Verification & benchmarks · v1.0.16

The numbers behind Pile Section

Pile Section makes two kinds of claim: that a section is strong enough, and that its cage is buildable. This page sets out the basis for both: the ACI 318-25 strength engine benchmarked against S-CONCRETE across 30 load cases, and the clear-spacing bands taken from the EFFC/DFI Guide to Tremie Concrete for Deep Foundations, together with the standard bar sizes and pile diameters the app is built on, and the assumptions and limits you should know before relying on either.

ACI 318-25 · EFFC/DFI 3rd Edition December 2024 · S-CONCRETE 2024.1.0, ACI 318-19 · 30 cases · reproducible with `pnpm benchmark`

load cases

3 sections × 2 grades × 5 loads

1.3%

median flexure |Δ|

mean 4.3%

1.0%

median shear |Δ|

mean 1.1%

26/30

equal or more conservative

flexure, vs S-Concrete

documented mechanisms

explain every residual

100 mm

green spacing line

per EFFC/DFI · 4 in

1 · Standard dimensions

What the app is built on

Every drawing, quantity and check starts from a standard schedule. These are the bar sizes and pile diameters Pile Section offers, in both unit systems, exactly as the application defines them.

Metric bars (29 sizes)

Bar	Ø mm	cm²	kg/m
Ø8	8	0.5	0.395
Ø10	10	0.79	0.617
Ø12	12	1.13	0.888
Ø14	14	1.54	1.208
Ø15	15	1.77	1.387
Ø16	16	2.01	1.578
Ø18	18	2.54	1.998
Ø20	20	3.14	2.466
Ø22	22	3.8	2.984
Ø24	24	4.52	3.551
Ø25	25	4.91	3.853
Ø26	26	5.31	4.168
Ø28	28	6.16	4.834
Ø30	30	7.07	5.549
Ø32	32	8.04	6.313
Ø34	34	9.08	7.127
Ø35	35	9.62	7.553
Ø36	36	10.18	7.99
Ø38	38	11.34	8.903
Ø40	40	12.57	9.865
Ø42	42	13.85	10.876
Ø43	43	14.52	11.4
Ø44	44	15.21	11.936
Ø45	45	15.9	12.485
Ø50	50	19.63	15.413
Ø55	55	23.76	18.65
Ø57.5	57.5	25.97	20.384
Ø63.5	63.5	31.67	24.86
Ø75	75	44.18	34.68

US bars (15 sizes)

Bar	Ø in	in²	lb/ft
#2b	0.249	0.049	0.166
#3	0.375	0.11	0.376
#4	0.5	0.196	0.668
#5	0.625	0.307	1.044
#6	0.75	0.442	1.503
#7	0.875	0.601	2.046
#8	1	0.785	2.673
#9	1.128	0.999	3.4
#10	1.27	1.267	4.311
#11	1.41	1.561	5.313
#14	1.693	2.251	7.66
#18	2.257	4.001	13.614
#20	2.5	4.909	16.703
#24	3	7.069	24.053
#28	3.5	9.621	32.739

Transverse reinforcement is offered from the lower part of each schedule: Ø8 to Ø22 in metric, #2b to #7 in US sizes.

Standard metric diameters (41)

30035040045050054060062065067070072075080082088090092010001050112011801200122013001400150016001700180018802000208021002200238024002500300035004000

mm · Manual override from 250 to 5000 mm.

Standard US diameters (40)

1214161820222425262830323436384042444648505254565860626466707278828496102108118138158

in · Manual override from 10 to 200 in.

2 · Clear spacing

Why the gap between bars decides the pile

“This pile failed its integrity test. The geotechnical design was right. The steel was right. The concrete mix was right. The cage was too tight for the concrete to flow through. … Your structural software will tell you the section is strong enough. It will not tell you the section is buildable. That check doesn't happen at the design desk. It happens on site, in concrete, at full cost.”Pile Section introduction

What the app measures

Clear spacing is the arc between the faces of two adjacent longitudinal bars, taken on the bar-centre circle. Where bars are bundled the arc runs between bundle envelopes, so a bundle is measured as the obstruction it actually is. Every gap in the section is evaluated and the governing (smallest) value is the one drawn and reported, live, as you edit the cage.

That value is what the concrete has to travel through to reach the shaft wall and embed the cage in the cover zone. It is the quantity the EFFC/DFI guide identifies as governing tremie flow past reinforcement.

Concrete cover and bar spacing. Clear spacing a between longitudinal bars, the nominal cover c(nom) to the excavated face, a spacer in the cover zone, and a three-bar bundle with its equivalent diameter. Redrawn after EFFC/DFI, Guide to Tremie Concrete for Deep Foundations, 3rd Edition, December 2024, Figure 3, p. 18.

The bands, and where they come from

Status	Metric	US	Basis
Green (clear)	a ≥ 100 mm	a ≥ 4 in	The guide's recommended minimum for vertical bars, to be met even in splice zones (§2.2, p. 17); ACI 336.1-01 §3.4.9; EN 1536 §7.5.2.6.
Amber (borderline)	80 ≤ a < 100 mm	3 ≤ a < 4 in	EN 1536 §7.5.2.7 allows 80 mm only over lap lengths, and only where D(max) ≤ 20 mm, with special consideration given to maintaining concrete flow. Something to justify, not something that passes.
Red (deficient)	a < 80 mm	a < 3 in	Below every published minimum. This is the region where voids, inclusions and necking become likely, and where the check is otherwise settled on site.

The published requirements, clause by clause

The guide collects the clear-spacing rules from the codes that govern bored piles. The app's green line at 100 mm and its amber floor at 80 mm come directly from these entries.

Clear spacing for bored piles and barrettes, after EFFC/DFI Table E.1
Clause	Value	Comment
ACI 336.1-01, 3.4.9	≥ 100 mm	Including at laps.
ACI 336.1-01, 3.4.9	≥ 4 × D(max)	Where D(max) is the maximum aggregate size, including at laps.
EN 1536:2010+A1, 7.5.2.6 and 7.6.3.3	≥ 100 mm	For single or bundles of longitudinal bars. The same value applies to horizontal (transverse) bars.
EN 1536:2010+A1, 7.5.2.7	≥ 80 mm	For lap length, provided that the maximum size of the aggregate ≤ 20 mm (special consideration must be given to the maintenance of sufficient concrete flow).
EN 1536:2010+A1, 7.5.2.9	≥ 1.5 × D(max) and ≥ 2.0 × Ds	For layers of bars, placed radially, where Ds is the bar diameter.
EN 1536:2010+A1, 7.5.2.5	≤ 400 mm	As wide as possible, but less than 400 mm.
EN 206:2013+A2:2021, Annex D.2.2	cs ≥ 4 × D(upper)	Where cs is the clear spacing between bars and D(upper) is the largest value of the upper sieve size for the coarsest fraction of aggregates permitted by the concrete specification.
AASHTO LRFD 5.12.9 (2020)	≥ 5 × D(max) and ≥ 125 mm	Where D(max) is the maximum aggregate size. Stricter than the 100 mm the app screens against.

Redrawn after EFFC/DFI, Guide to Tremie Concrete for Deep Foundations, 3rd Edition, December 2024, Table E.1 “Clear spacing for bored piles and barrettes”, p. 71, together with the recommendation in §2.2, p. 17. Reproduced for reference; the guide remains the authority and all rights in it belong to the EFFC/DFI Concrete Task Group. Clause references are to the editions current when the guide was published; check that none has been superseded for your project.

What the check does not do

Aggregate size governs too

Every code pairs the absolute minimum with an aggregate-proportional one: ACI 336.1 requires ≥ 4 × D(max), EN 206 ≥ 4 × D(upper), AASHTO ≥ 5 × D(max). Pile Section does not know your mix, so it screens the absolute limit only. Check the aggregate rule against your concrete specification separately.

AASHTO is stricter

AASHTO LRFD 5.12.9 requires ≥ 125 mm. Where AASHTO governs, green begins at 125 mm rather than 100, and the app's green band is not sufficient on its own.

80 mm is a lap-zone concession, not a target

EN 1536 permits 80 mm only over lap lengths and only where the maximum aggregate size is 20 mm or less, with explicit attention to maintaining concrete flow. That is why the app treats the 80–100 mm band as something to justify rather than something that passes.

Transverse bars are outside this check

The guide recommends 200 mm [8 in] clear spacing on horizontal bars to optimise flow (§2.2). Pile Section reports the governing vertical-bar spacing and does not assess the transverse pitch against that recommendation.

Cover has its own execution minimum

The guide recommends a nominal cover of at least 75 mm [3 in] for execution (a 50 mm minimum plus a 25 mm construction tolerance), and FHWA GEC 10 raises that for large shafts: 75 mm up to 1 m diameter, 100 mm above 1 m, and 150 mm above 1.5 m.

A screen, not a specification

The bands follow the guide's recommendation and the ACI 336.1 and EN 1536 minima. They are a design-desk screen intended to catch a problem early, and they do not replace project specifications, the concrete mix design, or the judgement of the responsible engineer.

Why clear space matters

From a congested cage that flags red to a buildable alternative that clears, checked at the design desk.

3 · Strength methodology

How the capacity is computed

The Strength module implements ACI 318-25 for circular reinforced-concrete sections, in metric and US customary units. This is the method in outline; the Technical Note inside the app gives the full derivation, and the white paper reproduces it.

Whitney stress block

§22.2.2.4: equivalent rectangular stress of 0.85 f′c over a depth a = β₁c, with β₁ from §22.2.2.4.3. Concrete in tension is ignored.

Strain compatibility

§22.2.1.2: plane sections remain plane, with a maximum concrete compressive strain εcu of 0.003 (§22.2.2.1). Steel is elastic–perfectly plastic.

Twenty-point interaction curve

Strain-controlled points from pure compression through the balanced region to pure bending, solved iteratively, closing at pure tension.

Strength reduction factors

Table 21.2.2: 0.75 spiral or 0.65 tied in compression, interpolated through the transition to 0.90 tension-controlled, with the φPn,max caps of §22.4.2.

Shear per §22.5

Circular sections with d = 0.8D and bw = D; Vc from Table 22.5.5.1 including the axial term, Vs = Av·fyt·d/s, and φ = 0.75.

A deliberately conservative SI transition

For fy = 500 MPa the SI engine ramps φ to 0.90 at 2.5 εy rather than ACI's εy + 0.003, which reaches 0.90 earlier. The result is a slightly lower φ in the transition, never an unsafe one. US units use the code form directly.

Utilisation bands

Green below 0.9, orange from 0.9 to 1.0, red at or above 1.0. N–M and shear are checked independently and both must pass for the section to be adequate.

Reinforcement ratio

Code limits of 0.5% to 8.0%, with a recommended working range of 1.0% to 4.0%; below that the section is flagged sparse, above it congested, on constructibility grounds.

Limitations

Slenderness and second-order effects are not included; the section is checked, not the member.
Biaxial bending is simplified to the resultant moment M = √(Mx² + My²).
Normal-weight concrete is assumed (λ = 1.0); lightweight concrete is not supported.
Deep-beam provisions and torsion interaction are not considered.
Seismic design to ACI 318-25 Chapter 18 may impose further detailing and capacity requirements.
Development length, splice and bar-spacing code checks are not performed.
Serviceability (crack control and deflection) is not included.
Fire resistance and durability are project-specific and outside the module.

Pile Section is intended for preliminary design, capacity verification and engineering cross-checks. Engage a suitably qualified structural engineer to confirm that any design complies with all applicable provisions of ACI 318-25, local regulations and project-specific requirements.Technical Note §1, Purpose and scope

4 · Benchmark

Measured against S-Concrete

Identical circular pile sections were designed in both programs and their utilisations compared, a code-to-code check of Pile Section, ACI 318-25 (SI) against S-CONCRETE 2024.1.0, ACI 318-19. Three sections (D600, D1200, D2500) at two concrete grades (40 and 50 MPa), five load points each: 30 cases, every one carrying a shear demand as well. Common parameters: fy = fyt = 500 MPa, spiral transverse reinforcement, uniaxial bending, clear cover measured to the spiral.

Utilisation is demand over capacity, so a higher figure is the conservative result. In flexure Pile Section returns a utilisation equal to or higher than S-Concrete in 26 of 30 cases. In shear it sits 1.1% lower on average, for a reason set out below.

Flexure: P–M utilisation

|Δ| ≤ 2% shown green · ≤ 5% blue · above 5% red

Case	Pile Section	S-Concrete	Δ
D600 · 40 MPa12N20 · N* -1,000 kN · M* 50 kN·m	0.682	0.589	+15.7%
D600 · 40 MPa12N20 · N* 500 kN · M* 300 kN·m	0.656	0.665	−1.3%
D600 · 40 MPa12N20 · N* 2,460 kN · M* 500 kN·m	0.890	0.946	−5.9%
D600 · 40 MPa12N20 · N* 5,464 kN · M* 200 kN·m	0.754	0.754	0.0%
D600 · 40 MPa12N20 · N* 6,500 kN · M* 50 kN·m	0.897	0.897	0.0%
D1200 · 40 MPa2x10N40 · N* -9,000 kN · M* 500 kN·m	0.896	0.796	+12.6%
D1200 · 40 MPa2x10N40 · N* 5,000 kN · M* 3,000 kN·m	0.587	0.566	+3.7%
D1200 · 40 MPa2x10N40 · N* 10,000 kN · M* 5,000 kN·m	0.965	0.953	+1.3%
D1200 · 40 MPa2x10N40 · N* 20,000 kN · M* 3,000 kN·m	0.705	0.633	+11.4%
D1200 · 40 MPa2x10N40 · N* 28,000 kN · M* 500 kN·m	0.875	0.876	−0.1%
D2500 · 40 MPa2x20N40 · N* -19,250 kN · M* 1,000 kN·m	0.891	0.851	+4.7%
D2500 · 40 MPa2x20N40 · N* 18,000 kN · M* 35,000 kN·m	1.002 ⚠	0.991	+1.1%
D2500 · 40 MPa2x20N40 · N* 50,000 kN · M* 45,000 kN·m	1.123 ⚠	1.111	+1.1%
D2500 · 40 MPa2x20N40 · N* 100,000 kN · M* 25,000 kN·m	0.907	0.824	+10.1%
D2500 · 40 MPa2x20N40 · N* 121,000 kN · M* 1,000 kN·m	0.997	0.997	0.0%
D600 · 50 MPa12N20 · N* -1,000 kN · M* 50 kN·m	0.679	0.589	+15.3%
D600 · 50 MPa12N20 · N* 500 kN · M* 300 kN·m	0.634	0.642	−1.3%
D600 · 50 MPa12N20 · N* 2,460 kN · M* 500 kN·m	0.796	0.845	−5.7%
D600 · 50 MPa12N20 · N* 5,464 kN · M* 200 kN·m	0.624	0.624	0.0%
D600 · 50 MPa12N20 · N* 6,500 kN · M* 50 kN·m	0.742	0.742	0.0%
D1200 · 50 MPa2x10N40 · N* -9,000 kN · M* 500 kN·m	0.893	0.796	+12.2%
D1200 · 50 MPa2x10N40 · N* 5,000 kN · M* 3,000 kN·m	0.549	0.529	+3.8%
D1200 · 50 MPa2x10N40 · N* 10,000 kN · M* 5,000 kN·m	0.870	0.864	+0.7%
D1200 · 50 MPa2x10N40 · N* 20,000 kN · M* 3,000 kN·m	0.573	0.527	+8.7%
D1200 · 50 MPa2x10N40 · N* 28,000 kN · M* 500 kN·m	0.737	0.737	0.0%
D2500 · 50 MPa2x20N40 · N* -19,250 kN · M* 1,000 kN·m	0.890	0.851	+4.6%
D2500 · 50 MPa2x20N40 · N* 18,000 kN · M* 35,000 kN·m	0.959	0.954	+0.5%
D2500 · 50 MPa2x20N40 · N* 50,000 kN · M* 45,000 kN·m	0.988	0.987	+0.1%
D2500 · 50 MPa2x20N40 · N* 100,000 kN · M* 25,000 kN·m	0.723	0.677	+6.7%
D2500 · 50 MPa2x20N40 · N* 121,000 kN · M* 1,000 kN·m	0.819	0.819	+0.1%

Shear: V/φVn utilisation

Case	Pile Section	S-Concrete	Δ
D600 · 40 MPa12N20 · V* 100 kN	0.406	0.415	−2.2%
D600 · 40 MPa12N20 · V* 250 kN	0.572	0.579	−1.3%
D600 · 40 MPa12N20 · V* 400 kN	0.582	0.587	−0.8%
D600 · 40 MPa12N20 · V* 150 kN	0.210	0.212	−1.1%
D600 · 40 MPa12N20 · V* 1,000 kN	1.398 ⚠	1.411	−0.9%
D1200 · 40 MPa2x10N40 · V* 250 kN	0.614	0.614	0.0%
D1200 · 40 MPa2x10N40 · V* 500 kN	0.253	0.256	−1.0%
D1200 · 40 MPa2x10N40 · V* 1,000 kN	0.383	0.386	−0.7%
D1200 · 40 MPa2x10N40 · V* 1,500 kN	0.555	0.561	−1.1%
D1200 · 40 MPa2x10N40 · V* 1,000 kN	0.370	0.374	−1.1%
D2500 · 40 MPa2x20N40 · V* 500 kN	0.162	0.167	−3.1%
D2500 · 40 MPa2x20N40 · V* 1,000 kN	0.128	0.129	−1.0%
D2500 · 40 MPa2x20N40 · V* 2,000 kN	0.174	0.176	−0.9%
D2500 · 40 MPa2x20N40 · V* 3,250 kN	0.283	0.286	−0.9%
D2500 · 40 MPa2x20N40 · V* 3,000 kN	0.262	0.264	−0.9%
D600 · 50 MPa12N20 · V* 100 kN	0.365	0.374	−2.3%
D600 · 50 MPa12N20 · V* 250 kN	0.538	0.545	−1.3%
D600 · 50 MPa12N20 · V* 400 kN	0.560	0.565	−0.9%
D600 · 50 MPa12N20 · V* 150 kN	0.192	0.193	−0.7%
D600 · 50 MPa12N20 · V* 1,000 kN	1.277 ⚠	1.290	−1.0%
D1200 · 50 MPa2x10N40 · V* 250 kN	0.614	0.614	0.0%
D1200 · 50 MPa2x10N40 · V* 500 kN	0.240	0.243	−1.2%
D1200 · 50 MPa2x10N40 · V* 1,000 kN	0.368	0.371	−0.9%
D1200 · 50 MPa2x10N40 · V* 1,500 kN	0.505	0.510	−1.1%
D1200 · 50 MPa2x10N40 · V* 1,000 kN	0.336	0.340	−1.1%
D2500 · 50 MPa2x20N40 · V* 500 kN	0.123	0.126	−2.4%
D2500 · 50 MPa2x20N40 · V* 1,000 kN	0.114	0.115	−1.3%
D2500 · 50 MPa2x20N40 · V* 2,000 kN	0.155	0.156	−0.5%
D2500 · 50 MPa2x20N40 · V* 3,250 kN	0.247	0.250	−1.1%
D2500 · 50 MPa2x20N40 · V* 3,000 kN	0.228	0.230	−0.8%

Every figure in both tables is computed when this page is built: the Pile Section column runs the live engine over the committed benchmark cases, and the reference column is read from the S-Concrete results file. Re-run it yourself with `pnpm benchmark`. S-CONCRETE is a product of Altus Group (S-FRAME Software); the benchmark is reproduced here for independent validation and all trademarks belong to their respective owners.

Flexure vs S-Concrete

Cases compared: 30
Average deviation: +3.3%
Average absolute deviation: 4.3%
Median absolute deviation: 1.3%
Maximum deviation: 15.7% (40MPa-D600-1)
Pile Section more conservative: 17 of 30
Identical within ±0.2%: 9 of 30
Pile Section less conservative: 4 of 30

Shear vs S-Concrete

Cases compared: 30
Average deviation: −1.1%
Average absolute deviation: 1.1%
Median absolute deviation: 1.0%
Maximum deviation: 3.1% (40MPa-D2500-1)
Pile Section more conservative: 0 of 30
Identical within ±0.2%: 2 of 30
Pile Section less conservative: 28 of 30

Where the differences come from

Both programs design to ACI, and the two remaining systematic differences have been identified and quantified. Neither is an error in either program.

The SI and imperial forms of ACI's concrete shear term differ

≈ 1% on the shear D/C, one-directional

ACI 318 publishes the concrete shear term as 2√f′c in psi and 0.17√f′c in MPa, and the SI value is a rounded-up conversion of the imperial one, 2.3% higher. This engine evaluates the SI form as published; S-Concrete evaluates the imperial form. Because Vs is unit-independent and often dominates Vn, the net effect on the ratio is about 1%. Substituting the imperial coefficients reproduces S-Concrete's Vc to within 0.1 kN, which confirms the mechanism rather than leaving it as a hypothesis.

Axial utilisation is taken with, or without, interaction

0–16% on the flexural D/C, always toward more capacity required

For axial-governed cases the two programs divide by different capacities. S-Concrete divides by the pure axial capacity, ignoring the coincident moment. This engine interpolates the axial capacity at the demand moment along the interaction curve, so a coincident moment reduces the capacity available. Dividing by the pure capacity reproduces S-Concrete's figure exactly on the four axial-governed cases, and the two programs agree to three decimals wherever the moment is small enough for interaction to be negligible, which isolates the mechanism.

A refinement we considered and rejected

The interaction curve is drawn as chords between computed points, and on the tension branch a straight chord is conservative, by about 2% at φP = −200 kN, 5% at −400 kN and 8% at −600 kN for the section we studied. We evaluated refining it and decided against: the straight tension chord is a shared industry convention rather than an approximation error, and every deviation it introduces is on the safe side.

5 · Open invitation

These defaults are a living standard.

The bar schedules, pile diameters and spacing bands built into Pile Section reflect the codes we implement and the mills and rigs we know about. Practice varies by market, by fleet, by specification. If your region rolls different bars, your rigs bore different diameters, or your specifications draw the amber line somewhere else, tell us. Practitioner feedback is how these defaults improve, and how the app keeps nudging designs toward cages that build cleanly on the first pour.

Suggest a revision

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References

EFFC/DFI Concrete Task Group (2024). Guide to Tremie Concrete for Deep Foundations, 3rd Edition. European Federation of Foundation Contractors and Deep Foundations Institute.
ACI Committee 318 (2025). Building Code Requirements for Structural Concrete (ACI 318-25) and Commentary. American Concrete Institute.
ACI Committee 336 (2001). Specification for the Construction of Drilled Piers (ACI 336.1-01). American Concrete Institute.
CEN (2010). EN 1536:2010+A1, Execution of special geotechnical works: Bored piles.
CEN (2021). EN 206:2013+A2:2021, Concrete: Specification, performance, production and conformity.
AASHTO (2020). LRFD Bridge Design Specifications, 9th Edition.
Brown, D.A., Turner, J.P., Castelli, R.J. & Loehr, E.J. (2018). Drilled Shafts: Construction Procedures and Design Methods (FHWA-NHI-18-024, GEC No. 10). Federal Highway Administration.
Altus Group / S-FRAME Software (2024). S-CONCRETE 2024.1.0.

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Standard dimensions, the EFFC/DFI spacing basis, the full strength methodology and all 30 benchmark cases, in one citable PDF.

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