Wave Force on a Pile

What is modelled

A slender pile does not change the wave much, so the force on each slice of it is found from the undisturbed water motion with the Morison equation: a drag force that follows the square of the water speed, and an inertia force that follows the acceleration. The wave comes from linear theory, and the forces are added up over the depth to give the total force and the overturning moment at the seabed.

Equations

• Morison f = ½ ρ Cd D u|u| + ρ Cm (πD2/4) ∂u/∂t.
• Linear wave u = (πH/T) cosh k(z+d) / sinh kd · cosθ, with ω2 = g k tanh kd.
• Inertia peak ρ g Cm π D2 H tanh(kd) / 8.
• Keulegan-Carpenter number KC = umax T / D.

Checks run in the page

• The wave-number equation and its limits.
• The inertia force and moment against closed forms.
• The drag force against its closed form.
• The peak of the sum against the bounds from its two parts.

Honest simplifications

Small-amplitude waves with the load integrated to the still-water level, no current, no breaking or slamming, no group effects from several piles, constant coefficients, and a solid timber pile with a single allowable stress. Real design uses nonlinear waves, wave-breaking loads and site-specific coefficients.

• Press Short steep chop and Long swell, thin pile and compare the Keulegan-Carpenter number.
• Press Fat pile, small waves: the inertia part dominates.
• Raise the wave height and see the moment grow faster than the height.