A 20-ft retaining wall is to be used to support a...

A 20-ft retaining wall is to be used to support a Terzaghi-Peck type I backfill (Figure 29). The wall cross section is similar to that shown in Illustration 3, exeept that the base is $8 \mathrm{ft}$ instead of $10 \mathrm{f}$. The backfill surface is level. Determine the factor of safety against overturning and against sliding (using a coefficient of friction between wall base and supporting soil. $\mu=0.5$ ) and the foundation pressure distribution (i.e., reaction against the base).

Key Concepts

Retaining Wall Stability

This concept refers to the structural integrity of retaining walls, ensuring that the wall can safely retain soil without failing due to excessive lateral earth pressure. Stability analysis typically considers various factors such as overturning, sliding, and bearing capacity to assess the overall performance and safety of the wall.

Factor of Safety

A factor of safety is a design criterion that provides a safety margin in engineering by comparing the strength or resisting forces against the applied loads or driving forces. In the context of retaining walls, separate factors are calculated for overturning and sliding to ensure that all potential failure modes are adequately resisted under expected loading conditions.

Overturning Analysis

Overturning analysis involves assessing the moments about a pivot point to ensure that the restoring moments provided by the wall's weight and design geometry exceed the overturning moments induced by lateral earth pressures, water pressures, and other forces. This analysis is crucial for preventing the wall from rotating or tipping over under load.

Sliding Analysis

Sliding analysis evaluates the horizontal forces acting on the retaining wall, comparing the resisting forces (such as friction at the base and, when applicable, passive earth pressures) to the sliding forces induced by the lateral earth pressures. The coefficient of friction between the wall base and supporting soil is a key parameter in this analysis to ensure that the wall does not slide forward.

Foundation Pressure Distribution

This concept involves determining how the reaction forces are distributed along the base of the retaining wall. A non-uniform pressure distribution can lead to localized overstress and potential failure of the foundation. Evaluating the distribution ensures that the foundation design can safely support the applied loads without excessive settlement or bearing capacity failure.

Earth Pressure Theories

Earth pressure theories, such as those proposed by Coulomb or Rankine, are used to estimate the lateral pressures exerted by the soil on retaining structures. These theories help in determining the active (and sometimes passive) pressures that must be resisted by the retaining wall, which are essential for performing both overturning and sliding stability analyses.

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