ZWAVE was Vulcan’s foray into the wave equation program field. It was an outgrowth of research that dated back to the late 1970’s on the magnitude of impact forces of its hammers on pile tops, so as to estimate both the loads on the equipment and the stresses on the piles. The first tangible result of this was a method and computer program based on numerical methods applied to semi-infinite pile theory; this was presented at the Offshore Technology Conference in 1987.

It became clear, however, that such a solution would not be as comprehensive as necessary, so ZWAVE was developed. Developed for MS-DOS computers, it’s “Preliminary Trial Release” (beta version) was released in 1987. The two proper releases (1.0 and 1.1) were done in 1988, after which time there was some work done the program but it had no further releases.  (The user’s manual for 1.0 can be downloaded here.)


Also in 1988 was the paper describing the program, “A New Type of Wave Equation Analysis Program,” presented at the Third International Conference on the Application of Stress-Wave Theory to Piles in Ottawa, Ontario, in May 1988. This paper is available in PDF format and can be downloaded by clicking the link below.

Click here to download “A New Type of Wave Equation Analysis Program”

Unfortunately ZWAVE’s copyright status makes it impossible to make the program available for download. The paper, however, shows many of the advanced features of the program which were both referenced by later authors and included in later wave equation programs.


Abstract for “A New Type of Wave Equation Analysis Program”

This paper describes a new wave equation analysis program called ZWAVE, which is a program specifically for external combustion hammers. The program is described in detail, the discussion dealing with topics concerning the program such as 1) the numerical method the program uses to integrate the wave equation, which is different from most other wave equation programs; 2) the modelling process of both cushioned and cushionless hammers; 3) the automated generation of mass and spring values for both hammer and pile; 4) the method of dealing with plastic cushions; 5) the use of a recently developed model for computing shaft resistance during driving; 6) the computation and generation of values based on basic soil properties such as shear modulus, Poisson’s Ratio and soil density; 7) the completely interactive method of feeding data to the program; 8) the method used to compute the anticipated rebound and the energy used to plastically deform the soil; and 9) the format of the interactive input of the program and the program’s output. Sample problems for the program, along with comparison of the program results with data gathered in the field, are presented.


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