Practice Question: Factor of Safety Against Overturning for a Retaining Wall

NCEES Civil PE Specification Soil Mechanics: Lateral Earth Pressure

Problem

You are designing a cantilever retaining wall for your new home in Beverly Hills, California. The hillside in your neighborhood is known for saturated soft clay that is prone to collapse and has already damaged the third guest house of many residents. Given the parameters in the following figure, determine the factor of safety against overturning for the retaining wall.

Ignore any lateral resistance provided by passive pressure but consider the weight of soil above the toe in your calculation.

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Solution

Answer: B) 3.8

The factor of safety against overturning is calculated by taking the ratio of the resisting moment to the overturning moment.

The resisting moment is caused by the self-weight of concrete and soil above the wall footing resisting the overturning of the wall.

The overturning moment is caused by the active pressure of soil retained by the wall.

Both overturning moment and resisting moment are calculated based on rotation about the toe. Moments are calculated in units of pound-foot per foot of the wall.

Calculate the resisting moment based on weight and distance to center of each component from toe:

Rankine active earth pressure coefficient, since ϕ = 0 (saturated clay):
$$ k_a=1 $$
Vertical pressure:
$$ p_v=\gamma\ \ast\ H=120\ pcf\ \ast\ \left(12\ ft+2.5\ ft\right)=1740\ psf $$
Active earth pressure:
$$ p_a=1740\ psf\ \ast\ 1-2\ast275\ psf\ast\sqrt1=1190\ psf $$
Resultant force due to active earth pressure:
$$ R_a=\frac{1}{2}\ \ast\ p_a\ \ast\ H=\frac{1}{2}\ \ast\ 1190\ psf\ \ast\ \left(12\ ft+2.5\ ft\right)=8627.5\ plf $$

Since the resultant force acts at H/3 above the base (triangular distribution), we can calculate the overturning moment as follows:
$$ M_{overturning}=R_a\ \ast\ \frac{H}{3}=8627.5\ plf\ \ast\ \frac{12\ ft+2.5\ ft}{3}=41699.6\frac{lb\ \ast\ ft}{ft} $$