Embedded-region benchmarks

The benchmark suite distinguishes centreline interaction for anchors and nails from the interaction-surface formulation for piles.

Interaction line

• Embedded anchor pull-out (2D)
• Embedded anchor pull-out (3D)
• Embedded anchor with Mohr–Coulomb capacity

These examples use *Embedded region, interaction. They do not verify the cylindrical interaction surface.

Interaction surface

• Exact fixed-host pull-out (A0): shaft quadrature, axial transfer, yielding and state update against a closed-form solution.
• Axially loaded pile (A1-A3): pressure source, stress recovery, base mobilisation, disk quadrature, ghost zone and combined shaft-base response against axisymmetric continuum models.
• Laterally loaded pile (H): unilateral separation, host-mesh convergence, interaction-stiffness sensitivity, pile-axis deformation and recovered normal stress against a three-dimensional continuum model.

The benchmarks A0-A3 and H are those of the manuscript An embedded beam formulation with an implicit interaction surface: design, implementation and numerical assessment (Machacek, 2026, submitted). Input files are provided for A0-A3.

The interaction-surface examples use *Embedded region, interaction-surface.