Pile Embedment Length for a Target Capacity (Alpha Method)
The inverse of the pile-axial-capacity tile: the embedded length that carries a target allowable load, L = (Qall x FS - Qp) / (alpha cu pi D), since the tip Qp is fixed by the diameter and the skin friction must supply the rest. A 16 in pile in cu = 1 ksf clay carrying 50 kip at FS 3 needs ~60 ft. Single pile, uniform clay. A design aid; the geotechnical engineer and a load test govern.
Formula and source
L = (Qall x FS - Qp) / (alpha cu pi D), with Qp = 9 cu (pi D^2/4); the alpha-method Qult = alpha cu (pi D L) + Qp solved for the embedded length.
The alpha (total-stress) method for a pile in clay, as compiled in the FHWA driven-pile manual and Das (Principles of Foundation Engineering), with the customary factor of safety of 2 to 3 without a load test, by name.
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