# «PILE DRIVING ANALYSIS BY THE WAVE EQUATION For technical assistance, contact: Dr. Lee L. Lowery, Jr., P.E. Department of Civil Engineering Texas A&M ...»

## PILE DRIVING ANALYSIS

BY THE

## WAVE EQUATION

**For technical assistance, contact:**

Dr. Lee L. Lowery, Jr., P.E.

Department of Civil Engineering

Texas A&M University

College Station, Texas 77843-3136

409-845-4395

e-mail: LLL2761@zeus.tamu.edu

(c) 1993 Wild West Software

2905 South College

Bryan, Texas 77801

Permission granted to copy both software and user's manuals so long as original author credits remain

## TABLE OF CONTENTS

CHAPTER 1. INTRODUCTIONCHAPTER 2. BASIC USES OF THE WAVE EQUATION

Introduction

Hammer Selection

Selection of Driving Accessories

Cushion Selection

Helmet Selection

Pile Size

Prediction of Pile Load Capacity

Initial Driving

Final Driving

Soil Set Up or Relaxation

Driving Stresses in Point Bearing Piles

Use of Wave Equation for Field Control

Basic Output

Input Data Summary

Solution Summaries

Selection of Allowable Stresses for Pile Materials

CHAPTER 3. INFORMATION REQUIRED FOR ANALYSIS

Introduction

Problem Information Forms

Example Problem

Discussion of Solution of Example Problem

Recommendations Based on Example Solution

CHAPTER 4. THE COMPUTER PROGRAM

Introduction

General

The Numerical Solution

Idealization of Hammers

The Ram

The Anvil and Helmet

Ram Velocity at Impact

Open-end diesel hammers

Closed-end diesel hammers

Double-acting air and steam hammers

Single acting air and steam hammers

Idealization of Cushions

Idealization of the Pile

Pile Segment Length

Pile Segment Weight

Pile Segment Springs

Limiting Forces Between Pile Segments

Slack in Joints

Idealization for Soils

Soil Quake and Damping

APPENDIX A - COMPUTER PROGRAM INPUT DATA

Introduction

Program Input Data

NOP(I) Functions

APPENDIX B - CODING SHEETS

APPENDIX C - HAMMER, CUSHION, AND SOIL PROPERTIES

TABLE C1 - Summary of Steam Hammer Properties

TABLE C2 - Summary of Diesel Hammer Properties

TABLE C3 - Summary of Constants for Commonly Used Cushion and Capblock Materials

TABLE C4 - SOIL PROPERTIES

APPENDIX D - SAMPLE PROBLEMS

Case I

Case II

Case III

Case IV

Case V

Case VI

Case VII

Case VIII

Case IX

Case X

Case XI

Case XII

Case XIII

Case XIV

Case XV

Case XVI

Case XVII

APPENDIX F - LIST OF SELECTED REFERENCES

APPENDIX G - MICROWAVE/EDITWAVE

Introduction - MICROWAVE

Program Operation

EDITWAVE

MICROWAVE

Sample Computer Session

To run the data using MICROWAVE

** LIST OF FIGURES**

Figure 1. RUT vs Blow Count Curves for Comparison of Different Pile Driving Hammers; Cases I, II, and III

** Figure 2. RUT vs.**

Blow Count Curves for Comparing the Effects of Varying Cushion Thickness Using a Delmag D-15 Hammer; Cases III, IV, and V

Figure 3. RUT vs Blow Count Curves for Comparing the Effects of Changing Helmet Weight Using a Delmag D-15 Hammer; Cases V and VI

Figure 4. RUT vs Blow Count Curves for Comparing the Influence of Changing a Pile's Crosssectional Area Using a Vulcan 010 Hammer; Cases VII, VIII, and IX

Figure 5. Pile Load Capacity vs Time After Driving to Determine Soil Set-up or Recovery of Strength After Driving in Cohesive Soil (After Reference 29)

Figure 6. RUT vs Blow Count for a Tapered Pile Driven with a Vulcan 010 Hammer to Full Penetration; Case X

Figure 7. Soil Resistance Distribution for a Tapered Pile During Driving and for Long Term Capacity; Cases XI and XII

** Figure 8. RUT vs Blow Count for a Tapered Pile Using a Vulcan 010 Hammer; Case XI.**

........ 18 Figure 9. RUT vs Blow Count for a Tapered Pile Using a Vulcan 010 Hammer; Case XII....... 19 Figure 10. RUT vs Blow Count for a Kobe K-25 Hammer Driving a 60 Foot Pipe Pile; Case XIII

Figure 11. RUT vs Blow Count for a Delmag D-44 Hammer Driving a 60 Foot Pipe Pile to 40 Foot Penetration; Case XIV

Figure 12. RUT vs Blow Count for a Vulcan 30C Hammer Driving a 10 Inch by 10 Inch Prestressed Concrete Pile; Case XV

Figure 13. RUT vs Blow Count for a Link Belt 312 Hammer Driving a 12" by 12" Prestressed Concrete Pile; Case XVI

Figure 14. RUT vs Blow Count for an MKT DE-30 Hammer Driving an HP8x36 Steel Pile; Case XVII

Figure 15. Cross-sectional View of a Drop or Steam Hammer for Representation of Various Sections

** Figure 16. Cross-sectional View of a Diesel Hammer for Representation of Various Sections.**

. 29 Figure 17. Cross-sectional View of a Pipe Pile with an Add-on Section

Figure 18. Penetration Below the Mudline for a Soil Boring Sample

Figure 19. Pile Penetration in Feet vs Resistance to Penetration in kips

** Figure 20. Assumed Soil Resistance Distribution for Problems 1&2, Distributed Along the Side and at the Point of the Piles for Varying Penetrations.**

** Figure 21. Wave Equation Results for Example Problems 1 & 2.**

Figure 22. Idealization of a Pile for Purpose of Analysis - Pile is Divided into Uniform Concentrated Weights and Springs

** Figure 23. Idealization of Steam Hammer with Capblock and Cushion in Hammer-Pile System 43 Figure 24.**

Idealization of Steam Hammer with Capblock Only in Hammer-Pile System........... 44 Figure 25. Idealization of Diesel Hammer with Capblock Only in Hammer/Pile System............ 45 Figure 26. Definition of Coefficient of Restitution for Cushioning Material

Figure 27. Soil Load/Deformation Characteristics

Figure 28. Idealization of Steam and Drop Hammers

Figure 29. Idealization of Diesel Hammers

Figure 30. Idealization for Case I

** Figure 31. Tapered Pile with a 5 Gage Wall Driven with a Vulcan 010 Hammer; Case X.**

........ 77 Figure 32. Raymond Step-Taper Pile Driven with a Vulcan 010 and Kobe K-25 Hammers to Full Embedment; Cases XI and XII

** LIST OF TABLES**

TABLE 1 - Stresses for Various Hammers

TABLE 2 - Stresses for Various Cushions

TABLE 3 - Stresses for Various Helmet Weights

TABLE 4 - Stresses in Point Bearing Pile - CASE XIV

TABLE C1 - Summary of Steam Hammer Properties

TABLE C2 - Summary of Diesel Hammer Properties

TABLE C3 - Summary of Constants for Commonly Used Cushion and Capblock Materials61 TABLE C4 - SOIL PROPERTIES*

** CHAPTER 1. INTRODUCTION**

During the past few years, the use of the wave equation to investigate the dynamic behavior of piling during driving has become more and more popular. Widespread interest in the method was started in 1960 by E.A.L. Smith who 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 the soil during driving. Since then, a vast amount of experimental data has been taken to determine just what input values should be used in the program, and numerous full-scale pile tests have been correlated which now permit engineering judgement to be coupled with the mathematical accuracy of the wave equation.

In recent years, the wave equation has been used extensively by both state highway departments and private contractors to predict the ability of given pile driving hammers to successfully install pile foundations.

In general, the computer solution is used to obtain the following information for a single

**blow of the hammer:**

1. To predict the driving stresses induced in the pile.

2. To determine the resulting motion of the pile during the impact.

3. To determine the resistance to penetration afforded by the soil at the time of driving.

**This information then enables the engineer to answer such questions as:**

1. Can a given hammer drive the pile to the required depth of penetration?

2. What rate of penetration will the hammer provide, i.e., how long will it take to install the pile?

3. To what maximum penetration can the pile be driven?

4. What is the maximum resistance to penetration that the hammer can overcome?

5. Will excessive stresses be set up in the pile or hammer during driving?

The wave equation is quite often used as an aid in design. For example, it is commonly

**used:**

1. To indicate the static resistance to penetration of the pile afforded by the soil at the time of driving. (Note that the wave equation only predicts the resistance to penetration at the time of driving since soil set up, group effect, negative friction, and other time effects may influence the long-term bearing capacity. Only the use of engineering soil mechanics can transform the resistance to penetration at the time of driving into the long-term bearing capacity).

2. To optimize the cushion, i.e., to determine which cushion will effectively limit the driving stresses induced in the hammer and pile, and yet will still produce the maximum possible permanent set per blow of the hammer.

3. To determine the correct size of the driving hammer. This reduces the chance of picking a very large and expensive hammer whose capacity is not needed, as well as the more unfortunate situation of picking a small hammer whose driving capacity is found to be inadequate to drive the pile to the required grade.

4. To design the pile itself, since the driving stresses can be determined. For example, tensile cracking of prestressed concrete piles, and the buckling of pipe piles are but two examples of driving failures which have been corrected by use of the wave equation. The choice of pile dimensions not only affects the driving stresses, but the drivability of the pile itself. For example, in some cases, a pile with a small cross-sectional area cannot be driven to grade, whereas a pile having a larger cross sectional area can. Thus, with the use of the wave equation the economic merit of being able to drive the stiffer pile to a greater depth can be studied.

5. To determine the influence of the driving accessories. It has been shown that in many cases the driving accessories absorb a major portion of the total energy output of the hammer. In some cases, these accessories account for a 50% reduction in the energy output of the hammer.

The use of the wave equation enables the selection of optimum driving accessories required to minimize these losses.

6. The wave equation is also a powerful engineering aid for the structural engineer, since numerous alternative designs can be quickly studied at very little expense. Such a study greatly increases the probability that the final design will be the most economical and least subject to installation problems.

In the discussions which follow, sample problems have been solved and the results plotted to demonstrate how the wave equation is utilized to solve various problems. Discussion of the method by which the given input data are utilized, and how values are assigned to the computer program are given in Appendix D.

Basically, the wave equation is used to describe how stress waves are transmitted in a long rod when a force is applied at one end of the rod. The idea of applying the wave equation to pile driving first came from D.V. Issacs, in 1931. But it was not until 1960 that widespread interest in this method was generated by E.A.L. Smith, who proposed a numerical solution to investigate the effects of such factors as ram weight, ram velocity, cushion and pile properties, and the dynamic behavior of the soil during driving. The theory behind the wave equation has not used until this time because the equations involved in the calculations were too difficult due to complications from the actions of the ram, the capblock, the pile, and the soil. However, the development of high-speed digital computers permitted the wave equation to be applied to practical pile driving problems.

In application, the hammer-pile-soil system is idealized as a series of concentrated weight connected by weightless springs. This idealization is described in detail in the users manual.

Whereas the wave equation accurately models the true dynamic behavior of driven piles, previous methods of analysis such as standard pile driving equations do not. Furthermore, standard pile driving equations cannot be used to predict the driving stresses generated in piles, as can the wave equation.

The purpose in developing this manual was to assist highway engineers in the understanding, use, and practical application of pile driving analysis by the wave equation. Thus, a simplified users manual with numerous example problems, including preparation of input data, and an interpretation of the results are included.

The previous users manuals prepared by the Texas Transportation Institute at Texas A&M University were written mainly for research use rather than production runs. Also, the previous manuals and programs include numerous options of no value to highway engineers, and were of research interest only. The current manual has been extensively simplified, and the computer program modified to run much faster than earlier versions.

## CHAPTER 2. BASIC USES OF THE WAVE EQUATION

Introduction The uses of the wave equation shown herein are hammer selection, selection of driving accessories, effect of pile size, prediction of pile load capacity, determination of driving stresses in point bearing piles, use of the wave equation for field control, basic output, and selection of allowable stresses for pile materials.**Hammer Selection**

The proper selection of the hammer to drive a given pile is necessary in order to insure the ability of the hammer to drive the pile to the desired penetration, and to prevent over stressing of the pile. The following cases have been analyzed using the wave equation to compare the differences between the drivability of three different hammers driving a typical concrete pile.