Converse-Labarre equation for pile group efficiency

A worked reduction-factor version of the formula that already ranks on the pile group efficiency hub. Geometric screening only. In clay, run the block check too. In driven sand, design practice caps η at 1.0.

Pile group efficiency is a reduction factor: η = Q_group / (n · Q_single). The Converse-Labarre equation is the usual way to get that factor from layout alone. It does not know the soil. Google already sends us people searching "converse labarre equation for group efficiency" and "pile group efficiency reduction factor". This page works the equation. The hub covers block failure and lateral p-multipliers.

The equation

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

θ = arctan(d / s) in degrees

• η — reduction factor on the sum of single-pile capacities
• n₁, n₂ — rows and piles per row
• d — pile diameter
• s — centre-to-centre spacing

The 90 is there because θ is in degrees. Bigger groups at the same spacing always come out less efficient, because the formula counts pile-to-pile interactions.

Worked reduction factors

Same equation as the hub. 0.6 m piles.

3×3 at s/d = 3 (s = 1.8 m)

θ = arctan(0.6/1.8) = 18.4°. Bracket = 12. Denominator = 810. η = 1 − 18.4 · 12/810 ≈ 0.73 (nine piles worth about 6.6 singles).

2×2 at s/d = 3

Bracket = 4. Denominator = 360. η = 1 − 18.4 · 4/360 ≈ 0.80

4×4 at s/d = 3

Bracket = 24. Denominator = 1440. η = 1 − 18.4 · 24/1440 ≈ 0.69

3×3 at s/d = 2

θ = 26.6°. η = 1 − 26.6 · 12/810 ≈ 0.61

Those match the hub table. Treat them as a geometric baseline, not soil truth.

What the reduction factor is not

It is not a soil model. In clay, the equivalent-block check often governs and an efficiency formula alone can overestimate a tight friction-pile group. In driven sand, measured η is often at or above 1.0 because driving densifies the soil; design practice still caps the group at the sum of the singles.

PileCalc's released vertical-group path is that driven-sand rule (η = 1, USACE EM 1110-2-2906). The block is printed as a diagnostic. Clay, rock, mixed, and weak-layer block-governing cases fail closed. Details are on the pile group efficiency hub and in the pile groups docs.

Lateral groups are not a single η. They use row p-multipliers (FHWA GEC 9 Table 7-1). That stays on the hub.

Design notes

Space at ≥ 3 diameters when you can. Below 2.5d, expect both a heavy geometric penalty and a governing block in clay. Efficiency is capacity. Check settlement separately.

The free pile group efficiency calculator runs this equation and the block comparison in the browser.

Sources: FHWA Soils and Foundations Reference Manual Vol. II (axial group efficiency and equivalent-block); WSDOT WA-RD 827.1 Eq. 2.29 (Converse-Labarre expression used on the hub). Engineering judgment stays with the user.