The Chartership Forum

Foundation Engineering / Laterally loaded piles

Capacity and deflection

Which one actually sizes the pile.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Corrections checked in this pass

  • Verified the short free-head pile equilibrium against FHWA equations. The model now shows mechanism load and required moment resistance.

Checks needed for project use

  • A geotechnical reviewer must confirm drainage and stress basis, bearing-factor formulation, correlations and settlement influence factors. Partial factors and project-specific ground conditions are outside these teaching checks.
  • Establish section moment resistance, whether the short-pile mechanism is admissible, head restraint, soil layering, cyclic loading and serviceability before deriving a design resistance.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Why this matters

A bridge pier that has not collapsed but has moved 60 mm at bearing level is a failed structure in every sense that matters. Lateral pile design is a serviceability problem far more often than a capacity one, and the two are calculated quite differently.

Broms-type lateral-pile methods use idealised limiting soil resistance and equilibrium, with different cases for head restraint, pile flexibility and section resistance. The short-pile clay model neglects near-surface resistance and uses a limiting pressure below that zone.

The short free-head uniform-clay equilibrium has been checked against FHWA/RD-85/106, equations 7.2–7.5. For D = 0.6 m, L = 4 m, su = 50 kPa and zero load height, the soil mechanism gives 242.5 kN and a maximum moment demand of 327.2 kNm. Raising the load by 1 m gives 179.4 kN and 400.4 kNm. These are mechanism results, not design resistances: the pile must resist the moment, and head restraint, ground profile, cyclic response, movement and factors need separate checks. Design resistance remains withheld until those checks are established.

Deflection is usually what governs. A pile that satisfies its ultimate lateral check by a comfortable margin may still move far more at working load than the structure will accept — Module 10's angular distortion argument, applied horizontally.

The subgrade reaction approach gives a deflection directly from kh, but its weakness is now exposed: a single spring constant cannot represent soil that is stiff at small strain and soft at large, and the answer is only as good as the kh chosen for the right movement.

The better tool is the p–y method: replace the single spring with a set of non-linear springs down the pile, each with its own load–deflection curve appropriate to its depth and soil. It is a numerical analysis rather than a formula, it is standard practice for offshore and bridge foundations, and it accommodates layering, cyclic degradation and head fixity in a way no closed-form solution can.

Check yourself

Why does raising the point of load application above ground level reduce a short pile's lateral capacity so much?

Practice

In a purely arithmetic comparison, two hypothetical resistance estimates are 530 kN and 376 kN. What percentage reduction does that represent? These values are not verified pile capacities.

Try it

Rigid or flexible?

The classification comes before any calculation, because the two mechanisms are completely different.

4.00 m
0.60 m
5000 kN/m²

The boundaries

  • L/T below about 2 — rigid. Above about 4 — flexible.
  • T takes the fourth root of EI, so doubling the section stiffness raises it by only 19%.
  • The free-head uniform-clay soil mechanism is shown at zero load height. Design resistance remains withheld until pile moment resistance and the applicable failure mode are checked.
rigidintermediateflexibleL/T = 1.610246
Second moment I
0.00636 m⁴
EI
190852 kN·m²
Stiffness factor T
2.49 m
L/T
1.61
Short-pile soil mechanism
242.5 kN
Moment demand at that load
327.2 kN·m
Design resistance
Section and applicability check required

Relatively rigid in this stiffness model. These thresholds illustrate relative stiffness. Head restraint, nonlinear ground response, load height and pile section resistance need separate checks.

Summary

  • T = (EI/kh)^¼ is a characteristic length in the stated line-spring model; L/T indicates relative stiffness
  • Below L/T ≈ 2 the pile rotates and fails in the soil; above ≈ 4 it hinges and fails in the pile
  • The same section was rigid at 4 m and flexible at 10 m
  • Assess load height through a verified lateral-response model; the previous capacity figures have been withheld
  • Deflection normally governs, and p–y analysis is the tool for it