Compute pile capacity of identical piles in the same soil A = cross-sectional of 20-in. square pile = 400 sq. in. (2580 cm²) L = length of the pile = 40 ft (12.2 m) W = weight of ram = 3.75 tons (33.4 kN) P = weight of pile = 8.25 tons (73.4 kN) h = fall of ram = 4.0 ft (1.22 m) H = 12 h, the

Question

Compute pile capacity of identical piles in the same soil
A = cross-sectional of 20-in. square pile = 400 sq. in. (2580 cm²)
L = length of the pile = 40 ft (12.2 m)
W = weight of ram = 3.75 tons (33.4 kN)
P = weight of pile = 8.25 tons (73.4 kN)
h = fall of ram = 4.0 ft (1.22 m)
H = 12 h, the fall of ramin. = 48 in. (121.92 cm)
S = penetration per blow = 0.15 in. (0.381 cm)
R = resistance of pile according to various formulas
E = modulus of elasticity of concrete (2,000,000 psi)[latex] 2 imes10^{6}[/latex] psi (13,789 MPa)
e = coefficient of restitution
k = hammer blow efficiency from Equation

Accepted Answer

1 By the Engineering News formula (Eq. (15.8))

[latex]R=\frac{2WH}{S+C}[/latex] (15.8)

[latex]R=\frac{2 imes 3.75 imes 4.0}{0.15+0.1} =120 tons \left(1067 kN ight)[/latex]

2 By the Modified Engineering News formula (Eq. (15.9))

[latex]R=\frac{2WH}{S+0.1\left(P/W ight) }[/latex] (15.9)

[latex]R=\frac{2 imes 3.75 imes 4.0}{0.15+0.1 \left(16,500/7500 ight) } =81 tons \left(720 kN ight)[/latex]

3 By the Terzaghi formula (Eq. (15.10))

[latex]\frac{AE}{L} =400 imes \frac{2,000,000}{40 imes 12} = 1,660,000 lb/in.\left(2907 kN/cm ight)[/latex]

[latex]WH\left(\frac{W+Pe^{2} }{W+P} ight)=7500 imes 48\left(\frac{7500+16,500 imes 0.5^{2} }{7500+16,500} ight) =174,000[/latex]

Then substituting in Equation (15.10):

[latex]R=\frac{AE}{L} \left[-0.15\pm \sqrt{0.15^{2}+\frac{2WH\left(W+Pe^{2} ight) /\left(W+P ight) }{AE/L} } ight][/latex] (15.10)

[latex]R=1660,000\left[-0.15\pm \sqrt{0.15^{2} }+\frac{174,000 imes 2}{1660,000} ight][/latex]
[latex]=1660,000\left(-0.15\pm 0.48 ight)[/latex]

Since the resistance cannot be a negative quantity,
R = 0.33 × 1,660,000 = 550,000 lb = 275 tons (2446 kN)
Comparison of computed pile capacities:
1 Engineering News formula 120 tons (1067 kN)
2 Modified Engineering News formula 81 tons (720 kN)
3 Terzaghi formula 275 tons (2446 kN).
Based on aforementioned results, there are significant variations, therefore, it should noted that pile driving formulas are only a guide to the engineer in predicting safe pile bearing capacities and should be used with caution and judgment.

Question 15.1: Compute pile capacity of identical piles in the same soil A ...

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