Adhesion of rigid rough contacts with bounded distribution of heights

We develop a "Bradley" (rigid) model for a rough surface with bounded or non-bounded distribution of heights. We observe a large effect of the distribution of heights: for example, for Weibull distributions, the decay from the theoretical strength becomes an inverse power law with the roughness amplitude normalized by the adhesion interaction distance. For Gaussian surfaces which are in principle unbounded distributions, only weak dependence is found on the details of the roughness spectrum. If the truncation comes from a natural process like wear where the height distribution is squashed at a certain truncation level, the latter factor dominates.