API: laterally loaded pile

Solves a laterally loaded single pile by the p-y method — a beam supported by nonlinear soil springs, solved with the COM624P finite-difference formulation (Wang & Reese, FHWA-SA-91-048), the same engine behind LPILE and RSPile. It returns head response, maxima, and the full deflection / moment / shear profile. The method and every input are explained in Laterally loaded piles (p-y); the same analysis runs interactively at the lateral tool.

Endpoint

POST

https://api.pilecalc.com/v1/lateral

GET

/v1/lateral?key=…&req=…&fields=…(for header-less callers)

The request has three required parts: the pile (uniform, or sectioned with depth-varying diameter/ei), the soil profile (a stack of layers, each tagged with a p-y model — Matlock soft clay, Reese stiff clay, Reese or API sand, weak rock, elastic, or user-defined curves), and the head boundary condition (five variants covering free, fixed, and rotationally restrained heads). Optional fields add an axial load, cyclic loading, distributed loads, ground slope, a p-multiplier, and free-field soil movement. Two more options change what comes back: sweep solves a series of proportionally scaled head loads (a pushover curve) in one call, and section + material replace the constant pile EI with the section's fiber-integrated moment–curvature stiffness (cracked-section nonlinear EI) — see Load sweep and Cracked section.

For cyclic loading, soil.cycles applies only to profiles containing Welch–Reese stiff clay above water (default N = 100). Omit it for fixed cyclic branches such as Matlock, RCK and sand. RCK layer.k and optional kBottom are initial moduli for the active loading state, not automatically reduced static inputs. Choose cyclic values from FHWA GEC 9 Table A-1 or justified site data.

Authentication, rate limits, and the error envelope are shared by every endpoint — see the API overview. Requests are unit-agnostic: any self-consistent unit system works, and results come back in the same units. The examples below use SI (m, kN, kPa, kN/m³).

Request fields

This table is generated from the same schema that validates the request, so it cannot drift. Where a field appears once per variant row, it belongs to that variant only.

Field	Type	Required	Constraints
`unitSystem`	"si" \| "us"	yes	Unit bundle for every dimensional input and output. "si": m, kN, kPa, kN/m³, kN·m, kN·m². "us": the kip–foot bundle — ft, kip, ksf, kip/ft³, kip·ft, kip·ft² (unit weights in kip/ft³, not pcf). Values are not converted, so every field must use the declared bundle.
`pile`	object	yes	Pile geometry and bending stiffness: kind "uniform" (one diameter and EI) or "sectioned" (a stack of prismatic and/or tapered sections).
`pile.kind = "uniform"`	variant	no	A prismatic pile with one constant diameter and EI (the default when kind is omitted).
`pile.length`	number	yes	> 0 — Total pile length from the head to the tip (m for si, ft for us), including any free length above grade.
`pile.diameter`	number	yes	> 0 — Pile width or diameter b (m for si, ft for us).
`pile.ei`	number	yes	> 0 — Flexural rigidity EI of the pile (kN·m² for si, kip·ft² for us).
`pile.groundSurfaceDepth`	number	no	≥ 0 — Depth of the ground surface below the pile head, i.e. the free (unsupported) pile length above grade (m for si, ft for us). Omit or use 0 when the head is at the ground surface.
`pile.kind = "sectioned"`	variant	yes	A pile built from a stack of prismatic and/or tapered sections that tile the pile from head to tip.
`pile.sections`	object \| object[]	yes	min 1 item — Pile sections ordered from the head down, contiguous with no gaps or overlaps. Each is prismatic (diameter + ei) or tapered (shape + diameterTop/diameterBottom + elasticModulus).
`pile.groundSurfaceDepth`	number	no	≥ 0 — Depth of the ground surface below the pile head, i.e. the free (unsupported) pile length above grade (m for si, ft for us). Omit or use 0 when the head is at the ground surface.
`soil`	object	yes	Layered soil profile below the ground surface; each layer selects a p-y model.
`soil.layers[]`	object[]	yes	min 1 item — Soil layers from the ground surface down, contiguous with no gaps or overlaps, each tagged with its p-y `model`. The last layer must reach at least the embedded pile tip.
`soil.layers[].model = "soft-clay"`	variant	yes	Matlock (1970) soft clay, for soft to medium clay below the water table.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].c`	number	yes	> 0 — Undrained shear strength (cohesion) c at the layer top (kPa for si, ksf for us).
`soil.layers[].cBottom`	number	no	> 0 — Cohesion c at the layer bottom (kPa for si, ksf for us); c varies linearly from the top value. Omit for a constant layer.
`soil.layers[].e50`	number	yes	> 0 — Strain at 50% of the maximum principal stress difference in an undrained triaxial test, ε₅₀ (dimensionless), at the layer top.
`soil.layers[].e50Bottom`	number	no	> 0 — ε₅₀ at the layer bottom (dimensionless); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].j`	number	no	> 0 — Matlock empirical depth factor J (dimensionless). Omitted defaults to 0.5; 0.25 is sometimes used for stiffer clays.
`soil.layers[].model = "stiff-clay-above-water"`	variant	yes	Welch & Reese (1972) stiff clay with no free water. Supplying k switches to the modified (Reese & Van Impe) form.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].c`	number	yes	> 0 — Undrained shear strength (cohesion) c at the layer top (kPa for si, ksf for us).
`soil.layers[].cBottom`	number	no	> 0 — Cohesion c at the layer bottom (kPa for si, ksf for us); c varies linearly from the top value. Omit for a constant layer.
`soil.layers[].e50`	number	yes	> 0 — Strain at 50% of the maximum principal stress difference in an undrained triaxial test, ε₅₀ (dimensionless), at the layer top.
`soil.layers[].e50Bottom`	number	no	> 0 — ε₅₀ at the layer bottom (dimensionless); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].j`	number	no	> 0 — Matlock empirical depth factor J (dimensionless). Omitted defaults to 0.5; 0.25 is sometimes used for stiffer clays.
`soil.layers[].k`	number	no	> 0 — Optional initial subgrade modulus k (kN/m³ for si, kip/ft³ for us). When present, the modified stiff-clay curve p = min(k·z·y, Welch–Reese backbone) is used; omit for the original Welch & Reese curve.
`soil.layers[].kBottom`	number	no	> 0 — Modified-model k at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from k. Omit for a constant layer.
`soil.layers[].model = "stiff-clay-below-water"`	variant	yes	Reese, Cox & Koop stiff clay below the water table.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].c`	number	yes	> 0 — Undrained shear strength c (kPa for si, ksf for us). Supported only as a constant strength equal to the surface-to-depth average: cBottom must equal c and, with direct layering, overlying layers must carry the same c.
`soil.layers[].cBottom`	number	no	> 0 — Cohesion at the layer bottom (kPa for si, ksf for us). Varying strength is rejected for this model, so omit it or set it equal to c.
`soil.layers[].e50`	number	yes	> 0 — Strain at 50% of the maximum principal stress difference in an undrained triaxial test, ε₅₀ (dimensionless), at the layer top.
`soil.layers[].e50Bottom`	number	no	> 0 — ε₅₀ at the layer bottom (dimensionless); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].k`	number	yes	> 0 — Initial modulus of subgrade reaction k for the active loading state (kN/m³ for si, kip/ft³ for us): the static value for static loading, the cyclic value for cyclic loading. It is not reduced automatically.
`soil.layers[].kSource`	"gec9-table-a1"	no	UI source-default selection provenance. k remains the explicit active-loading modulus used by the engine; the UI restores source selection only when k matches the default for the original loading and unit system.
`soil.layers[].kBottom`	number	no	> 0 — Subgrade modulus k at the layer bottom for the active loading state (kN/m³ for si, kip/ft³ for us); varies linearly from k. Omit for a constant layer.
`soil.layers[].model = "sand-reese"`	variant	yes	Reese, Cox & Koop (1974) sand (wedge and flow-around model).
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].phi`	number	yes	0 – 60 — Drained friction angle φ at the layer top, in degrees (0–60).
`soil.layers[].phiBottom`	number	no	0 – 60 — Friction angle φ at the layer bottom, in degrees (0–60); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].k`	number	yes	> 0 — Initial modulus of subgrade reaction k at the layer top (force/length³: kN/m³ for si, kip/ft³ for us).
`soil.layers[].kBottom`	number	no	> 0 — Subgrade modulus k at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].model = "sand-api"`	variant	yes	API RP-2A / O'Neill & Murchison (1983) sand (hyperbolic-tangent curve).
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].phi`	number	yes	0 – 60 — Drained friction angle φ at the layer top, in degrees (0–60).
`soil.layers[].phiBottom`	number	no	0 – 60 — Friction angle φ at the layer bottom, in degrees (0–60); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].k`	number	yes	> 0 — Initial modulus of subgrade reaction k at the layer top (force/length³: kN/m³ for si, kip/ft³ for us).
`soil.layers[].kBottom`	number	no	> 0 — Subgrade modulus k at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].model = "weak-rock"`	variant	yes	Reese (1997) weak rock. Static loading only.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].qu`	number	yes	> 0 — Uniaxial (unconfined) compressive strength of the intact rock qu at the layer top (kPa for si, ksf for us).
`soil.layers[].quBottom`	number	no	> 0 — qu at the layer bottom (kPa for si, ksf for us); varies linearly from qu. Omit for a constant layer.
`soil.layers[].eir`	number	yes	> 0 — Initial rock-mass modulus Eir at the layer top (force/length²: kPa for si, ksf for us).
`soil.layers[].eirBottom`	number	no	> 0 — Eir at the layer bottom (kPa for si, ksf for us); varies linearly from eir. Omit for a constant layer.
`soil.layers[].rqd`	number	yes	0 – 100 — Rock Quality Designation at the layer top, as a percentage (0–100).
`soil.layers[].rqdBottom`	number	no	0 – 100 — RQD at the layer bottom, as a percentage (0–100); varies linearly from rqd. Omit for a constant layer.
`soil.layers[].krm`	number	no	> 0 — Rock strain factor k_rm (dimensionless), typically 0.0005 to 0.00005. Omitted defaults to 0.0005.
`soil.layers[].model = "elastic"`	variant	yes	Linear-elastic (Winkler) subgrade: p = E_py·y, independent of deflection.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].esTop`	number	yes	≥ 0 — Soil-reaction modulus E_py at the layer top (force/length²: kN/m² for si, kip/ft² for us).
`soil.layers[].esBottom`	number	no	≥ 0 — E_py at the layer bottom (kN/m² for si, kip/ft² for us); varies linearly from esTop. Omitted means constant E_py = esTop.
`soil.layers[].model = "user"`	variant	yes	User-defined resistance: a constant linear modulus es, or measured p-y curves at given depths.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].es`	number	no	≥ 0 — Constant soil modulus E_py for a linear Winkler spring p = es·y (force/length²: kN/m² for si, kip/ft² for us). When supplied it is used instead of curves.
`soil.layers[].curves[]`	object[]	no	Depth-tagged p-y curves. Resistance is interpolated linearly along each curve and between curves in depth; above the first or below the last curve depth, the nearest curve applies.
`soil.layers[].curves[].depth`	number	yes	≥ 0 — Depth of this p-y curve below the ground surface (m for si, ft for us); must lie within the layer and increase strictly from curve to curve.
`soil.layers[].curves[].points[]`	object[]	yes	min 2 items — The curve's (y, p) points, starting at (0, 0).
`soil.layers[].curves[].points[].y`	number	yes	≥ 0 — Lateral deflection y (m for si, ft for us). The first point is 0; values must be strictly increasing.
`soil.layers[].curves[].points[].p`	number	yes	≥ 0 — Soil resistance p per unit pile length (kN/m for si, kip/ft for us) at deflection y. The first point is 0; values must be nondecreasing, and p is held constant beyond the last point.
`soil.layers[].model = "liquefied-sand"`	variant	yes	Rollins et al. (2005a) fully liquefied sand; resistance depends on depth only, with no strength inputs. Requires a pile diameter of at least 0.3 m within the layer.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].units`	"SI" \| "US"	yes	Working-unit tag for the dimensional Rollins constants. Must match the request's unitSystem: "SI" for si, "US" for us.
`soil.layers[].model = "silt-cphi"`	variant	yes	Reese et al. (1974) silt or cemented c-φ soil with both cohesion and friction.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].c`	number	yes	> 0 — Cohesion c at the layer top (kPa for si, ksf for us).
`soil.layers[].cBottom`	number	no	> 0 — Cohesion c at the layer bottom (kPa for si, ksf for us); c varies linearly from the top value. Omit for a constant layer.
`soil.layers[].phi`	number	yes	0 – 60 — Drained friction angle φ at the layer top, in degrees (0–60).
`soil.layers[].phiBottom`	number	no	0 – 60 — Friction angle φ at the layer bottom, in degrees (0–60); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].k`	number	yes	> 0 — Initial modulus of subgrade reaction k at the layer top (force/length³: kN/m³ for si, kip/ft³ for us).
`soil.layers[].kBottom`	number	no	> 0 — Subgrade modulus k at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from the top value. Omit for a constant layer.
`soil.layers[].j`	number	no	> 0 — Matlock J factor for the cohesive wedge (dimensionless). Omitted defaults to 0.5.
`soil.layers[].model = "piedmont-residual"`	variant	yes	Simpson & Brown (2003) Piedmont residual soil (residual silty sands and saprolite). Static loading only.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].esi`	number	yes	> 0 — Initial modulus of subgrade reaction Eₛᵢ at the layer top (force/length³: kN/m³ for si, kip/ft³ for us). Simpson & Brown (2003) Eq. 5.6 correlations, in pci: 22·N with N the uncorrected SPT blow count per 30 cm (not N₆₀, p. 64), 0.118·q_c (q_c in kPa), 0.076·E_DMT and 0.235·E_PMT (moduli in psi).
`soil.layers[].esiBottom`	number	no	> 0 — Eₛᵢ at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from esi. Omit for a constant layer.
`soil.layers[].lambda`	number	no	> 0 — Secant-modulus degradation constant λ (dimensionless). Omitted defaults to 0.23 (Simpson & Brown 2003).
`soil.layers[].model = "iso-clay"`	variant	yes	ISO 19901-4 / Jeanjean et al. (2017) clay, the offshore alternative to Matlock. Static loading only.
`soil.layers[].top`	number	yes	≥ 0 — Depth to the top of the layer below the ground surface (m for si, ft for us). The first layer starts at 0 and each later layer starts at the previous layer's bottom.
`soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m for si, ft for us). The last layer must reach at least the embedded pile tip.
`soil.layers[].gamma`	number	yes	> 0 — Unit weight at the layer top used to build the effective vertical stress: total unit weight above the water table, buoyant (effective) unit weight below it (kN/m³ for si, kip/ft³ for us).
`soil.layers[].gammaBottom`	number	no	> 0 — Unit weight at the layer bottom (kN/m³ for si, kip/ft³ for us); varies linearly from gamma. Omit for a constant layer.
`soil.layers[].su`	number	yes	> 0 — Undrained shear strength sᵤ on a Direct Simple Shear (DSS) basis at the layer top (force/length²: kPa for si, ksf for us).
`soil.layers[].suBottom`	number	no	> 0 — sᵤ (DSS basis) at the layer bottom (kPa for si, ksf for us); varies linearly from su. Omit for a constant layer.
`soil.layers[].alpha`	number	no	0 – 1 — Pile–soil adhesion factor α (0–1); sets the deep bearing factor N_pd = 9 + 3α. Omitted defaults to 1.
`soil.layers[].gap`	"open" \| "closed"	no	Gapping behind the pile: "open" adds the σ′ᵥ/sᵤ overburden term, "closed" doubles the wedge factor. Omitted defaults to "open".
`soil.layers[].clayType`	"soft" \| "stiff"	no	Jeanjean (2017) normalized backbone family keyed on strength: "soft" (sᵤ up to about 100 kPa) or "stiff" (above). Used only when ocr is omitted; omitted defaults to "soft".
`soil.layers[].ocr`	number	no	≥ 1 — Over-consolidation ratio (≥ 1). Selects the ISO 19901-4:2025 default normalized p-y curve, tabulated for OCR ≤ 2, 4 and 10 (between them the softer, higher-OCR curve is used; above 10 the OCR = 10 curve). Replaces the clayType table; do not send both.
`soil.layers[].plasticityIndex`	number	no	0 – 200 — Plasticity index Ip in percent; selects the ISO 19901-4:2025 Ip > 30 % or Ip ≤ 30 % curve group. Requires ocr. Omitted with ocr uses the softer Ip > 30 % group.
`soil.layers[].suTeDssRatio`	number	no	0 – 1.5 — Average triaxial-extension to DSS strength ratio sᵤTE/sᵤDSS within the wedge depth. With an open gap, applies the ISO 19901-4:2025 strength-anisotropy correction to the wedge bearing factor (ISO recommends 0.9 for very soft and soft Gulf-of-Mexico-type clays). Omitted with an open gap: the ISO default 0.9 is applied (declare 1 for isotropic strength). Not used with gap "closed".
`soil.cycles`	number	no	integer, > 0 — Cycle count N for Welch–Reese stiff clay above water only; omitted defaults to 100. Matlock, RCK and sand cyclic branches do not depend on N.
`head`	object	yes	Pile-head boundary condition: `kind` selects which two quantities are prescribed at the head.
`head.kind = "shear-moment"`	variant	yes	Prescribed head shear and moment (a free head when moment is 0).
`head.shear`	number	yes	Lateral shear (horizontal load) applied at the pile head (kN for si, kip for us).
`head.moment`	number	yes	Bending moment applied at the pile head (kN·m for si, kip·ft for us); 0 for a free, concentrically loaded head.
`head.kind = "shear-slope"`	variant	yes	Prescribed head shear and slope (a fixed head when slope is 0).
`head.shear`	number	yes	Lateral shear (horizontal load) applied at the pile head (kN for si, kip for us).
`head.slope`	number	yes	Prescribed pile-head rotation (slope dy/dx) in radians; 0 fixes the head against rotation.
`head.kind = "shear-rotational"`	variant	yes	Prescribed head shear with a rotational spring restraint (a partially fixed head).
`head.shear`	number	yes	Lateral shear (horizontal load) applied at the pile head (kN for si, kip for us).
`head.rotationalStiffness`	number	yes	≥ 0 — Rotational spring stiffness at the head, moment per radian (kN·m/rad for si, kip·ft/rad for us); 0 is a free head and large values approach a fixed head.
`head.kind = "deflection-moment"`	variant	yes	Prescribed head deflection and moment.
`head.deflection`	number	yes	Prescribed lateral pile-head deflection (m for si, ft for us).
`head.moment`	number	yes	Bending moment applied at the pile head (kN·m for si, kip·ft for us); 0 for a free, concentrically loaded head.
`head.kind = "deflection-slope"`	variant	yes	Prescribed head deflection and slope (slope 0 for a fixed head).
`head.deflection`	number	yes	Prescribed lateral pile-head deflection (m for si, ft for us).
`head.slope`	number	yes	Prescribed pile-head rotation (slope dy/dx) in radians; 0 fixes the head against rotation.
`tip`	object	no	Pile-tip boundary condition. Omitted means a free tip with zero shear and moment.
`tip.shear`	number	no	Prescribed shear at the pile tip (kN for si, kip for us). Omitted defaults to 0.
`tip.moment`	number	no	Prescribed moment at the pile tip (kN·m for si, kip·ft for us). Omitted defaults to 0.
`axialLoad`	number	no	Axial load carried down the pile, compression positive (kN for si, kip for us), included as a P-Δ second-order term. Omitted defaults to 0.
`loadType`	"static" \| "cyclic"	no	Build static (monotonic) or cyclic p-y curves. Omitted defaults to "static". weak-rock, piedmont-residual and iso-clay layers support static loading only.
`increments`	number	no	integer, 10 – 800 — Number of finite-difference segments the pile is divided into (10–800). Omitted defaults to 100.
`layering`	"direct" \| "georgiadis"	no	Layered-soil treatment: "direct" builds each layer's p-y curves at their actual depth (original COM624P); "georgiadis" uses Georgiadis (1983) equivalent depths for lower layers and does not accept elastic, user, liquefied-sand or piedmont-residual layers. Omitted defaults to "direct".
`groundSlopeDeg`	number	no	0 – 45 — Ground-surface slope in degrees (0–45), sloping down and away in the direction of loading; upslope loading is not supported. A nonzero slope is supported only for soft-clay, stiff-clay-above-water, stiff-clay-below-water, sand-reese and silt-cphi layers; with clay or silt-cphi layers it requires static loading, and it must not exceed the minimum friction angle of any sand-reese or silt-cphi layer. Omitted defaults to 0 (level ground).
`pMultiplier`	number	no	0 – 1 — Constant p-multiplier (0–1] scaling the soil resistance of every p-y curve, e.g. for pile-group shadowing. Omitted defaults to 1 (single pile); ignored when pMultiplierProfile is given.
`pMultiplierProfile[]`	object[]	no	min 2 items — Depth-varying p-multiplier, linearly interpolated between points and held constant beyond the first and last depths. Takes precedence over pMultiplier.
`pMultiplierProfile[].depth`	number	yes	≥ 0 — Depth below the ground surface (m for si, ft for us); strictly increasing.
`pMultiplierProfile[].factor`	number	yes	0 – 1 — p-multiplier at this depth (0–1].
`tipShearCurve[]`	object[]	no	min 2 items — Base shear versus tip deflection, applied as a restoring spring at the pile tip (e.g. an enlarged or belled base). Starts at (0, 0) and is linearly interpolated.
`tipShearCurve[].deflection`	number	yes	≥ 0 — Tip deflection magnitude (m for si, ft for us); strictly increasing from 0.
`tipShearCurve[].shear`	number	yes	≥ 0 — Mobilized base shear magnitude at that deflection (kN for si, kip for us); nondecreasing from 0.
`distributedLoad`	object	no	Uniform distributed lateral load over a depth band of the pile, added to the head loads. Omit for none.
`distributedLoad.intensity`	number	yes	Lateral load per unit pile length (kN/m for si, kip/ft for us).
`distributedLoad.top`	number	no	≥ 0 — Depth below the pile head where the load starts (m for si, ft for us). Omitted means the pile head.
`distributedLoad.bottom`	number	no	≥ 0 — Depth below the pile head where the load ends (m for si, ft for us); must exceed top. Omitted means the pile tip.
`soilMovement`	object	no	Free-field soil movement (passive loading): the soil displaces by a constant amount from the ground surface down to a sliding depth and is stationary below. Omit for none.
`soilMovement.magnitude`	number	yes	Free-field lateral soil displacement, constant from the ground surface to the sliding depth (m for si, ft for us).
`soilMovement.slidingDepth`	number	yes	> 0 — Depth of the sliding surface below the ground surface (m for si, ft for us); soil below it does not move.
`sweep`	object	no	Pushover sweep: also solve at proportionally scaled head loads and return the load–response curve. Requires a shear-moment, shear-slope or shear-rotational head.
`sweep.steps`	number	yes	integer, 2 – 50 — Number of load levels (2–50); step i is solved at i/steps of the target loads.
`sweep.maxShear`	number	no	Target head shear reached at the last step (kN for si, kip for us). Omitted defaults to the head condition's shear.
`sweep.maxMoment`	number	no	Target head moment reached at the last step (kN·m for si, kip·ft for us), used only with a shear-moment head. Omitted defaults to the head condition's moment.
`section`	object	no	Structural cross-section for a cracked-section (nonlinear EI) analysis. Supply together with material; not combinable with eiCurve.
`section.kind = "solid-circular"`	variant	yes	Solid circular section; pair it with a steel material.
`section.diameter`	number	yes	> 0 — Outside diameter of the solid section (m for si, ft for us).
`section.kind = "pipe"`	variant	yes	Circular hollow pipe section; pair it with a steel material.
`section.outerDiameter`	number	yes	> 0 — Outside diameter of the pipe (m for si, ft for us).
`section.wallThickness`	number	yes	> 0 — Pipe wall thickness (m for si, ft for us); less than half the outside diameter.
`section.kind = "rectangular"`	variant	yes	Solid rectangular section; pair it with a steel material.
`section.width`	number	yes	> 0 — Section width b perpendicular to the bending plane (m for si, ft for us).
`section.height`	number	yes	> 0 — Section height h in the bending plane (m for si, ft for us).
`section.kind = "round-concrete"`	variant	yes	Round reinforced or prestressed concrete section (drilled shaft or round pile), optionally composite with a steel casing and/or core; pair it with a concrete material.
`section.diameter`	number	yes	> 0 — Concrete diameter (m for si, ft for us). With a casing it must equal the casing inside diameter (casing outerDiameter − 2 × wallThickness).
`section.cage`	object	no	Circular ring of longitudinal bars or strands; omit for plain concrete.
`section.cage.count`	number	yes	integer, 1 – 200 — Number of identical longitudinal bars or strands, equally spaced on the bar circle.
`section.cage.area`	number	yes	> 0 — Cross-sectional area of one bar or strand (m² for si, ft² for us).
`section.cage.barDiameter`	number	yes	> 0 — Physical outside diameter of one bar or strand (m for si, ft for us), used to check that bars lie inside the concrete, do not overlap, and clear any steel core.
`section.cage.barCircleRadius`	number	yes	> 0 — Radius of the circle through the bar centres (m for si, ft for us), i.e. D/2 − cover − bar radius.
`section.cage.yieldStress`	number	yes	> 0 — Yield stress fy of the reinforcement, or fpy for a strand (kPa for si, ksf for us).
`section.cage.elasticModulus`	number	yes	> 0 — Elastic modulus Es of the reinforcement (kPa for si, ksf for us).
`section.cage.effectivePrestrain`	number	no	≥ 0 — Effective prestrain of prestressing strands after ALL losses, ε_pe = f_pe/Es (dimensionless tensile strain): f_pe is the strand stress in the finished member at zero external load, so the engine places the strand reference at the decompression strain and the strands carry exactly f_pe at zero thrust. Omit or use 0 for ordinary reinforcing bars.
`section.cage.hardeningRatio`	number	no	0 – 1 — Post-yield hardening ratio E_tangent/Es (0–1); omitted means 0 (elastic–perfectly-plastic).
`section.cage.tensionRuptureStrain`	number	no	> 0 — Tensile strain magnitude at which the reinforcement ruptures (dimensionless); must exceed the yield strain fy/Es and effectivePrestrain. Omit when rupture is not modelled.
`section.cage.strandGrade`	250 \| 270	no	Prestressing-strand grade fpu in ksi (250 or 270). When set, strand stress follows the PCI stress–strain relation (PCI MNL-116, 2nd ed., Fig. 2.2.5.1, p. 2-8) instead of an elastic–perfectly-plastic branch at yieldStress; elasticModulus must then equal 28,500 ksi (196,500 MPa) within 1 % and hardeningRatio must be omitted. Omit for ordinary reinforcing bars.
`section.rebarConcreteDisplacement`	"subtract" \| "overlap"	no	Required when a cage is present. subtract: bars replace their area of concrete (physical net section). overlap: concrete is not reduced, reproducing OpenSees patch-plus-layer sections.
`section.casing`	object	no	Permanent steel casing wrapping the concrete; its steel annulus lies outside the concrete diameter.
`section.casing.outerDiameter`	number	yes	> 0 — Outside diameter of the steel tube (m for si, ft for us). A casing's inside diameter (outerDiameter − 2 × wallThickness) must equal the concrete diameter; a core must be smaller than the concrete diameter.
`section.casing.wallThickness`	number	yes	> 0 — Radial wall thickness of the tube (m for si, ft for us); less than half the outside diameter.
`section.casing.yieldStress`	number	yes	> 0 — Yield stress Fy of the tube steel (kPa for si, ksf for us).
`section.casing.elasticModulus`	number	yes	> 0 — Elastic modulus Es of the tube steel (kPa for si, ksf for us).
`section.casing.hardeningRatio`	number	no	0 – 1 — Post-yield hardening ratio E_tangent/Es (0–1); omitted means 0 (elastic–perfectly-plastic).
`section.casing.tensionRuptureStrain`	number	no	> 0 — Tensile strain magnitude at which the tube steel ruptures (dimensionless); must exceed the yield strain Fy/Es. Omit when rupture is not modelled.
`section.core`	object	no	Concentric steel tube at the centre; the concrete inside its outside diameter is treated as void. It must clear the bar cage.
`section.core.outerDiameter`	number	yes	> 0 — Outside diameter of the steel tube (m for si, ft for us). A casing's inside diameter (outerDiameter − 2 × wallThickness) must equal the concrete diameter; a core must be smaller than the concrete diameter.
`section.core.wallThickness`	number	yes	> 0 — Radial wall thickness of the tube (m for si, ft for us); less than half the outside diameter.
`section.core.yieldStress`	number	yes	> 0 — Yield stress Fy of the tube steel (kPa for si, ksf for us).
`section.core.elasticModulus`	number	yes	> 0 — Elastic modulus Es of the tube steel (kPa for si, ksf for us).
`section.core.hardeningRatio`	number	no	0 – 1 — Post-yield hardening ratio E_tangent/Es (0–1); omitted means 0 (elastic–perfectly-plastic).
`section.core.tensionRuptureStrain`	number	no	> 0 — Tensile strain magnitude at which the tube steel ruptures (dimensionless); must exceed the yield strain Fy/Es. Omit when rupture is not modelled.
`section.kind = "rectangular-concrete"`	variant	yes	Rectangular or square reinforced or prestressed concrete section; pair it with a concrete material.
`section.width`	number	yes	> 0 — Section width b perpendicular to the bending plane (m for si, ft for us).
`section.height`	number	yes	> 0 — Section height h in the bending plane (m for si, ft for us).
`section.reinforcement`	object	no	Symmetric perimeter bars or strands; omit for plain concrete.
`section.reinforcement.layout`	"perimeter"	yes	Symmetric straight-sided perimeter layout (the only layout).
`section.reinforcement.barsPerFace`	number	yes	integer, 2 – 100 — Identical bars on each of the top and bottom faces (the faces spanning the width, at the extremes of the bending direction), including the two corner bars.
`section.reinforcement.barsPerSide`	number	yes	integer, 0 – 99 — Additional identical bars on each of the two side faces, excluding the corner bars already counted in barsPerFace.
`section.reinforcement.area`	number	yes	> 0 — Cross-sectional area of one bar or strand (m² for si, ft² for us).
`section.reinforcement.barDiameter`	number	yes	> 0 — Physical outside diameter of one bar or strand (m for si, ft for us), used for cover, containment and overlap checks.
`section.reinforcement.clearCover`	number	yes	> 0 — Clear distance from the concrete face to the outside of the bar (m for si, ft for us); bar centres sit at clearCover + barDiameter/2 from each face.
`section.reinforcement.yieldStress`	number	yes	> 0 — Yield stress fy shared by every bar, or fpy for strands (kPa for si, ksf for us).
`section.reinforcement.elasticModulus`	number	yes	> 0 — Elastic modulus Es shared by every bar (kPa for si, ksf for us).
`section.reinforcement.effectivePrestrain`	number	no	≥ 0 — Effective prestrain of prestressing strands after losses, ε_pe = f_pe/Es (dimensionless tensile strain). Omit or use 0 for ordinary reinforcing bars.
`section.reinforcement.hardeningRatio`	number	no	0 – 1 — Post-yield hardening ratio E_tangent/Es (0–1); omitted means 0 (elastic–perfectly-plastic).
`section.reinforcement.tensionRuptureStrain`	number	no	> 0 — Tensile strain magnitude at which the reinforcement ruptures (dimensionless); must exceed the yield strain fy/Es and effectivePrestrain. Omit when rupture is not modelled.
`section.reinforcement.strandGrade`	250 \| 270	no	Prestressing-strand grade fpu in ksi (250 or 270). When set, strand stress follows the PCI stress–strain relation (PCI MNL-116, 2nd ed., Fig. 2.2.5.1, p. 2-8) instead of an elastic–perfectly-plastic branch at yieldStress; elasticModulus must then equal 28,500 ksi (196,500 MPa) within 1 % and hardeningRatio must be omitted. Omit for ordinary reinforcing bars.
`section.rebarConcreteDisplacement`	"subtract" \| "overlap"	no	Required when reinforcement is present. subtract: bars replace their area of concrete (physical net section). overlap: concrete is not reduced, reproducing OpenSees patch-plus-layer sections.
`section.confinedCore`	object	no	Optional rectangular confined core, bounded by coverDepth on all four faces, with its own concrete material.
`section.confinedCore.coverDepth`	number	yes	> 0 — Distance from every concrete face to the confined-core boundary (m for si, ft for us); perimeter bar centres must lie in this cover or on the core boundary.
`section.confinedCore.material`	object	yes	Concrete material for the confined core; the cover concrete outside the core uses the main concrete material.
`section.confinedCore.material.kind`	"concrete"	yes	Concrete fiber material; pair it with a round-concrete or rectangular-concrete section.
`section.confinedCore.material.compressiveStrength`	number	yes	> 0 — Concrete cylinder compressive strength f′c as a positive magnitude (kPa for si, ksf for us).
`section.confinedCore.material.elasticModulus`	number	no	> 0 — Concrete elastic modulus Ec (kPa for si, ksf for us). Omitted for hognestad/todeschini: the ACI value 4700·√f′c (f′c in MPa), converted to the request's units. For concrete01 Ec is 2·f′c/peakStrain, and a supplied value must equal that.
`section.confinedCore.material.peakStrain`	number	no	> 0 — Compressive strain ε0 at peak stress f′c (dimensionless). Omitted for hognestad/todeschini: 1.7·f′c/Ec. Required for concrete01.
`section.confinedCore.material.ultimateStrain`	number	no	> 0 — Extreme-fiber compressive strain limit εcu (dimensionless), greater than peakStrain. Hognestad/todeschini: the ACI crushing strain at which the nominal moment Mn is read; omitted means 0.003. Concrete01 (required): the strain at which the stress has descended to residualStrength.
`section.confinedCore.material.descendingStrain`	number	no	> 0 — Hognestad only: strain at which the linear post-peak branch reaches 0.85·f′c (dimensionless), greater than peakStrain; omitted means 0.0038. Not accepted by todeschini or concrete01.
`section.confinedCore.material.tensileStrength`	number	no	≥ 0 — Modulus of rupture fr, the tensile stress at which the concrete cracks, as a positive magnitude (kPa for si, ksf for us). Omitted for hognestad/todeschini: the ACI value 0.62·√f′c (MPa), converted to the request's units. Concrete01 carries no tension: omit it or use 0.
`section.confinedCore.material.model`	"todeschini" \| "hognestad" \| "concrete01"	no	Compression stress–strain envelope. hognestad (default, LPILE-compatible): parabola to f′c, then a linear descending branch. todeschini: smooth Todeschini curve. concrete01: zero-tension Kent-Scott-Park envelope as in the OpenSees benchmark; requires peakStrain, ultimateStrain and residualStrength.
`section.confinedCore.material.residualStrength`	number	no	≥ 0 — Concrete01 only (required there): residual compressive stress reached at ultimateStrain, between 0 and compressiveStrength (kPa for si, ksf for us).
`material`	object	no	Material model for `section`: concrete sections need a concrete material, steel/elastic sections a steel material. Supply together with section.
`material.kind = "concrete"`	variant	yes	Concrete fiber material; pair it with a round-concrete or rectangular-concrete section.
`material.compressiveStrength`	number	yes	> 0 — Concrete cylinder compressive strength f′c as a positive magnitude (kPa for si, ksf for us).
`material.elasticModulus`	number	no	> 0 — Concrete elastic modulus Ec (kPa for si, ksf for us). Omitted for hognestad/todeschini: the ACI value 4700·√f′c (f′c in MPa), converted to the request's units. For concrete01 Ec is 2·f′c/peakStrain, and a supplied value must equal that.
`material.peakStrain`	number	no	> 0 — Compressive strain ε0 at peak stress f′c (dimensionless). Omitted for hognestad/todeschini: 1.7·f′c/Ec. Required for concrete01.
`material.ultimateStrain`	number	no	> 0 — Extreme-fiber compressive strain limit εcu (dimensionless), greater than peakStrain. Hognestad/todeschini: the ACI crushing strain at which the nominal moment Mn is read; omitted means 0.003. Concrete01 (required): the strain at which the stress has descended to residualStrength.
`material.descendingStrain`	number	no	> 0 — Hognestad only: strain at which the linear post-peak branch reaches 0.85·f′c (dimensionless), greater than peakStrain; omitted means 0.0038. Not accepted by todeschini or concrete01.
`material.tensileStrength`	number	no	≥ 0 — Modulus of rupture fr, the tensile stress at which the concrete cracks, as a positive magnitude (kPa for si, ksf for us). Omitted for hognestad/todeschini: the ACI value 0.62·√f′c (MPa), converted to the request's units. Concrete01 carries no tension: omit it or use 0.
`material.model`	"todeschini" \| "hognestad" \| "concrete01"	no	Compression stress–strain envelope. hognestad (default, LPILE-compatible): parabola to f′c, then a linear descending branch. todeschini: smooth Todeschini curve. concrete01: zero-tension Kent-Scott-Park envelope as in the OpenSees benchmark; requires peakStrain, ultimateStrain and residualStrength.
`material.residualStrength`	number	no	≥ 0 — Concrete01 only (required there): residual compressive stress reached at ultimateStrain, between 0 and compressiveStrength (kPa for si, ksf for us).
`material.kind = "steel"`	variant	no	Elastic–(bilinear-)plastic steel material; may be omitted. Pair it with a solid-circular, pipe or rectangular section.
`material.elasticModulus`	number	yes	> 0 — Young's modulus E of the section material (kPa for si, ksf for us).
`material.yieldStress`	number	yes	> 0 — Yield stress Fy of the section material (kPa for si, ksf for us).
`material.hardeningRatio`	number	no	0 – 1 — Post-yield hardening ratio E_tangent/E (0–1); omitted means 0 (elastic–perfectly-plastic).
`material.ultimateStrain`	number	no	> 0 — Symmetric extreme-fiber strain magnitude that ends the moment–curvature response (dimensionless); must exceed the yield strain Fy/E. Hardening steel (hardeningRatio > 0) needs this or, in a moment-curvature request, maxCurvature.
`eiCurve[]`	object[]	no	min 2 items — User-defined moment–curvature table; the pile EI at each node is M/κ interpolated from it at the local moment. Above the last point PileCalc uses 0.05 × the last secant EI, a numerical continuation with no published basis, and the response carries a warning. An alternative to section + material.
`eiCurve[].moment`	number	yes	> 0 — Bending moment (kN·m for si, kip·ft for us); strictly increasing.
`eiCurve[].curvature`	number	yes	> 0 — Curvature at that moment (1/m for si, 1/ft for us); strictly increasing.
`momentCapacity`	number \| object[]	no	Plastic moment capacity Mcap (kN·m for si, kip·ft for us), either one constant value or a capacity-versus-depth table interpolated linearly. Where the moment reaches it a plastic hinge forms. Omit for an elastic pile.
`lrfd`	object	no	LRFD load-combination check: each case factors the unfactored loads, runs the analysis with a shear-moment head at the factored loads, and checks the maximum moment and shear against φ_b·Mn and φ_v·Vn.
`lrfd.loads[]`	object[]	yes	min 1 item — Unfactored pile-head loads, each tagged by load type.
`lrfd.loads[].type`	"dead" \| "live" \| "earthquake" \| "impact" \| "wind" \| "water" \| "ice" \| "soil-pressure" \| "live-roof" \| "rain" \| "snow" \| "temperature" \| "special"	yes	Load type; each case's factors are keyed by these types.
`lrfd.loads[].shear`	number	yes	Unfactored lateral shear at the pile head (kN for si, kip for us).
`lrfd.loads[].axial`	number	no	Unfactored axial load, compression positive (kN for si, kip for us). Omitted defaults to 0.
`lrfd.loads[].moment`	number	no	Unfactored bending moment at the pile head (kN·m for si, kip·ft for us). Omitted defaults to 0.
`lrfd.loads[].distributed`	number	no	Unfactored uniform distributed lateral load along the whole pile (force/length: kN/m for si, kip/ft for us). Omitted defaults to 0.
`lrfd.cases[]`	object[]	no	min 1 item — Load-and-resistance combinations. Omitted uses the preset 1.4D; 1.2D + 1.6L + 0.5Lr; 1.2D + 1.6Lr + 1.0L, in which case every nonzero load must be dead, live or live-roof.
`lrfd.cases[].name`	string	yes	Label for the combination, e.g. "1.2D + 1.6L".
`lrfd.cases[].factors`	object	yes	Load factor per load type; types not listed get a factor of 0.
`lrfd.cases[].phiFlexure`	number	yes	0 – 1 — Flexural resistance factor φ_b applied to the nominal moment Mn.
`lrfd.cases[].phiShear`	number	no	0 – 1 — Shear resistance factor φ_v applied to the shear capacity Vn. Required when lrfd.shearCapacity is supplied.
`lrfd.phiFlexure`	number	no	0 – 1 — Flexural resistance factor φ_b for the preset combinations (used only when cases is omitted). Omitted defaults to 0.9.
`lrfd.phiShear`	number	no	0 – 1 — Shear resistance factor φ_v for the preset combinations (used only when cases is omitted). Omitted defaults to 0.75.
`lrfd.nominalMoment`	number	no	> 0 — Nominal moment capacity Mn (kN·m for si, kip·ft for us). Required unless section + material is supplied, in which case the section's nominal moment (concrete) or plastic moment is used.
`lrfd.shearCapacity`	number	no	> 0 — Nominal shear capacity Vn (kN for si, kip for us). Omit to skip the shear check.

Response fields

Field	Type	Description
`converged`	boolean	Whether the nonlinear p-y iteration converged. Treat a non-converged result as unusable.
`iterations`	number	Iterations the solver needed.
`head.deflection`	number	Pile-head lateral deflection (m for si, ft for us).
`head.slope`	number	Pile-head slope (rad).
`head.moment`	number	Moment at the head (kN·m for si, kip·ft for us).
`head.shear`	number	Shear at the head (kN for si, kip for us).
`maxMoment.value`	number	Largest-magnitude bending moment along the pile (kN·m for si, kip·ft for us).
`maxMoment.depth`	number	Depth of the maximum moment, from the pile head (m for si, ft for us).
`maxDeflection.value / .depth`	number	Largest-magnitude deflection and its depth (both m for si, ft for us).
`maxShear.value / .depth`	number	Largest-magnitude shear (kN for si, kip for us) and its depth (m for si, ft for us).
`equilibrium.residual`	number	Unbalanced force after convergence (kN for si, kip for us) — a solution-quality check against equilibrium.applied.
`equilibrium.applied`	number	Total applied lateral load (kN for si, kip for us).
`nodes[]`	object[]	The full solution, one entry per finite-difference node from head to tip.
`nodes[].depth`	number	Depth from the pile head (m for si, ft for us).
`nodes[].soilDepth`	number	Depth below the ground surface (m for si, ft for us) — differs from depth when the head is above grade.
`nodes[].deflection`	number	Lateral deflection y (m for si, ft for us).
`nodes[].slope`	number	Slope dy/dz (rad).
`nodes[].moment`	number	Bending moment (kN·m for si, kip·ft for us).
`nodes[].shear`	number	Shear force (kN for si, kip for us).
`nodes[].soilReaction`	number	Mobilized soil reaction p (kN/m for si, kip/ft for us); opposes the deflection.
`warnings[]`	string[]	Present only when the result rests on a modelling choice that no published source determines (for example the up-slope sand wedge where it is undefined, an ISO-clay strength profile with no positive mudline intercept, or Georgiadis layering with an ISO-clay strength gradient). Each entry names the conservative choice that was made.
`sweep[]`	object[]	Present when the request set `sweep` — one entry per pushover step, each an independent solution at the proportionally scaled head load: `shear`, `moment`, `headDeflection`, `headSlope`, `maxMoment`, `maxMomentDepth`, `maxDeflection`, `converged`.
`sectionProperties`	object	Present when the request set `section` + `material` (cracked-section nonlinear EI): the fiber-integrated section's `elasticEI` (kN·m² for si, kip·ft² for us), `yieldMoment`, and `plasticMoment` (kN·m for si, kip·ft for us).

Code examples

A complete, runnable request. Replace YOUR_API_KEY (or set PILECALC_API_KEY in your environment).

POST /v1/lateral

curl https://api.pilecalc.com/v1/lateral \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
  "unitSystem": "si",
  "pile": {
    "kind": "uniform",
    "length": 15,
    "diameter": 0.61,
    "ei": 143000,
    "groundSurfaceDepth": 0
  },
  "soil": {
    "layers": [
      {
        "model": "soft-clay",
        "top": 0,
        "bottom": 4,
        "gamma": 8.5,
        "c": 24,
        "e50": 0.02
      },
      {
        "model": "sand-reese",
        "top": 4,
        "bottom": 15,
        "gamma": 9.5,
        "phi": 34,
        "k": 16300
      }
    ]
  },
  "head": {
    "kind": "shear-moment",
    "shear": 312,
    "moment": 0
  },
  "axialLoad": 1200,
  "loadType": "cyclic",
  "layering": "direct",
  "increments": 120
}'

The GET variant returns head.deflection,maxMoment.value as a plain-text CSV line — made for Excel's WEBSERVICE() and Sheets' IMPORTDATA() (see Use PileCalc in Excel). Omit fields to get the full JSON response.

Interpreting results

Check converged first. If false, the pile is likely failing (soil fully mobilized) or too short — the numbers are not an equilibrium solution.
Deflections and moments follow the sign of the applied load; see Units & sign conventions.
nodes has increments + 1 entries (default 101: omitted increments means 100). For plots, use nodes[].depth vs. deflection/moment/shear.
equilibrium.residual should be small relative to equilibrium.applied; a large residual with converged: true is a red flag worth reporting.

Sizing runs

For load–deflection curves, set sweep (e.g. { "steps": 20 }) instead of sweeping head.shear across calls — the whole pushover curve comes back in sweep[] and costs a single request of your monthly quota.