(All factors of safety have been removed)

Engineering News

u RUF = 5 + c

Michigan Engineering News

Eytelwein

u 5 + 0.1 (~)

Navy-McKay

u

1 + 0.3 ( ;: ) Hiley

RU, ~ + o~~~~C,+C,~ @:! Terzaghi

RUF AE[ ---r- - 5 +

;:'] v 52 + 2U Wr + AE/L Wr +

Redtenbacher

RUF ~Cs +

wJ] v 52 + 2U Wr AE/L Wr +

PAGE FOUR

Pacific Coast

Canadian Building Code

RUF = -5 + V 52 + 4 (Can 1)

2(Can 2)

(Can 2)

Rankine

Gates

where:

RU~,

RUw

u

5

c

e

K

A

E

L

Can 1

Can 2

2 Ai{-s+ v 52 + u

AE/L

247 ( yU) ( log ~O )

Ultimate load capacity of pile at time of driv­ing predicted by the driving formula (lbs),

Ultimate resistance to penetration at the time of driving given by the wave equation.

Rated energy output of hammer (in. lbs),

Mechanical efficiency of hammer,

Permanent set of pile per blow (in.),

0.1 for steam and diesel hammers and 1.0 for drop hammers,

Coefficient of restitution of cushion,

= Weight of nim (lbs),

Weight of pile (lbs) ,

0.1,

RUF AE.,

0.20 ~F'

.0.25 for steel piles and .10 for concrete piles,

Cross-sectional area of pile (in.2 ),

Modulus of elasticity of pile (psi),

Pile length (in.),

U ( ~r : ~: P ) , and

l 1 2AE/L + 20,000A

Correlation Procedure During the course of this investigation, a total of

13 different methods were used to predict the resistance to penetration for each of the previously mentioned problems.

In each case, the wave equation was first used to solve the problem to determine the dynamic behavior of the pile for a single blow of the hammer. This solution gave information regarding the permanent set of the pile, temporary compression of the capblock, cushion block, and pile, elastic rebound of the pile, and all other variables required as input by the dynamic pile driving formulas. These values were then substi­tuted into each dynamic pile-driving formula to deter­mine its prediction for resistance to penetration, RUF, for that case. The resistance to penetration RUw pre­dicted by the wave equation was then divided by the value ·predicted by the formula being considered.

For example, assume that a 100 ft. long steel pile with an area of 10 in.2 is driven by a Vulcan No. 1 hammer against a soil resistance RUw of 50 kips, and that this resistance acts at the point of the pile (no side friction) . When this problem is analyzed by the wave

equation, the resulting permanent set is found to be 1.21 in. (see Table A1). Therefore, according to the Engi­neering News Formula given in Table 4, the ultimate load capacity of the pile at the time of driving will be:

RU = (15,000) (12) = 137 k' F 1.21 + 0.1 IpS

Thus, for this particular case, the ultimate soil resistance to penetration at the time of driving predicted by the Engineering News Formula is high. Calculating the ratio of

RUw RUF

50 kips 137 kips

= 0.364,

this point is plotted in Figure 5 under steel piles with a cross-sectional area of 10 sq. in. and a length of 100 ft.

Similarly, the values predicted by the other 10 formulas were determined, and their ratios RUw/RUF plotted.

Thus, by using these graphs, the engineer can readily determine the relative agreement between the pile driving formulas considered and the wave equation.

Discussion of Results The results of the correlations between the wave

equation and the dynamic formulas are both surprising and extremely informative. As noted in Figures 5 through 7 the ratio of the resistance predicted by the Engineering. News Formula and the wave equation is amazingly constant. This is not to say that the results are accurate, since the curves are consistently grouped around RUw/RUF = 0.5. This would indicate that at least for these cases the Engineering News Formula consistently predicts an ultimate value approximately twice the true resistance to penetration, such that when the recommended safety factor of 6 is applied to the equation, the true factor of safety would only be 3.

Nevertheless, the consistency of this formula is quite surprising, especially considering the amount of research which has recently been published condemning the meth­od.15· 16 This is not to imply that the Engineering News Formula is without proponents. In 1965, the Michigan State Highway Commission17 completed an exhaustive research program designed to obtain a better under­standing of the complex problem of pile driving, and to evaluate a number of pile driving formulas. Their re­search led them to modify the Engineering News For­mula as noted in Table 2. This modification has been noted herein as the Michigan Engineering News Formula.

It is important to note that the entire Michigan research program dealt with long, slender, and relatively lightweight steel piling. As noted in Figures 8 through 10, it is seen that their proposed pile-driving formula gives results which are as consistent and accurate as the Engineering News Formula, for lightweight steel pil­ing at least. However, Figures 8 through 10 also point out the complete inadequacy of the Michigan Formula for predicting capacities for heavy concrete piles. Simi­lar results were found when attempting to predict the bearing capacity for extremely heavy steel piles, and for

lightweight shell piles driven by heavy solid steel man­drels. For example, as noted in Figure 8, if a concrete pile having an area of 400 in.2 and a length of 100 ft. was to be driven to a side frictional resistance of 50 kips by a Vulcan No. 1 hammer, the Michigan Formula would not indicate satisfactory resistance to penetra-

. tion until an actual resistance of 115 kips was obtained. Thus, there would be an unseen factor of safety of 2.3 beyond the factor normally used.

This is by no means meant to detract from the use­fulness of the Michigan Formula, but rather to empha­size the potential danger of extrapolating such equations which were derived using only a certain type of pile under certain conditions.

As seen in Figures ll through 16, the Eytelwein and Navy-McKay Formulas are relatively inconsistent.

The results for the Hiley Formula noted in Figures 17 through 19 are extremely interesting. Although the angle and spread of the curves is much greater than that for the Engineering News Formula, notice that they in general center about a ratio of RUw/RUF = 1.0, es­pecially for steel piles with hard driving resistance at point. Predictions for long and/ or heavy concrete piles show far less agreement, as would be expected from pre­vious experience. None-the-less, the method's popularity is clearly indicated for steel point bearing piles since it comes closer to predicting the true average pile capacity for a greater variety of steel piles and soil conditions than any of the other formulas analyzed.

Figures 20 through 22 illustrate the results obtained for the Terzaghi Formula. Here again, the results vary, agreeing with the wave equation only for certain cases within certain ranges.

The Redtenbacher, Pacific Coast, and Canadian

PAGE FIVE

Building Code Formulas seem to show the least agree­ment of the pile-driving formulas studied in this in­vestigation.

Figures 32 through 34 illustrate the results of the Rankine Formula and indicate that they, like the Engi­neering News Formula are remarkably well banded and consistent, although they also are relatively inaccurate. However, it seems probable that constants could be applied to either the Rankine Formula or the Engineer­ing News Formula in order to greatly increase their

accuracy and_ usefulness, at least within the range of problems studied in this report.

The results obtained for the Gates Formula are il­lustrated in Figures 35 through 37. Although the re­sults are not as closely grouped as some of the previ­ously mentioned formulas, they are remarkably consistent considering the lack of variables accounted for, and it appears that it might be possible to modify the formula somewhat in order to obtain closer agreement with the wave equation.

Conclusions

For the cases shown, the Engineering News and Rankine Formulas are generally in better agreement with the wave equation than any of the other formulas studied in this report. For the cases analyzed, both formulas predicted bearing capacities around twice that given by the wave equation. There were several exceptions for the Engineering News Formula, these being for extremely large, heavy concrete piles driven by a Vulcan No. l hammer, and for long steel piles with extremely small cross-sectional areas, driven by Vulcan 80C hammer. The Rankine Formula, however, had exceptions only when driving long concrete piles of large cross-sectional area with the Vulcan No. l hammer.

Because the results obtained by these two formulas are quite consistent, the formulas can be multiplied by the factor (RUw/RUF) to bring the formulas into agreement with the wave equation. The factor RUw/RUF can be found from the figures presented. This factor, when applied to the formula in question, will produce a predicted safety factor of 1.0. For the Engineering News Formula, the equation with the appropriate constant becomes:

_ ( U ) ( RUw) RUF- s + c RUF

where the equation should be applied only to piles and hammers analyzed in this report.

Other simplified dynamic formulas can be treated in a similar manner. Note that an appropriate factor of safety should then be applied to the modified for­mulas.

It must be emphasized that throughout this report the authors have limited their considerations to pile capacity immediately after driving, (hence the term "resistance to penetration") since it is widely recog­nized that neither the wave equation nor any dynamic formula can account for time-dependent variables which

PAGE SIX

might influence the capacity of a pile. Time effects can only be determined by the application of soil mechanics.

LEGEND: POINT RESISTANCE! SIDE RESISTANCE

EASY DRIVING -Q----0---0- -()---{)- --o-HARD DRIVING -D--0-0- -o---D---D-

STEEL PILES CONC. PILES

AREA=301N.' . AREA=400 IN.2

2.0

1.0

- _ _.._....,-= -'-~- ---- ::.:::.::::.

~====: ·=-0.0

AREA=2DIN.' AREA=27p !r1i2

2.0

~ a: ' ~ a: 1.0

,---o ---o 1==----.=j ----:.-; --"" ----:::: - -----o

0.0 AREA=IO IN! AREA=I50 IN}

2.0

1.0

--- --.d -

-30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 5. The Engineering News Formula vs the wave equation-Vulcan No. 1 hammer.

LEGEND: POINT RESISTANCE' SIDE RESISTANCE LEGEND: POINT RESISTANCE' SIDE RESISTANCE

EASY DHIVING --o----o-o- --Q---0---0- EASY DRIVING -o--cr---o- -o---o.--o-HARD DRIVING --D-D-D- --G--G---G- HARD DRIVING -{J--0-[)- --G--o---o-

STEEL PILES CONC. PILES STEEL PILES CONC. PILES

AREA•30 IN2 AREA•400 IN.2 AREA•30 IN. 2 AREA• 400 IN. 2

/ 20 20 /

//v

0.0 AREA• 20 IN. 2

2.0

=> a: ..... "' :::>

!I: 1.0

»::.-- - --=-

0.0 1---+--+---+---1-+--+--lcc---+---+-1 AREAeiO IN.2 AREA•I50 IN.2

2.0 1---t---t----1----1-+---+---+----+---+-1

1.0 1---t---1----1----1-+---+---+----+---+-1

---- ---

--- I}-

O.OOL_ __ ~3r0==~6tO::~~IJO~O====I4=0~JOL_ __ j3LO __ _j6_0 ______ 101o------1~1,oJ PILE LENGTH (FT)

Figure 6. The Engineering News Formula vs the wave equation-Vulcan BOC hammer.

LEGEND: POINT RESISTANCE I SIDE RESISTANCE

EASY DRIVING --o----o-o- -Q--.0.--Q-

I HARD DRIVING I -o-o--o-·r -o---o---a-

STEEL PILES CONC. PILES

AREA•30 IN. 2 AREA" 400 IN.2

2.0

1.0

----r==-. - - ---....:: ..,..~ -

0.0 AREA•201N.2 AREA•275 IN.2

2.0

=> a: ..... "' :::>

a: 1.0

--- ,_ __ ~- ==B - - -

0.0 AREAeiO IN.2 AREA•I50 IN.2

2.0

1.0

--- r---- p----· ---e- D -i--

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 7. The Engineering News Formula vs the wave equation-Delmag D-22 hammer.

.-' t/ ------ ---- - ~ D

......,_-::::::..=:-.= ;:;...---~----,_

0.0 AREA•201N:2 AREA•27~ IN.2

2.0 /

/

:1 a: ..... "' :::>

a: 1.0

/ _,. / / V------~ -,..::::.-----<

-~~ -==--=.-:.:; v ~--=:=.--.'="

0.0 AREAeiO IN.2 AREA•150 IN.2

20

"

1.0

,...... ....... _,... .--.::::-~-

?" .... ~ ~

p-

--- ----

30 60 100 140 0 30 60 100 140

PILE LEI~GTH (FT)

Figure 8. The Michigan Engineering News Formula vs the wave equation-Vulcan No. 1 hammer.

:1

LEGEND: POINT RESISTANCE' SIDE RESISTANCE

~·~·~~~D~R~IV~IN~G ____ ~--o----o-o-~~~ ~ -0---0-HARO DRIVING --D-0--0- -G--Q- -Q-

STEEL PILES CONC. PILES

AREAe30 IN.2 AREAe400 IN2

2.0 1---t--t----t--++---+---+---!-------:7\---1 ,-"'

/

----~: /~ 1.0 '---+---t-----+-----++-----1~>'--s-~--lii--;:.:.-,::..--:::::::_-+'-------+--1

I ~ -=---... --

0.0 f---1---:!----+---++---l---":----+---I-AREA•20 IN! AREA•275 IN.2

2.or---r---r---J---t-+--+-+--+----f-l

!;:: 11::::::::.:::.::::: ~ -~~~v--' a: 1.0 r---+-_-_-_+_-_-_--+_. _---~---__ -_H---lv""::.-:-~IJ='~;,;:~L..--+-1

o.o 1--+---l---+---H--1---1---1---+-1 AREA:IO IN.2 AREA• I 50 IN.2

2.0 1---T---+---1---t-+--+--+--+----f-l

..-.:;:-.:i

1.0 f--+----l------+-----++---1---+...,.,s:-::..::::~:::::~----l--l :::-~b---9·-===------~=-q --- ---- ----

30 60 100 140 0 30 60 100 140 PILE LENGTH (FT)

Figure 9. The Michigan Engineering News Formula vs the wave equation-Vulcan BOC hammer.

PAGE: SE:VE:N

LEGEND: POINT RESISTANCE! SIDE RESISTANCE

EASY DRIVING -o-0--0- -Q---Q---0-HARD DRIVING -D--0-----0- _I. -G- -D---D--

STEEL PILES CONC. PILES

AREA=30 IN} AREA= 400 IN2

2.0 r---r---+---+---t-+---t----11----t---H

1.0 r----r--+---+---t-+---t----11----t---H -=--.: ==--= ==- --- ---- ==---'

0.0 AREA=201N2 AREA=275 IN2

2.0

~ 0:: ..... " :::>

0:: 1,0

O.Of----t---+----t----H---t---11----t---H AREA=IO IN! AREA=I50 IN2

2.0 -+--+---+---++--+---t----t-----IH

1.0 1-----t---+---+---++---+--+---+----+-l

o.o o._ _ _,3.,0--6"'"o:----l-'o-o--14-o'-'o--3.J..o ___ 6Lo---~o.J..o ___ l_,4_,o

PILE LENGTH (FT)

Figure 10. The Michigan Engineering News Formula vs the wave equation-Delmag D-22 hammer.

LEGEND: POINT RESISTANCE! SIDE RESISTANCE

~DI:IVING -o-0--0- -()- --()- --o-DRIVING --o-o-o- -D---o-- -o--

STEEL PILES CONC. PILES

AREA=301N.2 AREA=400 IN}

2.0

~ ....-~1-"" _.. ..-<

---~ ~ I~ ~ -~ --==- __....... 1.0

·-0.0

AREA=201N.2 AREA=275 IN.'

2.0 .. :::> 0::

' _..p " :::> 0:: 1.0

~

~ ""' -- --==~- --- ...,: ~~----0.0 AREA=IO IN! AREA=I50 IN}

2.0

1.0

~~ -- ---~ --- - .... --30 60 100 140 0 30 60 100 140·

PILE LENGTH (FT)

Figure 11. The Eytelwein Formula vs the wave equation -Vulcan No. 1 hammer.

PAGE EIGHT

LEGEND: . POINT RESISTANCE! SIDE RESISTANCE

EASY DRIVING -o-0--0- -o--.0·--Q-HARD DRIVING -D--0-----0- -o-- -o- --a-

STEEL PILES CONC. PILES

AREA=301N." AREA= 400 IN.'

2.0

1.0 _,~

_..._.;:::;-

~ - --~ __....,.= 14<;;.;:, ~--:>--

0.0 AREA=201N.2 AREA=275 IN.'

2.0

~ 0:: ..... "' :::>

0:: 1.0 -· ~~ s:::=----- --- ----- !;(::::.--

0.0 AREA•IO IN! AREA=I50 IN.'

2.0

1.0

- ·~"__....-. g~-=----' -,_ ..... ....... ~

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 12. The Eytelwein Formula vs the wave equation -Vulcan BOC hammer.

LEGEND: POINT RESISTANC~~ISTANCE EASY DFIIVING -o-o-o- -o---o---o-HARD DniVING -D--0-----0- -o-- -o- --a-

STEEL PILES COI'-JC. PILES

~3o1N.2 AREA= 400 IN2

2.0

//I

/ ~

£ ,,

r-._ ,.._.,- --- -- ---1.0

=-== 0.0 -

AREA=201N} AREA=275 IN2

2.0

~ 0::

-~ --- ,:::-,-, I~ ,_ __

..... " :::>

a: 1.0

I-==< -'"AREA•IO IN! AREA=I50 IN}

0.0

2.0

i 1.0

--- --- --- -..,.. .... , --:::;. ~~ -___:_j __ L '' ----~~ --- --·--

30 60 100 1~;0 0 30 60 100 140

PILE LENGTH (FT)

Figure 13. The Eytelwein Formula vs the wave equation -Delmag D-22 hammer.

~ a: ' ~ a:

LEGEND: POINT RESISTANcd SIDE RESISTANCE

EASY DRIVING --o--o-o- -o---o---o-HARD DRIVING --D---0---0- -D-- -o---o-

STEEL PILES CONC. PILES

AREA=30 IN} AREA=400 IN} I 2.0 1--t---t---t---11-t---+--,-J--f-~---1-l \ 1/

)/ 1.0 1---+--+---t----::_""'_-.Q---t--+/~---:ll:___-+---:----;~

t:::.-:: :::::.,;:: : :::.:-- := ? ::::-:::-::=-·~

0.0 AREA=201N.2

2.0

to

--=--- :::.--- -::..::::~

AREA=275 IN2

/ /

/ /

/

0.0 1--+--:+---t---lr+--+---1---+---H AREA=IO IN.2 AREA= I 50 IN}

2.0 1--t--+---t---1'--1---+---1---+---l-1

/

1.0 f--+--f---+----t-+--1--+---:-J,:...L:_/~...Q--1 -::::::.::::;.-:::..:-..::~

..... ------r-----~-----

O.O 0'--=-30,.-----,6:':0:----:I.J.0.,-0--I-:4..JOLL0--3LO-_j6.,.0---IOL0---14.J.O..J

PILE LENGTH (FT)

Figure 14. The Navy-McKay Formula vs the wave equa­tion-Vulcan No. 1 hammer.

LEGEND: POINT RESISTANCE~ SIDE RESISTANCE

EASY DRIVING --o--o-o- -o---o- -o-HARD DRIVING --D---0---0- --D-- -o- --o-

STEEL PILES CONC. PILES

AREA=301N2 AREA=400 IN2

2.0 /

//

.......... -/ r--- -- y.-,....

~ :::---~--= --- ::..::::-:::: --- -1.0

;::::;::::::. - - ~::...-

0.0 AREA=201N.2 AREA=275 IN2

2.0

~

.,""' ,.--/

--- --- -::;:;;: ~ i~ --- -----a: ' "' ::> a: 1.0

r.::---- -0.0

AREA=IO IN." AREA=I50 IN2

2.0

---- --- -- ---- --::c -· - ---1.0

--c -- ~

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 15. The Navy-McKay Formula vs the wave equa­tion-Vulcan BOC hammer.

LEGEND: POINT RESISTANCE~ SIDE RESISTANCE

EASY DRIVING --o--o-o- -o---o---o-HARD DRIVING --D---0---0- -o----o---o--

STEEL PILES CONC. PILES

AREA=301N." A REI'.= 400 IN2

2.0 .

---~ .......... /

--- --- --- ~ ~ -- ---1.0

....__, :::;::=:::::::: ---0.0

AREA=20 IN.2 AREA=275 IN 2

2.0

~ -· ~ :::-::. d

,__ __ ..---- )-.-~

~ --- ~

a: ' ~ a: 1.0

,:::=-- --0.0

AREA=IO IN.2 AREA=I50 IN."

2.0

1-- --- -- ---~ --- -:::;.::;

1.0

--- --- - a::--i- ---

30 60 100 140 0 30 60 100 1~-0

PILE LENGTH (FT)

Figure 16. The Navy-McKay Formula vs the wave equa­tion-Delmag D-22 hammer.

LEGEND:· POINT RESISTA~CE~.: RESISTAN~ --~y DHIVItJG -0--0--0-~-0---D--·0-

DD:11Vit~- -o~---0= ::0.--o--D---- -.:=.......=..-.

STEEL. PILES COf·JC. PILES

2.0

----~-r------ -------, ----r---AREI\o30 11~2 . AREA=400;fJ~I

/ p

-- - ~ / 1.0

--- / --~-~ -

~--- I

0.0

2.0 .. ::> n:: ...... ~ n:: 1.0

AREA=201N. 2 AHEA=275 IN.:%

~ //

_..., o~~ "/ / --- ~ :~ ----l~ ·--o.o

2.0

AREA=IO IN.' AREA=I50 IN.~/~' ,_.....-:/ /

/

///' / _ ... " ...... ,....-'

1.0

---- / ..... _______.-' ..--L--'~ / --- - / /

;:=-:::=:c /

-30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 17. Vulcan No.

The Hiley Formula vs the wave equation­] hammer.

PAGE NINE

LEGEND: POINT .RESISTANCE! SIDE RESISTANC~ . -EASY DRIVING -()----{)---0-- -o- --o- --o-HARD DRIVING --D-D~D- --o-- -o- --Q-

STEEL PILES CONC. PILES -

2.0

AREA=30 IN.2

AREA=:7t _,-'"/ - v --/ v -- ..-- /

~ v- ----

1>---- / ---,__-~

-I>-

1.0

AREA=201N2 AREA=275 l.ll<l~ /

'i / ..... ..--

l/ --[________-/

./ ------ ::-- ~ v --- ----------:-: ---'----

0.0

2.0

::') 0:: '-" ;:)

0:: 1.0

AREA=IO IN.' AREA= I 50 IN.://V

/ v ---1/./ ----- --

0.0

2.0

~---------V., -- ~__.....-<

-:::-- :::-::=.---

__ ....

----------- s----=- v 1.0

)-

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 1B. The Hiley Formula vs the wave equation­Vulcan BOG hammer.

LEGEND: POINT RESISTANCE' SIDE RESIST.t'.NCE

EASY DRIVING -0--0--0- -0---o---o-r---------..L I~HA::::R.D DRIVIf'G I --D-D-0-_L_-o---o---o-

STEEL PILES CONC. PILES

AREA=30 IN.2 AREA= 400 IN2

LEGEND: POINT RESISTANCE! SIDE RESISTANCE

r EASY DRIVING -()----{)---0-- -o- --o---o-HARD DRIVING -o-o-o- I -o-- -o---o-

STEEL PILES CONC. PILES

2.0

AREA=301~ AREA= 400 IN2 I / /

/ v / /

/ v ./ ---- b ~~ r-~-:::: ~ -=-===-::::

1.0

0.0 AREA=2.01N.2 AREA=275 IN 2

.//-/ 2.0

/ / ,

y./ ~ -- ..?"~

1.:::--:::__::; ~~ I~ ~ v---

::') 0:: '-" ;:)

0:: 1.0

AREA=IO IN.' AREA=I50 IN.2 0.0

2.0

-::: ?"

- ~:::=~ ;....----~ ---~-~-----~ ---· ~ :::..= 1.0

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 20. The Terzaghi Formula vs the wave equation -Vulcan No. 1 hammer.

LEGEN.O: POINT RESISTANCE' SIDE RESISTANCE

~lYING -()----{)---0--J -o-- -o- --o-RIVING --D-D-0- --o-- -o- -D-

STEEL PILES CONC. PILES

AREA=30 IN.2 ---A~400IN2

w ~ /

::') 0:: '-

~----

O.O t-A-R_E_A+-=2_0_1_N-:!.Z---t----·H-A-R_E_A+=-27_5_1_N-1::2---t---H

2.0 t----+----+---f---H--+---1----+----1--l

~ o:: 1.0 r--+-+--+---=H---Jt-.... -_-_-_t-~---:::-::::-="'.±:::=~~

-_-;;~ _,::: ---- b_::::.::.- ---~l-- --1

o.o 1---+--+--+----H----1--1-----1----+1 AREA=I50 IN2 AREA=IO IN.2

2.0 1---+---+---+---+-l---+--+---+-----+-1

1.0 f---+---+---+---1--l---+--+--~~~9-1

OD 0'----3.L0--6.LO ___ I_i0_0 __ 1~-,o.L..0'----3L0--6L0---1_10_0 ___ 14-'--0-~

PILE LENGTH (FT)

Figure 19. The Hiley Formula vs the wave equation­Delmag D-22 hammer.

PAGE TEN

/ ./

--- -- ,.-:_:;. ~ ~ ~~

,-:::::::._ __ ~ ~

1-AREA=20 IN.Z AREA=275 IN2

0.0

2.0

~

..... -.::: p ~ -- ___. .- --

~ p v &=---

~ -----

:!) 0:: '-" ;:)

0:: 1.0

0.0 Ar~EA=IO IN.2 AREA=I50 IN.'

2.0

.,...,... .........

1---// --::::-

,~ --ld 1::::-:"' ---- ~

~ -::-....., ---"' --1.0

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 21. The Terzaghi Formula vs the wave equation -Vulcan BOG hammer.

LEGEND: POINT RESISTANCE! SIDE RESISTANCE

EASY DRIVING --o--o-o- I -o- --o- --o-HARD DRIVING --o---o--o- -G--o---o-

STEEL PILES CONC. PILES

AREt:'.•30 IN.zr-- ARE/\•400 IN2

2.0

---::-~ ~ :-- === ~-= ~·

1.0

0.0 AREA•201N. 2 ARE/\•275 IN.2

2.0

~ 0::

' "' --~

:-"::..~ ~ =-==-:?>- ---- ~--<

:::> 0:: 1.0

0.0 AREA•IO IN.2 AREA•I50 IN2

2.0

.....

-- -:;::.:::--- --~

1.::::---__ ---- >;:;_.:;:;;:. ~ f--· 1.0

1- -30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 22. The Terzaghi Formula vs the wave equation -Delmag D-22 hammer.

LEGEND: -~NT RESISTANCE! SlOE RESISTA~;; [EAsYDRiV~ --o--o-o--1---?---o---o-

HARD DRIVING -Q----0---D- J --[J---D---D-_

STEEL PILES CONC. PILES

AREA•301N2 -----~-~----·

AFlEA"~·OO IN2

2.0 / /

/ / 0 '/ __.;;/ // ~// / / v 'i ~ .,/'/_

~: ~ v 1.0

AREA•201N.2 AREt,•275 IN2 //

/ / /

/,/ / ll/ / /

0.0

2.0

~

----- / \~ v ~ ........ ~--

~ ~ b~ v

0::

' "' :::> 0:: 1.0

AREA•IO 11" 2 AREA•I50 IN2 / /

=Lf /

i / ~ /

I _..

./_;; ~ I -- --~ ---1 . --~ _ ___r~-

_rJ L_

0.0

2.0

1.0

30 60 100 140 0 30 60 100 140

PILE LE!~GTH (FT)

Figure 23. The Redtenbacher Formula vs the wave equa­tion-Vulcan No. 1 hammer.

LEGEND: IPDIIH RESISTM:c~:SIDE RESISTAtJCE

~SY D!<IW!G --~-0---0--0- -0--.0.~ r-··------·- .Ri1~~~vii~o-----·-.:::-o=:-o::..n-:.=r-g-- -Q---~=

----,-· ~:~:r::~~~~---J-~Oi-!C. PILES AP.E/\•30ii-J. 2 ?\REI\•4001N2

/

2.0 / I

/,/ / II / -~ /

/~ ??' ..-/ ' "" ----r% -~ y 1.0

~---------f-------ARE/\•20 IN. 2 .l\I-1EA=275 IN.2

< V/. ---· <~~ v

/ / / / / ~'d

~ v // -9"\ //

~ ~ ,..-----" ?? ..-'

0.0

2.0

~ 0::

' " :::> 0:: 1.0

-AIXEA•IO IN 2 Af,EA•I50 IN2

0.0

/ /

/~ y 2.0

_.....-v /-:/ ~?__...-v ~

11::::..--- -~

,..-./

·----1---1.0

·------·-'--- ------30 60 100 140 0 30 60 100 1~-0

PILE LEf~GTH (FT)

Figure 24. The Redtenbacher Formula vs the wave equa­tion-Vulcan BOG hammer.

~ 0::

' "' :::> 0::

2.0

1.0

0.0

2.0

1.0

0.0

2.0

1.0

0.0 0

LEGEND: POINT RESISTANCE! SIDE RES!STAt!CE

EASY DRIVING -o---o---o- I -o---o---o-HARD 0111\!ING -o---o-o-- I -a-- -o---o-

STEEL PILES CONC. PILES

AREA•301N2 AREA• 40J.rf>.i2 I

-' // / ........ ,.,._/ L ---:-' /;:;:-~ ~ ,/

/ ......-· / / ):._ v

AREA•201N.2 AREA•275 IN2 j / /' :/ /// / /0

,/'

r~---- (/}• / /~: -

~ :~ 1------

AREA•IO IN.2 ARE/\•150 IN2 / /'J /

-----::- //~ / /~

v---_ ---- /;'/ V/ ~ ~ ---- ~ ,/

30 60 100 140 0 -:>0 60 100 140

PILE LENGTH (FT)

Figure 25. The Redtenbacher Formula vs the wave equa­tion-Delmag D-22 hammer.

PAGE ELEVEN

LEGEND: POINT RESISTANCE! SIDE R~SIST~N_CE EASY DRIVING --o-o-----o-- -o---o---o-HARD DRIVING ~ -o--o- -o-

STEEL PILES CONC. PILES

2.0

AREA=30 IN.2 AREA=4001N.>/ I

i -; .... / ~ I ....

1.0 -~ ~~ ~ --~ sp li"" _,--- (/'

" -~ 0.0

AREA=201N.Z AREA=275 IN.2 /

/ / 2.0

u. 0 0:: ..... ;,

::> 1.0 0::

/ r ~ .... - / / /

/ ~· ./ ;~ ....--::..---- / / /

v ---~· ~ ___. - .-<

0.0 AREA=IO IN.2 AREA= I 50 IN.Z /

2.0 ----/ / .-' ----

,.

1.0 -- (::.:.:---- v ~ -~ ,...-::: -· ~ -- ~- .

~ ,_ __ , -- ~

1----

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 26. The Pacific Coast Formula vs the wave equation-Vulcan No. 1 hammer.

LEGEND: POINT RESISTANCE' SIDE RESISTANCE

EASY DRIVING --o-o-----o-- -o---o---o-HARD DRIVING -D-0-0- -o--o---o-

STEEL PILES CONC. PILES

AREA=30IN2 AREA= 400 IN2 / ' ,"

2.0 ......... y /

/ ,.--/ "";P ·~ .- ~ v

--~ --- ::./ ~~ - ,______. ~

~--1.0

AREA=201N.Z AREA=275 IN.Z v/ ,-:;::. ~/ / ;'

/

0.0

2.0

"-::>

;/ // v v ---- ,_·---~ .... ~·--

[.?--~

0:: ..... ;.

::> 0:: 1.0

AREA=IO IN.2 AREA=I50 IN.Z ./' ,"' L_

,/ /

~ ,-' / // .-'.

0.0

2.0

.--/" l/

/~ ~ ........... -"' ~ -' ---- - ~ ,......-,.......------1.0

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 27. The Pacific Coast Formula vs the wave equa­tion-Vulcan 80C hammer.

PAGE TWELVE

LEGEND: POINT RESISTANCE I SlOE RESISTANCE_

EASY DRIVING --o-o-----o-- -o---o---o-HARD DRIVING -D-0-D- -o-- -o- --a-

STEEL PILES - cor~ c. PILES

AREA=301N2 AREA= 400 IN2

......... ---2.0 /

_, 0~ ,_ ____

/-___ ....

n/ / -1.0

""'-- 7 ~y ~,...

----------/ -----0.0

2.0

::3' 0:: ..... ~ 0:: 1.0

AREA=201N.Z AREA=275 IN2

//

.... y-,"'/I --,... --... ~'--, / /~

!0- --~ ,---' -

0.0

2.0

AREA=IO IN.2 AREA=I50 IN.Z / . ..-: /

.-;:. y //A---""'

1.0

l~ / h~"" ~ -:/ ---- ,...~ ~--' -- :--- v ~/ ---~-- ~

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 28. The Pacific Coast Formula vs the wave equa­tion~Delmag D-22 hammer.

LEGEND: POINT RESISTANC~~ SIDE RESISTANCE

EASY DRIVING --o-o-----o-- -o---o---o-HARD DRIVING -D-0-0- -o--o---o-

STEEL PILES CONC. PILES

2.0

AREA=301N.Z AREA= 400 IN.Z /I // {I

/ 1 -~ ~-- cl/ -- -- .--::::--

~ ~ \:;..- :? -

1.0

0.0 AREA=201N.Z AREA=275 IN.Z

// I /

// /...------- ,.,-"'"' & ;:.....-----

,. ---~ ~I --- y -

2.0

"-::> 0:: ..... ;,

::l 0:: 1.0

~

0.0 AREA=IO IN.Z AREA=I50 IN.Z

/ ,/_,/ >-:''

2.0

-- --- ,;/? :::::::-~ ~

=::-- -"" ~ ~=--1.0

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 29. The Canadian Building Code Formula vs the wave equation-Vulcan No. 1 hammer.

LEGEND: POINT RESISTANCE' SIDE RESISTANCE

EASY DRIVING --o--o--o-- -o---o- --o-HARD DRIVING --o-o----a-J -o-- -a---a-

STEEL PILES CONC. PILES

AREA•301N.2 AREA• 400 IN2

2.0 /

" ----~/ ,...,..

--- _,/ v --~ /-~ -·~ p:-- -- ~ .----

1.0

AREA•201N. AREA•275 IN} 0.0

/~ __ ,. ~

~ /' ~ / .- <------ /

~ ~- -- v

2.0

=> 0:: ..... ;.

::> 1.0 0::

0.0 AREA•IO IN.2 AREA•I50 IN2

2.0 "" "' .. / _,... ..

------- ~ \ .......... - ~

~ l:"------·-·- ~ ;_-----

1.0

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 30. The Canadian Building Code Formula vs the wave equation-Vulcan 80C hammer.

lEGEND: POINT RESISTANCE' SIDE RESISTANCE

l EASY DRIVING --o--o--o-- -o---o- --o-HARD DRIVING --o-o----a- -o-- -a- --a-

STEEL PILES CONC. PILES

AREA•301N2 ~4001N2

2.0

---- - --:;:;::= -- - -y-:..:-~ ---- ---:: ~ ---c.-- ~ I

1.0

-0.0

AREA•201N} ARE/1•275 IN}

2.0

=> --- ---:::::::- -- :::---- -- 7--::.~ ---

-,...r.:. ~ ---- ~~ a~ -!::=:-::

0:: ..... ~ 0:: 1.0

0.0 AREA•IO IN.2 AREA•I50 IN}

2.0

_;;:::-::-~ .... ::::--_,. _.. _...

~ 5----- -:;:;; g..?' --- ___., -1.0

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 31. The Canadian Building Code Formula vs the wave equation-Delmag D-22 hammer.

LEGEr:m: POIHT RES!STANCEI SIDE RESISTANCE

fEASYDm=v::,Nc:.G:---+'--o--o-~~.:; o- I -o---o---<c_ ,----------'-[HA_.:.:.UA.:;.:RROOO DRIVING --D-D-----D- _:-0---D---D- _

STEEL PILES CONC. PILES

~30\N:r ~4001N2

2.0 1---+---+-----f---j'--f--J---+----+---+-1

1.0 f-----+---f----f----+-+---+---+---+---+--1

----- - :_:::.:: =---

0.0 ARE/\•201N.2 AREA•275 IN 2

2.0

=> 0:: ..... ;.

::> 0:: 1.0

-0.0 1---+---+----\---H--+----f----+-----+-1

Af~EA=IO IN.2 AREA= 150 IN}

2.0 1---t---+----j--

1.0 f------1---+----t----+-+---f----+----+---+-l

--- - =-==-=-~ --- =---0.00~--3L0---6LO ____ IJ0_0 ____ 14-0L-01~--~3L0--~6-0-----10-'-0------I~~,C~

PILE LEf~GTH (FT)

Figure 32. The Rankine Formula vs the wave equation -Vulcan No. 1 hammer.

LEGEND: POINT RESISTANCEI_SIDE RESISTANCE

IEAS'YDRivu~G --o--o--o-- -o---o- -o--~RIVIN_G1__L-p----o-----o-_j -o---o----o-

STEEL PILES CONC. PILES

AREA=30 IN.2 AREA•400 IN.2

2.0

1.0

---- - --.; ,_ ... ---~

AREA•201N.Z AREA=275 IN2 0.0

2.0

=> 0:: ..... ;.

::> 0:: 1.0

-~ --;;:;;:! ---~ - ---

0.0 AREA•IO IN.2 AREA= I 50 IN2

2.0

1.0

~i -- ___ _,

i==-~ -----~ r--· -

30 60 100 140 0 30 60 100 140

PILE LENGTH (FT)

Figure 33. The Rankine Formula vs the wave equation -Vulcan 80C hammer.

PAGE THIRTEEN

LEGEND: POINT RESISTANCE! SIDE RESISTANCE

IEAsYDRtVING --o--o---o- -o---{)- --{)-HARD DRIVING I --o-o-o- -o- -o- -o-

STEEL PILES CONC. PILES

AREA=301N2 AREA= 400 IN2

2.0

1.0 ,.__ - ---?::><::::- - - ----- - -

0.0 AREA=201N.' AREA=275 IN2

2.0 ...

:::> 0::

' ;. :::> 0: 1.0

---- ---1>--~ - - - -0.0

AREA=IO IN.2 AREA=I50 IN2

2.0

1.0

1>- -- =-== ~ -;:..::::::::. .J/1> ... - - ---~

30 60 100 140 0 30 60 100 1~0

PILE LENGTH (FT)

Figure 34. The Rankine Formula vs the wave equation -Delmag D-22 hammer.

LEGEND: POINT RESISTANCE' SIDE RESISTANCE

I ____ ~AS'(_DRIVII~G __ 1_=5?~ -o----o- -o-IHARODf>tVING -~~ -o---o---o-·

STEEL PILES CONC. PILES

AREA=400 IN2

2.0 1-----+-----+----1---H--+---+---+---i-1

--- 0---- ----

1.0 1------1---l--l--W--1'===!!:====1pi"='"_ ·==----=--:;~k--o---t>--- ___ c --__::..p--

0.0 f---+--+--+--+-1---+---+:----+---1---1 AREA=201N2 AREA=275 IN2

2.0 f----1--+--+--+-1--+---+---t---1--i :::) 0:: ·-' 1>---- ---- --- --- ----------~ o: I.Oi---+--t----j---H---1--+---t---t-t

1>---- -- ---- )-- - --::.:

0.0 f----I---1----1---H---1--1-----t---t-1 AREA 10 IN 2 AREA=I50 IN.' = . I

2.0 I

~-- ---- 1>--- 1---P'-----¢ 1.0 ~--'i===i==~~~~H---~--+--+----1--1

>----

30 60 100 140 0 30 60 100 14·0

PILE LENGTH (FT)

Figure 35. The Gates Formula vs the wave equation­Vulcan No. 1 hammer.

PAGE FOURTEEN

LEGEND: POINT RESISTANCE!_ SIDE RESISTANCE

EASY DRIVING --o--o---o- -o---{)- --{)-HARD DRIVING --o---o--o- -D---o- -o-

STEEL PILES CONC. PILES

AREA=301N.' AREA-400 IN.'

2.0 I

--- ---- -?- >- ----1.0

0.0 AREA=201N.' AREA=275 IN2

2.0 -- ---- ---!----I ...

:::> 0::

' ;. :::> 0:: 1.0 .,__ -

AREA=IO IN.2 AREA=I50 IN2 0.0

- --2.0

' ~ -~

~:-sj - r-- - -1.0

\

\ \

30 60 100 140 0 -.:>0 60 100 140

PILE LENGTH (FT)

Figure 36. The Gates Formula vs the wave equation­Vulcan 80C hammer.

:::) 0::

'

LEGEND:

EASY DRIVING

HARD DRIVING

STEEL PILES

AREA=301N.'

POINT RESISTANCE! SIDE RESISTANCE

--o--o---o- -o- --o- --{)-

CONC. PILES

AREA= 400 IN2

I 2.0 f----krr--=---_+_-_-_-_+p----++--+~+--+_-_-_-_+119

~==::.~>----•

1.0 f--+~'--:::o:,.....-k=--+--H---t:---t---t----t--' ----..._

O.O AREA=20 IN.'

2.0

---- -- ---- ,_ --

AREA=275 IN 2

---J-

~ o: 1.0 1-----'1-=1=-::_~_+-_--_-_-_-1-1---9=--=±----t---H

0.0 f---l----:l---t--+-1---1--+;:---t---H AREA=IO IN.2 AREA=I50 IN.'

2.of---+--+---t--++--+--_+-_-_-_+~--;H --,_ __ -----:. __ _

1.0 1---t-=r-:..:·-:..:-~=~+~~H--1""""-::'.:._±--'-----±---+-1

0·0 0L--:l3l:-0--6='"o=----:-:l ol:o:-~14:-:o~o:----:3::l:o::---:6~0:---:-I o;:o;:---1:-;4';::'0

PILE LENGTH (FT)

Figure 37. The Gates Formula vs the wave equation­Delmag D-22 hammer.

References 1. McClelland, B., John A. Focht, Jr., and William J.

Emrich, "Problems and Design and Installation of Heavily Loaded Pipe Piles," Prese'1ted to ASCE Specialty Conference on Civil Engineering in the Oceans, San Francisco, September 1967.

2. Chellis, R. D., "Pi'e Foundations," McGraw-Hill Book Company, New York, 1961, p. 24.

3. Smith, E. A. L., "Pile Driving Analysis by the Wave Equation," Journal of the Soil Mechanics and Foun­dations Divisions, Proceedings, ASCE, Paper No. 2574, SM4, August 1960.

4. Hirsch, T. J., "Computer Study of Variables Which Affect the Behavior of Concrete Piles During Driv­ing," Report of the Texas Transportation Institute, Texas A&M University, August 1963.

5. Hirsch, T. J., and Thomas C. Edwards, "Impact Load-Deformation Properties of Pile Cushioning Materials," Report of the Texas Transportation In­stitute, Texas A&M University, July 1965.

6. Chan, P. A., "A Laboratory Study of Dynamic Load­Deformation and Damping Properties of Sand Con­cerned with a Pile-Soil System," A Dissertation, Texas A&M University, January 1967.

7. Airhart, Tom P., T. J. Hirsch, and H. M. Coyle, "Pile-Soil System Response in Clay as a Function of Excess Pore Water Pressure and Other Soil Prop­erties," Report of the Texas Transportation Insti­tute, Texas A&M University, September 1967.

8. Lowery, Lee L., Jr., T. J. Hirsch, and C. H. Samson, Jr., "Pile Driving Analysis-Simulation of Ham­mers, Piles, and Soils," A Report of the Texas Transportation Institute, Texas A&M University, August 1967.

9. Hirsch, T. J., "Stresses in Long Prestres~ed Con­crete Piles During Driving," A Report of the Texas Transportation. Institute, Texas A&M University, September 1962.

10. Samson, C. H., T. J. Hirsch, and L. L. Lowery, Jr., "Computer Study of Dynamic Behavior of Piling," Journal of the Structural Division, ASCE, Volume 89, No. ST4, Proceedings Paper 3608, August 1963.

11. Hirsch, T. J., "Field Tests of PreJtressed Concrete Piles During Driving," Report of the Texas Trans­portation Institute, Texas A&M University, August 1963.

12. Chellis, R. D., "Pile Foundations," McGraw-Hill Book Company, New York, 1961, p. 24.

13. Chellis, R. D., and A. F. Zaskey, Discussion of "Pile­Driving Analysis by the Wave Equation," by E. A. L. Smith, Transactions, ASCE, Vol. 127, 1962, Part I. p. 1145.

14. Lowery, Lee L., Jr., T. J. Hirsch, and C. H. Samson, Jr., "Pile-Driving Analysis-Simulation of Ham­mers, Piles, and Soils," A Report of the Texas Tram:­portation Institute, Texas A&M University, August 1967.

15. Olson, R. E., and K. S. Flaate, "Pile-Driving For­mulas for Friction Piles in Sand," Journal of the Soil Mechanics and Foundations Division, Proceed­ings, ASCE, November 1967, Paper No. 5604.

16. Agerschou, Hans A., "Analysis of the Engineering News Pile Formula," Journal of the Soil Mechanics and Foundations Division, Proceedings, ASCE, Pro­ceedings Paper 3298, October 1962.

17. Michigan State Highway Commission, "A Perform­ance Investigation of Pile Driving Hammers and Piles," Lansing, Michigan, March, 1965.

PAGE FIFTEEN

, TABLE A.l. PERMANENT SET OF PILE PER BLOW PREDICTED BY THE WAVE EQUATION-STEEL PILES >

Gl J11 Area Length Vulcan No. 1 Hammer Vulcan 80-C Hammer Delmag D-22 Hammer Cll

>< of of Pile Soil Resistance Soil Resistance Soil Resistance Soil Resistance Soil Resistance Soil Resistance

-i Pile (ft.) at point (kips) on side (kips) at point (kips) on side (kips) at point (kips) on side (kips) J11 (in.) 2 J11 z 50 200 50 200 100 400 100 400 100 400 100 400

30 1.23 0.23 1.88 0.38 1.16 0.08 1.73 0.18 1.45 0.15 2.53 0.25 [JJ

10 60 1.22 0.17 1.93 0.35 1.19 0.01 1.75 0.05 1.41 0.14 2.50 0.21 c:: 100 1.21 0.12 1.96 0.31 1.21 0.00 1.75 0.00 1.47 0.08 2.16 0.16 ::= 140 1.22 0.13 1.80 0.28 1.20 0.00 1.82 0.00 1.45 0.08 2.18 0.17 ::= 30 1.19 0.28 1.88 0.42 1.12 0.15 1.70 0.30 1.24 -0:26 2.19 0.18 >

20 60 1.18 0.27 2.01 0.43 1.09 0.13 1.73 0.28 1.17 0.29 1.86 0.14 ~ 100 1.20 0.27 1.87 0.44 1.08 0.13 1.83 0.27 1.09 0.13 1.64 0.28 140 1.20 0.27 1.85 0.42 1.20 0.13 1.80 0.26 1.09 0.13 1.61 0.29 0 30 1.18 0.28 1.93 0.41 1.09 0.18 1.66 0.33 1.28 0.24 2.53 0.36 >Tj

30 60 1.32 0.30 1.96 0.40 1.08 0.21 1.76 0.34 1.18 0.17 1.938 0.35 ""0 100 1.25 0.30 1.81 0.40 1.08 0.21 1.78 0.35 1.05 0.18 1.56 0.35 t:rj 140 1.30 0.28 1.93 0.37 1.15 0.22 1.70 0.36 1.05 0.18 1.46 0.30 ::0

::= > :.z: t:rj :.z: o-3 [JJ t:rj

o-3 > [JJ"CS

""0 "CS ::0 ~ t:rj = 0 ~ (=) ~ o-3 t:rj 0 to

TABLE A.2. PERMANENT SET OF PILE PER BLOW PREDICTED BY THE WAVE EQUATION-CONCRETE PILES >-<: o-3

Area Length Vulcan No. l Hammer Vulcan 80-C Hammer Delmag D-22 Hammer ::c: t:rj

of of Pile Soil Resistance Soil Resistance Soil Resistance Soil Resistance Soil Resistance Soil Resistance Pile (ft.) at ooint (kips) on side (kips) at point (kips) on side (kips) at point (kips) on side (kins) ~ (in.)' >

50 200 50 200 100 40() 100 4.00 100 400 100 400 < t:rj

30 1.20 0.26 1.69 0.37 1.03 0.15 1.57 0.27 1.30 0.18 2.15 0.31 t:rj

150 60 1.23 0.27 1.71 0.35 1.09 0.20 1.58 0.28 0.96 0.19 1.75 0.31 ,Q 100 1.25 0.27 ,. 1.57 0.3.5 1.11 0.21 1.61 0.32 1.16 0.21 1.68 0.30 ~ 140 1.34 0.27 1.93 0.33 1.12 0.17 1.65 0.31 1.18 0.21 1.51 0.34 o-3 30 1.21 0.23 1.74 0.31 1.09 0.18 1.51 0.27 1.32 0.22 2.04 0.34 0

275 60 1.26 0.22 1.68 0.26 1.12 0.23 1.58 0.26 1.23 0.25 1.74 0.28 :.z: 10.0 1.36 0.23 1.85 0.27 1.13 0.23 1.52 0.29 1.50 0.26 1.89 0.31 140 1.96 0.24 2.56 0.29 1.20 0.24 1.76 0.27 1.10 0.27 1.28 0.30

30 1.19 0.21 1.62 0.28 1.08 0.18 1.52 0.25 1.23 0.22 1.80 0.31 400 60 1.34 0.19 1.79 0.22 0.10 0.21 1.49 0.23 1.16 0.22 1.57 0.24

100 1.97 0.18 2.59 0.20 1.15 0.21 1.50 0.22 1.09 0.23 1.29 0.25 140 2.70 0.20 3.23 0.23 1.38 0.22 1.94 0.24 1.06 0.24 1.07 0.26