Thirty Years of Experience with the Wave Equation Solution Based on the Method of Characteristics

"This paper will describe a brief history of the method of characteristics as an accurate solution of the wave equation, and the author's experiences with the method of characteristics over a period of 30 years.As a result of the offshore pile driving activities associated with the development of the North Sea oil fields in the 1970's, two Dutch companies initiated extensive research efforts. Heerema started to research the dynamic behavior of soil during driving and HBG (Hollandsche Seton Groep) extended the method of characteristics with a straightforward theoretical solution for the shaft friction along a pile.The research institute TNO started the development of the wave equation program TNOWAVE in the late 1970's based on HBG's friction model extension for the method of characteristics. Today the program has a worldwide application in the field of pile testing. This paper will describe its development and application over time and its relation to today's applications for driveability studies for impact hammers (PDPWAVE) and vibratory hammers (VDPWAVE), signal matching for Dynamic Load Testing (DL TWAVE), Pile Integrity Testing signal matching (SITWAVE), and Statnamic simulation (STNWAVE).The paper will highlight that these developments have been the result of multi-disciplinary and multi-national efforts and encourage geotechnical engineers to seek further developments of the wave equation program in a similar manner. Finally, the paper will indicate some areas where such further developments are required."