Understanding finite element analysis for pile caps

Inspired by: Understanding finite element analysis for pile caps | CROSS (Report ID: 1152)

The application of two-dimensional (2D) Finite Element (FE) shell elements for modelling planar structures, such as concrete slabs or walls, requires careful consideration regarding the element's thickness relative to its overall dimensions. The underlying theory used in the formulation of these elements, like Mindlin-Reissner plate theory, suggests limits on the thickness-to-span ratio (e.g., generally a maximum ratio of thickness to panel dimension around 3, or a Eurocode limit of 5, or a span needing to be more than 10 times the depth for certain flat slabs). The CROSS Safety Report highlights significant concerns that designers frequently employ 2D FE shells to model structural components such as pile caps, combined bases, and large ground bearing structures, where the element depth is substantial and exceeds these accepted limits. For such thick elements, the underlying structural theory is no longer strictly valid, and the results from the FE analysis cannot be relied upon, as the model may be over-constrained, and the crucial effects of shear may be underestimated.

When elements exhibit a high depth-to-span ratio, such as deep beams or pile caps, their behaviour is dominated by shear rather than bending, meaning they function more effectively as strut-and-tie systems. If FE analysis is used in these cases without sufficient thought and understanding, the subsequent design derived from potentially inaccurate forces may result in an unsafe structure, or cause the section's performance to transition abruptly from ductile to brittle under overload due to insufficient reinforcement calculated for the actual demands. Consequently, for deep structural elements, alternative analysis and design approaches, such as the Strut-and-Tie method, are strongly recommended, necessitating sound engineering judgment alongside any software application.

The MasterFrame Finite Element Analysis (FE) module is designed to model continuum structures such as slabs and walls using 2D FE surfaces. To offer flexibility, MasterFrame FE employs finite elements formulated on the basis of the Mindlin-Reissner plate theory, a thick plate formulation that incorporates shear deformation effects.

However, when modelling structural elements where the depth is significant, such as pile caps, combined bases, and large foundation structures, careful consideration must be given to the limits of the underlying 2D FE theory. These elements are typically thick, stiff units that often behave more like deep beams, where shear significantly influences behaviour.

1. The Limits of Applicability of 2D FE Models

The validity of using 2D FE analysis hinges on the element's span-to-depth (or span/thickness) ratio:

Recommended Upper Limit: The upper advised limit for the span/thickness ratio of a structural element modelled using MasterFrame FE is 3–5. The Mindlin-Reissner theory suggests a maximum thickness-to-panel dimension ratio of around 3.
Unreliable Results: For elements where the thickness is so large that the span/thickness ratio falls below this 3–5 limit, the fundamental theory governing the finite elements is no longer valid, and the analysis results cannot be reliably used.
Shear Predominance: When FE analysis is used outside its range of applicability for thick elements (like pile caps), the results may be inaccurate because the analysis often assumes the structure primarily works in bending, leading to an underestimation of shear effects.

2. Recommended Alternative Design Methodology

For structures explicitly recognised as deep beams or elements where the span/thickness ratio dictates caution (i.e., less than 5), alternative analysis and design methods should be employed.

Strut-and-Tie Method: The highly recommended approach for the design of non-standard concrete elements like corbels, pile caps, and deep beams is the Strut-and-Tie design method. A deep beam is defined as one whose span is less than 3 times the beam depth.
MasterSeries Dedicated Pile Cap Design Module: MasterSeries includes a separate module for Pile Cap Design, which can be accessed via the Design menu in MasterFrame and includes Strut and Tie / Deep Beam checks.

3. Best Practice and Validation when using MasterFrame FE

If the MasterFrame FE module is used for slabs or bases with thickness ratios near or within the critical 3–5 range, engineers must exercise caution and apply sound engineering judgement.

Validation and Checks:

Independent Verification: Always understand the probable behaviour of the structure irrespective of the FE analysis output. Perform 'order of magnitude' checks against simplified formulas to ensure the results are sensible and of the correct scale (Verifying results is crucial to confirming the model is correctly set up).
Graphical Output Tools: Utilise the graphical results within the MasterFrame FE module to fully interrogate the model. The FE results can be displayed as colour-coded contour outputs, but Section Line Diagrams are also available and are particularly useful for checking support reactions or internal forces.
Understanding Element Theory: Before using any FE software, the designer must know the underlying theory used for the elements and understand the potential impact of dimensional limitations.

Addressing Localised Stress Peaks:

When modelling elements like pile caps (which involve point loading from columns on the slab surface), localised high stresses (singularities) can occur at the column/FE surface interaction point. MasterFrame provides tools to manage these effects:

Slab Stiff Column/Wall Mesh Regions: Use the Slab Stiff Region feature to modify the mesh locally over the column footprint, accounting for the 2-dimensional nature of the intersection and modifying the element stiffness.
Punching Shear Design: The MasterKey FE Slab Design module offers the option to determine the shear force for punching checks directly from the FE Shear Forces (linear elastic analysis) rather than solely relying on the Code method (plastic distribution). This is generally considered more accurate for complex slabs but requires understanding that the FE forces are derived from a linear elastic analysis.
Peak Smoothing: This feature reduces the impact of singularities by averaging results over a defined radius around the peak value. Note that if column/wall stiff regions are applied, peak smoothing is not appropriate.

See Also