A masonry gravity retaining wall 5 m high has a cross section as shown by Figure 25 and sapport

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A masonry gravity retaining wall 5 m high has a cross...

A masonry gravity retaining wall $5 \mathrm{~m}$ high has a cross section as shown by Figure 25 and sapports a clay soil backfill that is level with the top of the wall. The top of the wall is $0.75 \mathrm{~m}$ wide and the base of the wall is $1.75 \mathrm{~m}$ wide. Check the stability of this wall against overturning and sliding using criteria indicated by Figure 18(b). Use a unit weight for the masonry equal to $22 \mathrm{kN} \times \mathrm{m}^3$. Use Terzaghi charts and Figure 29 to obtain values for $P_b$ and $P_{r^{\prime}}$. Assume that the unit resistance to slid. ing along the base is equal to the value for the clay cohesion, determaned from shear strength testing as $35 \mathrm{kPa}$.

Key Concepts

Shear Strength and Base Friction

The shear strength of the soil, which includes parameters such as cohesion and friction angle, directly affects the friction available at the interface between the wall base and the supporting soil. This friction provides critical resistance against sliding. Evaluating the shear strength properties of the soil enables engineers to estimate the unit resistance along the base, which is essential for designing a wall that is stable against sliding forces.

Earth Pressure and Load Distribution

Earth pressure theories determine the lateral pressure distribution acting on retaining structures. These methods, often based on soil mechanics principles (such as Rankine or Coulomb theories) and supplemented by empirical charts like Terzaghi’s, help estimate both the magnitude and distribution of active earth pressures on the wall. Understanding this distribution is key to analyzing both overturning and sliding stability.

Sliding Stability Analysis

Sliding stability is concerned with evaluating whether the lateral forces acting on the wall (for instance, due to soil pressure) can be adequately resisted by friction and any other stabilizing mechanisms at the base of the wall. This involves calculating the horizontal force component and comparing it to the frictional resistance provided by the wall’s base, ensuring that a critical safety factor against sliding is achieved.

Overturning Stability Analysis

Overturning stability refers to the assessment of whether the moment generated by lateral loads (such as earth pressure) about the wall’s base exceeds the resisting moment provided by the wall’s weight. Analysis involves calculating the moments about a pivot point and ensuring that a prescribed safety factor is maintained, so that the wall does not rotate or overturn under imposed loads.

Gravity Retaining Wall Design

Gravity retaining walls rely primarily on their mass to resist lateral earth pressures. The design involves carefully selecting the wall’s geometric dimensions to ensure that the self-weight produces sufficient stabilizing moment to counteract external forces from the backfill soil, without the need for additional mass reinforcement or tiebacks.

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