1. Code framework

Calculations are performed in accordance with the Eurocode framework adopted for foundation design in the UK and EU. The controlling standards are:

Reference	Title / scope
EN 1990	Basis of structural design
EN 1991-1-1	Actions on structures — densities, self-weight, imposed loads
EN 1993-1-1	Steel structures — general rules
EN 1993-5	Steel structures — Piling (corrosion, slender pile sections)
EN 1997-1	Eurocode 7 — Geotechnical design, Part 1 General rules
EN 1997-2	Eurocode 7 — Geotechnical design, Part 2 Ground investigation
EN 1999-1-1	Aluminium structures — general rules
EN 14199	Execution of special geotechnical work — Micropiles
BS EN ISO 22476-3	Standard penetration test

The UK / IE / DE national annexes are followed for partial factors. Design Approach 1 (DA1) is used with two combinations checked side by side.

2. Partial / capacity reduction factors

2.1 Action partial factors (γ_F)

Action	Symbol	A1 set	A2 set
Permanent unfavourable	γG	1.35	1.0
Permanent favourable	γG,inf	1.0	1.0
Leading variable unfavourable	γQ	1.5	1.3
Variable favourable	—	0	0

2.2 Material partial factors (M1 set, used for both combinations)

Soil parameter	Symbol	M1 value
Angle of shearing resistance	γφ'	1.0
Effective cohesion	γc'	1.0
Undrained shear strength	γcu	1.0

2.3 Resistance partial factors

Quantity	Symbol	R1 set (DA1-1)	R4 set (DA1-2)
Base resistance	γb	1.0	1.7
Shaft resistance (compression)	γs	1.0	1.5
Shaft resistance (tension)	γs,t	1.25	2.0

3. Load distribution to inclined piles

The pile cap is assumed to distribute the resultant action evenly between the n piles in the group. The piles are sufficiently spaced that single-pile group efficiency factors are not applied (a deliberate conservatism). For a cap of radius r with n piles arranged on a circle:

The worst-pile vertical share, combined with the cap moments M_x and M_y, uses the envelope distance x_m = r/√2 (which corresponds to the pile at 45° from the moment axis, where M_x and M_y contributions superimpose):

Per-pile horizontal shares include the torsion contribution:

The piles are installed at an angle α = 25° from vertical (specifying a fixed rake reduces parameter complexity for designers). At the pile head, the vertical and horizontal force components from the cap are resolved into the pile's axial (along-axis) and shear (perpendicular-to-axis) components:

4. Pile section — structural capacity

4.1 Steel piles — properties

Property	Symbol	S355	Notes
Yield strength	fyk	355 N/mm²	EN 10025
Modulus of elasticity	E	210 000 N/mm²	EN 1993-1-1
Available diameters	OD	48.4, 60.3 mm	Hot-rolled CHS
Available wall thicknesses	tnom	3.0, 4.0, 5.0, 6.3 mm	—

Section properties for a circular hollow section with corroded wall t_DWL:

4.2 Aluminium piles — properties

The aluminium pile is a 6082-T6 extrusion with 6 internal longitudinal ribs at 60° spacing (verified against measured mass per metre). Two sizes are offered:

Size	OD (mm)	Wall (mm)	A (mm²)	I (mm⁴)	W (mm³)	Mass (g/m)
AluPile 48	48.0	3.6	651.3	151 674	6320	1758
AluPile 60	60.0	4.5	1017.0	370 299	12 343	2747

Material property	Symbol	6082-T6	Notes
Yield strength	fyk	250 N/mm²	EN 755-2 (≥ 5 mm)
Modulus of elasticity	E	70 000 N/mm²	EN 1999-1-1

4.3 Capacity formulas

Slender-member buckling reduction χ = 0.30 is applied to both materials (placeholder calibrated for the EN 1993-1-1 buckling curve at the relevant slenderness):

4.4 Corrosion approach

The two pile materials corrode by fundamentally different mechanisms, and are modelled separately. Steel corrodes uniformly enough to be treated as a year-on-year wall-thickness deduction. Aluminium corrodes by localised pitting — stochastic, sparse, and a poor fit for a uniform-loss approach — and is modelled through the FDOT pit-progression service-life envelope.

4.4.1 Steel piles — uniform corrosion deduction. Per EN 1993-5 Annex D / Table 4-1, scaled linearly with the design working life L_D:

Soil category	60-yr loss (mm)
Undisturbed natural soils	0.60
Non-compacted non-aggressive fills	1.20
Polluted natural / industrial	1.50
Aggressive natural soils	1.75
Non-compacted aggressive fills	3.25

4.4.2 Aluminium piles — FDOT pit-progression model. Aluminium does not corrode uniformly. Once the natural oxide layer is breached, attack proceeds as a small number of localised pits that grow downward roughly logarithmically. The wall around each pit stays essentially intact. The implications:

• Average mass loss is small, but maximum pit depth grows faster than the area-mean section loss — the deepest pit at any time is typically 3 to 5 times deeper than the average loss (Bushman & Lytton ratio, FHWA-RD-89-186).
• The classical engineering failure point for a pipe is “first pit-through” — one pit reaches the inner wall and the pipe leaks. For a pile this is not a structural failure: a 60 mm OD pile with a 0.5 mm hole has lost < 0.001% of cross-sectional area, with no measurable effect on axial, moment, or elastic-length capacity.
• A uniform Δt · L_D deduction therefore overstates the structural impact of pitting by an order of magnitude. This calculator does not apply a uniform aluminium corrosion deduction.

Instead, the calculator reports a service-life envelope per the Florida Department of Transportation method published in the FDOT Drainage Design Guide, Appendix M (January 2024) — the most thorough public-domain treatment of buried aluminium infrastructure:

The FDOT table is published for 16 ga aluminium pipe (~1.5 mm wall). The calculator scales linearly with the actual wall thickness of the RapidRoot pile (T_p/1.5).

4.4.3 Soil corrosivity tiers. The user’s soil corrosivity selection is mapped silently into one of five aluminium-durability tiers. Resistivity values shown are typical ASTM G57 ranges:

Soil category	Tier	Typical resistivity	AluPile 48 (3.6 mm) SL	AluPile 60 (4.5 mm) SL
Undisturbed natural soils	Optimal	> 5,000 Ω·cm	~480 yrs	~600 yrs
Non-compacted non-aggressive fills	Mild	2,000–5,000 Ω·cm	~240 yrs	~300 yrs
Polluted / industrial	Moderate	700–2,000 Ω·cm	~144 yrs	~180 yrs
Aggressive natural soils	Aggressive	200–700 Ω·cm	~96 yrs	~120 yrs
Non-compacted aggressive fills	Severe	< 200 Ω·cm	Out of scope — not recommended

4.4.4 Threshold checks shown on Results. Rather than reporting a precise design-life year (which would imply more precision than the stochastic pitting model can deliver), the calculator reports two binary checks at thresholds well above typical building design life (50–60 yrs):

• ≥ 75-year durability envelope: passes for Tiers 1–4 on both AluPile sizes. Generally a non-issue.
• ≥ 100-year durability envelope: passes for Tiers 1–3 on both sizes; AluPile 60 also passes Tier 4. For AluPile 48 on a Tier 4 site, the result is flagged “Marginal” with a recommendation to upgrade to AluPile 60 or switch to steel.

5. Geotechnical capacity — Meyerhof SPT method

Meyerhof (1976) SPT correlation for unit shaft friction in cohesionless soils, with the standard upper cap at N = 50: Meyerhof (1976) SPT correlation for unit base resistance, with the standard upper bound at fully developed end bearing in dense sand (≈ 4 N MPa, i.e. 40 N at full penetration depth ratio): Characteristic shaft and base resistances are then: Where the embedment passes through multiple soil layers, the SPT-N value used in equations (7) and (8) is the average weighted by the thickness of each layer intersected by the pile:

6. Lateral analysis — Reese-Matlock T-method

The elastic-foundation characteristic length T is computed for both cohesive and non-cohesive sub-models, and the larger of the two is used (conservative envelope on mixed profiles):

Depth to maximum moment, capped at 1.3 T:

Worst-case bending moment combining cantilever stickup and in-ground peak:

7. Reactive / expansive soils

7.1 Why this matters

Expansive (reactive) clays undergo cyclical volume change with seasonal moisture content. As the soil swells in the wet season it engages the pile shaft in uplift, generating tension in the pile and the cap connection; as it shrinks in the dry season the shaft friction in the upper soil is lost. A pile that is bonded entirely within the active zone will translate up and down with the seasons, taking the building with it.

7.2 Site classification

The user selects a site classification from the standard band system used in the controlling code (§7.6 below). Each class carries a characteristic surface ground movement y_s and an assumed active zone depth H_a. Both can be overridden by the user when a site-specific geotechnical investigation provides better values.

7.3 Triangular suction profile

The disruption to shaft friction follows the suction-change profile, which is approximately triangular — full disturbance at the surface, zero at the bottom of the active zone H_a. Integrating the triangle gives an average disruption factor of exactly 0.5 across the active zone. This calculator therefore uses an effective active-zone depth of:

7.4 Effective shaft length

Shaft friction in equations (10) and (15) uses L_eff rather than L_ent when the calc determines the active zone is engaged.

7.5 Swelling uplift force on the pile

where q_s,swell is a class-specific unit uplift friction (8 to 50 kPa, increasing with site class). This force is added to the tension demand on the pile.

7.6 Anchor depth check

Independent of disruption magnitude, the pile must reach stable ground below the full active zone. The calc applies:

with anchor margin = 1.0 m for EU/AUS and 3 ft (0.91 m) for US.

7.7 NC soil override

Non-cohesive (sand, gravel) soils do not swell. If every layer that intersects the active zone has layer type = NC, the reactive adjustments are switched off automatically — regardless of the selected class. This avoids penalising a sand site that happens to share a classification with a clay site.

7.8 Hard reject for severe sites

The two highest reactivity classes (VH and P; AS 2870 H2, E and P) trigger a hard reject. With a 3 m pile-length envelope (10 ft in US) the pile cannot be reliably anchored below an active zone that exceeds ~2.5 m. The calc displays an out-of-scope notice with the recommended response: longer pile system, or project-specific load test.

7.9 Site classification table

Class	PI band	ys	Ha default	qs,swell	Status
VL	< 15	< 5 mm	0 m	0 kPa	Pass — no adjustment
L	15–25	5–20 mm	1.2 m	8 kPa	Pass with adjustment
M	25–35	20–40 mm	1.5 m	15 kPa	Pass with adjustment
H	35–55	40–60 mm	2.0 m	25 kPa	Pass with adjustment
VH	> 55	> 60 mm	3.0 m	40 kPa	OUT OF SCOPE
P	variable	site-specific	3.5 m	50 kPa	OUT OF SCOPE

8. Serviceability — settlement check

Serviceability is checked using a 1.0G + 1.0Q service load combination (no factors) per the simplified approach in EN 1997-1 §2.4.8 / AS 2159 §8.4 / IBC §1810.3.3.3.

8.1 Elastic shaft compression

Assuming linear load transfer to the shaft (the average axial load along the shaft is N_service/2):

8.2 Tip movement

Empirical, proportional to base mobilisation. Per Tomlinson (1994) and AS 2159 commentary, tip movement at full base mobilisation is approximately D/100 for small-diameter piles:

8.3 Total and permissible settlement

The user sets δ_max on the Inputs tab (default 25 mm / 1.0 in).

9. Limitations of this calculator

• Pile diameter restricted to 48 mm and 60 mm equivalents.
• Maximum pile embedment 3 m (10 ft).
• Group efficiency factor not applied (single-pile resistance summed across the cap).
• Project-specific static load testing is not modelled. The code permits favourable adjustment of resistance factors on the basis of load test; that adjustment is the engineer's call.
• Refusal on rock, soil reinforcement, and pile-cap moment transfer are not modelled.
• Output is a preliminary sizing only. A qualified design professional must verify the methodology, the input parameters, and the conclusions before any construction work proceeds.

10. References

1. EN 1990: Basis of structural design.
2. EN 1991-1-1:2002: Actions on structures — general actions.
3. EN 1993-1-1:2005: Design of steel structures, Part 1-1.
4. EN 1993-5:2007: Design of steel structures, Part 5 — Piling.
5. EN 1997-1:2004: Geotechnical design, Part 1 General rules.
6. EN 1997-2:2007: Geotechnical design, Part 2 Ground investigation.
7. EN 1999-1-1:2007: Design of aluminium structures.
8. EN 14199:2005: Execution of special geotechnical work — Micropiles.
9. Meyerhof, G. G. (1976). Bearing capacity and settlement of pile foundations. J. Geotech. Eng. Div., ASCE 102(GT3), 197–228.
10. Reese, L. C., & Matlock, H. (1956). Non-dimensional solutions for laterally loaded piles. 8th Texas Conf. on Soil Mechanics.
11. Davisson, M. T. (1970). Lateral load capacity of piles. Highway Research Record 333.
12. NAVFAC DM-7.2 (1986). Foundations and Earth Structures.
13. Tomlinson, M. J., & Woodward, J. C. (2015). Pile Design and Construction Practice, 6th ed.
14. Bostani-Taleshani, S. A., Evans, R., Gad, E., & Disfani, M. M. (2020). Performance of driven battered mini-pile group against expansive soil induced ground movement. E3S Web of Conferences 195, 01030.