Lab: pile group efficiency (Converse-Labarre)

A course-lab / practice drill for Converse-Labarre pile group efficiency. Geometric screening only — not a PE stamp, not a design example for a real project. Work the hub's 3×3 case by hand, then confirm it in the live pile group efficiency calculator. Theory and the published η table live on the pile group efficiency hub; the formula walk-through is on Converse-Labarre equation.

Given (hub worked example)

Copy these inputs. Do not invent a different η — the hub already published this case.

• Rows m = 3, columns n = 3 (3×3 group)
• Pile diameter d = 0.6 m
• Centre-to-centre spacing s = 1.8 m (s/d = 3)

Hub result at s/d = 3 for a 3×3 group: η ≈ 0.73 (nine piles worth about 6.5 piles' capacity).

Step 1 — Compute η by hand

Same Converse-Labarre form as the hub and calculator:

η = 1 − θ · [(n₁ − 1)·n₂ + (n₂ − 1)·n₁] / (90 · n₁ · n₂)

θ = arctan(d / s) in degrees

With n₁ = n₂ = 3, d = 0.6 m, s = 1.8 m:

• θ = arctan(d/s) = arctan(0.6/1.8) = 18.4°
• bracket = (3 − 1)·3 + (3 − 1)·3 = 12
• denominator = 90 · 3 · 3 = 810
• η = 1 − 18.4 · 12/810 ≈ 0.73

Check: 0.73 · 9 ≈ 6.5 — nine piles worth about 6.5 piles' capacity. That matches the hub table cell for s/d = 3, 3×3 group.

Step 2 — Confirm in the live calculator

1. Open the pile group efficiency calculator.
2. Enter Rows m = 3, Columns n = 3, Spacing s = 1.8 (m), Pile diameter d = 0.6 (m).
3. Confirm the reported η is about 0.73 — the same geometric screening result as Step 1 and the hub.

Step 3 — What this η is not

Converse-Labarre is layout-only. It does not cover:

• Clay equivalent-block failure — check separately; it can govern below ~3d. An efficiency factor alone can overestimate a tight friction-pile group in clay.
• Lateral group action — that is p-multipliers / shadowing (FHWA GEC 9), not a single axial η.

PileCalc's released vertical-group tool is the driven-sand path (η = 1) with the block printed as a diagnostic. Details and caveats are on the hub.

Optional stretch — other spacings from the hub table

Keep d = 0.6 m. Change s so s/d = 2 (s = 1.2 m) and s/d = 6 (s = 3.6 m). Run the calculator (and/or the formula) for 2×2, 3×3, and 4×4, then compare to the hub table — quote those cells; do not invent new ones:

• s/d = 2: η = 0.70 (2×2), 0.61 (3×3), 0.56 (4×4)
• s/d = 6: η = 0.90 (2×2), 0.86 (3×3), 0.84 (4×4)

Full table and commentary: pile group efficiency, explained.

References

• Live calculator (rows, columns, spacing, diameter)
• Pile group efficiency hub
• Converse-Labarre equation

Geometric screening only. Engineering judgment stays with the user — this lab is not a PE stamp and is not a design example for a real project.