Practice Question: Retaining Wall Factor of Safety Against Sliding

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Solution

Answer: B) 1.8

Total Height of Wall:
\[H=8 \ ft+2 \ ft=10 \ ft\]
Unit Weight of Soil:
\[γ=115 \ pcf\]
Active Earth Pressure Resultant:
\[P_a=1.8 \ k/ft\]

Weight of Soil Above Wall Footing:

\[W_{soil}=5 \ ft × 8 \ ft ×115 \ pcf=4600 \ k/ft\]
Weight of Wall:
\[W_{wall}=[2 \ ft × (10 \  ft)+2 \ ft × 5 \ ft]×150 \ pcf\]

\[W_{wall}=4.5 \ k/ft\]\[μ=0.35\]Horizontal Shear Demand:
\[V_{demand}=P_a=1.8 \ k/ft\]

Friction Force Resisting Sliding:
\[V_{resist}=(W_{wall}+W_{soil})×μ\]

\[V_{resist}=3.185 \ k/ft\]
Safety Factor:

\[SF=\frac{V_{resist}}{V_{demand}}\]

\[SF= \frac{3.185 \ k/ft}{1.8 \ k/ft}≈1.8\]
 

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