Question 11.9: For Prob. 11.4, determine the downdrag load on the concrete ...
For Prob. 11.4, determine the downdrag load on the concrete piers due to settlement of the sand during the earthquake. For the loose sand layer, the friction angle Φ = 30°, total unit weight \gamma_{t} = 17 kN/m³, and use the equation k_{0} = 1 – sin Φ’. The groundwater table is well below the bottom of the sand layer.
From Prob. 11.3, the thickness of the loose sand layer subjected to settlement during the earthquake is 3 m, or L = 3 m. The diameter of the pier = 0.6 m. There is no groundwater, hence u = 0 and \sigma_{v}^{\prime}=\sigma_{v}.
\sigma_{v}^{\prime}=\sigma_{v} and using average conditions at z = 1.5 m
\sigma_{v}^{\prime}=\sigma_{v} = (1.5 m)(17 kN/m³) = 25.5 kPa
For a concrete pier: \phi_{w}=3 / 4 \phi=3 / 4\left(30^{\circ}\right)=22.5^{\circ}
k_{0}=1-\sin \phi^{\prime}=1-\sin 30^{\circ}=0.5
Substituting these values into Eq. (11.14) and therefore Q_{D} equals:
Q_{D}=(2 \pi R L)\left(\sigma_{v}^{\prime} k \tan \phi_{w}\right)= (2π)(0.3 m)(3 m)(25.5 kPa)(0.5)(tan 22.5°)
= 30 kN