Compression of soil around roots

A simplified model is developed for soil compression around plant roots. The main assumptions are that the root volume is accommodated by loss of porosity in the surrounding soil; that there is a minimum soil porosity below which soil will not be compressed; and that the density decreases exponentially with distance from the roots surface with an exponent which is a constant multiple of the root diameter. These assumptions lead to simple, practical expressions for the soil porosity around roots and for the amounts of materials such as nutrients or organisms which lie within certain distances from a root surface.