Rather exotic, but hydrophobic cellulose expands upon drying, by a factor of 4 or 6 the first time it gets wet then dries. After a few wet-dry cycles it seems to settle around 3.5 times. Just a quick look shows the extra volume may be air, so strength could be a problem for your application.
A chemically modified hydrophobic cellulose material was wetted by force in vacuo and allowed to dry under ambient conditions. Most known materials shrink upon drying and swell upon wetting, a phenomenon known as dry-shrinkage; and thus are characterized by a dry-shrinkage coefficient either...
(above found with a Google search of: material that expa
I just entered the above string and picked one of Google's search suggestions.)
There are several grout formulations used for this purpose (popular in sinkhole country). There are also recipes used for actual demolition - they expand so much that they break up the slab/rock under which they are injected. I'm not aware of any 'soil' that expands when dry, but the soil from my garden seems to uniformly distribute around the interior of my house if I don't properly wipe my feet (according to my wife).
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