Pile Group

A group does not carry n times what one pile carries. Two separate questions have to be answered, and they come from different mechanisms and different sources: how much the axial capacity drops, and how the rows share the load under lateral loading.

The two are computed independently. For single-pile behaviour, see Single Pile Analysis.

Axial: two mechanisms#

The lesser of the two governs (GEC 12 §7.2.2.2 item 4; GEC 10 Eq. 14-2 writes the efficiency itself as $R_{block} / \sum R_n \le 1$). The block check can be switched off; the result and the report then state that it was.

Which efficiency rule applies#

The controlling stratum is the one that provides most of the resistance, not the one with the most thickness (GEC 12 §7.2.2). If the toe bears in sand with a thick, very weak clay above it, the group still follows the cohesionless rule.

The two cohesionless rows differ because the installation does: driving densifies the sand, drilling removes soil. At three diameters a driven group gets 1.0 and a bored one 0.77.

Block failure is not checked in a profile with no cohesive soil under the toe, so a bored group in clean sand is reduced by $\eta$ alone.

$\eta$ multiplies the whole single-pile resistance — shaft and toe together, as GEC 12 Eq. 7-35 defines it.

Below 2.5 diameters the value is held, not extrapolated. AASHTO does not allow that spacing, so no value is published there. The calculation holds 0.65, warns that the true efficiency is lower, and asks you to widen the spacing or enter your own factor.

The 2 ksf boundary on $s_u$, the undrained strength that selects the cohesive rule, is handled the same way. At exactly 2 ksf the more critical branch is taken.

Entering your own efficiency#

Efficiency can also be entered by hand. The result reports it as a user value, attributed to you, which is the route for a specification that mandates one of the older empirical formulas. Converse-Labarre, Los Angeles and Seiler-Keeney are not implemented: they are fits from the 1940s-50s and appear in none of the documents above. For a driven group in sand at $s \ge 3D$, Converse-Labarre gives roughly 12 % less than the full sum GEC 12 §7.2.2.1 allows.

Block failure#

Three sources state the same model (GEC 12 Eq. 7-36/7-37, GEC 10 Eq. 14-3, O'Neill & Reese Eq. B.66). None of them states how to read $s_{u1}$ and $s_{u2}$ off a layered profile; this calculation reads them as follows:

• $B$ and $Z$ reach the outside of the perimeter piles (GEC 12 Figure 7-31): the block contains the piles, so $(n-1)s + D$. $B$ is always the smaller dimension, because the shape term presumes it.
• $s_{u1}$ is integrated node by node, not averaged per layer, and a cohesive layer contributes its full $s_u(z)$, not $\alpha \cdot s_u$: the block's failure surface runs through the soil around the piles, where there is no pile-soil adhesion. A cohesionless layer contributes its unit shaft resistance instead.
• The block's faces do not take over a bored pile's top-exclusion zone. Near-surface clay separates from the shaft's concrete — and the block's surface runs through soil.
• $s_{u2}$ is averaged from the toe down to $2B$, over the cohesive soil only (GEC 12 §7.2.2.3). One equation therefore covers both named cases: a group standing in clay, and a group founded in sand over a weak clay.
• The profile has to be defined down to that depth. If it stops at the pile toe, the result says "not applicable" and states the depth it has to reach.
• No cohesive soil in the base zone also returns "not applicable". Block failure is a soft-clay mechanism.

Lateral: the p-multiplier, row by row#

Axially, a pile sheds load through friction all round its shaft, so a neighbour's influence is roughly the same whichever side it sits on, and one average factor summarises it. Laterally it is not: all of the resistance comes from a wedge of soil on the side the pile pushes towards, so position stops being symmetric. The pile in the leading row pushes into undisturbed ground; a pile behind it pushes into ground the leading pile has already displaced. That is shadowing, and the factor applied to a shadowed pile's whole p-y curve is the p-multiplier $P_m$.

A rigid cap forces every pile to the same head deflection, so the rows do not share the load equally. The leading row is the stiffest, therefore takes the largest share, therefore carries the largest bending moment.

FHWA-HIF-18-031 Table 7-1 (from AASHTO 2014), with spacing measured in the direction of loading and valid for vertical piles only:

Which spacing is read is settled by Figure 7-5 in three sketches: a multi-row array uses the in-line spacing; a line of piles loaded along the line is one pile per row; and a line loaded across the line is all Row 1, read at the side-by-side spacing.

Table 7-1 covers 3B–5B only. Outside that range nothing is published, so the end values are held rather than extrapolated. Above 5B holding is conservative: a widely spaced group is credited with less than it will develop. Below 3B the real shadowing is stronger, so the group comes out stiffer than it will be. The calculation raises a warning there and asks you to widen the spacing or enter your own multiplier.

Solving row by row#

FHWA-HIF-18-031 gives two methods. The first builds each row's load-deflection curve with its own $P_m$, adds them into the group's curve, finds the deflection that carries the applied total, and reads every row's moment there. The second (Brown et al.) solves once at a single averaged $P_m$ and adds an overstress allowance to the moment (×1.20 at 3B, ×1.15 at 4B, ×1.05 at 5B) because averaging understates the leading row.

The row-by-row method is used, and it gives the leading row's moment directly rather than through a correction factor. The averaged method is reported alongside it as a cross-check.

The solve is deflection-controlled: the cap is what the rows have in common, it imposes the movement, and each row's share of the load falls out of its own stiffness. Each row is solved as a single pile with a reduced p-y curve — which is also why any row can be pulled into Single Pile Analysis and examined there in full, with its own moment diagram, p-y curves and step-by-step working.

Verification#

Every equation and rule on this page is a printed closed form, so each is compared against hand-computed values as an equality rather than through a tolerance band: $N_c$, both terms of the block equation, the 2 ksf conversion, all four efficiency curves at their end and interpolated points, Table 7-1's values, and Figure 7-5's layout rules.

Cross-check against the averaged method#

The row-by-row solve never uses the averaged method's overstress allowance. It nevertheless reproduces that allowance to within 0.04 across 36 configurations: the published empirical correction and the directly computed ratio agree. The difference is largest at 5B, where the computed ratio runs about 0.025 above the published 1.05.

Comparison against field tests#

The three datasets below compare the cohesionless efficiency rule for bored piles (AASHTO 10.8.3.6.3; 0.65 at 2.5D → 1.0 at 4D) against field measurements. What is under test is the rule itself, which this calculation implements as published, so the deviations in the table describe the conditions that rule was calibrated over. No published group tests exist for the other rules on this page.

The Senna and Ismael groups were not loaded to failure, so their measured value is a lower bound, not an equality: it shows the rule claims no more than the ground delivered.

The Garg series is the only one in GEC 10 Figure 14-5 that runs against the rule; every other series in that figure measures above it at every spacing. Those are under-reamed model shafts, and bell-to-bell interference at close spacing is a different mechanism from the straight-shaft stress overlap the AASHTO rule was fitted to. GEC 10 prints the figure and still recommends 0.65 → 1.0 at 4 diameters, which is what is implemented here. For an under-reamed, suspended-cap, closely spaced group, enter a lower efficiency by hand.

What this calculation does not cover#

Endpoints#

The axial group check also runs as a group block added to a single-pile axial request, answered under result.group. The group's axial and lateral analyses are independent of each other.