CVEN 686

Offshore and Coastal Structures
Pile Driving Analysis by the Wave Equation

Class 1 - 3/21/16:  Flipped class - Watch an introductory video regarding Wave Equation Analysis for Driven Offshore Piles by clicking here (MP4) or here (MOV).  The video was recorded a couple of years ago when such things weren't nearly the quality we get today, so you will probably want to download the corresponding class notes to follow the video discussion.  Click here for the class notes.  Also, please glance through the classic paper on Pile Driving Analysis by the Wave Equation by E.A.L. Smith.  Click here for the paper.

Notes for Class 1:

The appropriate time interval for use in different materials with a pile segment length around 8 to 10 feet is given in Smith's paper.  See reference papers "Z" below, page 1165.

Total number of time intervals to run ~ length of pile * 4 (up and down twice) / (speed of wave * time interval used).  So for a 500 foot long steel pile:
                     = 500 feet*4/(16,700 ft/sec * (1 sec/4000 iterations))
                     ~ 500 iterations

You will note me messing around looking for information in a couple of tables in the video.  These tables are listed in the Data and Help files below.

Class 2 - 3/23/16:  Flipped class - Watch a video regarding setting up cases to run using the Wave Equation by clicking here (MP4) or here (MOV).  Click here for the corresponding class notes.  

Notes for Class 2:

Homework assignments:

  1. Due on 4/10/16 - Please email your solution in a single document to using CVEN 686 Pile Driving Homework as the subject line.

  2. Due on 4/15/16 - Again, email your solution.

Questions?  Email me at or see my office hours at

Ready to try the program?  See "The Microwave Programs" below, under Student Resources.


MICROWAVE - A computer program to study the behavior of piles during driving
Written by: Lee L. Lowery, Jr., PhD, P.E.
Department of Civil Engineering
Texas A&M University
College Station, Texas 77843-3136
Phone 979-845-4395

Data and help files

  1. Hammer data
  2. Helmet data
  3. Cushion properties
  4. Blank input calculation forms (PDF)
  5. Typical pile model
  6. Input Forms (XLS) for printing only - will not form data sets.
  7. Example input data set (ASCII text file ready to run under MW88)
  8. Example output set (ASCII text file)
  9. Problem to work in class

Computer programs for running the wave equation:

  1. The Microwave programs and other supporting programs including Editpad and DOSBox.  Note:  Do not left-click on this link.  Right click on it and then click on "Save Target As".  Then save it in a folder on your hard drive, or on a thumb drive.  It will save in your folder or thumb drive.  Then go to that folder and double-click on  It will make a "686Wave - Copy" folder with the files in it.  Double click on that folder to access the files.  Then copy those files and folders to a working folder of your choice, I suggest C:\686Wave.  Microwave (MW88.exe or MW87.exe - both the same) and other useful programs are in there, including Editpad (an ASCII editor for generating datasets) and DOSBox (a 32 bit program emulator.  You should also put your data in that folder and run everything from there.  
  2. MWMANWRD.doc - This is a Microsoft Word version of the user's manual, including all figures.  Simply right-click on this file, click on "Save Target As", and put it in a folder on your computer.
  3. MWMANUAL.htm - HTML version of the user's manual.
  4. MWMANUAL.pdf - The user's manual in pdf format, courtesy of Don C. Warrington who maintains an excellent site regarding pile driving analysis by the wave equation - a must read for serious practitioners. Don also has written an excellent paper regarding a closed form solution to limited cases for the wave equation.
  5. How to DOSBox - How to run Microwave (MW88.exe) using DOSBox.
  6. DOSBox - They also have Mac OS X, and other versions.  Take your pick.  The only one I have above is for Windows.  DOSBox is necessary to run the wave equation when using Windows 7, 64 bit computers.  Click on "Downloads" to download the DOSBox installer you need.  Put it in a known directory on your hard drive. Then run it from there.  I would suggest that you make a directory on your hard drive called "C:\686Wave".  Put the DOSBox installer there, and also download the MW88.exe program and all of your data files there.  It makes it easier to run everything.  Included in the package above.
  7. EditPad Lite - An ASCII text editor useful in generating wave equation data sets.  Included in the package above.

Hammer information sites:

  1. Don C. Warrington's excellent site

Reference Papers:

  1. The original E.A.L. Smith paper: Pile-Driving Analysis by the Wave Equation, ASCE Paper No. 3306, Vol. 127, 1962, Part I
  2. The original Samson, Hirsch and Lowery paper: Computer Study of Dynamic Behavior of Piling, ASCE Paper No. 3608, Aug. 1963
  3. Lowery's dissertation: Dynamic Behavior of Piling, Texas A&M University, May 1967
  4. A Comparison of Dynamic Pile Driving Formulas with the Wave Equation - 1968
  5. Driving Practices for Prestressed Concrete Piles - 1966
  6. Impact Load-Deformation Properties of Pile Cushioning Materials - 1966
  7. Pile Driving Analysis - State of the Art - 1969 - THE User's Manual for running MW87, Pile Driving Analysis by the Wave Equation
  8. Applications of Wave-Equation Analysis to Offshore Pile Foundations - OTC Paper 1055 - 1969
  9. Increasing the Ability to Drive Long Offshore Piles - OTC Paper 1064 - 1969
  10. Jonggeun Choe and Hans Juvkam-Wold Paper on Bottom-Hammering of Piles
  11. Pile Drivability Analysis - Fenske, Carl S. and Hirsch, T.J.  What happens when you hit sand lenses?
  12. 8th International Conference on the Application of Stress Wave Theory to Piles
  13. Application of Stress Wave Theory to Piles  One of a series.
  14. Driving pipe piles - potential for plugging during driving, page 74 

CVEN 686 - Historical Papers - Note: These papers were collected back in the 60's for use in research on pile driving. If you are the author of any of these papers and feel that it should not be included for student use in this historical summary, please email me at and I will remove it.

CVEN 686 4-18-11 - Class presentation back on 4-18-11