A concrete pile of 40 cm diameter is driven into a homogeneous mass of cohesionless soil. The pile carries a safe load of 650 kN. A static cone penetration test conducted at the site indicates an average value of qc = 40 kg/cm^2 along the pile and 120 kg/cm^2 below the pile tip. Compute the length

Question

A concrete pile of 40 cm diameter is driven into a homogeneous mass of cohesionless soil. The pile carries a safe load of 650 kN. A static cone penetration test conducted at the site indicates an average value of [latex]q_{c}=40 kg / cm ^{2}[/latex] along the pile and 120 [latex]kg / cm ^{2}[/latex] below the pile tip. Compute the length of the pile with [latex]F_{s}=2.5[/latex]. (Fig. Ex. 15.19)

Accepted Answer

From Eq. (15.51a)

[latex]q_{b}=q_{p} ext { (cone) }[/latex] (15.51a)

[latex]q_{b} ext { (pile) }=q_{p} ext { (cone) }[/latex]

Given, [latex]q_{p}=120 kg / cm ^{2}[/latex], therefore,

[latex]q_{b}=120 kg / cm ^{2}=120 imes 100=12000 kN / m ^{2}[/latex]

Per Section 15.12, [latex]q_{b}[/latex] is restricted to 11,000 [latex]kN / m ^{2}[/latex].

Therefore,

[latex]Q_{b}=A_{b} q_{b}=\frac{3.14}{4} imes 0.4^{2} imes 11000=1382 kN[/latex]

Assume the length of the pile = L m

The average, [latex]\bar{q}_{c}=40 kg / cm ^{2}[/latex]

PerEq. (15.52a),

[latex]f_{s}=\frac{\bar{q}_{c}}{2}( kPa )[/latex] (15.52a)

[latex]f_{s}=\frac{\bar{q}_{c}}{2} kN / m ^{2}=\frac{40}{2}=20 kN / m ^{2}[/latex]

Now, [latex]Q_{f}=f_{s} A_{s}=20 imes 3.14 imes 0.4 imes L=25.12 L kN[/latex]

Given [latex]Q_{a}=650 kN ext {. With } F_{s}=2.5, Q_{u}=650 imes 2.5=1625 kN[/latex].

Now, [latex]1625=Q_{b}+Q_{f}=(1382+25.12 L) kN[/latex]

or [latex]L=\frac{1625-1382}{25.12}=9.67 m ext { or say } 10 m[/latex]

The pile has to be driven to a depth of 10 m to carry a safe load of 650 kN with [latex]F_{s}=2.5[/latex].

Question 15.19: A concrete pile of 40 cm diameter is driven into a homogeneo...

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