Pile Point-Bearing Capacity Formula and Calculator

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Pile Point-Bearing Capacity Formula and Calculator

Civil Engineering Application & Design Resources

Theoretical Pile Point-Bearing Capacity Equations and Calculator

The theoretical point-bearing capacity (also known as the tip resistance and point capacity), Q_p, of a single pile can be calculated in much the same manner as for a footing. Since the pile size, B, is small, the (1/2) · γ · B · N_γ term is generally omitted.

Preview: Pile Point-Bearing Capacity Calculator

Eq. 1a,
SI Units
Q_p = A_p ( 0.5 · ρ · g · B · N_γ + c · N_c + ρ ·g · D_f · N_q )

Eq. 1b,
US Imperial units
Q_p = A_p ( 0.5 · γ · B · N_γ + c · N_c + γ · D_f · N_q )

For cohesionless (granular) soil, c = 0. For sands and silts, the tip point-bearing capacity increases down to a critical depth, D_c, after which it is essentially constant. For loose sands (i.e., with relative densities less than 30%) and loose silts, the critical depth is taken as 10B. For dense sands (relative densities above 70%), and dense silts, the critical depth is 20B. Between relative densities of 30% and 70%, the critical depth can be interpolated between 10B and 20B.

Eq. 2a
SI Units
cohesionless; D ≤ D_c
Q_p = A_p · ρ · g · D_f · N_q

Eq. 2a
US Imperial units
cohesionless; D ≤ D_c
Q_p = A_p · γ · D_f · N_q

For cohesive soils with θ = 0°, N_q = 1 and the γ · D_f term is approximately cancelled by the pile weight. N_c = 9 for driven piles of virtually all conventional dimensions. (See Table 1 and Table 2.)

Eq. 3
cohesive
Q_p = A_p · c · N_c ≈ 9 · A_p · c

Where

Q_p = capacity lbf, N
A_p = pile contact area ft², m²
ρ = density, lbm/ft³, kg/m³
g = acceleration of gravity, ft/sec², m/s²
B = diameter or width, ft, m
N_γ = capacity factor, Table 3
c = cohesion, lbm/ft², kg/m²
N_c = capacity factor
D_f = pile depth, ft, m
N_q = capacity factor
γ = specific weight
Φ =

Table 1 Meyerhof Values of N_q for Piles*

Φ	0°	25°	28°	30°	32°	34°	36°	38°	40°	42°	45°
driven	8	12	20	25	35	45	60	80	120	160	230
drilled	4	5	8	12	17	22	30	40	60	80	115

Table 2 Values of N_c for Driven Piles*
(square and cylindrical perimeters)

D_f / B	N_c
0	6.3
1	7.8
2	8.5
≥ 4	9

Table 3
Terzaghi Bearing Capacity Factors

Φ	N_γ
0°	0.0
5°	0.5
10°	1.2
15°	2.5
20°	5.0
25°	9.7
30°	19.7
35°	42.4
40°	100.4
45°	297.5

Table 4
Recommended Values of Adhesion, (piles in clay)

Pile Type	consistency	cohesion, c ( lbf/ft² (kPa) )
timber or concrete	very soft	0–250 (0–12)
	soft	250–500 (12–24)
	medium stiff	500–1000 (24–48)
	stiff	1000–2000 (48–96)
	very stiff	2000–4000 (96–192)
steel	very soft	0–250 (0–12)
	soft	250–500 (12–24)
	medium stiff	500–1000 (24–48)
	stiff	1000–2000 (48–96)
	very stiff	2000–4000 (96–192)

*Significant variation in N_q has been reported by various researchers. The actual value is highly dependent on # and the installation method.

Derived from Foundations and Earth Structures Design Manual, NAVFAC DM-7.2, 1986, Fig. 2, p. 7.2-196.

Source

Civil Engineering Engineering Reference Reference Manual for the PE Exam for the PE Exam
Fourteenth Edition
Michael R. Lindeburg, PE