The force exerted by unbroken surface waves on a cylindrical object, such asa pile, which extends from the bottom upward above the wave crest, is made upof two components, namely:

  1. A drag force proportional to the square of the velocity which may berepresented by a drag coefficient having substantially the same value as forsteady flow, and

  2. A virtual mass force proportional to the horizontal component of theaccelerative force exerted on the mass of water displaced by the pile.

These relationships follow directly from wave theory and have been confirmedby measurements in the Fluid Mechanics Laboratory of the University ofCalifornia, Berkeley.

The maximum force exerted by breakers or incipient breakers is impulsive innature, reaching a value much greater than that produced by unbroken waves butenduring for only a short time interval. This impulsive force represents theultimate development of the accelerative force and is produced by the steepwave front and large horizontal acceleration at the front of a breaker. Thisimpulsive force greatly exceeds the drag force computed from the particlevelocities of the breaker.

The reader is cautioned that these preliminary results are applicable only tosingle piles without bracing and are likely to be modified somewhat wheremultiple piles are driven, one within the influence of the other or wheremultiple piles are connected by submerged bracing. This paper is essentially apreliminary report submitted at this time because of the current importance ofwave forces in the design of offshore structures. An extended series ofadditional experiments is planned for the near future.

Theoretical Relationships

For the sake of simplicity of treatment, the theory will be developed fromthe equations for waves of small amplitude.


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