Deep Pile Axial Capacity in Clay (Alpha Method)
The analytical pile capacity beside helical-pile's torque correlation: in clay the alpha method takes Qult = alpha cu (pi D L) skin friction plus 9 cu (pi D^2/4) end bearing. A 16 in pile 40 ft into cu = 1 ksf clay carries 105 kip ultimate (88% in skin friction) and 35 kip allowable at FS 3 - and doubling the length nearly doubles it while the tip term stays put, which is why a friction pile is lengthened, not fattened. Single pile, uniform clay, total-stress method. A design aid; the geotechnical engineer and a load test govern.
Formula and source
As = pi D L; Ap = pi D^2/4; Qs = alpha cu As; Qp = 9 cu Ap; Qult = Qs + Qp; Qall = Qult / FS.
The alpha (total-stress) method for the static axial capacity of a pile in clay -- skin friction alpha cu over the shaft plus end bearing Nc cu (Nc = 9) at the tip -- with the adhesion factor alpha (~1.0 soft to ~0.5 stiff) as compiled in the FHWA driven-pile manual and Das (Principles of Foundation Engineering), and the customary factor of safety of 2 to 3 without a load test, by name.
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