Pile-head springs your structural model can actually use.
A signed reciprocal lateral–rotation tangent matrix and both vertical secant and tangent stiffness at one explicit service state — with convergence, reciprocity and refinement evidence visible.
Every structural model of a building or bridge on piles needs the foundation response at its service state. PileCalc runs the nonlinear p-y solution at the service state and four centered perturbations, forms a signed reciprocal flexibility Jacobian, and inverts it to the coupled lateral–rotation tangent matrix.
The same explicit vertical service load is evaluated on the t-z/q-z response. Both Q/s secant stiffness and local dQ/ds tangent stiffness are reported, and every result carries its convergence, reciprocity and mesh-refinement evidence — a nonconverged or mesh-sensitive run is rejected explicitly rather than silently dropped.
Explicit service state
Q, V and M are mandatory; zero lateral actions remain valid because tangent derivatives do not require component ratios.
Signed reciprocal coupling
Kyy, Kyθ, Kθy and Kθθ preserve the clockwise-positive work-conjugate sign convention.
Vertical secant and tangent
Q/s reproduces total service settlement; local dQ/ds describes incremental response.
Convergence diagnostics
All five lateral solves, raw reciprocity and fine/half-resolution vertical response are checked on every run.
Validated against published benchmarks
Every figure below is produced by the engine on the cited published problem — closed-form solutions, design-manual tables, or independent codes — and reproduced by the test suite on every release.
Signed service-state tangent matrix plus vertical secant/tangent response
| Quantity | PileCalc | Reference | Agreement |
|---|---|---|---|
| Semi-infinite homogeneous Winkler signed head matrix, EI=10⁸ and es=1000Crispin & Mylonakis (2022), Eq. 8; independently evaluated closed form | Automated Kyy, Kyθ, Kθy and Kθθ gate | 25,148.7; −316,227.8; −316,227.8; 7,952,707.3 | within 0.25% |
| Vertical service interpolation: (Q,s)=(0,0),(100,.01),(160,.03), Qs=130FHWA GEC 12 load-transfer service-response basis | s=.02; Ksec=6500; Ktan=3000 | Independent piecewise-linear algebra | machine precision algebraic gate |
The numbers, published
PileCalc's engine is checked term-by-term against the reference codes. A representative sample of the benchmarks — every intermediate value is visible in the app so you can reproduce them yourself.
Foundation stiffness (springs): common questions
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Free to start — no install, no dongle, every input explained and every result visible.
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