The analysis for anchored pile walls can be performed either by free-earth or fixed-earth conditions, dependent on the capacity of the available solver.
1. Free-earth method: When penetration depth (D) is small, passive earth pressure below the excavation can't provide sufficient support for sheet pile movement. The sheet pile can be assumed as rigid and rotate freely about anchor point (A), as shown in Fig. 9-12 (a). Applying Rowe's moment reduction chart can reduce the design bending moment. This method is not recommended for soft soil layers as base stability can't be assured.
2. Fixed-earth method takes advantage of the more considerable embedded depth of the sheet pile to add redundancy to the pile wall system (Figs 9-12, b and c). It provides a solution more relevant to the actual design and construction using considerable pile depth, especially in the Bangkok clay region. Furthermore, using an inflection point gives less bending moment and shear force for section design. Therefore, the fixed earth method usually leads to a more economical section of sheet pile walls.
Ref: Sheet Pile Design by Pile Buck