PileCalc

Slope stabilization

Strict pile-row demand/capacity checks across declared candidate slip surfaces, with explicit distributed demand and convergence evidence.

PileCalc evaluates a declared row of piles crossing candidate slip surfaces. For each candidate it solves one pile's lateral p-y and axial t-z response to imposed soil movement, resolves that resistance tangent to movement, aggregates the supported row, and compares it with an explicit distributed driving demand. The surface with the largest demand/capacity ratio governs.

Pile-row check — not a global slope-stability solution

The tool does not search for a critical limit-equilibrium surface or calculate global factor of safety. Candidate-surface demand must come from a separate slope-stability model. See Validation & provenance for the evidence behind the method.

Method and boundary

Soil above each candidate surface receives a free-field movement δ tangent to the slip. The movement is resolved into lateral and axial components for the two component solvers.

δ_l = δ cos θ,  δ_a = δ sin θ,  R_t = R_l cos θ + R_a sin θ
Movement and work-conjugate single-pile resistance

R_l is the pile shear at the candidate surface from the lateral p-y analysis. R_a is the internal axial force there from t-z/q-z load transfer. The tangent projection R_t is used for demand/capacity; the vector magnitude is reported only as a diagnostic.

The released interaction method is independent-wide-spacing: piles must be normal to movement and spaced at least six pile diameters. Its interaction factor is exactly 1.0. PileCalc rejects closer spacing because it does not yet implement a calibrated shadowing, soil-flow, or strain-wedge interaction model for this tool.

Pile row

C_row = n · η · R_t,  η = 1.0
Row capacity inside the declared wide-spacing envelope
LPile lengthlength
The pile must cross every candidate surface and extend into the stable mass below it.
bPile diameterlength
Diameter controls both component response and the minimum released spacing of 6b.
EIFlexural rigidityforce · length²
Flexural rigidity is used by the p-y component solver.
EElastic modulusforce / length²
Elastic modulus and the section-dependent structural area form axial stiffness EA(z). Section changes are not replaced by the head area.
nPile countcount
Number of identical piles represented by the row.
sSpacinglength
Center-to-center spacing. Requests below six maximum pile diameters fail validation.
WTributary widthlength
Width of slope represented by the supplied distributed demand and this pile row.

Candidate surfaces and distributed demand

Every candidate surface has a stable ID, crossing depth, and driving demand per unit row width. The API accepts an arbitrary demand at every surface. The interactive UI provides a convenience sweep that linearly interpolates between declared shallow and deep values.

D_i = q_i W,  DCR_i = D_i / C_row,i,  governing = arg max_i(DCR_i)
Candidate demand, capacity ratio, and governing surface

Selecting the largest sampled resistance is incorrect: a surface with more resistance can still govern if its driving demand rises faster. Candidate IDs must be unique, depths must be strictly ordered, and no crossing may lie below the pile tip.

Applied soil movement

δDisplacementlength
The free-field movement tangent to the candidate surface. The public request carries an explicit lateral displacement cap in its declared unit system; no hidden 0.3 m/0.3 ft default is used.
θSlip angledegrees
Inclination of movement from horizontal. The released domain is strictly between 0° and 90°.

Soil profiles

The lateral and axial profiles describe the same ground through different constitutive models. Both must start at depth zero, remain ordered and contiguous, and cover the full pile length and bearing stratum. Lateral and axial pile length and diameter must agree at every depth. Explicit groundwater unit weight is required whenever a water table affects the axial model.

Buried/free-head coordinate transformations and cyclic slope degradation are outside the released method and fail validation rather than being silently ignored.

Reading the results

Summary quantities

  • Governing DCR — the largest total-demand / row-capacity ratio and its candidate surface. A value above 1 means the declared row resistance is below the supplied pile demand; it is not a global factor of safety.
  • Row capacity — the full row's tangent resistance at the governing surface inside the declared wide-spacing envelope.
  • Demand / margin — supplied total demand and capacity minus demand at the governing surface.

Profiles, trace, and convergence

The chart compares row capacity, total demand, and single-pile tangent resistance. The table retains component forces, DCR, margin, and iteration evidence for every candidate. A public result is returned only when both the p-y and t-z solutions converge at every surface; otherwise the request fails with an actionable engine error.

Evidence and limits

Public evidence anchors include FHWA GEC 9, the UTCA road-embankment study, the Purdue/INDOT pile-stabilized-slope report, and CDOT's driven-pile slope study. These sources — together with RSPile comparisons — support the problem framing, distributed demand, pile-spacing sensitivity, and public comparison targets; they do not justify a universal close-spacing interaction factor, which is why closely spaced rows are rejected.