API: slope stabilization

POST /v1/slope and GET /v1/slope run the strict pile-row demand/capacity method. The request requires the named applied-displacement and NAVFAC/Reese– O'Neill component methods, a complete lateral and axial pile/soil model, a declared wide-spacing row, explicit numerical controls, and an ordered demand for every candidate surface. See Slope stabilization for the scientific boundary.

Endpoint

POST

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

GET

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

method, axial.method, unitSystem, water unit weight where applicable, the movement cap, and all solver controls are required. Candidate surfaces use { id, slidingDepth, distributedDemand, slipAngleDeg? }. The optional local slipAngleDeg overrides the shared request angle for both displacement resolution and tangent force projection. Each angle must be between 0° and 90° (exclusive). Demand is force per unit row width in the declared SI or US bundle; total demand is calculated with row.tributaryWidth.

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.
`method`	"applied-displacement-independent-wide-spacing"	yes	Slope pile-row method: applied soil displacement with independent, widely spaced piles.
`lateral`	object	yes	Lateral (p-y) model of one pile. Ground surface must be at the pile head (no buried head) and cyclic degradation is not supported; the soil profile must cover the full pile length.
`lateral.pile`	object	yes
`lateral.pile.kind = "uniform"`	variant	no	A prismatic pile with one constant diameter and EI (the default when kind is omitted).
`lateral.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.
`lateral.pile.diameter`	number	yes	> 0 — Pile width or diameter b (m for si, ft for us).
`lateral.pile.ei`	number	yes	> 0 — Flexural rigidity EI of the pile (kN·m² for si, kip·ft² for us).
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil`	object	yes
`lateral.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.
`lateral.soil.layers[].model = "soft-clay"`	variant	yes	Matlock (1970) soft clay, for soft to medium clay below the water table.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].c`	number	yes	> 0 — Undrained shear strength (cohesion) c at the layer top (kPa for si, ksf for us).
`lateral.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.
`lateral.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.
`lateral.soil.layers[].e50Bottom`	number	no	> 0 — ε₅₀ at the layer bottom (dimensionless); varies linearly from the top value. Omit for a constant layer.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].c`	number	yes	> 0 — Undrained shear strength (cohesion) c at the layer top (kPa for si, ksf for us).
`lateral.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.
`lateral.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.
`lateral.soil.layers[].e50Bottom`	number	no	> 0 — ε₅₀ at the layer bottom (dimensionless); varies linearly from the top value. Omit for a constant layer.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.soil.layers[].model = "stiff-clay-below-water"`	variant	yes	Reese, Cox & Koop stiff clay below the water table.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.soil.layers[].e50Bottom`	number	no	> 0 — ε₅₀ at the layer bottom (dimensionless); varies linearly from the top value. Omit for a constant layer.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.soil.layers[].model = "sand-reese"`	variant	yes	Reese, Cox & Koop (1974) sand (wedge and flow-around model).
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].phi`	number	yes	0 – 60 — Drained friction angle φ at the layer top, in degrees (0–60).
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].model = "sand-api"`	variant	yes	API RP-2A / O'Neill & Murchison (1983) sand (hyperbolic-tangent curve).
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].phi`	number	yes	0 – 60 — Drained friction angle φ at the layer top, in degrees (0–60).
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].model = "weak-rock"`	variant	yes	Reese (1997) weak rock. Static loading only.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].eir`	number	yes	> 0 — Initial rock-mass modulus Eir at the layer top (force/length²: kPa for si, ksf for us).
`lateral.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.
`lateral.soil.layers[].rqd`	number	yes	0 – 100 — Rock Quality Designation at the layer top, as a percentage (0–100).
`lateral.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.
`lateral.soil.layers[].krm`	number	no	> 0 — Rock strain factor k_rm (dimensionless), typically 0.0005 to 0.00005. Omitted defaults to 0.0005.
`lateral.soil.layers[].model = "elastic"`	variant	yes	Linear-elastic (Winkler) subgrade: p = E_py·y, independent of deflection.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].model = "user"`	variant	yes	User-defined resistance: a constant linear modulus es, or measured p-y curves at given depths.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.soil.layers[].curves[].points[]`	object[]	yes	min 2 items — The curve's (y, p) points, starting at (0, 0).
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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.
`lateral.soil.layers[].model = "silt-cphi"`	variant	yes	Reese et al. (1974) silt or cemented c-φ soil with both cohesion and friction.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].c`	number	yes	> 0 — Cohesion c at the layer top (kPa for si, ksf for us).
`lateral.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.
`lateral.soil.layers[].phi`	number	yes	0 – 60 — Drained friction angle φ at the layer top, in degrees (0–60).
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].j`	number	no	> 0 — Matlock J factor for the cohesive wedge (dimensionless). Omitted defaults to 0.5.
`lateral.soil.layers[].model = "piedmont-residual"`	variant	yes	Simpson & Brown (2003) Piedmont residual soil (residual silty sands and saprolite). Static loading only.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.soil.layers[].lambda`	number	no	> 0 — Secant-modulus degradation constant λ (dimensionless). Omitted defaults to 0.23 (Simpson & Brown 2003).
`lateral.soil.layers[].model = "iso-clay"`	variant	yes	ISO 19901-4 / Jeanjean et al. (2017) clay, the offshore alternative to Matlock. Static loading only.
`lateral.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.
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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).
`lateral.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.
`lateral.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.
`lateral.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".
`lateral.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".
`lateral.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.
`lateral.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.
`lateral.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".
`lateral.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.
`axial`	object	yes	Axial (t-z/q-z) model of the same pile, vertical only; length and diameter must match the lateral pile at every depth.
`axial.method`	"navfac-dm7-reese-oneill"	yes	Axial method: NAVFAC DM-7 capacity with Reese & O'Neill t-z/q-z load transfer.
`axial.pile`	object	yes
`axial.pile.kind = "uniform"`	variant	no	Pile geometry type: "uniform" is one diameter over the full length (the default).
`axial.pile.length`	number	yes	> 0 — Pile length below the pile head (m for si, ft for us).
`axial.pile.diameter`	number	yes	> 0 — Pile width or diameter B (m or ft).
`axial.pile.tipArea`	number	no	> 0 — End-bearing (tip) area (length², in the request's unit system). Defaults to π·B²/4 using the tip diameter (a closed circular tip).
`axial.pile.batterDeg`	number	no	0 – 45 — Batter angle from vertical in degrees (0–45, default 0). Some analyses (axial, downdrag, drilled shaft) accept vertical piles only.
`axial.pile.elasticModulus`	number	yes	> 0 — Young's modulus E of the pile material (kPa for si, ksf for us); controls elastic shortening under load.
`axial.pile.unitWeight`	number	yes	≥ 0 — Unit weight of the pile material (kN/m³ for si, kip/ft³ for us). Sets the pile self-weight credited to uplift resistance; the buoyant value is used below the water table.
`axial.pile.displacement`	boolean	no	true for a driven displacement pile, false for a drilled/bored (non-displacement) pile. Selects the Nq end-bearing factor and, in the axial service solve, driven (API RP2A) vs bored (Reese–O'Neill) t-z/q-z curves. Omitted means true, except in the drilled-shaft analysis, which rejects true and always treats the shaft as non-displacement.
`axial.pile.material`	"steel" \| "concrete" \| "timber"	no	Pile material for the NAVFAC DM-7.02 defaults: the interface friction angle δ (Fig. 1 cont., p. 7.2-194: steel 20°, concrete and timber ¾φ) and the clay adhesion C_A (Fig. 2, p. 7.2-196: steel column vs timber-and-concrete column). When omitted, the lower (conservative) table value is used: δ = min(20°, ¾φ) and the steel adhesion column. deltaDeg, frictionFactor and a layer's ka override these defaults. Not accepted by the drilled-shaft method.
`axial.pile.deltaDeg`	number	no	0 – 60 — Pile–soil interface friction angle δ in degrees for cohesionless side friction; may not exceed the layer's phi. When omitted, δ = frictionFactor × phi, or the NAVFAC material default (see material) when frictionFactor is also omitted.
`axial.pile.frictionFactor`	number	no	0 – 1 — Ratio δ/φ used to derive the interface friction angle when deltaDeg is omitted (0–1). When omitted, the NAVFAC DM-7.02 material default applies (see material).
`axial.pile.kind = "sectioned"`	variant	yes	Pile geometry type: "sectioned" gives the pile as contiguous depth sections with their own diameter, perimeter and area.
`axial.pile.sections[]`	object[]	yes	min 1 item — Pile sections ordered from the head down, starting at depth 0 with no gaps or overlaps.
`axial.pile.sections[].top`	number	yes	≥ 0 — Depth to the top of this section below the pile head (m for si, ft for us). The first section starts at 0 and sections must be contiguous.
`axial.pile.sections[].bottom`	number	yes	> 0 — Depth to the bottom of this section below the pile head (m or ft); must exceed top. The last section's bottom is the pile length.
`axial.pile.sections[].diameter`	number	yes	> 0 — Section width or diameter B (m or ft).
`axial.pile.sections[].perimeter`	number	no	> 0 — Surface perimeter used for side resistance (m or ft). Defaults to π·B (circular).
`axial.pile.sections[].area`	number	no	> 0 — Structural cross-sectional area used for elastic shortening and pile self-weight (length², in the request's unit system). Defaults to π·B²/4.
`axial.pile.tipArea`	number	no	> 0 — End-bearing (tip) area (length², in the request's unit system). Defaults to π·B²/4 using the tip diameter (a closed circular tip).
`axial.pile.batterDeg`	number	no	0 – 45 — Batter angle from vertical in degrees (0–45, default 0). Some analyses (axial, downdrag, drilled shaft) accept vertical piles only.
`axial.pile.elasticModulus`	number	yes	> 0 — Young's modulus E of the pile material (kPa for si, ksf for us); controls elastic shortening under load.
`axial.pile.unitWeight`	number	yes	≥ 0 — Unit weight of the pile material (kN/m³ for si, kip/ft³ for us). Sets the pile self-weight credited to uplift resistance; the buoyant value is used below the water table.
`axial.pile.displacement`	boolean	no	true for a driven displacement pile, false for a drilled/bored (non-displacement) pile. Selects the Nq end-bearing factor and, in the axial service solve, driven (API RP2A) vs bored (Reese–O'Neill) t-z/q-z curves. Omitted means true, except in the drilled-shaft analysis, which rejects true and always treats the shaft as non-displacement.
`axial.pile.material`	"steel" \| "concrete" \| "timber"	no	Pile material for the NAVFAC DM-7.02 defaults: the interface friction angle δ (Fig. 1 cont., p. 7.2-194: steel 20°, concrete and timber ¾φ) and the clay adhesion C_A (Fig. 2, p. 7.2-196: steel column vs timber-and-concrete column). When omitted, the lower (conservative) table value is used: δ = min(20°, ¾φ) and the steel adhesion column. deltaDeg, frictionFactor and a layer's ka override these defaults. Not accepted by the drilled-shaft method.
`axial.pile.deltaDeg`	number	no	0 – 60 — Pile–soil interface friction angle δ in degrees for cohesionless side friction; may not exceed the layer's phi. When omitted, δ = frictionFactor × phi, or the NAVFAC material default (see material) when frictionFactor is also omitted.
`axial.pile.frictionFactor`	number	no	0 – 1 — Ratio δ/φ used to derive the interface friction angle when deltaDeg is omitted (0–1). When omitted, the NAVFAC DM-7.02 material default applies (see material).
`axial.soil`	object	yes
`axial.soil.layers[]`	object[]	yes	min 1 item — Soil and rock layers ordered from the ground surface down, starting at depth 0 with no gaps or overlaps.
`axial.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 layers must be contiguous.
`axial.soil.layers[].bottom`	number	yes	> 0 — Depth to the bottom of the layer below the ground surface (m or ft); must exceed top. The deepest layer should reach at least the pile tip.
`axial.soil.layers[].gamma`	number	yes	> 0 — Total unit weight γ of the layer (kN/m³ for si, kip/ft³ for us); builds the vertical stress profile.
`axial.soil.layers[].type`	"cohesive" \| "cohesionless" \| "rock"	yes	Behavioural class that selects the resistance method: cohesive (clay, undrained strength), cohesionless (sand), or rock. It also decides which strength fields are required or allowed.
`axial.soil.layers[].cohesion`	number	no	≥ 0 — Undrained shear strength Su of a cohesive layer (kPa for si, ksf for us). Give exactly one of cohesion or qu for cohesive layers; not allowed on cohesionless or rock layers.
`axial.soil.layers[].phi`	number	no	0 – 60 — Drained friction angle φ in degrees (0–60) for cohesionless layers. Required by the axial (NAVFAC) soil profile; in the layer where the pile tip bears it must be 26–40°, the range NAVFAC DM-7.02 tabulates Nq for. NAVFAC's table footnotes (p. 7.2-194) limit φ to 28° for jetted piles, and for drilled-pier end bearing where a bailer or grab bucket is used below groundwater; enter φ accordingly. The drilled-shaft method uses sptN instead and rejects phi.
`axial.soil.layers[].sptN`	number	no	≥ 0 — SPT blow count N (blows per 0.3 m) for cohesionless layers. Required by the drilled-shaft method (0 < N ≤ 50); not accepted by the axial (NAVFAC) soil profile.
`axial.soil.layers[].qu`	number	no	≥ 0 — Unconfined compressive strength qu (kPa for si, ksf for us). Required for rock layers; for cohesive layers it is the alternative to cohesion, with Su = qu/2. The axial, capacity-vs-length, downdrag, slope and stiffness analyses reject rock within the pile length (no rock t-z/q-z service curves, and no static method for driven piles in rock, FHWA GEC 12 §7.2.1.4); analyse a cast-in-place rock socket with the drilled-shaft method, which limits qu to the concrete strength f′c (FHWA-IF-99-025 Eq. 11.24).
`axial.soil.layers[].rockJointCondition`	"massive-intact" \| "closed" \| "open-or-gouge-filled"	no	Rock-mass joint condition from FHWA-IF-99-025 Table 11.4, required on rock layers: massive-intact, closed joints, or open/gouge-filled joints. Jointed conditions reduce socket side resistance by RQD; jointed rock at the pile tip is rejected.
`axial.soil.layers[].rqd`	number	no	0 – 100 — Rock Quality Designation in percent. Required (20–100, the published Table 11.4 range) for closed or open/gouge-filled rock; must be omitted for massive-intact rock.
`axial.soil.layers[].kDown`	number	no	> 0 — Layer override of the lateral earth-pressure ratio K = σ'h/σ'v for downward (compression) side friction in cohesionless layers (NAVFAC method). When omitted, the analysis-level value applies. The drilled-shaft and helical methods do not use it and reject it.
`axial.soil.layers[].kUp`	number	no	> 0 — Layer override of K for uplift side friction (NAVFAC method). When omitted, this layer's kDown is used, then the analysis-level value.
`axial.soil.layers[].kc`	number	no	> 0 — Adhesion factor Kc multiplying cohesive side adhesion (fs = Kc·Ka·Su) in the NAVFAC method; default 1. Not allowed on cohesionless layers, or by the drilled-shaft and helical methods.
`axial.soil.layers[].ka`	number	no	> 0 — Adhesion ratio Ka = Ca/Su override for cohesive side friction in the NAVFAC method. When omitted it follows the NAVFAC DM-7.02 Figure 2 recommended-adhesion table (p. 7.2-196) for the pile material: C_A = Su up to 250 psf, then 480/750/950/1300 psf (timber and concrete) or 460/700/720/750 psf (steel, also used when material is omitted) at Su = 500/1000/2000/4000 psf, interpolated between band limits and held above 4000 psf. Not allowed on cohesionless layers.
`axial.soil.waterTableDepth`	number	no	≥ 0 — Depth of the water table below the ground surface (m for si, ft for us). Omit for a dry profile; when given, waterUnitWeight is required.
`axial.soil.waterUnitWeight`	number	no	> 0 — Unit weight of water γw used for pore pressure and buoyancy: 9.81 kN/m³ for si or 0.0624 kip/ft³ for us (never pcf). Required when waterTableDepth is given.
`axial.capacity`	object	yes	Axial capacity options that set the ultimate side and tip resistance for the t-z/q-z springs.
`axial.capacity.segments`	number	yes	integer, 20 – 500 — Number of integration segments along the embedded length for the axial capacity calculation.
`axial.capacity.penetrationRatioSide`	number	yes	> 0 — Penetration ratio z/B defining the limiting depth for side friction.
`axial.capacity.penetrationRatioTip`	number	yes	> 0 — Penetration ratio z/B defining the limiting depth for end bearing.
`axial.capacity.kDown`	number	yes	> 0 — Lateral earth-pressure ratio K (dimensionless) for downward side friction, used for layers that omit their own kDown.
`axial.capacity.kUp`	number	yes	> 0 — Lateral earth-pressure ratio K (dimensionless) for uplift side friction, used for layers that omit their own kUp and kDown.
`row`	object	yes	Pile row stabilizing the slope.
`row.pileCount`	number	yes	integer, > 0 — Number of identical piles in the row crossing the candidate surfaces.
`row.spacing`	number	yes	> 0 — Center-to-center pile spacing along the row (length, in the request's unit system). Must be at least 6 times the maximum lateral pile diameter.
`row.tributaryWidth`	number	yes	> 0 — Width of slope represented by this row and its distributed demand (length). Total demand = distributedDemand × tributaryWidth; it cannot be less than the row's outside-pile centerline span.
`row.orientation`	"normal-to-movement"	yes	Row orientation; only a row normal to the slope movement is supported.
`row.interactionMethod`	"independent-wide-spacing"	yes	Pile-row interaction method; only independent wide spacing (interaction factor 1.0) is supported.
`surfaces[]`	object[]	yes	min 1 item, max 60 items — Candidate slip surfaces, ordered by strictly increasing sliding depth, with unique IDs.
`surfaces[].id`	string	yes	Unique, stable lowercase identifier for this candidate surface (e.g. "s1").
`surfaces[].slidingDepth`	number	yes	> 0 — Depth below the ground surface where this candidate slip surface crosses the pile (length). Surfaces must be listed in strictly increasing depth and may not lie below the pile tip.
`surfaces[].distributedDemand`	number	yes	> 0 — Driving force per unit row width that the pile row must resist on this surface, from a separate slope-stability analysis (force/length, e.g. kN/m in SI or kip/ft in US).
`surfaces[].slipAngleDeg`	number	no	0 – 90 — Local slip-surface inclination from horizontal at this crossing, in degrees. Omit to use the request's shared slipAngleDeg.
`soilDisplacement`	number	yes	> 0 — Magnitude of the free-field soil movement tangent to the slip surface, applied to soil above each candidate surface (length, in the request's unit system).
`slipAngleDeg`	number	yes	0 – 90 — Shared inclination of the slip surface and soil movement from horizontal, in degrees; used by surfaces without their own slipAngleDeg.
`maxDisplacementCap`	number	yes	> 0 — Cap on the lateral (horizontal) component of the soil displacement (length, in the request's unit system). The lateral component is min(δ·cos θ, cap); the axial component is not capped. Required; there is no default.
`increments`	number	yes	integer, 20 – 800 — Number of finite-difference increments along the pile for the lateral p-y solve.
`axialSegments`	number	yes	integer, 20 – 800 — Number of axial load-transfer elements along the pile for the t-z solve.
`convergenceTolerance`	number	yes	0 – 0.01 — Relative convergence tolerance shared by the lateral and axial nonlinear solvers.
`lateralRelaxation`	number	yes	0 – 1 — Picard under-relaxation factor for the lateral p-y iteration (1 = full update, no relaxation); the solver may reduce it if iterations stall.
`axialRelaxation`	number	yes	0 – 1 — Picard under-relaxation factor for the axial t-z iteration (1 = full update, no relaxation).
`maxIterations`	number	yes	integer, 2 – 5000 — Maximum nonlinear iterations for each lateral and each axial solve. A solve that does not converge fails the request.
`layering`	"direct" \| "georgiadis"	yes	Layered-soil treatment for lateral p-y curves: "direct" builds each layer's curves at actual depth (as in COM624P); "georgiadis" uses the Georgiadis (1983) equivalent-depth method.
`lateralShearReadout`	"equilibrium" \| "finite-difference"	no	How the lateral resistance (pile shear at the slip) is read. "equilibrium" (default): the equilibrium shear −∫p dz from the head to the slip, second order in the element length, used for design. "finite-difference": the central-difference shear RSPile and LPile print; it is first order in the element length and below the mesh-converged shear on coarse meshes, so it is only for reproducing published values at the publishing program's own mesh (the response then carries a warning).

Response fields

Field	Type	Description
`method`	object	Exact released method, edition, interaction selector, and minimum spacing in pile diameters.
`assessment`	object	globalFsAssessed and structuralCapacityAssessed are both false: this endpoint supplies mobilized pile resistance only.
`row`	object	Echoed row definition plus the computed minimum independent spacing in request length units.
`points[]`	object[]	One successful lateral-plus-axial solve per candidate surface, in declared depth order.
`points[].surfaceId`	string	Stable candidate-surface identifier from the request.
`points[].slipAngleDeg`	number	Resolved local slip angle in degrees, from the candidate override or shared request angle.
`points[].slidingDepth`	number	Depth where the candidate surface crosses the pile, in the declared unit system.
`points[].lateralResistance`	number	Single-pile p-y shear at the candidate surface.
`points[].axialResistance`	number	Single-pile t-z internal axial force at the candidate surface.
`points[].resultant`	number	Vector magnitude of component resistance, reported as a diagnostic only.
`points[].tangentResistance`	number	Work-conjugate single-pile resistance tangent to slip movement; used for capacity.
`points[].rowCapacity`	number	Pile count × interaction factor × tangent resistance.
`points[].totalDemand`	number	Distributed driving demand × declared tributary width.
`points[].demandCapacityRatio`	number	Total candidate demand divided by row capacity.
`points[].capacityMargin`	number	Row capacity minus total demand.
`points[].lateralIterations`	integer	Nonlinear iterations used by the p-y solve.
`points[].axialIterations`	integer	Nonlinear iterations used by the t-z solve.
`governingSurface`	object	Candidate with the largest demand/capacity ratio, not the largest resistance.
`convergence`	object	Successful all-surface convergence stamp and maximum component iteration counts.

Code examples

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

POST /v1/slope

curl https://api.pilecalc.com/v1/slope \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
  "unitSystem": "si",
  "method": "applied-displacement-independent-wide-spacing",
  "lateral": {
    "pile": {
      "kind": "uniform",
      "length": 12,
      "diameter": 0.61,
      "ei": 143000,
      "groundSurfaceDepth": 0
    },
    "soil": {
      "layers": [
        {
          "model": "soft-clay",
          "top": 0,
          "bottom": 5,
          "gamma": 8.5,
          "c": 28,
          "e50": 0.02
        },
        {
          "model": "sand-reese",
          "top": 5,
          "bottom": 12,
          "gamma": 9.5,
          "phi": 34,
          "k": 16300
        }
      ]
    }
  },
  "axial": {
    "method": "navfac-dm7-reese-oneill",
    "pile": {
      "kind": "uniform",
      "length": 12,
      "diameter": 0.61,
      "elasticModulus": 200000000,
      "unitWeight": 77,
      "displacement": true
    },
    "soil": {
      "layers": [
        {
          "top": 0,
          "bottom": 5,
          "gamma": 18,
          "type": "cohesive",
          "cohesion": 28
        },
        {
          "top": 5,
          "bottom": 12,
          "gamma": 19,
          "type": "cohesionless",
          "phi": 34
        }
      ]
    },
    "capacity": {
      "segments": 120,
      "penetrationRatioSide": 20,
      "penetrationRatioTip": 20,
      "kDown": 1,
      "kUp": 1
    }
  },
  "row": {
    "pileCount": 5,
    "spacing": 3.66,
    "tributaryWidth": 18.3,
    "orientation": "normal-to-movement",
    "interactionMethod": "independent-wide-spacing"
  },
  "surfaces": [
    {
      "id": "surface.01",
      "slidingDepth": 1,
      "distributedDemand": 45
    },
    {
      "id": "surface.02",
      "slidingDepth": 2,
      "distributedDemand": 55
    },
    {
      "id": "surface.03",
      "slidingDepth": 3,
      "distributedDemand": 65
    },
    {
      "id": "surface.04",
      "slidingDepth": 4,
      "distributedDemand": 75
    },
    {
      "id": "surface.05",
      "slidingDepth": 5,
      "distributedDemand": 85
    },
    {
      "id": "surface.06",
      "slidingDepth": 6,
      "distributedDemand": 95
    },
    {
      "id": "surface.07",
      "slidingDepth": 7,
      "distributedDemand": 105
    },
    {
      "id": "surface.08",
      "slidingDepth": 8,
      "distributedDemand": 115
    }
  ],
  "soilDisplacement": 0.05,
  "slipAngleDeg": 30,
  "maxDisplacementCap": 0.3,
  "layering": "direct",
  "increments": 120,
  "axialSegments": 120,
  "convergenceTolerance": 1e-7,
  "lateralRelaxation": 0.4,
  "axialRelaxation": 0.5,
  "maxIterations": 1000
}'

The GET variant returns governingSurface.demandCapacityRatio,points.0.rowCapacity 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

Use governingSurface.demandCapacityRatio for the supplied pile-row check. It is not the slope's global factor of safety. The endpoint also does not check pile structural capacity; verify bending and shear strength separately.
points[].resultant is not the design capacity. The declared capacity uses the work-conjugate tangentResistance and the explicit row aggregation at the declared movement. The response retains resolved angles in points[].slipAngleDeg and governingSurface.slipAngleDeg.
The API never returns a successful point with converged: false. Any failed lateral or axial solve produces an actionable engine error for the request.
Spacing below six maximum pile diameters, unsupported orientation/interaction, mismatched component geometry, cyclic input, buried coordinates, unordered surfaces, and incomplete soil coverage fail contract validation.

Close-spacing interaction is not modeled

independent-wide-spacing has interaction factor 1.0 only inside its declared envelope. Do not emulate shadowing by altering pile count or spacing; rows spaced closer than the declared envelope are rejected explicitly.