Soil-Structure Interaction

Standard plant piping is supported by discrete, localized restraints (shoes, guides, anchors). Buried pipelines, however, are continuously supported and restrained by the surrounding soil.

To capture this soil-structure interaction, the engine combines an automated meshing algorithm with the soil spring formulations of the ALA (2001) Guidelines for the Design of Buried Steel Pipe, Appendix B — modelled as bilinear (elastic-perfectly-plastic) springs with direction-dependent vertical behaviour.

4.1 Burial Depth from Geometry

Burial depth is not a fixed input — it is computed per element from the model geometry:

$H = \text{Ground Elevation} - z_{centreline}$

evaluated at each sub-segment's midpoint, where Ground Elevation is set in Settings (default 0). Consequences:

• An inclined or vertical riser automatically receives shallower (softer, weaker) springs near the surface and stiffer ones at depth.
• Any part of a buried element at or above ground level receives no soil restraint — the air/soil transition falls out of the geometry naturally.
• A buried element that computes $H \leq 0$ over its whole length triggers a named warning (shown by Check Model and with analysis results) instead of silently going unrestrained.

4.2 Automated Discretization

When an element is assigned a soil profile, the preprocessor subdivides it into segments no longer than

$L_{max} = \max(0.5\text{ m}, \min(2.0\text{ m}, 5 D_o))$

and attaches soil springs at every generated node, each covering its tributary length. Bend arcs inherit burial from their adjacent elements, so a buried elbow's discretised arc is soil-restrained along its full length.

4.3 ALA Spring Formulations

Inputs from the Soil tab: density $\rho$ (kg/m³, $\gamma = \rho g$), friction angle $\phi$, cohesion $c$ (kPa), and coating factor $f$ (interface friction angle $\delta = f\phi$; ~0.6 rough steel, up to 1.0 concrete). Sand and clay terms are both evaluated, so $c$–$\phi$ soils are handled.

1. Axial ($T_u$)

Adhesion plus interface friction on the mean overburden pressure:

$T_u = \pi D \alpha c \;+\; \pi D H \gamma\,\frac{1 + K_0}{2}\,\tan(f\phi), \qquad K_0 = 1 - \sin\phi$

with the adhesion factor $\alpha(c)$ per ALA Eq. B-1. Yield displacement $\Delta_t$ = 3 mm (sand) / 8 mm (clay). A $\phi = 0$ undrained clay correctly retains only the adhesion term.

2. Lateral ($P_u$)

$P_u = N_{ch}\, c\, D + N_{qh}\, \gamma H D$

$N_{ch}$ (clay, ≤ 9) and $N_{qh}$ (sand, function of $\phi$ and $H/D$) are the ALA Appendix B factors — not the Rankine passive coefficient, which underestimates lateral resistance several-fold at typical burial ratios. Yield displacement $\Delta_p = 0.04(H + D/2) \leq 0.15 D$.

3. Vertical Bearing ($Q_d$) — pipe moving down

$Q_d = N_c\, c\, D + N_q\, \gamma H D + \tfrac{1}{2} \gamma D^2 N_\gamma$

with the classical bearing factors $N_q = e^{\pi\tan\phi}\tan^2(45° + \phi/2)$, $N_c = (N_q - 1)/\tan\phi$ (5.14 at $\phi = 0$), $N_\gamma = e^{0.18\phi - 2.5}$. Yield displacement $0.1 D$ (sand) / $0.2 D$ (clay).

4. Vertical Uplift ($Q_u$) — pipe moving up

N_{cv} = \min\!\big(2\tfrac{H}{D},\,10\big), \quad N_{qv} = \min\!\Big(\frac{\phi H}{44 D},\, N_q\Big)$$ Yield displacement $\min(0.015H, 0.1D)$ sand / $\min(0.15H, 0.2D)$ clay. Uplift is by far the weakest direction — typically well under half the bearing resistance at plant burial depths. ## 4.4 Bilinear Springs & One-Way Vertical Behaviour Each direction is an **elastic-perfectly-plastic** spring: elastic stiffness $k = F_{ult}/\Delta$ up to the ultimate resistance, then a constant force with a plastic datum moved by radial return mapping — the same scheme the solver uses for [support friction](./1.3-boundary-conditions.md). This matters wherever movements exceed the small yield displacements (axial yields at just 3–8 mm): near risers, at buried bends, and along the virtual-anchor zone, a purely linear spring would overestimate soil restraint without bound. The **vertical direction is one-way**: downward movement engages the bearing stiffness and capacity, upward movement the (much softer and weaker) uplift values. The solver switches the branch by the node's displacement sign, with a deadband and an anti-chatter freeze; occasional-load overlays inherit the operating-state branch. For **inclined pipe**, each node's spring set is built in an untwisted local frame — axial along the pipe, one pure-lateral horizontal direction, and a bearing/uplift direction blended by inclination ($\cos^2\alpha$ vertical / $\sin^2\alpha$ lateral). A vertical riser degenerates correctly to two horizontal lateral springs plus axial friction along the pipe. :::info[Convergence & determinism] Soil yield statuses join the same convergence criteria as gaps and friction: the solve is accepted only when every spring's branch and yield state is stable and the residual displacement creep is below tolerance. The procedure is deterministic — the same model always produces the same converged state. ::: :::note[Modal analysis] Dynamic matrices use the elastic (unyielded) soil stiffnesses with the bearing-side vertical branch — the pipe vibrates about its gravity-loaded operating position. :::