Steel core piles are often regarded as the “Rolls-Royce” of foundation systems: they are highly capable, but also expensive, and their production and transportation come with a considerable carbon footprint. That alone makes optimal design not merely desirable, but necessary. Yet current practice is often far from optimal. In many cases, steel core piles are designed only for the elastic capacity of the steel core, while the contribution of the concrete infill and the steel casing is simply ignored. Structurally, this is difficult to justify. The pile is a composite member, and there is no fundamental reason why its resistance should not be assessed on that basis, particularly when corrosion losses in the casing can be accounted for explicitly, as is already done for steel pipe piles, and when the steel core can be detailed to ensure adequate interaction with the concrete.

For some time, I have been reflecting on this inconsistency and about six years ago I developed a simplified method for estimating the capacity of steel core piles, which I refer to as the pseudo-elastic approach and would like to share here. The aim of the method is to provide a practical and reasonable estimate of composite pile capacity without requiring a full elasto-plastic section analysis. It builds on the relative simplicity of establishing the fully plastic capacity of the composite cross-section. The procedure begins by constructing the fully plastic M–$N$ interaction diagram of the pile, in which all materials in the cross-section are assumed to reach their plastic resistance. In this formulation, steel contributes in both tension and compression, the tensile resistance of concrete is neglected, and the effect of corrosion on the steel casing is taken into account through a reduced effective casing thickness.

Once this plastic capacity diagram has been established, the pseudo-elastic capacity is derived by calibrating an elastic-shaped composite interaction curve to the plastic composite response. First, the steel-only shape factor at zero axial force is determined as$$r_{\text{steel}} = \frac{M_{pl,\text{steel}}(N=0)}{M_{el,\text{steel}}(N=0)}$$

This ratio expresses the relationship between the plastic and elastic moment capacities of the steel core alone. Next, the plastic composite moment resistance at zero axial force, $M_{pl,\text{comp}}(N=0)$, is obtained from the fully plastic composite interaction diagram. The pseudo-elastic composite moment resistance at zero axial force is then defined as$$M_{pe,\text{comp}}(N=0) = \frac{M_{pl,\text{comp}}(N=0)}{r_{\text{steel}}}$$

In this way, the pseudo-elastic composite curve is assigned the same plastic-to-elastic ratio at $N=0$ as the steel core alone. The axial intercepts of the pseudo-elastic curve are taken directly from the plastic composite interaction diagram, so that$$N_{0,+} = \max\!\left(N_{pl,\text{comp}}\right), \qquad N_{0,-} = \min\!\left(N_{pl,\text{comp}}\right)$$

The pseudo-elastic interaction is then defined piecewise by linear branches between these axial intercepts and the calibrated moment intercept at $N=0$:

$$M_{pe}(N) = M_{pe,\text{comp}}(0)\left(1-\frac{N}{N_{0,+}}\right), \qquad N \ge 0$$$$M_{pe}(N) = M_{pe,\text{comp}}(0)\left(1-\frac{|N|}{|N_{0,-}|}\right), \qquad N < 0$$

with$$M_{pe}(N) \ge 0$$The result is a simplified composite interaction curve that preserves the axial capacity of the plastic composite solution while reducing its bending resistance to a level more consistent with an elastic design philosophy. The pseudo-elastic approach therefore provides a rational intermediate estimate: it is less conservative than designing for the elastic capacity of the steel core alone, yet less ambitious than adopting the full plastic capacity of the entire composite section. I further assume that the actual elasto-plastic capacity of the pile will lie between the pseudo-elastic and fully plastic capacities. On that basis, the pseudo-elastic model may be regarded as a better lower-bound approximation than the elastic capacity of the steel core alone, provided that the effects of corrosion, concrete strength, and the low tensile capacity of concrete are properly taken into account. As such, it offers a simple and transparent means of accounting for part of the beneficial contribution of both the concrete infill and the steel casing in practical design.

From a cost point of view, if the same design demand can be met with less steel, smaller sections, or fewer piles, then fabrication, transport, handling, and installation effort would usually fall as well. That is where the pseudo-elastic approach could support better optimization.

From a carbon-dioxide point of view, the argument is similar. A design that uses less steel and possibly fewer pile elements would generally reduce embodied emissions from:

• steel production,
• transport of heavy elements,
• site handling and installation,
• and potentially grout/concrete quantities as well.

So the environmental significance is that a less conservative but still cautious structural model can help avoid overdesign, and overdesign in steel foundations usually means unnecessary cost and unnecessary emissions.

However, the pseudo-elastic method is still a proposed engineering simplification, not a validated standard method. So the right conclusion is not “this guarantees savings,” but rather: it may offer a much better lower-bound design basis than elastic steel-core-only design, and that improved realism creates room for meaningful cost and carbon optimization where structural section capacity is the controlling criterion. Its use in practical design must therefore be regarded as exploratory, and any engineer choosing to apply it does so at their own risk.

Classical pile buckling analysis commonly relies on Engesser’s solution, which assumes a uniform lateral support stiffness along the embedded pile length. While this analytical approach is useful for rapid checks and conceptual understanding, its applicability is limited to idealized soil conditions. In practice, soil stiffness varies with depth and is often characterized by layered profiles in which weak strata of finite thickness are interbedded with stronger layers. In such cases, the governing buckling behavior is controlled not by an average stiffness value, but by the spatial variation of soil stiffness and the corresponding deformation modes of the pile. PBuckle.V0 addresses these limitations through a finite element–based formulation that allows depth-dependent lateral stiffness defined directly by the user, supports piecewise-constant or linearly interpolated stiffness profiles, explicitly captures local buckling modes triggered by weak layers, and accurately identifies the true minimum critical buckling load—even when it occurs at a higher buckling mode rather than the first mode.

PBuckle.V0 is provided as an engineering analysis and research tool intended to support understanding of pile buckling behavior under idealized modeling assumptions. While care has been taken in the development and verification of the program, the results produced are dependent on user input, modeling choices, and assumptions regarding soil and structural behavior. The software does not replace professional engineering judgment, independent verification, or project-specific design checks. Any use of PBuckle.V0 in engineering projects is undertaken at the user’s own responsibility and accountability, and the developer assumes no liability for the application of the results in design, construction, or decision-making processes.

Find the application following the link

https://drive.google.com/file/d/1Gy3PBlHYF4huelK8u9lil0M8_9oPlyst/view?usp=drive_link