Pile group analysis solves two separate problems. The first is how far the axial capacity falls in a pile group (efficiency and block failure); the second is how the lateral load is shared between the pile rows. The two checks arise from different mechanisms and rest on different sources. Their verification differs as well.
Every step of the group calculation is checked against the formulas and worked examples in the source literature. The bearing capacity factor and block resistance equations are compared with hand-computed values, and the efficiency rules and lateral row multipliers are checked against the specification's own values. The results agree. Measured group tests published in the literature are also compared with the calculation, and each comparison is summarised here.
The measured tests have no connection to StructuralMind. Each is independent work carried out and published by the institution that ran it. The single-pile counterpart of this page is Single Pile — Verification.
Axial group: the source equations
Bearing capacity factor (GEC 12 Equation 7-37)
| Hand computation | Source | Calculation | |||
|---|---|---|---|---|---|
| 6 m | 4 m | 10 m | 7.02 | 7.0200 | |
| 3 m | 3 m | 5 m | 6.72 | 6.7200 | |
| 10 m | 2 m | 2 m | , capped | 9.00 | 9.0000 |
The cap on the third row is the source's own: is generally taken as 9, and the equation only ever serves to reduce it.
Block resistance (GEC 12 Equation 7-36)
= 3 m, = 3 m, = 5 m, = 40 kPa, = 60 kPa and = 6.72 (the second row above, an uncapped value, so the equation runs end to end):
| Term | Hand computation | Source | Calculation |
|---|---|---|---|
| Side | 1,920 kN | 1,920 kN | |
| Base | 6,048 kN | 6,048 kN | |
| Total | 7,968 kN | 7,968 kN |
The same block model is printed independently in three sources (GEC 12 Eq. 7-36, GEC 10 Eq. 14-3, O'Neill & Reese Eq. B.66), and all three are the same model.
Axial group: the efficiency rules
As Equation 7-35 defines it, the efficiency factor multiplies the sum of the single pile's shaft and toe resistance.
| Rule | Source | Anchor points | Interpolated check | Calculation |
|---|---|---|---|---|
| Cohesive, suspended cap, 2 ksf | GEC 12 §7.2.2.2 (AASHTO 10.7.3.9) | 0.65 (2.5D) → 1.0 (6D) | = 4.25 | 0.8250 |
| Cohesive, cap in firm contact | GEC 12 §7.2.2.2 | 1.0 | — | 1.0000 |
| Cohesive, 2 ksf | GEC 12 §7.2.2.2 | 1.0 | — | 1.0000 |
| Cohesionless, driven | GEC 12 §7.2.2.1 | 1.0 | — | 1.0000 |
| Cohesionless, drilled | GEC 10 §14.4.1.2 (AASHTO 10.8.3.6.3) | 0.65 (2.5D) → 1.0 (4.0D) | = 3 | 0.7667 |
The last row is the only branch this macro reduces below 1.0 at normal spacing, and every measurement below belongs to it. In cohesionless soil the efficiency factor for a drilled shaft rises from 0.65 to 1.0 as the spacing goes from 2.5 to 4 diameters. A factor of 1.0 means no reduction is left on the efficiency side, so the group carries the sum of the single-pile capacities. In cohesive soil with a suspended cap the same rise is not complete until 6 diameters. The two values come from different specification clauses.
Two points the source does not state explicitly:
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 , the undrained strength that selects the cohesive rule, is handled the same way. At exactly 2 ksf the more critical branch is taken.
Axial group: assembling the equation's inputs from a layered profile
Equation 7-36 is written for a single homogeneous clay. How and are read off a layered profile is our decision, so each rule is stated and tested separately.
| Quantity | Rule | Reason |
|---|---|---|
| , | To the outside of the perimeter piles: | GEC 12 Figure 7-31; the block contains the piles |
| / | is always the smaller dimension | Equation 7-37's term presumes it; the same group entered rows-first or columns-first must give one answer |
| The closest spacing in the array | A single row is governed by the spacing within it and nothing else | |
| , cohesive layer | itself, not | The block's failure surface is the group's outer envelope and runs through soil, not along the pile shafts. The enclosed soil sinks with the block and never shears |
| , cohesionless layer | That layer's unit shaft resistance | GEC 12 §7.2.2.3 substitutes it explicitly |
| Averaged over the cohesive soil only, from the toe down to | The source's own restriction; it is what lets one equation serve both a group in clay and a group in sand over weak clay | |
| Controlling stratum | By resistance, not thickness | GEC 12 §7.2.2: "the stratum that provides the majority of the nominal geotechnical resistance" |
The row is the rule in this table that changes the answer most: using understates the block resistance by up to a factor of two and makes the block govern when it does not.
In two situations the calculation refuses to produce a number. If the profile ends at the pile toe, no block capacity is given, with the reason and the depth required. If there is no cohesive soil in the base zone, the result comes back as "not applicable" and that is the answer: GEC 12 §7.2.2.3 states that block failure is a design consideration only for groups in soft cohesive soils or in cohesionless soils underlain by a weak cohesive layer.
Measured group tests
All three datasets come from GEC 10 §14.4.1.2 and all three are drilled shafts in sand, the branch where the efficiency rule falls below 1.0.
Senna et al. (1993)
Bored piles, 250 mm diameter and 6 m long, in lateritic clayey sand in Brazil; in every configuration, caps in contact with the ground (the reported efficiency includes the cap's own bearing).
| Configuration | Measured | Calculated | Direction |
|---|---|---|---|
| 2-shaft bent | 1.10 | 0.767 | conservative by 30 % |
| 3-shaft row | 1.10 | 0.767 | conservative by 30 % |
| 3-shaft triangular | 1.04 | 0.767 | conservative by 26 % |
| 2×2 square group | 1.00 | 0.767 | conservative by 23 % |
Ismael (2001)
Bored piles in weakly cemented sand, Kuwait, cap in contact.
| Measured | Calculated | Direction | |
|---|---|---|---|
| 2.0 | 1.20 | 0.65 (the held floor) | conservative by 46 % |
| 3.0 | 1.90 | 0.767 | conservative by 60 % |
In both datasets the calculation stays below the measured efficiency. GEC 10 points the same way (p. 14-9): there are circumstances in which the AASHTO specifications give a conservative estimate of group resistance.
Garg (1979): the series where the calculation sits above the measurement
GEC 10 Figure 14-5. Model-scale, under-reamed (belled) drilled shafts in moist silty sand.
| 2-shaft, cap in contact | 2-shaft, suspended | 4-shaft, cap in contact | 4-shaft, suspended | Calculated | |
|---|---|---|---|---|---|
| 3.75 | 1.43 | 1.24 | 0.95 | 0.77 | 0.9417 |
| 5.00 | 1.53 | 1.39 | 1.03 | 0.99 | 1.0000 |
| 6.20 | 1.99 | 1.77 | 1.52 | 0.94 | 1.0000 |
Most series in the figure measure above the calculated value at every spacing. The one exception is the four-shaft group with the cap suspended: at 3.75 diameters the measured efficiency is 0.77 against a calculated 0.942, so the calculation sits +0.17 (about 22 %) above it. At 5.0 and 6.2 diameters the same series measures 0.99 and 0.94, and the gap closes to 1–6 % as the spacing opens.
Why the rule is not changed:
- These are model-scale, under-reamed shafts. Bell-to-bell interference at close spacing is a different mechanism from the straight-shaft stress overlap the rule addresses.
- GEC 10 prints this figure and then still recommends 0.65 → 1.0 at 4 diameters. What is implemented here is the code.
- The direction this figure points in runs against the section's own overall assessment. GEC 10 §14.4.1.2 notes that in some circumstances the group resistance computed to AASHTO comes out lower than the real one. Within its own source, the Garg series is the exception.
An engineer whose case resembles Garg's (belled shafts, suspended cap, close spacing) can enter
their own value through efficiency_override; it is used verbatim and attributed to the user.
Lateral group: Table 7-1
On the lateral side the group is solved by a rigid cap forcing every pile to the same deflection. The leading row pushes into undisturbed ground while the rows behind it stand in its shadow, so the load does not divide equally. Each row is solved with its own p-multiplier.
Spacing is measured in the direction of loading, and the values are for vertical piles only.
| Centre-to-centre spacing | Row 1 | Row 2 | Row 3 and higher |
|---|---|---|---|
| 3B | 0.8000 | 0.4000 | 0.3000 |
| 4B (interpolated) | 0.9000 | 0.6250 | 0.5000 |
| 5B | 1.0000 | 0.8500 | 0.7000 |
The table only gives values between 3B and 5B. Outside that range the value at the nearer end is held rather than extrapolated. Below 3B the real shadowing is stronger than the table gives, so the result falls on the unconservative side. Above 5B the opposite holds and the result is conservative. Which case applies is reported as a warning.
For a single pile the p-multiplier is 1.0. The table covers interaction between piles, so with no second pile to interact with there is no reduction.
Every pile in a single row standing across the direction of loading counts as Row 1, and the table is entered with the side-by-side spacing. The source notes that side-by-side interaction is not significant at 5B or more, and the table's Row 1 value at 5B is exactly 1.0, so the two statements agree.
Lateral group: the strongest check
The source states that when a single weighted-average multiplier is used instead of solving the rows, the computed moment falls short of the real one, and it publishes an overstress allowance to compensate: 1.20 at 3B, 1.15 at 4B, 1.05 at 5B.
Our row-by-row solve computes that same ratio from the p-y physics, having never seen the allowance. So one question has two independent answers:
| Ratio the calculation produces | Published allowance | Difference | |
|---|---|---|---|
| 3B | 1.2204 | 1.20 | +0.020 |
| 4B | 1.1391 | 1.15 | −0.011 |
| 5B | 1.0750 | 1.05 | +0.025 |
This is the strongest check on the page, because the two numbers being compared are produced in ignorance of each other.
⚠️ Recorded deviation: at 5B the calculated ratio runs about 0.025 above the published 1.05, meaning the published allowance slightly under-corrects at wide spacing. It is small and does not affect the primary answer: the row-by-row path computes the leading row's moment directly and never uses the allowance.
Measured row multipliers: Rollins et al. (1998)
Row multipliers measured in a full-scale pile group lateral load test, plotted against pile head deflection.
| Head deflection | Front row | Middle row | Back row |
|---|---|---|---|
| 5 mm | 1.05 | 0.65 | 0.83 |
| 10 mm | 0.89 | 0.54 | 0.70 |
| 17 mm | 0.82 | 0.49 | 0.61 |
| 29 mm | 0.81 | 0.51 | 0.60 |
| 41 mm | 0.80 | 0.49 | 0.60 |
| 56 mm | 0.75 | 0.47 | 0.55 |
The measurement confirms two features of the behaviour.
The ordering. The front row exceeds both trailing rows at every measured deflection. That ordering is the entire justification for solving the rows separately.
The plateau. The source states that the multipliers settle above about 19 mm, and the data show it (the front row flat within 0.10 beyond that). The small-deflection values are higher, so applying the table's plateau values at a small deflection is conservative.
⚠️ The measurement shows behaviour no row-multiplier table can reproduce. In this test the back row measured higher than the middle row at every deflection (0.55–0.83 against 0.47–0.65). Table 7-1's values fall steadily from the front row backwards, so it cannot produce that ordering. The source records the effect ("in some cases the outer elements appear to take more load than the interior elements") and still recommends taking each row's multiplier from the table. The calculation follows that recommendation and carries the same limit.
What this calculation covers
The macro computes the group's axial capacity and its lateral load sharing. The following are outside its scope, with the direction each omission works in.
Group settlement. A group settles appreciably more than a single pile at the same load per pile. Settlement is a separate calculation and this macro does not give it.
The load distribution over the piles. Every pile is assumed to carry the same load. Eccentric loading, and separating out what each pile in the cap takes, are outside the scope.
The cap's own lateral resistance. The source records that a cap can carry 40–50 % or more of a group's lateral resistance through passive pressure on its face and shear on its sides. It is not modelled, and omitting it works in the conservative direction.
Uplift. Group uplift rests on a different model, so the API refuses the request rather than returning an approximate answer.
The classical efficiency formulas. Converse-Labarre, Los Angeles and Seiler-Keeney are not
implemented; none of the five documents in the source library contains them. An engineer who
wants their own value can enter it through efficiency_override.
Time effects. GEC 12 §7.2.2.2 records short-term group efficiencies of 0.4–0.8 in clay while driving-induced pore pressure dissipates (1–2 months, up to a year for a very large group). This is not modelled.
What the measurements cover. All three datasets above are drilled shafts in sand above the water table, which is also the branch this macro reduces below 1.0.