Pile Bearing Capacity from SPT

Theory: Piles

How Aoki-Velloso's and Décourt-Quaresma's semi-empirical methods estimate a pile's bearing capacity from the N values of an SPT boring, and how the allowable load follows.

Bearing capacity

An axially loaded pile passes its load to the soil through friction along its shaft and the resistance under its tip. At failure, its capacity is the sum of the two.

R = R_p + R_l = r_p A_p + U \sum r_l\, \Delta l

r_p: unit tip resistance · A_p: tip area · U: shaft perimeter · r_l: unit shaft friction in each stretch of length Δl

In Brazil, r_p and r_l usually come from correlations with the SPT's N, a test run on almost every site. The methods are semi-empirical: calibrated on load tests of certain pile types and soils, they should be used within that context.

Aoki-Velloso

Aoki and Velloso (1975) started from the cone penetration test (CPT), taking the pile's tip as a full-scale cone. The cone's tip resistance relates to N through K, and its sleeve friction to its tip resistance through α; the factors F₁ and F₂ account for the difference in scale and the way the pile is built.

r_p = \frac{K N_p}{F_1}

N_p: N at the tip's depth · N_l: N of each stretch of the shaft

Soil	K (MPa)	α (%)
Sand	1.00	1.4
Silty sand	0.80	2.0
Silty clayey sand	0.70	2.4
Clayey sand	0.60	3.0
Clayey silty sand	0.50	2.8
Silt	0.40	3.0
Sandy silt	0.55	2.2
Sandy clayey silt	0.45	2.8
Clayey silt	0.23	3.4
Clayey sandy silt	0.25	3.0
Clay	0.20	6.0
Sandy clay	0.35	2.4
Sandy silty clay	0.30	2.8
Silty clay	0.22	4.0
Silty sandy clay	0.33	3.0

Pile	F₁	F₂
Franki	2.50	5.00
Precast concrete	1 + D/0.80	2F₁
Steel	1.75	3.50
Bored	3.00	6.00
CFA and root	2.00	4.00

Décourt-Quaresma

Décourt and Quaresma (1978) related N directly to the resistances of precast concrete piles. At the tip, N_p is the mean of the N at the tip and those just above and below; along the shaft, N_l is the mean along it, without those used at the tip, each N between 3 and 50.

r_p = \alpha\, C\, N_p

C: coefficient of the soil at the tip · α and β: factors for the pile type (Décourt, 1996)

Soil at the tip	C (kPa)
Clays	120
Clayey silts (residual soil)	200
Sandy silts (residual soil)	250
Sands	400

Pile	α clay / silt / sand	β clay / silt / sand
Driven	1.00 / 1.00 / 1.00	1.00 / 1.00 / 1.00
Bored	0.85 / 0.60 / 0.50	0.80 / 0.65 / 0.50
CFA	0.30 / 0.30 / 0.30	1.00 / 1.00 / 1.00
Root	0.85 / 0.60 / 0.50	1.50 / 1.50 / 1.50

Allowable load

P_a = \frac{R}{\mathrm{FS}}

NBR 6122 asks for FS = 2 when the capacity comes from semi-empirical methods, without load tests

In bored piles, NBR 6122 holds the tip's share to 20% of the allowable load, as the base is hard to clean: the shaft must carry the rest.
The two methods often differ, sometimes widely; comparing them, and with load tests from the region, gives a measure of the uncertainty.
The pile's allowable load also depends on its settlement and the structural strength of its shaft, which this app doesn't check.

References

Aoki, N.; Velloso, D. A. An approximate method to estimate the bearing capacity of piles. In: Panamerican Conference on Soil Mechanics and Foundation Engineering, 5., Buenos Aires, 1975. v. 1, p. 367–376.
Décourt, L.; Quaresma, A. R. Capacidade de carga de estacas a partir de valores de SPT. In: Congresso Brasileiro de Mecânica dos Solos e Engenharia de Fundações, 6., Rio de Janeiro, 1978. v. 1, p. 45–53.
Décourt, L. et al. Análise e projeto de fundações profundas. In: Hachich, W. et al. (ed.). Fundações: teoria e prática. São Paulo: Pini, 1996.
Cintra, J. C. A.; Aoki, N. Fundações por estacas: projeto geotécnico. São Paulo: Oficina de Textos, 2010.
ABNT. NBR 6122: Projeto e execução de fundações. Rio de Janeiro, 2019.

Enter the pile — type, section, size and length —, the soil layers and the N values of an SPT boring to estimate the bearing capacity and allowable load by Aoki-Velloso's and Décourt-Quaresma's methods.

Pile

Type

Section

Diameter, DmLength, Lm

Tip area A_p = 0.1257 m², perimeter U = 1.257 m. The pile's head is at the surface.

Layers

From the top down, each layer with its soil in Aoki and Velloso's classification and the depth of its bottom. They must reach the tip.

SPT boring

Depth (m)	N_SPT

One N per test, usually every meter. They must reach the tip; the one just below it counts in Décourt-Quaresma's tip.

Design

Global FSWorking load, PkN

P_a = R/FS; NBR 6122 asks for FS = 2 with semi-empirical methods. Allowable loads below P are marked.

Each N stands for the stretch between its test and the one above (the first from the surface); the pile's head is at the surface, and its tip takes the N of the stretch it's in.
Aoki-Velloso: r_p = K·N_p/F₁ and r_l = α·K·N/F₂, with K and α from each stretch's soil (Aoki and Velloso, 1975) and F₁ and F₂ from the pile type (Cintra and Aoki, 2010).
Décourt-Quaresma: r_p = α·C·N_p, N_p being the mean of the N at the tip and just above and below it; r_l = β·10(N_l/3 + 1), N_l being the mean along the shaft without the N used at the tip, each between 3 and 50. α and β from Décourt (1996) for bored, CFA and root piles; 1 for driven ones.
N above 50 is taken as 50. The allowable load is R/FS (NBR 6122 asks for FS = 2 with semi-empirical methods); in bored piles, the tip carries at most 20% of it.
The length chart puts the tip at each test's depth, with the same pile and profile.
The 3D is an illustration: the bars over the head of cast-in-place piles (φ16) and the Franki pile's base show the work as built but aren't designed here, and the base isn't counted in the capacity.