You've also missed passive erosion. Obviously, specific numbers can't be given because the effect varies with the specifics of each beach. But it's not really r

You've also missed passive erosion. Obviously, specific numbers can't be given because the effect varies with the specifics of each beach. But it's not really rocket science, at least if you have ever lived close to a beach. To preserve a beach, you need the waves to leave behind as much solid material as possible. In an open beach, you can observe much of the wave being "absorbed" by the beach rather than "pulling back" in the sea. When the wave is "absorbed", any solids carried by the wave settle on the beach. If you place a wall on the beach: (a) you prevent the waves from reaching further inlands where they have been attenuated so they can be "absorbed" and leave the solids they carry behind, (b) you force them to "pull back" while they still carry a lot of energy, which will also carry away some of the existing solid material on the beach. Or, if you prefer a mathematical explanation, the waves shape the beach so that its vertical gradient is a continuous function. If you force a discontinuity (wall) in the gradient, the waves will shape the beach so that there is no discontinuity. I.e. either the wall will be destroyed, or the beach will erode and the waters will become deeper.