Parameter tables¶

The coefficients of the semi-empirical methods, according to Cintra & Aoki, Fundações por estacas: projeto geotécnico.

Coefficients with the same name, different meanings

\(\alpha\) appears in all three methods meaning different things:

In Aoki-Velloso it is the friction ratio \(f_s/q_c\), dimensionless, in %.
In Décourt (1996) it is a toe correction factor, dimensionless.
In Teixeira it is a stress, in kPa, that multiplies \(N_{SPT}\).

The same goes for \(\beta\). They are not interchangeable.

Aoki-Velloso¶

Coefficient K and friction ratio α¶

Table 1.3 — Aoki and Velloso (1975).

Soil	\(K\) (MPa)	\(\alpha\) (%)
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

K and α are inversely related

Clean sand has a high \(K\) (1.00 MPa) and a low \(\alpha\) (1.4 %): it resists a lot at the toe and little by friction. Clay is the opposite — 0.20 MPa and 6.0 %. That is why a pile in clay works by its shaft and a pile in dense sand works by its toe.

Correction factors F1 and F2¶

Table 1.5 — updated values, adapted from Aoki and Velloso (1975).

Pile type	\(F_1\)	\(F_2\)
Franki	2.50	\(2F_1\)
Steel	1.75	\(2F_1\)
Precast	\(1 + D/0.80\)	\(2F_1\)
Bored	3.0	\(2F_1\)
Root, CFA and Omega	2.0	\(2F_1\)

The factors are divisors: the larger they are, the lower the capacity. The scale reflects the effect of construction on the soil — driven piles densify the ground and get the smallest factors; bored piles, which relieve stresses, get the largest.

Where the updated values came from

The original table (1975) only had Franki 2.50, Steel 1.75 and Precast 1.75.

Precast: Aoki (1985) found that the method was too conservative for small diameters and proposed \(F_1 = 1 + D/0.80\), with \(D\) in metres — the diameter or side of the shaft section.
Bored: \(F_1 = 3.0\) and \(F_2 = 6.0\), from Aoki and Alonso (1991).
Root, CFA and Omega: \(F_1 = 2.0\) and \(F_2 = 4.0\), from Velloso and Lopes (2002).

Décourt-Quaresma¶

Characteristic soil coefficient C¶

Table 1.6 — Décourt and Quaresma (1978). Fitted with 41 load tests on precast concrete piles.

Soil type	\(C\) (kPa)
Clay	120
Clayey silt *	200
Sandy silt *	250
Sand	400

* weathered rock — residual soils.

Décourt's α and β factors (1996)¶

Tables 1.7 and 1.8. Note that the classification is in three families — clays, intermediate soils and sands —, not by the full soil code.

Factor α, on the toe resistance:

Soil type	Bored in general	Bored (bentonite)	CFA	Root	Grouted under high pressure
Clays	0.85	0.85	0.30 *	0.85 *	1.00 *
Intermediate soils	0.60	0.60	0.30 *	0.60 *	1.00 *
Sands	0.50	0.50	0.30 *	0.50 *	1.00 *

Factor β, on the shaft resistance:

Soil type	Bored in general	Bored (bentonite)	CFA	Root	Grouted under high pressure
Clays	0.80 *	0.90 *	1.00 *	1.50 *	3.00 *
Intermediate soils	0.65 *	0.75 *	1.00 *	1.50 *	3.00 *
Sands	0.50 *	0.60 *	1.00 *	1.50 *	3.00 *

* indicative values only, given the small amount of data available.

The direction of the variation: clay on top, sand at the bottom

In \(\alpha\), clay gets the highest value (0.85) and sand the lowest (0.50). It is counter-intuitive for those who expect sand to resist more — but the factor does not measure resistance; it measures how much of the original method can be used in that soil with that construction method. Boring relieves the toe more in sand than in clay, and that is what the factor penalises.

Swapping the rows reverses the result: a bored pile in sand would get 70 % more toe resistance than it should.

Three types are left out

Precast, steel and Franki piles keep \(\alpha = \beta = 1\) — the original 1978 method, without correction.

Teixeira¶

Valid for \(4 < N_{SPT} < 40\).

Parameter α (kPa)¶

Table 1.9 — Teixeira (1996). It depends on the soil and on the pile type.

Soil	Precast and steel section	Franki	Open bored	Root
Silty clay	110	100	100	100
Clayey silt	160	120	110	110
Sandy clay	210	160	130	140
Sandy silt	260	210	160	160
Clayey sand	300	240	200	190
Silty sand	360	300	240	220
Sand	400	340	270	260
Sand with gravel	440	380	310	290

Parameter β (kPa)¶

Table 1.10 — it depends only on the pile type.

Pile type	\(\beta\) (kPa)
Precast and steel section	4
Franki	5
Open bored	4
Root	6

Shaft friction in soft sensitive clay¶

Table 1.11 — for the case in which the method does not apply: floating precast concrete piles in thick layers of soft sensitive clay, with \(N_{SPT}\) normally below 3. Here \(r_L\) is tabulated directly, by the nature of the sediment.

Sediment	\(r_L\) (kPa)
Fluvial-lagoonal clay (SFL)	20 to 30
Transitional clay (AT)	60 to 80

SFL — Holocene fluvial-lagoonal and bay clays, down to about 20 to 25 m deep, with \(N_{SPT} < 3\), dark grey, slightly overconsolidated.

AT — Pleistocene transitional clays, underlying the SFL, with \(N_{SPT}\) from 4 to 8, sometimes light grey, with higher preconsolidation stresses than the SFL.

The program's table covers more types than the source

Teixeira tabulated four pile types. SPX offers seven, and the remaining three — bored with slurry, CFA and Omega — receive extrapolated values, not published by the author.

Record this in the calculation report when using the method for these types.

Coefficient m for Kh¶

Used in the soil reaction, not in the bearing capacity. Selected by the dominant fraction — sandy and silty soils use the sand table, clayey soils the clay table.

Sands and silts (kN/m⁴)¶

\(N_{SPT}\)	Density	\(m\)
1–6	Loose	1500 – 2750
7–39	Medium dense	3000 – 7850
40–49	Dense	8000 – 14300
50	Very dense	15000

The table is defined point by point for each integer \(N_{SPT}\), with a linear progression per range: about 154 kN/m⁴ per blow in the medium dense range and 700 in the dense range.

Clays (kN/m⁴)¶

\(N_{SPT}\)	Consistency	\(m\)
0	Semi-liquid	250
1–2	Very soft	750 – 1125
3–5	Soft	1500 – 2500
6–11	Medium	3000 – 4667
12–21	Stiff	5000 – 6800
22–29	Very stiff	7000 – 8750
30	Hard	9000

Capping outside the range

Above the last tabulated \(N_{SPT}\) — 50 for sands, 30 for clays — the program adopts the last value, without extrapolating. A clay with \(N = 45\) receives the same \(m\) as one with \(N = 30\).

It is the conservative decision, but it means that, in very strong soils, the model underestimates the horizontal stiffness and overestimates the displacements.

Soil deformation modulus¶

Used in settlement. Aoki (1984):

Pile type	\(E_0\)
Driven	\(6 \, K \, N_{SPT}\)
CFA	\(4 \, K \, N_{SPT}\)
Bored	\(3 \, K \, N_{SPT}\)

with \(K\) from the Aoki-Velloso table.