Van der Merwe’s method, which was first introduced in the 1960’s, is a simple method for estimating the vertical movement of expansive soils. The method at its most basic is described in publications such as Foundations in Expansive Soils, and basically looks like this:
The problem with this presentation is that it is entirely in “Imperial” units, which were the standard in the South Africa of van der Merwe’s day. We need to convert this to make it usable in SI units as well. First we present the potential expansion chart, from Soil Mechanics:
Then we reconstruct van der Merwe’s equation to make it applicable for SI units as well as US (or Imperial) units:
Note that the swell potential is now in the denominator. That’s a convenience to make the PE values of a reasonable order of magnitude. But now it’s dimensionless. Also note that the depth reduction factor has a different exponent for SI units than it does for US units.