Equation (1d) is a form of Miner's Rule (see Wikipedia). The fifth power comes from Markl's fatigue curve.

Your math looks right but I don't know if you can work this with half cycles. Wikipedia mentions that Miner's may fall apart when there is a big excursion followed by small excursions.

Some Codes address one-time displacements (settlement) directly. The stress (range) from a single, one-time displacement is limited to 3Sh.