Stage 6 / pile capacity

Stage 6 axial pile capacity.

The pile-capacity route is a CPT-based screen for the axial compression resistance and the serviceability settlement of a single pile founded in Belgian soils. It implements the four-stage De Beer scale-effect transformation for the unit base resistance, the Belgian η*p table for the unit shaft friction, the full Eurocode 7 / Belgian factor chain (γRd, ξ3 / ξ4, γb, γs), a slip-method and analogy-method screening of negative skin friction, and the Allani–Huybrechts (2022) load-transfer model with hyperbolic t-z and q-z springs for the SLS settlement.

Scope and intent

1. Problem class and engineering purpose

The pile route is an axial-compression ULS and SLS screen for a single pile founded on the interpreted CPT section. It is the deep-foundation counterpart of the bearing capacity chapter: shallow-foundation bearing resistance is replaced by the sum of pile-base resistance Rb and pile-shaft resistance Rs, both derived directly from the CPT qc profile through the Belgian semi-empirical method. The route reports the full ULS factor chain end-to-end and a load-transfer SLS settlement estimate against a user-defined allowable.

Model class. Single-pile axial compression under Eurocode 7 with the Belgian National Annex, Buildwise Dimensioneringsmethode 20 (DM20), and ATG-with-certification factors where available. Tension / uplift, lateral loading, seismic, buckling, pile-group settlement (equivalent raft), and structural pile design are out of scope for this screen.
Primary quantities
Rb, Rs, Rc
Calculated pile base, shaft, and total compression resistance [kN].
Rc,cal, Rc,k, Rc,d
Calibrated, characteristic, and design pile compression resistance [kN].
qb
Unit pile base resistance from the De Beer transformation [kPa].
qs,i
Unit shaft friction in layer i [kPa].
Fc,d, Frep
ULS design load and SLS representative load on the pile [kN].
Fnk,d
Design negative-skin-friction load on the pile [kN].
shead
Pile-head settlement under Frep [mm].

Hierarchy

2. Belgian design hierarchy

The pile route follows the Belgian design hierarchy stated in BUtgb-UBAtc Informatieblad 2025/3 [1] and the Belgian practice report [3]:

  1. NBN EN 1997-1 with the Belgian National Annex (2022) [6]; NBN EN 1997-2:2007 with its national annex remains applicable in Belgium pending the ANB to NBN EN 1997-2:2024 [7].
  2. Buildwise Dimensioneringsmethode 20 (2020) [2] for the geotechnical ULS design of axially loaded piles and micropiles from CPTs.
  3. ATG-with-certification factors for the specific pile system, where available [1], [8].
  4. Project specifications such as Standaardbestek 260 (Flemish) [9] for execution and reporting; SB260 does not replace the geotechnical ULS calculation route.

The screening tool ships with public DM20 factor tables as defaults. An ATG override block exposes user-entered αb, αs, γRd, and γb for production calculations on systems with a current ATG. A static-load-test (SLT) selector switches the γRd row between γRd1 (no SLT), γRd2 (SLT in comparable conditions), and γRd3 (SLT on the job site).

Geometry

3. Pile geometry

Ab,circular = π Db² / 4
Ab,square = a²
Ab,rect = a · b
Db,eq,circular = Db
Db,eq,rect (b ≤ 1.5 a) = √(4 a b / π)
Db,eq,rect (b > 1.5 a) = √(6 a² / π)
χs,circular = π Ds, χs,square = 4 a, χs,rect = 2 (a + b)
Notation
Ds, Db
Pile shaft and base diameter (or equivalents) [m].
Db,eq
Equivalent base diameter used in the De Beer transformation [m].
Ab, Ap
Base bearing area and pile axial-stiffness cross-section [m²]. They differ for open tubes and steel sections; closed concrete piles use Ap = Ab.
χs
Shaft perimeter [m].
  • Open-ended tubes, sheet piles, plugged tubes, and steel profiles use DM20 / ATG-specific geometry rules and are out of scope for this screen.
  • The pile head depth zhead defaults to ground level but can be moved down for piles started in an excavation. The pile length is L = ztoe − zhead.

De Beer transformation

4. Unit base resistance qb — De Beer scale-effect method

The De Beer method is the Belgian standard procedure to convert the CPT qc profile into the unit pile-base resistance qb for a pile of equivalent diameter Db,eq. It is a four-stage algorithmic procedure described in [3] and detailed in the BGGG reference document [4]; it is not a single closed-form equation and must not be replaced by qc at the toe nor by a simple average over a depth window.

The implementation resamples the raw qc profile from its native ~0.02 m sampling to 0.20 m bins (BGGG performs the calculation at exactly 0.20 m), then applies the four stages in order:

Stage 1 (homogeneous): qh(z) = qc(z)
Stage 2 (downward): ratio = Dc / Db,eq, Dc = 0.0357 m
if qh(z) ≤ qd(z − Δz): qd(z) = qh(z)
else: qd(z) = qd(z − Δz) + ratio · (qh(z) − qd(z − Δz))
Stage 3 (upward): symmetric, iterated from the deepest bin upward, with the same ratio
Stage 4 (mixed): qp(z) = min[ qd(z), qu(z) ]
qb = linear interpolation of qp at ztoe
Implementation note — Stage 1. The screening tool implements Stage 1 as the identity transformation qh(z) = qc(z). The full BGGG homogeneous-conversion equations are not in the public source set [3]; the diameter scale-effect is applied entirely through the Stages 2 and 3 gradient limits. Production calculations should use the BGGG / DM20 reference algorithm or audited software calibrated against the BGGG worked examples.
Implementation note — Stages 2 and 3. The fraction-of-the-gap form used here is a screening simplification of the BGGG gradient limit. The fraction equals the cone-to-pile diameter ratio Dc / Db,eq, so a larger pile climbs more slowly into a strong layer. The implementation is verified against the BGGG worked examples to within 5 % relative error on qb (the BGGG examples are tabulated to 0.1 MPa, which limits cross-check precision).
  • Mechanical-cone qc values are reduced by the ω factors of [3] before the resampling step (ω = 1.30 for M1 and M2 in tertiary clay, 1.15 for M4 in tertiary clay, 1.00 elsewhere). The default cone is CPT-E (electric, ω = 1.00).
  • If ztoe is below the deepest CPT reading, the deepest layer's qc is used as a fall-back and a warning note flags the extrapolation.

Base resistance

5. Base-resistance closure

Rb = αb · eb · β · λ · Ab · qb
Notation
αb
Installation factor for base resistance, by pile type and soil category. Defaults are screening values; production calculations must use DM20 / ATG values via the override block.
eb
Scale / fissuring factor. eb = 1.0 for most soils; for tertiary over-consolidated clay (Boom, Ypres): eb = max[0.476, 1 − 0.01 (Db,eq / Dc − 1)].
β
Shape factor. Circular / square: 1.0; rectangular: (1 + 0.3 a / b) / 1.3.
λ
Relaxing-base reduction. λ = 1.0 for non-relaxing enlarged bases and standard shafts; relaxing prefab enlarged bases (Db > Ds + 0.05 m on a driven pile) require a manual override since the explicit DM20 reduction is not in the public source set.
αb and αs screening defaults. The exact installation factors for each pile system are published in DM20 [2] and in the certified ATG documents [1], [8]. They are not reproduced in the public Belgian practice report [3], so the screening tool ships with internal defaults at conservative midpoints commonly cited in Belgian pile design practice. The defaults are intended for screening only; production calculations must use the actual DM20 / ATG values for the specific pile system, entered through the ATG override block. The runtime emits a warning note when the defaults are used without an override.

Shaft resistance

6. Shaft resistance and the η*p table

Rs = χs · Σi αs,i hi qs,i
qs,i = η*p,i · qc,m,i · 1000 [kPa, with qc,m in MPa]

qc,m,i is the layer-mean cone resistance over the intersection of layer i with the pile shaft (zhead ≤ z < ztoe). η*p depends on soil type and on qc,m through the public Belgian table [3] §A.1:

Clay: 1 ≤ qc,m ≤ 4.5 MPa: η*p = 1/30; qc,m > 4.5: qs = 150 kPa cap
Loam / silt: 1 ≤ qc,m ≤ 6 MPa: η*p = 1/60; qc,m > 6: qs = 100 kPa cap
Sandy clay / clayey sand: 1 ≤ qc,m ≤ 10 MPa: η*p = 1/80; qc,m > 10: qs = 125 kPa cap
Sand: 1 ≤ qc,m ≤ 10: η*p = 1/90; 10 < qc,m ≤ 20: qs = 110 + 4 (qc,m − 10) kPa; qc,m > 20: qs = 150 kPa cap
  • Layers whose layer-mean qc,m is below 1 MPa are excluded from positive shaft friction [3].
  • Peat / organic layers are also excluded regardless of qc,m.
  • Cyclic compression / tension loading triggers an αs reduction by 1.33 per [3]; the screening tool does not apply this reduction automatically. Cyclic loading users must reduce αs manually via the ATG override.
  • The η*p mapping from the Stage 3 NEN6740 classification is approximate. The UI exposes a per-layer override.

Factor chain

7. Model, correlation, and partial-resistance factors

Rc = Rb + Rs
Rc,cal = Rc / γRd
Rc,k = Rc,cal / max(ξ3, ξ4) (single-CPT branch — see callout)
Rb,k = Rc,k · Rb / Rc, Rs,k = Rc,k · Rs / Rc
Rc,d = Rb,k / γb + Rs,k / γs
Single-CPT correlation factor. The full Eurocode 7 / Belgian rule is Rc,k = min[(Rc,cal)avg / ξ3, (Rc,cal)min / ξ4]. With one CPT in scope, the average and the minimum collapse to the single calculated value, so the governing branch is max(ξ3, ξ4). In every cell of the public ξ tables [3] §A.3, ξ3 ≥ ξ4, so ξ3 governs the single-CPT case. Genuine multi-CPT statistical treatment (Rc,cal,j per CPT, separate average and minimum branches) is out of scope for this screen.
Public values from [3]
γRd
Driven / jacked: 1.00 / 1.00 / 1.00. Screw: 1.30 / 1.10 / 1.00. CFA: 1.35 / 1.20 / 1.10. Bored: 1.20 / 1.20 / 1.10. Columns are γRd1 (no SLT) / γRd2 (SLT comparable) / γRd3 (SLT on job site).
ξ3, ξ4
Five-column table by CPT density (1 CPT / 10 m² … 1 CPT / 1000 m²) and three rows by pile count (1–3, 4–10, > 10). Reproduced verbatim from [3] §A.3.
γb, γs
Without QA: γb = 1.00 (driven), 1.07 (screw), 1.10 (CFA), 1.20 (bored); γs = 1.00 for all. With QA (verified quality conditions via ATG): γb = γs = 1.00 for all.

The ULS check is Fc,d + Fnk,d ≤ Rc,d; Fnk,d contributes only when downdrag is selected (see §8). Per [3], the negative-friction action need not be combined simultaneously with transient loads — the screening tool reports the worse of the transient combination and the long-term downdrag combination.

Negative skin friction

8. Fnk — slip and analogy methods

When the soil around the pile may settle relative to the pile, positive shaft friction is replaced by a downward dragging action over the affected layers. The screening tool offers a downdrag preset (none / moderate / severe) that follows the [3] settlement trigger logic, plus a user-entered neutral-plane depth zNP. Layers above zNP lose positive friction and contribute to Fnk by the larger of two methods.

Fnk,slip = χs · Σi ↑ hi · K0,i · tan(δi) · σ′v,i
Fnk,analogy = χs · Σi ↑ αs,i hi qs,i
Fnk,rep = max[ Fnk,slip, Fnk,analogy ]
Fnk,d = γF · multiplier · Fnk,rep, γF = 1.0 per [3]
Notation
K0,i
Earth-pressure-at-rest coefficient: K0 = 1 − sin φ′.
δi
Pile-soil interface friction angle. δ = φ′ for cast-in-situ concrete piles; δ = 0.75 φ′ for precast concrete and steel piles. The product K0 · tan(δ) is floored at 0.25.
σ′v,i
Effective vertical stress at the layer mid-depth, computed from the Stage 4 unit weights and the Stage 1 / user water table.
multiplier
1.0 for the severe preset (full Fnk), 0.5 for the moderate preset (half Fnk) per the [3] settlement-trigger rule.
  • The settlement-trigger rule: > 10 cm or not calculated → full Fnk; 4–10 cm → half Fnk; 2–4 cm → no negative load but exclude positive friction in the affected layers; < 2 cm → may be neglected (designer decides whether positive friction may be counted in the affected layers).
  • The screening tool does not itself compute the surface settlement; the user selects the preset that matches an external settlement analysis under fill, surcharge, or groundwater lowering.

SLS settlement

9. Single-pile settlement — Belgian load-transfer method

The SLS settlement implements the Allani–Huybrechts (2022) load-transfer model [5]: hyperbolic shaft (t-z) and base (q-z) springs are calibrated to the Belgian ULS resistance convention (ultimate resistance corresponds to a base settlement of 10 % of Db). An axial-force-and-displacement march along the pile, with bisection on the trial base settlement zb, recovers the pile-head settlement under the representative SLS load Frep.

Shaft (t-z): t(w) = w / (1/ks + w/tmax)
Base (q-z): q(zb) = zb / (1/kb + zb/qmax)
t10%,i = αs,i · qs,i, qb,10% = Rb / Ab
tmax,i = t10%,i · (1 + 10 Ms,i)
qmax = qb,10% · (1 + 4.55 / Mb)
ks,i = tmax,i / (Ms,i · Ds)
kb = Eb / βb, βb ≈ 0.455 Db
Notation
Ms,i, Mb
Dimensionless shaft and base flexibility / stiffness factors from the > 100-instrumented-load-test database in [5]; tabulated by pile type and soil group (sand / mixed / clay).
Eb
Soil modulus at the base level under the SLS stress state. Default: oedometric modulus from the Stage 4 Hardening-Soil law evaluated at σ′v(ztoe) + 0.5 qb,10%; falls back to a CPT correlation Eb ≈ αE · qc,b · 1000 (αE = 3 in sand, 5 in mixed, 7 in clay) when Stage 4 parameters are absent. User-overridable.
βb
Calibrated coefficient from [5]; equivalent to ½ (1 − ν²) Db at ν = 0.3, the average flexible-circle approximation zb ≈ q Db (1 − ν²) / (2 Eb).

The pile is discretized into segments of length Δz = min(0.20 m, L / 50). At each trial zb, a single FD march from the toe upward integrates the load-transfer ODE:

d²w/dx² = (χs / (Ep · Ap)) · t(w(x))
N(L) = q(zb) · Ab, N(L − Δz) = N(L) + χs · ti(w) · Δz
w_local += N · Δz / (Ep · Ap) (sign: pile in compression, w grows toward the head)

An outer bisection on zb drives Nhead to Frep within tolerance. The pile-head settlement is shead = zb + Σi Ni · Δzi / (Ep Ap). The SLS pass criterion is shead ≤ sallow.

  • Layers above the neutral plane (when downdrag is set) are inert in the t-z march: they do not mobilize positive friction, so N is conserved through them and w grows only by elastic compression.
  • An optional simplified typical-curve method is offered for short, homogeneous-profile piles; a warning flags pile lengths > 15 m or strongly heterogeneous profiles for which the method is not suited.

Interactive section view

10. Interactive section view

The pile capacity panel includes a dedicated interactive SVG section view of the pile and the soil column, intended as the engineer's primary visual cue. The view is independent of the slope-stability canvas; it shares only the low-level pan-zoom-snap utilities of the Stage 6 canvas family.

  • Drag the pile toe handle vertically to set ztoe; drag the head handle to set zhead; drag the shaft / base edge handles to change Ds / Db.
  • Click any soil layer to snap the toe to its top, mid, or bottom. Layer-boundary snap applies within ±0.10 m; otherwise a 0.10 m grid snap fires. Hold Shift during a drag to disable snapping.
  • Hover any layer to see qc,m, η*p, qs, αs, and the per-layer Rs contribution (or "above neutral plane — excluded from positive friction").
  • The active-shaft band (green) marks the layers that contribute to Rs; the downdrag band (red hatch) marks the layers above the neutral plane when downdrag is selected. The neutral plane itself is a draggable dashed orange line.
  • All numeric inputs in the left column stay synchronized with the drag gestures and vice versa; on each change the analysis recomputes and the four Chart.js panels (De Beer transformation chain, per-layer shaft friction, load–settlement curve, axial-force distribution) update.

Outputs and limitations

11. Deliverables and boundaries of validity

  • Rb, Rs, Rc, Rc,cal, Rc,k, Rc,d with the full factor-chain audit, and the ULS utilisation (Fc,d + Fnk,d) / Rc,d.
  • qb, the De Beer transformation chain (qc, qh, qd, qu, qp) overlay vs depth, and the per-layer shaft friction profile.
  • Fnk,slip, Fnk,analogy, and the design Fnk,d when downdrag is selected.
  • shead at Frep, the load–settlement curve, the axial-force distribution N(z), and the SLS utilisation shead / sallow.
  • Multi-CPT statistical treatment (separate ξ3-on-average and ξ4-on-minimum branches across multiple CPTs) is out of scope.
  • Tension / uplift, lateral loading, seismic, buckling, pile-group settlement (equivalent raft), and structural pile design are out of scope.
  • αb, αs, γRd, γb defaults are screening midpoints from public Belgian practice; production calculations must use the actual DM20 / ATG values via the override block.
  • De Beer Stage 1 is implemented as identity; the diameter scale-effect is captured entirely through the Stages 2 / 3 gradient limits.

References

References

References were verified against their primary sources on 2026-05-06. URLs are reproduced for traceability.

  • [1] BUtgb-UBAtc. Informatieblad 2025/3: Ontwerp van palen en micropalen, versie van 16 september 2025. PDF.
  • [2] Buildwise. Richtlijnen voor de toepassing van de Eurocode 7 in België volgens de NBN EN 1997-1 ANB. Deel 1: het grondmechanische ontwerp in de uiterste grenstoestand (UGT) van axiaal belaste funderingspalen en micropalen op basis van statische sonderingen (CPT's) — Dimensioneringsmethode 20, 2020. Publication page; document access requires Buildwise registration.
  • [3] Huybrechts, N., De Vos, M., Bottiau, M., and Maertens, L. Design of piles — Belgian practice, Buildwise / BBRI national report, 2016. PDF.
  • [4] BGGG-GBMS. Reference document for the application of the De Beer method for the prediction of the ultimate unit pile base resistance from CPT; the version cited internally in the document is dated 11-09-2002. PDF.
  • [5] Allani, M. and Huybrechts, N. Pile settlement under vertical static load: SLS design method based on Belgian experience. Proc. 20th International Conference on Soil Mechanics and Geotechnical Engineering (ICSMGE), Sydney, 2022. PDF.
  • [6] Buildwise (publication info). NBN EN 1997-1 ANB: Eurocode 7 — Geotechnisch ontwerp — Deel 1: Algemene regels — Nationale bijlage, publication date 2022. Publication info.
  • [7] NBN. NBN EN 1997-2:2024 — published on the NBN catalogue but not yet applicable in Belgium pending publication of its Belgian National Annex. NBN EN 1997-2:2007 with its national annex remains applicable during the transition; the first-generation Eurocodes are scheduled to be withdrawn on 30 March 2028.
  • [8] BCCA. Publication ATG texts — Foundation piles, 8 May 2023. News item; the first 12 ATG dossiers covering soil-displacement screw piles were issued on 2 May 2023.
  • [9] Vlaanderen, Departement Mobiliteit en Openbare Werken. Standaardbestek 260 voor kunstwerken en waterbouw, versie 3.0, July 2025. Publication page.