Most cantilever retaining walls are designed by structural engineers, based on the soil parameters provided by a geotechnical consultant. The structural engineer needs whatever parameters are required to compute the loads and resisting forces. IBC (Table 1610.1) and other publications specify these load parameters in terms of equivalent active and at-rest/passive pressures. CRSI uses Rankine formulas to end up with a design based on, essentially, the equivalent fluid pressures. These may be excessive simplifications, but they have proven sufficient for a great many walls over several decades.
That said, I am in the middle of an update to the CRSI Design Handbook chapter 14 on cantilever retaining walls. If you have specific issues, I would really like to hear about them now (before the new edition is published), so we can be as useful as possible.
John Turner CSP PE
CRSI Greater Southwestern Regional Manager