H-piles are driven to 7 m depth in homogeneous sand. Pile surface area is 3 m² per metre length. The effective friction angle is 32° and wall-friction angle $\delta=23^\circ$. The water table is 2 m deep; soil unit weights above and below it are 16 and 19 kN/m³. Take earth-pressure coefficient $K=1$. Find total axial frictional resistance in kN, to one decimal place.
Use shaft resistance $dQ_s=K\sigma_v\prime\tan\delta\,p\,dz$ with perimeter $p=3$ m. With $\gamma_w=10$ kN/m³, effective stress is $16z$ for $0<z<2$ and $32+9(z-2)$ for $2<z<7$. Its depth integral is $16(2^2)/2+32(5)+9(5^2)/2=304.5$ kN/m. Therefore $Q_s=3\tan23^\circ(304.5)=387.8$ kN. The friction angle of the sand is not substituted for the separately supplied interface angle.
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