Example (6): A square footing of \( 1.8 \times 1.8 \mathrm{~m} \) is loaded with axial load of \( 1780 \mathrm{kN} \) and subjected to \( M_{x}=267 \mathrm{kN}-\mathrm{m} \) and \( M_{y}=160.2 \mathrm{kN}-\mathrm{m} \) moments. Undrained triaxial tests of unsaturated soil samples give \( \phi=36^{\circ} \) and \( c=9.4 \mathrm{kN} / \mathrm{m}^{2} \). If \( D_{f}=1.8 \mathrm{~m} \), the water table is at \( 6 \mathrm{~m} \) below the G.S. and \( \gamma=18.1 \mathrm{kN} / \mathrm{m}^{3} \), what is the allowable soil pressure if \( \mathrm{SF}=\mathbf{3 . 0} \) using (a) Hansen bearing capacity and (b) Meyerhof's reduction factors.

Step 1 ：1. Calculate the net effective load: \( \mathrm{Q}_{\mathrm{net}}=\frac{1780}{1.8^{2}}= \) 547.222 kN/\( \mathrm{m}^{2} \)

Step 2 ：2. Calculate the modified axial load: \( \mathrm{Q}_{\mathrm{mod}}=\frac{\mathrm{Q}_{\mathrm{net}}}{3 . 0}= \) 182.407 kN/\( \mathrm{m}^{2} \)

Step 3 ：3a. Use Hansen's bearing capacity equation: \( q_{\mathrm{permit}}=c N_{\mathrm{c}} \mathrm{s}_{\mathrm{c}} \mathrm{d}_{\mathrm{c}} \mathrm{i}_{\mathrm{c}}+\mathrm{D}_{\mathrm{f}} \left(1 - 0.5 d_{\mathrm{f}} / \mathrm{D}_{\mathrm{F}} \right) \gamma N_{\mathrm{q}} \mathrm{s}_{\mathrm{q}} \mathrm{d}_{\mathrm{q}} \mathrm{i}_{\mathrm{q}} + 0.5 \gamma \mathrm{B} N_{\mathrm{\gamma}} \mathrm{s}_{_{\gamma}} \mathrm{d}_{_{\gamma}} \mathrm{i}_{_{\gamma}} \), \( q_{\mathrm{allowable}}= q_{\mathrm{permit}} - \mathrm{Q}_{\mathrm{mod}} \)

Step 4 ：3b. Use Meyerhof's reduction factors: Apply equation to Meyerhof: \( q_{\mathrm{permit}}=c N_{\mathrm{c}} \mathrm{s}_{\mathrm{c}} \mathrm{d}_{\mathrm{c}} \mathrm{i}_{\mathrm{c}}+\mathrm{D}_{\mathrm{f}} \left(1 - 0.5 d_{\mathrm{f}} / \mathrm{D}_{\mathrm{F}} \right) \gamma N_{\mathrm{q}} \mathrm{s}_{\mathrm{q}} \mathrm{d}_{\mathrm{q}} \mathrm{i}_{\mathrm{q}} + 0.5 \gamma \mathrm{B} N_{\mathrm{\gamma}} \mathrm{s}_{_{\gamma}} \mathrm{d}_{_{\gamma}} \mathrm{i}_{_{\gamma}} \), \( q_{\mathrm{allowable}}= q_{\mathrm{permit}} - \mathrm{Q}_{\mathrm{mod}} \)

Step 5 ：4a. Calculate bearing capacity using Hansen's formula.

Step 6 ：4b. Calculate bearing capacity using Meyerhof's formula.

Step 7 ：5. Compare the bearing capacity in both cases and report the lower value as the final allowable soil pressure.