Pile Buck has a good text that dicusses earth loads, including seismic. And earth suppoort theories, including free earth. They really are two seperate issues unless you are looking for a paper on performanvce of free earth walls durring earthquakes. Compute your loads for earthquake (Monobe-Okabe is often used) as well as your other loads and apply to free earth analysis. Since free earth allows deflection of the toe of the sheet, and requires less embedment, liquifaction near the toe would be a concern to be investigated.
Hope that helps.
