Pile group efficiency: formulas, p-multipliers, block failure

Pile group efficiency is the ratio of a group's capacity to the sum of its piles' individual capacities: η = Q_group / (n · Q_single). Because closely spaced piles mobilize overlapping zones of soil, η is typically 0.6–0.8 at 2–3 diameter spacing and approaches 1.0 near 6 diameters. Vertical groups are checked with efficiency formulas plus a block-failure check; lateral groups use row-by-row p-multipliers instead.

Why closely spaced piles carry less than the sum of the parts

A single friction pile transfers load into a bulb of stressed soil around its shaft and below its tip. Put a second pile one or two diameters away and the two bulbs overlap: both piles are now shearing partly the same soil, and the group settles as if it were a single, much larger foundation. The consequences are twofold. First, ultimate capacity: in cohesive soil the individual shear surfaces can merge, so the group fails as a monolithic block of soil and piles rather than as n independent shafts. Second, settlement: the group stresses soil to a much greater depth than a single pile, so even a group that loses no capacity settles more than one pile under the same per-pile load.

The effect is strongly soil-dependent. In soft to firm clay, overlap is the dominant story and efficiency below 1.0 should be assumed until checked. In cohesionless soil, driving piles at close spacing densifies the sand between them, and measured group efficiencies for driven piles at conventional spacing are often at or above 1.0 — which is why codes tend to cap η at 1.0 rather than let you claim a bonus.

The Converse-Labarre formula

The most widely used efficiency equation for vertical capacity is the Converse-Labarre formula. It is purely geometric — it knows nothing about the soil — and reduces efficiency in proportion to how many pile-to-pile interactions the layout contains:

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

θ = arctan(d / s)   (in degrees)

• η — group efficiency (multiply the sum of single-pile capacities by it)
• n₁, n₂ — number of rows and number of piles per row (a 3×4 group has n₁ = 3, n₂ = 4)
• d — pile diameter
• s — centre-to-centre spacing
• θ — arctan(d/s) expressed in degrees, which is why the 90 appears in the denominator

Worked example: a 3×3 group of 0.6 m piles at 1.8 m centres (s/d = 3). θ = arctan(0.6/1.8) = 18.4°. The bracket is (3 − 1)·3 + (3 − 1)·3 = 12, and the denominator is 90·3·3 = 810. So η = 1 − 18.4 · 12/810 ≈ 0.73 — the nine piles are worth about 6.5 piles' capacity. Because the formula counts interactions, bigger groups always come out less efficient at the same spacing.

Efficiency vs spacing: typical values

The table below is the Converse-Labarre formula evaluated at common spacing ratios. Read it as a geometric baseline, not soil truth — for driven piles in sand many engineers take η = 1.0 at s ≥ 3d, while for friction piles in clay the block check below often governs instead.

You can reproduce any of these — and see the block check alongside — in the free pile group efficiency calculator.

Block failure in clay: the check that actually governs

For closely spaced groups in cohesive soil, an efficiency factor is not enough — you must also check failure of the group as an equivalent block: a prism of soil and piles with plan dimensions B_x × B_y (outside face to outside face) and the piles' embedded length L. Its capacity is perimeter shear plus base bearing:

Q_block = 2 · L · (Bₓ + Bᵧ) · c̄ᵤ  +  N_c · cᵤ · Bₓ · Bᵧ      (N_c ≤ 9)

Two details matter and are easy to get wrong. The perimeter shears soil on soil, not pile on soil — so the full undrained strength c̄ᵤ applies along the sides (no Tomlinson adhesion reduction α), and in cohesionless layers the full friction angle φ applies rather than a reduced interface angle δ. And the design capacity is the lesser of the two modes: min(n · Q_single, Q_block). At wide spacing the block is huge and the individual piles govern; squeeze the spacing and the block takes over — that crossover is what group efficiency is really measuring. For a refresher on where single-pile capacity itself comes from, see skin friction vs end bearing.

Lateral groups are different: p-multipliers and shadowing

Lateral group action does not reduce to a single η, because the interaction is directional. When a group is pushed sideways, the leading row pushes into fresh soil, but each trailing row pushes into soil already disturbed and displaced by the row ahead of it — the "shadowing" effect. The standard treatment scales down the p-values of each row's p-y curves by a row-specific p-multiplier less than 1. Deflections stay compatible (the cap forces a common head deflection), but trailing rows attract less shear.

PileCalc uses the row-specific multipliers of FHWA GEC 9 (2018), Table 7-1, which tabulates values at 3B and 5B loading-direction spacing, linearly interpolated between them:

So a 3×3 group at s/B = 3 runs its leading row at 0.8 and its trailing rows at 0.4 and 0.3 — the trailing rows deliver less than half the leading row's resistance at the same deflection. PileCalc applies the table over its published 3B–5B range and reports pile resistance only, conservatively leaving any cap/soil contribution out.

Primary sources for the group checks

Use the public FHWA manuals to confirm the method domain before applying a screening result to design:

• Soils and Foundations Reference Manual, Volume II: axial group efficiency and the equivalent-block failure expression in cohesive soil.
• FHWA GEC 9, Design and Analysis of Laterally Loaded Deep Foundations: lateral pile-group shadowing and the Table 7-1 row p-multipliers.
• FHWA GEC 12 driven-pile manuals and design examples: driven-pile group capacity, settlement, construction, and verification context.

What PileCalc computes

The group module implements both checks exactly as described, and shows its work:

• Vertical: single-pile capacity (NAVFAC DM-7.02), the equivalent block with soil-on-soil perimeter shear and base bearing over B_x · B_y, the efficiency η = Q_ult,group / (n · Q_ult,single), and separate ultimate, ASD allowable and optional LRFD factored resistances.
• Group settlement: single-pile settlement at the service load scaled by the USACE sand-group factor √(B_group/B_pile) — the group always settles more.
• Lateral: the cap imposes a common head deflection (free- or fixed-head); each row is solved with the full COM624P finite-difference method using its own p-multiplier, and the group load is the sum of the rows' head shears — with the per-row moment and deflection profiles available, not just the total.

The inputs, factors, and intermediate quantities are all visible in the output, so you can trace η back to the numbers that produced it. Details are in the pile groups documentation.

Design guidance

• Space at ≥ 3 diameters. The customary 3d minimum centre-to-centre spacing exists precisely to keep efficiency losses and driving interference manageable. Below 2.5d, expect both a heavy efficiency penalty and a governing block check in clay.
• In clay, always run the block check. An efficiency formula alone can overestimate closely spaced friction-pile groups; the block is the physically meaningful failure mode.
• In sand, don't take credit above 1.0. Densification from driving often produces measured η ≥ 1, but design practice caps the group at the sum of the singles.
• Check settlement separately. Efficiency is a capacity concept. A group can pass every capacity check and still settle several times more than a single pile.
• For lateral load, think in rows. If your layout is long in the load direction, most added rows arrive at the row-2 and row-3+ multipliers — 0.4 and 0.3 at 3B spacing. Widening the group (more piles per row) is usually more efficient than lengthening it.

Common questions

What is a typical pile group efficiency?

For friction piles at conventional 3-diameter spacing, geometric formulas like Converse-Labarre give roughly 0.7–0.8, dropping toward 0.55–0.65 at 2-diameter spacing and rising toward 0.85–0.9 at 6 diameters. Driven piles in sand frequently test at or above 1.0 because driving densifies the soil, but design practice caps efficiency at 1.0.

Does the Converse-Labarre formula apply to sand?

It can be applied — the formula is purely geometric — but it is generally conservative for driven piles in cohesionless soil, where densification between piles often makes the group as strong as the sum of the singles. Its natural home is friction-pile groups in clay, checked alongside (not instead of) an equivalent-block failure calculation.

What is a p-multiplier?

A p-multiplier is a factor, typically between 0.3 and 1.0, that scales down the soil resistance (the p-values) of a pile's p-y curves to account for group interaction under lateral load. The leading row keeps the highest multiplier; trailing rows, pushing into soil disturbed by the row ahead, get smaller values that grow back toward 1.0 as spacing increases. Under FHWA GEC 9 Table 7-1, row 1/2/3+ multipliers run from 0.8/0.4/0.3 at 3B spacing to 1.0/0.85/0.7 at 5B.

Why do trailing rows in a pile group carry less lateral load?

Because of shadowing: the row in front displaces and softens the soil wedge that the trailing row must push against. At a shared cap deflection the trailing row therefore mobilizes less soil reaction and less head shear. At 3-diameter spacing the reduction is severe — FHWA GEC 9 Table 7-1 assigns row 2 a multiplier of 0.4 and row 3+ a multiplier of 0.3 — and it eases toward 0.85 and 0.7 by 5 diameters.

Want the numbers for your own layout? The free pile group efficiency calculator runs the Converse-Labarre formula and the block comparison in your browser — and the full app adds the row-by-row lateral analysis with per-pile moment and deflection profiles.