RapidRoot™ Design Calculator — US

IBC 2021 | ASCE 7-22 LRFD | AISC 360-22 & ADM 2020 | FHWA NHI-05-039

Pile selection

Pile material

Pipe size (NPS)

Schedule (wall)

Piles per cap

Embedded length L_ent (ft)

Stickup L_ext (ft)

Number of pile caps

Pile cap reference

RR8

—

Service loads — per cap (ASCE 7-22 nominal)

D — dead vertical (kips)

L — live vertical (kips)

Wx — lateral X (kips)

Wy — lateral Y (kips)

Mx — moment X (kip-ft)

My — moment Y (kip-ft)

Mz — torsion (kip-ft)

Strength combo used: 1.2D + 1.6L + 1.0W on horizontals. Uplift case: 0.9D minus moment effects (per ASCE 7-22 §2.3.1).

Design parameters

Design working life (yrs)

Soil corrosivity (steel only)

n_h — subgrade modulus (pci)

Max settlement δ_max (in)

Groundwater

Water table

No groundwater correction applied.

Site classification — expansive soils (ASTM D4829 / IBC §1803.5.3)

Expansion class (EI band)

Active zone depth H_a (ft)

Characteristic y_s

< 1/4 in

Class VL (Very Low): no reactive-soil adjustments applied. The calc runs as a standard bearing-capacity check.

Soil data source

Enter SPT-N blowcounts (blows/foot per ASTM D1586) per layer. Leave unused rows blank.

Soil layers (up to 10)

#	Thick. (ft)	Type	γ (pcf)	SPT-N	C_u (psf)	φ′ (°)	DPM-30/20 raw blows	N_SPT equiv (×0.006842)

Appendix — typical soil parameter ranges (US units)

Guidance only. Always prefer measured values from a geotechnical investigation.

Cohesive soils (C) — c_u (psf)

Very soft clay	< 250
Soft clay	250 – 500
Firm clay	500 – 1,000
Stiff clay	1,000 – 2,000
Very stiff clay	2,000 – 4,000
Hard clay / weak claystone	> 4,000

Non-cohesive (NC) — φ′ (°)

Loose silty sand	25 – 30
Loose sand	28 – 32
Medium dense sand	32 – 36
Dense sand	36 – 40
Very dense sand	40 – 45
Sandy gravel (medium dense)	34 – 38
Dense well-graded gravel	38 – 45

SPT-N (blows/ft)

Very loose sand	N < 4
Loose	4 – 10
Medium dense	10 – 30
Dense	30 – 50
Very dense	> 50
Soft clay (N)	2 – 4
Firm clay	4 – 8
Stiff clay	8 – 15
Hard clay	> 30

Unit weight γ (pcf)

Peat / organic	65 – 90
Soft clay	100 – 115
Firm / stiff clay	115 – 135
Loose sand	95 – 125
Dense sand	115 – 140
Sandy gravel	120 – 140
Made ground / fill	100 – 125

n_h (pci)

Loose sand	5 – 9
Medium dense	18 – 28
Dense sand	44 – 74

Steel corrosion (60-yr loss)

Undisturbed natural soil	24 mils
Below water table	36 mils
Non-aggressive fill	47 mils
Polluted / industrial	59 mils
Aggressive natural soil	69 mils
Aggressive fill	128 mils

References: Terzaghi (1955); Reese & Matlock (1956); Davisson (1970); NAVFAC DM-7.2; FHWA NHI-05-039; AASHTO LRFD Bridge Design Specifications.

LRFD utilisation checks — worst-case pile

Pile section at end of design life

Auto design — service loads (LRFD-factored internally)

Soil data is read from the Soil profile tab. Results show minimum pile length for each cap/pile combination, ranked by cost efficiency.

D — dead vertical (kips)

L — live vertical (kips)

Wx — lateral X (kips)

Wy — lateral Y (kips)

Mx — moment X (kip-ft)

My — moment Y (kip-ft)

Soil parameters — from soil profile tab

SPT-N, c_u and DPM data are read automatically from the Soil profile tab.

Weighted avg SPT-N

— enter layers in Soil profile tab

Weighted avg c_u (psf)

—

Data source

—

n_h (pci)

Soil corrosivity (steel)

Design working life (yrs)

Minimum pile length

Maximum pile length

Pile options to include

Steel A572 Gr50 — NPS 2 Sch 40 Steel A572 Gr50 — NPS 1½ Sch 40 Alu 6061-T6 — ~OD 2.36 in Alu 6061-T6 — ~OD 1.89 in

Calculation methodology

This page documents the engineering basis used by this calculator so a qualified design professional can audit the approach against the project context, the controlling code, and their own check calculations.

1. Code framework

Calculations follow the US LRFD building-code framework. The controlling standards are:

Reference	Title / scope
IBC 2021 Ch. 18	Soils and Foundations
IBC §1803.5.3	Expansive soils investigation
ASCE 7-22 §2.3	Strength load combinations
AISC 360-22	Specification for Structural Steel Buildings
ADM 2020	Aluminum Design Manual
ASTM A572 Gr 50	Steel pile material specification
ASTM B221 6061-T6	Aluminum pile material specification
ASTM D1586	Standard penetration test
ASTM D4829	Expansion Index (soils)
FHWA NHI-05-039	Micropile Design and Construction Reference Manual
AASHTO LRFD §10.7.5	Steel pile corrosion deduction

All calculations are performed internally in SI units and converted to US customary (ft, in, kips, ksi, psf) at the input/output boundaries.

2. Partial / capacity reduction factors

2.1 Load combinations (ASCE 7-22 §2.3.1)

Combination	Use
1.2D + 1.6L + 0.5(L_r or S or R)	Strength (compression)
1.2D + 1.0W + 1.0L + 0.5(L_r or S or R)	Strength (lateral)
0.9D + 1.0W	Uplift

The calc uses 1.2D + 1.6L on verticals, 1.0W on horizontals and moments, and 0.9D for the counter-action in tension/uplift checks.

2.2 Resistance factors

Quantity	Symbol	Value	Source
Steel flexure	φ_b	0.90	AISC 360-22 F8
Steel compression	φ_c	0.90	AISC 360-22 E1
Steel shear	φ_v	0.90	AISC 360-22 G2
Aluminium flexure	φ_b	0.85	ADM 2020 F.1
Aluminium compression	φ_c	0.75	ADM 2020 H.1
Geotechnical compression	φ_g	0.60	FHWA NHI-05-039 Table 5-4
Geotechnical tension	φ_g,t	0.50	FHWA NHI-05-039 Table 5-4

Buckling-reduction χ = 0.30 is applied in addition to φ to cover the slender-pile case at maximum embedment. This is a calibrated placeholder; for a stamped design the engineer should compute χ from AISC 360-22 E3 using the actual slenderness ratio kL/r.

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:

Σ x_i² = (n/2)·r²(1)

Σ (x_i² + y_i²) = n·r²(2)

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):

H_z,gov = F_d/n + (x_m·M_y,d + x_m·M_x,d) / Σx_i²(3)

Per-pile horizontal shares include the torsion contribution:

H_xi = H_x,d/n + (x_m·M_z,d) / Σ(x_i² + y_i²)(4)

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:

N_axial = H_z,gov·cosα + √(H_xi² + H_yi²)·sinα(5)

V_shear = √[(H_xi·cosα)² + (H_yi·cosα)² + (H_z,gov·sinα)²](6)

All subsequent capacity checks compare these axial and shear forces against the corresponding axial and shear capacities along/across the pile axis. Action and resistance are projected to the same frame; group efficiency factors are not applied.

4. Pile section — structural capacity

4.1 Steel piles — ASTM A572 Gr 50

Property	Symbol	Value	Notes
Yield strength	F_y	50 ksi (345 MPa)	ASTM A572
Modulus of elasticity	E	29 000 ksi (200 GPa)	AISC 360-22
Available sizes	NPS	1½, 2	OD 1.900 in (48 mm), 2.375 in (60 mm)
Available wall	t	Sch 40 / Sch 80	Sch 40: 0.145–0.154 in; Sch 80: 0.200–0.218 in

Section properties for the corroded annulus follow equations (12)–(14) from §4.1 above. Internal SI math, displayed in US customary in the Results tab.

4.2 Aluminium piles — ASTM B221 6061-T6

The aluminium pile is a 6061-T6 extrusion with 6 internal longitudinal ribs at 60° spacing. Two sizes are offered (areas verified against measured mass per metre):

Size	OD (in)	Wall (in)	A (in²)	I (in⁴)	S (in³)
~OD 1.89 in (48 mm)	1.89	0.142	1.009	0.364	0.386
~OD 2.36 in (60 mm)	2.36	0.177	1.577	0.890	0.753

Material property	Symbol	6061-T6	Notes
Yield strength	F_y	35 ksi (240 MPa)	ADM 2020
Modulus of elasticity	E	10 100 ksi (70 GPa)	ADM 2020

4.3 Capacity formulas

φ·P_n = φ_c · χ · F_y · A(15)

φ·M_n = φ_b · F_y · S_x(16)

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 AASHTO LRFD Bridge Design Specifications §10.7.5, scaled linearly with the design working life L_D:

Environment	60-yr loss (mils)
Undisturbed natural soil (above WT)	24
Soil below water table	36
Non-compacted non-aggressive fill	47
Polluted / industrial	59
Aggressive natural soil	69
Non-compacted aggressive fill	128

t_DWL = max(t_nom − Δt · L_D/60, 0.5 mm)(17a)

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:

SL = T_p / (R_pH + R_r) [years to first pit-through](17b)

where
T_p = wall thickness (mm)
R_pH = pit-progression rate from soil pH (mm/yr)
R_r = pit-progression rate from soil resistivity (mm/yr)

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.

The 75-yr and 100-yr thresholds are deliberately coarser than the corresponding steel deduction. The intent is to give the designer a clean go/no-go on aluminium suitability rather than to suggest the calc can predict pile life to a year. Aluminium pit depth at any point in time is best understood as a distribution — the FDOT formula gives the median/expected first-perforation time, and real-world maximum pit depth could be reached earlier or later by a factor of 2–3 (Gumbel extreme-value distribution, Aziz & Godard 1989).

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:

q_s = 2·min(N, 50) [kPa](7)

The cap at N = 50 reflects field observation that shaft friction does not continue to scale linearly above this density level (Tomlinson 1994). The factor of 2 is the original Meyerhof value, consistent with NAVFAC DM-7.2 for driven small-diameter piles.

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):

q_b = min[0.4·N·(L/D), 40·N] [kPa](8)

The (L/D) ratio is the penetration ratio of the pile into the bearing stratum, capped at 100 by the second term. For small-diameter micropiles (D ≈ 0.05 m) the L/D term grows quickly and the cap is reached at modest embedment.

Characteristic shaft and base resistances are then:

R_s,k = q_s·π·D·L_eff(10)

R_b,k = q_b·π·D²/4(11)

where
D = pile outside diameter (m)
L_eff = effective shaft length (m), equal to L_ent in non-reactive ground; reduced for reactive sites — see §7

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:

N_avg = Σ_i(N_i·t_i) / Σ_i t_i(9)

Layers beyond the pile toe are not included (the weighting is clipped to the actual embedment depth). This avoids overstating capacity when a strong stratum sits below the pile toe.

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):

T_clay = (EI / (67·c_u))^1/4(17)

T_sand = (EI / n_h)^1/5(18)

Depth to maximum moment, capped at 1.3 T:

Z_o = min[(0.25 + 0.8·ln(L_ent/T))·T, 1.3·T](19)

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

M_max = V·L_ext + 0.64·V·Z_o(20)

L_ext is the pile stickup above ground; the 0.64 coefficient is the Broms / Reese-Matlock dimensionless moment maximum for a fixed-head flexible pile.

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:

H_a,eff = 0.5 · H_a(20)

This is materially less conservative than treating the active zone as fully disengaged. The 0.5 factor is consistent with AS 2870 Appendix D, EN 1997-1 Annex H and the FHWA-IF-99-025 guidance on drilled piers in expansive soils. Bostani-Taleshani et al. (2020) field-measured 70% movement attenuation on a 1.2 m pile in H2 ground — i.e. effective engagement of ~30%. The 0.5 factor sits between this measurement and the fully-conservative uniform model.

7.4 Effective shaft length

L_eff = L_ent − H_a,eff = L_ent − 0.5·H_a(21)

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

P_swell = q_s,swell · π·D·H_a,eff·cosα(22)

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:

L_ent ≥ H_a + (anchor margin)(23)

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	EI band	y_s	H_a default	q_s,swell	Status
VL	0–20	< 1/4 in	0 ft	0 psf	Pass — no adjustment
L	21–50	1/4–1/2 in	4 ft	170 psf	Pass with adjustment
M	51–90	1/2–1 in	5 ft	310 psf	Pass with adjustment
H	91–130	1–2 in	6.6 ft	520 psf	Pass with adjustment
VH	> 130	> 2 in	10 ft	835 psf	OUT OF SCOPE
P	variable	site-specific	11.5 ft	1045 psf	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):

δ_shaft = N_service·L_ent / (2·A·E)(24)

where A and E are the pile section area and Young's modulus.

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:

δ_tip = (N_service / R_n)·D/100(25)

8.3 Total and permissible settlement

δ_total = δ_shaft + δ_tip ≤ δ_max(26)

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

International Building Code (IBC) 2021, Chapter 18.
ASCE/SEI 7-22: Minimum Design Loads and Associated Criteria.
ANSI/AISC 360-22: Specification for Structural Steel Buildings.
Aluminum Association ADM 2020: Aluminum Design Manual.
ASTM A572: Standard Specification for High-Strength Low-Alloy Steel.
ASTM B221: Standard Specification for Aluminum Extruded Bars, Rods, Wire.
ASTM D1586: Standard Test Method for Standard Penetration Test (SPT).
ASTM D4546 / D4829: Expansive soils tests and Expansion Index.
FHWA NHI-05-039: Micropile Design and Construction Reference Manual (2005).
AASHTO LRFD Bridge Design Specifications, §10.7.5 corrosion deduction.
Meyerhof, G. G. (1976). Bearing capacity and settlement of pile foundations. ASCE.
Reese, L. C., & Matlock, H. (1956). Non-dimensional solutions for laterally loaded piles.
Davisson, M. T. (1970). Lateral load capacity of piles.
NAVFAC DM-7.2 (1986). Foundations and Earth Structures.
Tomlinson, M. J., & Woodward, J. C. (2015). Pile Design and Construction Practice, 6th ed.

Disclaimer. This app is for use by qualified design professionals only, who have reviewed the design methods and verified the output with their own calculations. It is a preliminary sizing tool, not a substitute for project-specific engineering judgement or stamped calculations.