A 10 -m-high concrete retaining wall (gravity type) having a...

A 10 -m-high concrete retaining wall (gravity type) having a vertical backface supports a cohesionless soil backfill sloping at an inclination of 30 s with the horizontal. The retained soil has the following properties: $\gamma=17 \mathrm{kN} \approx \mathrm{m}^3$, $\phi=35^{\circ}$. (a) Cakulate $P_A$ using the Rankine theory. (b) Calculate $P_A$ using the Coulomb theory, assuming a wall-friction angle equal to $30^{\circ}$.

A 10 -m-high concrete retaining wall (gravity type) having a vertical backface supports a cohesionless soil backfill sloping at an inclination of 30 s with the horizontal. The retained soil has the following properties: $\gamma=17 \mathrm{kN} \approx \mathrm{m}^3$, $\phi=35^{\circ}$.
(a) Cakulate $P_A$ using the Rankine theory.
(b) Calculate $P_A$ using the Coulomb theory, assuming a wall-friction angle equal to $30^{\circ}$.

Key Concepts

Retaining Wall Design

Retaining wall design involves ensuring that structures designed to hold back soil masses are stable under various loading conditions, including active earth pressures. The design process uses theories like Rankine and Coulomb to assess the forces acting on the wall, considering factors such as soil properties, backfill geometry, and wall friction, to prevent failure and ensure long-term stability.

Soil Properties (Unit Weight and Friction Angle)

The unit weight of soil is a measure of its density and is central to calculating gravitational forces in soil mechanics. The friction angle represents the inherent shear strength of the soil due to particle interlocking and frictional resistance. Both properties are critical in determining the magnitude and distribution of lateral earth pressures acting on retaining structures.

Coulomb Earth Pressure Theory

Coulomb's theory extends the analysis of earth pressures by incorporating the effect of wall friction and geometry, including the inclination of the wall and the backfill surface. This theory considers the equilibrium of a soil wedge and is used to calculate earth pressures when additional factors such as wall roughness or inclined backfill surfaces influence the soil-structure interaction.

Rankine Earth Pressure Theory

Rankine's theory provides a simplified method for estimating active and passive earth pressures in a soil mass by assuming a state of plastic equilibrium and neglecting wall friction. It uses the soil's friction angle and unit weight to derive earth pressure coefficients, which are essential for calculating the resultant lateral force acting on vertical or near?vertical retaining structures.

Active Earth Pressure

Active earth pressure refers to the lateral pressure exerted by soil when a retaining structure moves away from the soil mass, leading to mobilization of the soil's shear resistance at a minimum state. This concept is critical in geotechnical engineering for designing retaining walls, as it determines the load that the wall must safely resist under conditions of potential wall movement.

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