7. Soil & piles

Ground support in Luma has three forms: distributed Winkler springs under a mat
(soil zones), discrete pile head springs with an optional meshed shaft
(piles), and their combination in a pile_supported model. This chapter
covers the mechanical models, how to choose stiffness values, the result
reads, and worked numbers.

7.1 Winkler support model

A soil zone adds a vertical spring at every meshed slab node inside it:

Kz = k × tributary area        [kN/m]
k  = subgrade modulus          [kN/m³]

The tributary area comes from the mesh; refining the mesh does not change the
total support stiffness. By default springs act in both directions. Tick
Compression only (no tension) on the zone (soil tool panel, Properties, or
the bulk editor) and the solver iterates the contact state instead: springs
where the slab lifts off are deactivated, so uplift shows as a zero-bearing
gap rather than suction. The run summary reports the lifted count and
iterations (Uplift (no-tension) row). Consequences:

• A uniform load on a uniform mat gives w = q/k almost everywhere
  (the exact solution for an infinite mat). Concentrations occur only within a
  few characteristic lengths of edges and load changes.
• With two-way springs, if the resultant of the loads moves outside the zone
  footprint, the far side goes into tension (negative bearing) - a modelling
  artefact. Either tick Compression only, extend the mat or zone, or switch to
  a pile-supported model.
• Equilibrium check: Σ(k·w·A) over the zone must equal the applied load
  (over the springs still in contact, for no-tension zones).

No-tension iteration

When any zone is compression-only, each analysis runs an outer contact loop
around the normal (elastic, cracked or long-term) solve: solve, deactivate
every no-tension spring whose node rose past 1 nm, reactivate lifted springs
back in compression, repeat until nothing changes (max 20 passes). It usually
settles in 2–4 passes; the summary flags (no conv.) if it hits the cap. Load
combinations are solved directly (never superposed) when no-tension zones are
present, since the contact state depends on the total load. If a load case has
net uplift the mat genuinely tips and the solve fails - that is the correct
answer, not a solver bug: add ballast, extend the mat, or tie it down.

Choosing k

Typical ranges for the modulus of subgrade reaction (long-term values):

If a geotechnical report gives a modulus of elasticity Es and Poisson's ratio
ν, a first estimate for a wide mat is

k ≈ Es / (B (1 − ν²))        per unit area, with B the mat width

Check the result: the differential settlement between the centre and edge of a
real mat should be within the geotechnical allowance (commonly ≤ 1/500 of the
span between columns). If not, re-examine k.

Bearing results

The ⏚ view shows abs(fz)/tributary at nodes plus k·abs(uz) inside
zones, in kPa. Compare the peak with the allowable bearing pressure - the
service load check is on the peak, not the average.

Anchor (slab-mat-soil): 8 × 8 m mat, t = 250 mm, k = 30 000 kN/m³,
q = 10 kPa → w = q/k = 10/30 000 = 0.333 mm; bearing ≈ 10 kPa;
ΣR = 640 kN.

7.2 Pile support model

A pile contributes in several ways:

If Diameter = 0 the pile is springs only (a "point spring" pile). With a
diameter, the shaft is meshed at ≈ 1 m segments (max 20) and connected to the
slab directly for a fixed head, or through a short head link for a pinned or
rotational-spring head. The auto bending stiffness is
EI = E·πd⁴/64 with E = 30 GPa; give an explicit EI for cracked, prestressed
or steel piles.

Head restraint

Choosing pile stiffness

For preliminary work:

Axial k ≈ (ultimate skin + tip capacity) / (working-load settlement)
        often 50–300 MN/m for 0.6 m bored piles; 100 000 kN/m is a reasonable start
Lateral k ≈ 3EI/L³ for a free-head pile in stiff ground, or get it from a p-y analysis
Rotational k ≈ 0 for pinned, or from the pile/cap connection

The tip bearing result is the tip spring reaction divided by the pile area:
q_b = N_tip / (π d²/4), comparable against the geotechnical end-bearing
pressure. The skin result is the mobilised kz·uz per metre run along the
shaft - integrate it (the summary shows Σ mobilised skin) and compare with
the shaft capacity.

Anchors:

• pile-settlement - single 100 kN pile, axial k = 100 000 kN/m, 8 m long
  → head deflection 2.00 mm (shaft plus spring), tip load 100 kN.
• pile-tip-bearing - 0.6 m shaft → tip bearing q_b = 100/(π×0.6²/4) = 353.68 kPa at the same head load.

7.3 Pile soil layers

Pile soil layers distribute support along the shaft, replacing the single head
spring with a more realistic profile. Open the editor from the pile tool or a
pile's Properties (Edit layers…).

The generator gives each meshed shaft node Kx = Ky = Lateral k × tributary length and Kz = Skin × tributary length, summable where the node sits in two
layers (shared boundary).

Deriving values from geotechnics

• Lateral: from a p-y curve for the layer, the initial modulus kh (kN/m³) is
  multiplied by the shaft diameter to give stiffness per metre of shaft:
  lateral k ≈ kh · d. Soft clay 2 000–6 000 kN/m³, stiff clay 6 000–20 000,
  loose sand 3 000–10 000, dense sand 10 000–30 000, rock 50 000+.
• Skin: skin ≈ (shaft perimeter × unit skin friction) / (slip at full mobilisation); a working estimate is skin ≈ 0.05–0.2 × the pile's axial k per metre of shaft. Alternatively start with a uniform 1 000 kN/m/m and
  adjust until the load distribution between layers looks geotechnically
  sensible.

Anchor (pile-layers): the shipped four-layer model mobilises
ΣKz = 59 200 and ΣKx = 48 000 across its shaft nodes - use these to verify
your own layer input against the same geometry.

Notes:

• Layer elevations are absolute (model Z), not depth below head; the editor's
  new-row defaults chain off the previous bottom.
• Layers are global to the model - all piles share them.
• A layer needs at least one of lateral/skin > 0; top must be above bottom.

7.4 Mats vs piles

A useful comparison workflow:

1. Solve the mat model and read the peak/mean bearing and differential
   settlement.
2. If either exceeds the geotechnical limits, switch to a pile-supported model
   with the same slab, place piles under columns, and re-run.
3. Compare the slab moments between models: piles attract load locally and
   reduce the global sagging moments but raise the local column-strip hogging;
   compare column reactions and punching utilisation between the two.

The program allows a soil zone in a pile-supported model; in that mode the soil
springs add to the pile stiffness and the bearing plot shows the sharing -
use it deliberately (e.g. a piled raft with ground contact), not accidentally.

7.5 Worked examples

Mat on Winkler soil (Verify S2)

• 8 × 8 m mat, t = 0.25 m, C32, k = 30 000 kN/m³, q = 10 kPa, no self weight
  (verification load case).
• Hand: w = q/k = 10/30 000 m = 0.333 mm; ΣR = q·A = 10 × 64 = 640 kN.
• App: Deflection shows 0.333 mm at the centre; ⏚ shows ≈ 10 kPa;
  the reactions table Σ ground = 640 kN, Applied ΣFz = −640 kN.

Single pile settlement (Verify P2)

• 100 kN point load at a pile head, axial k = 100 000 kN/m.
• Hand for the spring alone: w = P/k = 1.0 mm; the shaft and head link add
  compliance, giving the published 2.00 mm.
• App: P⌀ → u-lat / N shows the head deflection; Tip reaction = 100 kN.

Tip bearing (Verify P3)

• Same pile, diameter 0.6 m.
• Hand: q_b = N_tip/(πd²/4) = 100/0.2827 = 353.68 kPa.
• App: P⌀ summary Tip bearing q_b.

Layered shaft (Verify P4)

• Four soil layers with lateral and skin stiffness; the shaft mobilises
  ΣKz = 59 200 kN/m and ΣKx = 48 000 kN/m, head load 100 kN.
• App: P⌀ → skin shows the friction profile; the layer table in the
  editor lists the inputs.

Reproduce any of these from the JSON files in
web/projects/verification/ - import one with Import from File and run
the analysis; each ships with its expected values.

7.6 Troubleshooting

→ Next: Chapter 8 - Worked examples