According to this site, "[t]he elephant's digestion system is quite inefficient and only around 50% of the fodder eaten is utilised." That means that elephant dung is full of undigested plant fibers. (A number of people make paper from the fiber recovered from elephant dung.) When the dung is trampled by elephants walking over it, the fibers are pushed down into horizontal randomly oriented layers. If the digested portion of the dung was dissolved or washed away by water, you would have layers of fibers, the "straw mats". All of this, of course, is my own analysis, and I can't add it to the article without a reliable source to cite.  Donald Albury