FEM analysis

The FEM analysis computes the internal forces along the pile for horizontal forces, moments and vertical forces applied at the head or at any elevation. The pile is a beam on Winkler elastic soil: beam elements with constant stiffness E·J and, at each node in the ground, a horizontal spring.

Enabling the analysis

In the Reinforcement and FEM analysis card tick Run the FEM analysis and the section design with Calculate. With the tick, Calculate also runs the FEM and the section check, and charges 5 more credits. If the analysis produces no results the FEM credit is not charged and the geotechnical calculation remains valid; the reason appears in the messages.

The model

Field	Meaning
Number of elements	segments the pile is divided into, protrusion included
First soil node	first node with a spring; 1 = the protrusion is not discretised separately
Subgrade modulus Ks	Bowles or Chiarugi-Maia
Ks varying with depth	with Bowles, Ks = As + Bs·z; unticked, constant Ks
Non-linear soil	iteratively removes the springs that are no longer effective
Xmax	maximum linear soil displacement [m]
First-spring reduction	factor on the spring at the first soil node
Max iterations	maximum number of cycles of the non-linear calculation
As, Bs, n	assigned Ks: with As > 0, Ks = As + Bs·zⁿ replaces the method

The stiffness of each spring is K_s(z)·D times the tributary length of the node, with half a step at the ends. The elastic modulus of the pile is that of the concrete class in the materials archive; the second moment of area is J = π·D⁴/64, or the J assigned. The axial force comes from the self-weight and the vertical forces.

Modulus of subgrade reaction K_s

• Bowles: K_s = A_s + B_s·z, with A_s = 40·(c·N_c + ½·γ·D·N_γ) and B_s = 40·γ·N_q, in kN/m³, with Hansen's bearing capacity factors. It is computed automatically from the layer parameters.
• Chiarugi-Maia: k_h from the oedometric modulus E_ed, Poisson's ratio ν of the layer and the pile-soil relative stiffness. Fill in E_ed and ν in the layer properties.
• Assigned: enter A_s, B_s and n. Use it for a K_s from tests or from the literature.

Linear and non-linear

In the linear calculation all springs work, in tension too. With Non-linear soil the program repeats the solution and removes the springs with a negative displacement (in tension) or one larger than X_max, up to the maximum number of iterations.

Reading the FEM analysis tab

Choose the combination from the drop-down. At the top the maxima: M_max, T_max, Max displacement and Max pressure. Then the five Internal-force diagrams, each with its maximum value and zoom controls:

• Soil pressures (p = K_s·y)
• Spring reactions
• Bending moment
• Shear
• Deflection

The Results per node table reports, for each node: elevation z, N, M, T, rotation, displacement, pressure p, K_s and reaction R. A load with z > 0 is applied to the node nearest to the given elevation: check in the table where it ended up.

The internal forces of each combination feed the section check node by node. The diagrams also go into the DXF drawing and the report.

Limits of the model

Large displacements

The Winkler model captures neither the interaction between springs nor soil yielding, beyond the removal of springs. For piles with large displacements you need analyses with p-y curves or continuum models, which MP NX does not offer.

The analysis concerns the single pile: it does not account for group effects. The structural check that follows holds for the circular reinforced-concrete section: the FEM accepts an assigned J for other sections, the ULS check remains that of the circular section of diameter D.

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