The force exerted on piles by waves is usually expressed as the sum of the drag force and the virtual mass force. When breaking waves act on piles, an impact force is added to the above forces. The impact force is produced by the collision of a vertical wave front which moves with the velocity of breaking wave celerity. Since the wave front loses a part of its forward momentum at the instant of collision, this change in the momentum yields a force of large magnitude.
　By assuming the height of the vertical wave front being ληc where ηc is the crest height above the mean water level, the total impact force on a pile has been calculated as:
　F1=γDHB2KBλ
in which KB is a factor related to the breaking wave celerity and crest height. The parameter λ may be called the curling factor of breaking waves.
　This impact force is characterized with the short duration: e.g., some 0.02 seconds for model piles. The resultant stress in a pile or the measured force on a model pile depends not only upon the magnitude of the impact force, but also upon the product of the duration time, τB, to the natural frequcncy of the system. f. Hence the effective impact force is expressed with the impact response factor Xmax(fτB) as (FI)e=FIXmax.
　Experiments have been done for four test piles of circular sections with the diameters of 4.3 and 7.6 cm, square section of 5.0 cm wide, and triangular section of 7.1 cm wide. For the waves with the period of 1.93 seconds breaking at a water depth of 15 cm on a steep slope of 1 to 10, the same value of λ=0.4 was found to be applied for the four piles tested. The maximum values of (FI)e/γDHB2, 1.6 for the circular piles, 3.6 for the square pile, and 1.3 for the triangular pile, were in good agrreement with the results of the theory.
　The magnitude of the curling factor λ was then investigated for various wave conditions. As the relative water depth h/L decreased from 0.10 to 0.06, the magnitude of λ increased gradually from the value of 0.3 to 0.4 on the steep slope of 1 to 10 and from 0.07 to 0.10 on the gentle slope of 1 to 100. This tendency agrees well with the general observation of breaking waves which show the strong curling and plunging as the wave steepness decreases and the bottom slope becomes steep.
　Based on the above analysis and experiments, the maximum breaking wave force acting on the total length of a pile has been formulated as the sum of the three forces of drag, virtual mass, and impact with the curling factor being the parameter of the summation.