### Abstract:

A numerical model is developed to estimate wave forces on A-Jacks armor units. The forces include drag, inertia, buoyancy, and slamming as the unit penetrates the free surface. The wave force model is used to determine the rigid body motions of the units. Bulk forces on a matrix of units are also estimated. Wave flume tests are used to provide preliminary verification of the wave force model.
The wave force model discretizes the A-Jacks into a number of small elements. The Morison equation is used for submerged elements with stretch linear wave theory employed for wave kinematics. For elements that penetrate the free surface, slamming force calculations are based on the von Karman method. The calculated wave forces are used to determine the rigid body rotation of a single, unrestrained A-Jacks. The axes of rotation are defined by the three contacts between the unit and the under layer. The model allows for an individual A-Jacks unit to rotate with one degree of freedom about
the axis of rotation with the minimum stability. Adjacent units do not restrain the rotation and interactions with other units in the matrix are not included. The equation of motion
is integrated in time to determine the rotation. This technique is used to determine the incipient motion conditions for a single, unrestrained A-Jacks. This is verified with experimental observations. The wave force model is found to be in agreement with the incipient rotational motion experiment results. The angular velocity at the instant when a lea of the unit rocks back and impacts the under layer can also be used to determine the impact force on the leg.
A single, unrestrained A-Jacks is a simplistic idealization. In reality, there is a high degree of interaction among the units. The interaction results in partial sheltering from wave forces and additional motion restraint. The bulk forces on a matrix of A-Jacks units are estimated by applying an empirical factor to the calculated forces to account for the sheltering effects among units. A calibration and preliminary verification of the bulk force models is obtained by measuring forces exerted on a matrix of units mounted on a load-frame. The A-Jacks were subjected to a variety of wave conditions in a 10 m wave flume. The measured bulk force on a matrix of units was fit with the numerical model output using a consistent set of sheltering coefficients.