Question 11.5: A site has the subsoil profile as shown in Fig. 11.21 and a ...
A site has the subsoil profile as shown in Fig. 11.21 and a bridge foundation consisting of piers will be installed at the location of B-25. The piers will be embedded 3 m into the sandstone. For the sediments above the sandstone, use an average buoyant unit weight \gamma_{b} = 9.2 kN/m³. For the sandstone, use an average buoyant unit weight \gamma_{b} = 11.7 kN/m³ and the effective shear strength parameters are c’ = 50 kPa and Φ’ = 40°. Use the bearing capacity factors from Fig. 11.22. Based on scour conditions (scour to elevation -10 m) and considering only end-bearing, determine the allowable pier capacity Q_{\text {all }} if the piers are 1.0 m in diameter and using a factor of safety of 3. Also determine the allowable pier capacity Q_{\text {all }} for seismic loading conditions assuming the sandstone will not be weakened by the earthquake.
Using Fig. 11.22 to obtain the bearing capacity factors:
For Φ’ = 40°, N_{c} = 84, N_{\gamma} = 100, and N_{q} = 72
From Eq. (8.4) with c’ = 50 kPa, B = 1 m, and assuming sandstone at elevation -19 m:
q_{ ult }=\frac{Q_{ ult }}{B L}=c N_{c}\left(1+0.3 \frac{B}{L}\right)+0.4 \gamma_{t} B N_{\gamma}+\gamma_{t} D_{f} N_{q} (8.4)
q_{ ult }=1.3 c^{\prime} N_{c}+0.4 \gamma_{b} B N_{\gamma}+\gamma_{b} D_{f} N_{q}= (1.3)(50)(84) + (0.4)(11.7)(1)(100) + [(9.2)(9) + (11.7)(3)](72)
= 14,400 kPa
q_{ all }=q_{ ult } / FS =14,400 kPa / 3=4800 kPa
Q_{\text {all }}=\left(q_{\text {all }}\right)\left(\pi r^{2}\right)=(4800 kPa )(\pi)(1.0 / 2)^{2}=3770 kN
Since the earthquake will not weaken the sandstone, a one-third increase in bearing pressure is often recommended, or:
Seismic q_{ all }=(4800 kPa )(1+0.333)=6400 kPa
Seismic Q_{\text {all }}=\left(q_{\text {all }}\right)\left(\pi r^{2}\right)=(6400 kPa )(\pi)(1.0 / 2)^{2}=5000 kN