Structural analysis¶
The pile is analysed as a 3D frame in finite elements, supported on an elastic foundation. The solver is PyNite, a matrix structural analysis library.
The result of this analysis — moments, shears and axial forces along the shaft — is what feeds the design.
The model¶
Discretisation¶
The pile is divided into nodes metre by metre, matching the borehole discretisation. This is no accident: each node needs a spring, and the spring comes from the soil layer at that metre.
The nodes go from the head to the toe, ordered from top to bottom. The head node receives the applied loads.
Section and material¶
Solid circular section:
The material is defined by \(E_c\), Poisson's ratio \(\nu\) (default 0.20) and a unit weight of 25 kN/m³, with
Elastic supports¶
Each node receives springs according to the soil reaction:
| Direction | Spring | When |
|---|---|---|
| DX, DY | \(K_h\) | Always |
| DZ | \(K_v\) | Only when the vertical springs are enabled |
Torsion (RZ) is restrained to stabilise the model — a circular pile under transverse load has no significant torsion, and leaving it free would create a rigid-body mode.
Surface nodes receive no spring
Nodes less than 0.10 m deep have their spring set to zero. The soil at the surface is the least confined and the most subject to erosion, excavation and seasonal variation — relying on its reaction is an optimism that practice does not confirm.
Head level below ground¶
When the pile head is embedded — cut off below ground level, the normal situation under a cap —, the head node has soil around it and receives the spring corresponding to its depth.
When the head is at ground level or above, it is left free. This is the case of a pile with an exposed length, which behaves like a column fixed in the soil.
A modelling precaution
The nodes are positioned at the borehole levels, not at distances measured from the pile head. It looks like a detail, but it is what ensures that the \(K_h\) of a given depth is applied at the right depth: positioning the nodes from the head would make the model sink with the pile, applying the 3 m stiffness at the 5 m level and lengthening the modelled member.
Raked piles¶
SPX models raked piles with two angles:
| Parameter | Meaning |
|---|---|
| Rake | Angle from the vertical |
| Azimuth | Direction of the rake in the horizontal plane |
The horizontal position of each node is obtained by projecting the drop from the head:
The projection is measured from the pile head, not from ground level — a pile cut off at 2 m only starts to depart from the vertical from there.
Individual rake
In a pile cap, each pile can have its own rake and azimuth. That is what allows fan arrangements to resist horizontal loads — the classic case of a bridge abutment or a structure under earth pressure.
Analysis per axis¶
The analysis is carried out per axis — one model for X and another for Y —, each with the shear and moment of its own direction. The two results are then combined in the design, which treats the bending as biaxial with axial force.
This separation is what allows one plane model to be used at a time, which is numerically more stable, without losing the biaxial interaction in the section check.
Results¶
The analysis produces, along the shaft:
- Horizontal displacement — the most widely used serviceability criterion for laterally loaded piles.
- Bending moment — usually at its maximum a few metres below the surface, and it is what designs the longitudinal reinforcement.
- Shear force — designs the stirrups.
- Axial force — decreasing with depth, due to the mobilised friction.
The charts are interactive and can be exported to the report.
Limits of validity¶
Range of application
- The model is linear elastic. The concrete does not crack and the soil does not yield. For service displacements this is acceptable; close to failure, it is not.
- The flexural stiffness uses the gross concrete section. NBR 6118 allows a reduction for cracking in second-order analyses, which would make the displacements larger and redistribute the moments.
- Winkler springs do not represent interaction between piles in the same cap. In a group with small spacing, the effective stiffness per pile is lower than calculated.
- The 1 m discretisation limits the resolution of the maximum moment. In short or very stiff piles, the peak may fall between nodes.