Laterally loaded pile (p-y)

A single vertical pile in layered soil under lateral load, head moment and axial compression, analysed by the p-y method of FHWA GEC 9 (2018): the pile is an elastic beam-column on nonlinear soil springs, solved by finite differences for every load combination. The type reports the deflection, slope, moment, shear and soil reaction along the pile, checks a steel pipe (or an entered section) for combined axial load and flexure, and checks the head deflection at the service loads against the engineer's limit. The Broms method stays in the Laterally loaded pile type.

Inputs of the p-y pile #

• Pile: head condition (free, or fixed against rotation by a cap: the engineer's judgment of the restraint), the height of the pile top above grade (the loads act at the top), the embedded length, and the section: a steel pipe (D, t, Fy, E) or an entered section (width, E, I, nominal Mn and Pn with φ or Ω). The width D is the one the p-y curves use.
• Soil: the water table (effective stresses below it use γsat − 62.4 pcf), static or cyclic curves, and the layers top down, each with its own p-y curve family and parameters:
  • Soft clay, Matlock (1970): su, ε50 and J (GEC 9 A.1; J = 0.5 soft, 0.25 medium);
  • Stiff clay without free water, Welch and Reese (1972): su and ε50 (GEC 9 A.3, Table A-2);
  • Sand, API: φ' and the initial modulus k (GEC 9 Table A-3: 25 / 90 / 225 pci above water, 20 / 60 / 125 pci below, for loose / medium / dense sand);
  • Linear: a constant subgrade modulus kh (Es = kh·D), for an elastic check.
• Loads: per load type, unfactored: H and M at the pile top and the axial compression P. The ASCE 7-22 2.3.1 (or 2.4.1) combinations give the strength cases; the 2.4.1 combinations give the service cases for the deflection.
• Head deflection limit: set by the supported structure.
• Pile segments: the number of finite-difference segments over the whole pile (100 by default, as LPILE).

Auto-design varies the embedded length in 2-ft steps (the shortest that passes). The section, soil, head and limits are kept. See Auto-design.

Checks performed #

The solver writes EI·y'''' + P·y'' + Es·y = 0 at each node with central differences, two imaginary nodes at each end, head shear EI·y''' + P·y' = H, head moment EI·y'' = M (free) or slope zero (fixed), and zero moment and shear at the tip. Es = p/y is the secant of each node's p-y curve, iterated until the largest change of deflection is below 10⁻⁵ in. (or 10⁻⁵ of the largest deflection); the step is halved if the iteration oscillates.

The drawings show the pile in its soil profile with the load and dimensions, and the deflection, moment and soil reaction along the pile under the governing strength combination.

Limitations #

• Stiff clay with free water (Reese et al. 1975) is not offered: its As and Ac factors are read from a chart. The Reese (1974) sand curve is replaced by the API tanh form, which uses the same ultimate resistance. Rock, liquefied sand and cemented soils are not offered.
• The API sand tanh form and its factor A are written from knowledge (API RP 2A is not on disk; to confirm against the code text).
• Group effects (p-multipliers), sloping ground, scour and cyclic degradation beyond the cyclic curves are the engineer's (enter reduced strengths).
• Constant EI: no cracking of a concrete pile (enter a cracked I) and no change of section along the pile.
• Buckling of the stick-up above grade under axial load is not checked separately.

Verification examples #

Verification status: 6 values compared in 3 examples (0 published, 3 hand calculations from the cited equations): 6 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.

No published p-y example with a complete input set is on disk (LPILE and COM624P manuals, Reese and Van Impe 2011 and FHWA-IP-84-11 are listed as needed documents). The solver and the curves are checked by hand calculation (backend/tests/test_verify_lateral_pile_py.py):