Contact mechanics: relation between interfacial separation and load

I study the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. I derive a relation between the (average) interfacial separation $u$ and the applied normal squeezing pressure $p$. I show that for non-adhesive inte raction and small applied pressure, p is proportional to exp (-u/u_0), in good agreement with recent experimental observation.