I'm looking for codes that can do this for saturated and/or unsaturated porous media. I expect there are a few that can handle the porosity changes easily, but predicting permeability changes seems much more complicated.
I'm not sure how much of sophistication you are after but very basic levels of porosity change is implemented in USGS's code PHREEQC. I think tools like TOUGHREACT has some extent of capability to incorporate porosity/permeability changes. However, I suspect that the codes used by petroleum engineering community should have better capability dealing with permeability changes because they deal with permeability more often than subsurface and/or mining people! My two cents...
Let us say, precipitation decrease porosity till clogs pores, the specific yield also decreased may reaches zero. Some times the specific yield amount can be considered as an effective porosity of media, which generally controls the permeability of sediments.
There are few noncommercial softwares that are able to simulate the effect of salt precipitation on soil porosity and mermeability. In these softwares, the Richards equation is resolved numerically and the soil permeability and porosity are assumed varying as fuction of the solute concentration.