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A Primer on Foundation Dispersive Wave Testing – Technical Note 117

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The Principles of Dispersive Wave Propagation

Dispersive wave propagation is the name of an area of science which considers how wave motion in solid materials is affected by the mechanical properties and geometry (i.e., boundaries, discontinuities) of the material. Any strike to the surface of a solid creates a disturbance that propagates throughout the solid as a wave. Ideally, if the velocity of the disturbance is constant and the speed and time required for it to travel up and down a solid could be measured, the physical length of the solid could be calculated as the product of velocity and travel time. A disturbance, or wave, in a solid material with bounded surfaces continuously changes its shape and elongates as time passes and a single speed cannot be determined. This phenomenon is known as dispersion.

To treat such behavior, dispersive waves in materials which have linear stress-strain diagrams can be represented mathematically as the algebraic sum of numerous separate frequencies, each traveling at its own velocity. It is different frequencies traveling at different speeds which cause the "change in shape" phenomenon. As they travel through a solid, the frequencies reflect and refract from internal boundaries (e.g. the foundation's tip or significant fractures or breaks). Thus, analyzing a dispersive wave to determine the distance to the foundation's tip, or to determine the location of a significant fracture or break, becomes the problem of determining the individual wave speeds of individual frequencies and determining the time needed for each to travel to, and reflect from, one of those boundaries.

The Testing Methodology

Foundation dispersive wave propagation tests are conducted by temporarily mounting accelerometers (gauges) at select locations in the foundations' exposed surface and then applying a strike impulse at various potential positions in the surface of the foundation. For a given foundation, an optimum impulse is selected as most effective for the given structural situations from the standpoint of clarity and transmission of the generated dispersive wave.

Schematic of a Typical Dispersive Wave Propagation Test

The waves created by the impulse propagate up and down the foundation's length with the reflections being recorded and stored on a digital storage oscilloscope as they return to the top. The data then is analyzed by digital signal processing techniques using special proprietary software. The analysis permits computation of the velocities of individual frequencies comprising the waves and for the time needed for them to travel from the gauges to the bottom of the concrete and back. The foundation's length then is computed from the product of frequency velocity and the time required for travel.

Typical Accelerometer Responses on Foundation Pile

The Results

Wave speed calculations are typically performed by mounting two gauges on or near the foundation's tops, and recording waves as they travel between the gauges. The time needed for various frequencies comprising the wave are determined with these times divided into the measured distances between the gauges. This leads to wave speed computations for the various frequencies that are used in the overall length computations.

Foundation length computations are performed by measuring the time needed for various frequencies to travel from a foundation's top to its bottom. The length so determined reflects the condition of the foundation in the following manner:

A) If the concrete within the foundation does not have any complete breaks, major voids, or severe cracks, (i.e., the concrete has continuity) the "computed length" will be the value for the distance from its top to its bottom.

B) If there were a break in the concrete, or major void, a strong return would be found on the record at the approximate location of the break. The computed length then would be the distance from the foundation's top to the location of such a material anomaly.


Computed vs. Recorded Foundation Pile Lengths

Applications For Dispersive Wave Propagation Testing

Foundation dispersive wave testing is versatile and non-destructive. Furthermore, unlike core drilling or excavations, only limited access is required to the foundation under test. This not only reduces the cost of testing and analysis, but also opens application areas where testing might not previously have been feasible.


Typical advantages of the dispersive wave testing are:

 Surrounding load bearing soils are not disturbed.
 Tower presence does not interfere with tests.
 No weather delays; testing can even be done underwater!
 Individual anchor piles under a common pile cap can be tested.
 Bracing or other foundation attachments do not affect results.
 Identifies major breaks, voids and areas of material deterioration.



  1. J.D. Holt, Tower Solutions: No More Guessing, Wireless Review, Intertec Publishing, February 15, 1998, pg. 156.
  2. R.A. Douglas and J.D. Holt, "Determining Length of Installed Timber Pilings by Dispersive Wave Propagation Methods," Final Report. Research Project Number 23241-92-2. North Carolina Department of Transportation, Federal Highway Administration, U.S. Department of Transportation, June 1993.
  3. J.D. Holt, S. Chen, and R.A. Douglas, Determining Lengths of Installed Timber Piles by Dispersive Wave Propagation," Transportation Research Board, National Research Council, Transportation Research Record No. 1447, pg. I 10.
  4. J.D. Holt, "Finding Lengths of Installed Steel Piles by Bending Wave Propagation," 5th International Conference on the Application of Stress Wave Theory to Piles, Orlando, FL, September 1996.
  5. H. Kolsky, "Stress Waves in Solids," Dover Publications, New York, 1963.





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