Pile Embedment Length for a Target Capacity (Alpha Method)
The embedded length that carries a target allowable load.
Example
You enter
- Target allowable capacity Qall (kip) 50
- Pile diameter D (ft) 1.33333
- Undrained shear strength cu (ksf) 1
- Adhesion factor alpha (~0.55 medium stiff) 0.55
- Factor of safety FS 3
You get
- Required embedded length L 59.7 ft
- End bearing Qp (Nc = 9) 12.6 kip
Checked against published worked examples from: Middle East Technical University, Dept. of Civil Engineering (CE 366).
Details, formula, and sources
ScopeL = (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 or tableL = (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.
Source and editionThe 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.
Free accessThe FHWA driven-pile design manuals are free at fhwa.dot.gov; the alpha-method relations are public in the standard foundation texts.
What governsEstimate. AHJ and licensed professional govern.
API field namesqall_target_kip, d_ft, cu_ksf, alpha, fs, l_ft, qp_kip
- Skin friction supplies the remainder L sized so alpha cu (pi D L) = Qall x FS - QpFHWA / Das alpha method
- End bearing qp = 9 cu over the tip area (Nc = 9 for a deep foundation in clay)Skempton / FHWA
- Safety factor the customary 2 to 3 on ultimate without a static load testFHWA driven-pile practice