MikeAll:
In your thinking process, you have to keep several things in mind. Your mats have to be properly proportioned w.r.t. each other, layer to layer, to work well together, you have to pay attention to alternating the spanning directions of the mats when they are made of something like individual 6x6 timbers, for example, and you have to consider the relative strength/stiffness of materials in the various layers. Your mat problem is really a gridwork of beams problem, a beam on spring supports problem, or a beam on an elastic foundation problem, and the engineering theory and thinking involved in these problems should color your approach. Look at some good Strength of Materials, Theory of Elasticity or Structural Design and Analysis textbooks, and/or Google those topics. The main ideas are to distribute the concentrated load to a larger bearing area with each successive layer downward, and that there must be compatibility of deflection from layer to layer for this to work.