Laterally loaded pile

The ultimate lateral resistance of a single vertical pile by Broms' method (1964a cohesive soil, 1964b cohesionless soil), checked against the service lateral load with the engineer's factor of safety, with an estimate of the deflection at grade. FHWA GEC 9 (2018) 6.5 presents the method and its limits: it suits short, stiff piles with a free head; long or fixed-head piles should be confirmed with a p-y analysis.

Inputs of the laterally loaded pile #

• Soil: cohesive (undrained shear strength cu; no resistance over the top 1.5D, then 9·cu·D per unit length) or cohesionless (effective unit weight γ' and friction angle φ'; 3·Kp·γ'·z·D per unit length with the Rankine Kp = tan²(45° + φ'/2)). One uniform soil; the values come from the geotechnical report.
• Pile: head condition (free, with the load at the height e above grade; or fixed by a cap at grade that prevents rotation: the engineer's judgment of the restraint), embedment L, the section: a steel pipe (D, t, Fy; My = Fy·Z with the plastic modulus Z = (D³ − di³)/6) or an entered section (width D, yield moment My, E, I; for a prestressed concrete pile FHWA HI-97-013 uses My = f'c·S), and the factor of safety on Hu (FHWA HI-97-013 9.7.3.2 uses 2.5; 2 to 3 is common).
• Loads: per load type, unfactored: H at the load point and, for a free head, a head moment M (same sense as H·e; it raises the effective load height to e + M/H). The ASCE 7-22 2.4.1 combinations give the service loads.
• Deflection estimate (optional): the horizontal subgrade modulus kh (clay, constant with depth; about 67·cu/D per Davisson) or its gradient nh (sand, kh = nh·z/D) and the deflection limit set by the supported structure.

Auto-design (editor toolbar) varies the embedment in 1-ft steps (the shortest that passes). The section, soil, head and factor of safety are kept: a long pile governed by its yield moment needs a stronger section, which the engineer chooses. See Auto-design.

Checks performed #

The intermediate depths follow the exact passive distribution (f = √(2H/(3γ'DKp)), the published 0.82 and 0.544 are its rounded coefficients). The drawings show the pile elevation (grade, soil, load, embedment, the 1.5D zone in clay) and the Broms soil reaction and moment along the pile at Hu, which stop at a plastic hinge.

Limitations #

• p-y analysis is not included. The free sources on hand (FHWA GEC 9, FHWA HI-97-013, GEC 12, EM 1110-2-2906) describe the p-y method but give no complete set of curves with a worked example the program could reproduce; FHWA-IP-84-11 (Reese 1984) and the COM624P manual (FHWA-SA-91-048), which have them, could not be obtained. Use a p-y program (LPILE, COM624P) for long, fixed-head or important piles.
• One uniform soil, level ground, static loads; no cyclic degradation, scour, layered soil or sloping ground.
• No axial load or P-delta; the pile's structural design and axial capacity are not checked.
• Group effects are not included (enter reduced soil values for close spacing).
• The deflection is an estimate (GEC 9 considers Broms' deflections rough); a free-head long pile in sand with the load above grade has a chart solution only and is not estimated.

Verification examples #

Verification status: 15 values compared in 4 examples (4 published, 0 hand calculations from the cited equations): 12 within tolerance, 3 recorded deviations. Code basis: partial. Only some provisions were read in the target edition; the rest rests on older editions, examples or summaries.

Published worked examples (backend/tests/test_verify_lateral_pile.py):

No free published example of a free-head pile in sand was found; that case is verified against the closed forms in backend/tests/test_lateral_pile.py.