Pile groups

Piles are almost never used alone — they are tied together by a cap and act as a group. A group is not simply the sum of its piles: closely spaced piles interact through the soil between them, so the group can be weaker, softer, and settle more than the same number of isolated piles. PileCalc builds the group analysis on top of the single-pile methods — axial capacity for vertical load and the p-y method for lateral load — and then layers the interaction effects on top. This page explains how, and every input on the groups tool.

Why groups differ from single piles

When piles are driven close together their zones of influence overlap. The mechanism is different for vertical and lateral load, but the cause is the same — neighbouring piles share the same soil:

Axially, the failure surfaces of adjacent piles merge. A tightly packed group can punch through the soil as one large block rather than as independent piles, and the overlapping stress bulbs make the whole group settle more.
Laterally, a pile pushes against soil that the pile ahead of it has already disturbed. Trailing piles sit in this shadow and mobilize less resistance, so the group carries less than the sum of its single piles for the same head movement.

Both effects are governed by the centre-to-centre spacing relative to the pile diameter — the spacing/diameter ratio, s/D. Closely spaced piles (small s/D) interact strongly; widen the spacing and the group recovers toward the sum of its independent piles.

Group layout

The group is a rectangular grid. You define how many rows there are in the direction of loading, how many piles sit in each row across the load, and the spacing each way. The tool shows the resulting pile count and the spacing/diameter ratio as you edit — for example s/D 3.0×2.0 — because s/D is what sets the interaction in both the axial and lateral analyses.

nₓRowscount

The number of pile rows in the loading direction.

Why it matters. For lateral groups the rows are what shadow one another: the first row leads, every row behind it sits in the shadow of the rows ahead and carries less. More rows means a softer, less efficient group.

n_yPiles per rowcount

The number of piles in each row, measured across the loading direction.

Why it matters. Piles side by side across the load share overlapping soil. Together with the rows it sets the total pile count nₓ · n_y and the equivalent block footprint.

s_xSpacing along the loadlength

Centre-to-centre spacing in the loading direction.

Why it matters. The ratio s_x/D sets the front (in-line) p-multiplier for lateral shadowing — wider spacing recovers efficiency. It also sets the block length for the axial check.

s_ySpacing across the loadlength

Centre-to-centre spacing across the loading direction.

Why it matters. The ratio s_y/D sets the side-by-side reduction and the equivalent block width. Closer side spacing means more overlap and a smaller group efficiency.

Vertical (axial) groups

The axial group capacity is the lesser of two failure modes. Either each pile fails individually — the group carries the sum of the single-pile capacities — or the whole group punches through the soil as one large block. PileCalc computes both and reports the one that governs.

Sum of single piles — n times the single-pile capacity from axial capacity. This is the upper bound: what the group would carry if the piles did not interact.
Block capacity — the capacity of an equivalent block that encloses the whole group, of plan dimensions Bₓ × B_y (set by the outer pile spacings), resisting on its base and perimeter as a single deep footing.

The ratio of the two is the group efficiency η:

η = Q_block ⁄ (n · Q_single)

Group efficiency — block capacity over the sum of single piles

When η ≥ 1 the sum of single piles governs and there is no reduction — the piles are far enough apart to act independently. When η < 1 the block governs: the piles are closely spaced and the group is weaker than the sum of its parts.

Spacing also amplifies settlement. Even when the piles act independently for capacity, their stress bulbs overlap deep in the soil, so the group settles more than a single pile at the same load per pile. PileCalc scales the single-pile settlement by the Vesić ratio:

s_group = s_single · √(B′ ⁄ D)

Group settlement ratio (Vesić, 1969)

where B′ is the group width and D the single-pile diameter. A wider group has more overlap and settles proportionally more.

Lateral groups

A rigid cap ties the pile heads together, so they all move sideways by the same amount. PileCalc imposes that one common head deflection on every pile and solves each as a single laterally loaded pile (the p-y method) — but with the soil resistance reduced by a p-multiplier that depends on where the pile sits in the group.

The leading (front) row pushes into undisturbed soil and gets a p-multiplier of about 1. Each trailing row pushes into soil already disturbed by the rows ahead — it sits in their shadow — and gets a smaller multiplier, combining the front (in-line) and side-by-side reductions. With softer soil springs, a shadowed pile develops less shear for the same head deflection.

The group lateral load is the sum of the head shears that develop across all piles. Because the trailing rows are softened, this total is lower than n times the single-pile shear — the shortfall is exactly the shadowing effect. PileCalc reports the result row by row: the row, its pile count, its p-multiplier, the shear each pile in it carries, and the maximum bending moment.

y_tHead deflectionlength

The common lateral deflection the cap imposes on every pile head.

Why it matters. A rigid cap forces all piles to the same head movement; the group load is the sum of the shears that develop to produce it. Set it to the serviceability displacement you want to check the group against.

—Head fixity

Whether the pile heads are fixed against rotation (cast into the cap) or free to rotate.

Why it matters. A fixed head develops more shear for the same deflection and shifts the peak moment up toward the cap, raising the group lateral load. A free head deflects more readily and carries less.

Where p-multipliers come from

The p-multipliers are set by the spacing/diameter ratio s/D, not chosen by hand. Closely spaced rows shadow each other strongly and get small multipliers; widening the spacing raises the multipliers back toward 1 and recovers the group's efficiency. At large spacing the piles stop interacting and the group approaches n independent piles.

Reading the results

The tool has two tabs — an axial group and a lateral group — and each reports its own summary.

Axial group

Group capacity — the governing ultimate capacity: the lesser of the sum of single piles and the equivalent block. This is what the group can actually carry.
Σ single piles — n × single-pile capacity, the upper bound with no interaction.
Block capacity — the capacity of the equivalent block enclosing the group; it governs when piles are closely spaced.
Efficiency η — block over Σ single. η ≥ 1 means the sum governs (no reduction); η < 1 means the block governs.
Settlement — the single-pile and group settlements side by side, with the group amplified by √(B′/D), plus the equivalent block dimensions Bₓ × B_y.

Lateral group

Group lateral load — the total load the group carries at the imposed head deflection: the sum of every pile's head shear, lower than n × single because of shadowing.
Head deflection — the common cap deflection shared by all piles.
Piles — the total pile count, nₓ rows × n_y per row.
Row-by-row shadowing — a table giving, for each row, its pile count, p-multiplier, pile shear, and maximum moment. The lead row (p-multiplier ≈ 1) attracts the most load; trailing rows are softened by the front and side reduction factors.