The monograph Anchored Sheet Pile Wall Analysis Using Fixed End Method Without Estimation of Point of Contraflexure, which appeared on this site very early in its existence (October 2007) has been very popular. The online routine described in the report, which you can use, is found here. The abstract for the paper is found here:
The fixed end method used for the design of anchored sheet pile walls has been used with success since before World War II; however, computational limitations have forced designers to use simplifications such Hermann Blum developed. The original method called for the use of an “elastic line” solution, where the penetration of the sheet piling below the excavation line was estimated using statically indeterminate beam theory. This paper develops the governing equations for the “elastic line” method for a simple case and presents the solution in two ways: parametrically using charts, and for specific cases using an online computer algorithm. Comparison with other solution techniques is presented, and suggestions for broader applications are made. The adjustment of the penetration for the residual toe load is also discussed, and the limitations of current practice in this adjustment are detailed.