Question 13.2: Use the data from Prob. 13.1 and an effective friction angle...
Use the data from Prob. 13.1 and an effective friction angle Φ’ between the pile surface and the surface soil layer and sand layer of 28°. Assume that k_{0} = 0.5 and that the last location for the earthquake-induced pore water pressures to dissipate will be just above the clayey fine sand layer. Further assume that the clayey fine sand layer and the silty fine sand layer are not anticipated to settle during the earthquake. If the piles are 0.3 m in diameter, calculate the downdrag load on each pile due to liquefaction at the site.
Divide the soil into two layers, as follows:
Layer 1:
Depth = 0 to 1.5 m
The first layer is located above the groundwater table. Consider conditions at the average depth = (0 + 1.5)/2 = 0.75 m. Assume pore water pressures are equal to zero above the groundwater table.
\sigma_{v}^{\prime}=\gamma_{t} z=\left(18.3 kN / m ^{3}\right)(0.75 m )=13.7 kPa
\sigma_{h}^{\prime}=k_{0} \sigma_{v}^{\prime}=0.5(13.7)=6.9 kPa
Downdrag load = (pile perimeter) (layer thickness) \left(\sigma_{h}^{\prime} \tan \phi^{\prime}\right)
= π (0.3 m) (1.5 m) (6.9 tan 28°) = 5.2 kN
Layer 2:
Depth = 1.5 to 6 m
The second layer is located below the groundwater table. Consider conditions at the average depth = (1.5 + 6)/2 = 3.75 m.
= (18.3 kN/m³) (1.5 m) + (9.7 kN/m³) (2.25 m) = 49.3 kPa
\sigma_{h}^{\prime}=k_{0} \sigma_{v}^{\prime}=0.5(49.3)=24.6 kPaDowndrag load = (pile perimeter) (layer thickness) \left(\sigma_{h}^{\prime} \tan \phi^{\prime}\right)
= π (0.3 m) (4.5 m) (24.6 tan 28°) = 55.5 kN
Total downdrag load = 5.2 + 55.5 = 61 kN