User friendly (classical) theories of earth pressure (Coulomb and Rankine) don't work well with single piles, partly because a pile is a small, three-dimensional object - rather than a two-dimensional wall. Also because active and passive earth pressures are not mobilized until complete failure.
However there are controversial ways that can be used, the easiest is a "Prescriptive Solution". See paragraph 7.2.2 of this State of Indiana DOT document (page 49 of the 75 page .pdf download) for both a warning and an answer to your question
Try the USACE.
They have a pretty good one for the lateral pile resistance.
Used mathcad to calculate the springs and the results from SAP matched exactly those from MPILE.
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