JNTU B.Tech III EARTH AND ROCKFILL DAMS AND SLOPE STABILITY Previous Question Paper (November/December - 2020 - R16)

An earthen dam is a massive structure constructed from compacted natural materials such as soil, sand, gravel, and clay. Its stability relies on its weight and the shear strength of the materials used. The general features of an earthen dam include the following components:

• Shell/Embankment: The outer zones of the dam, usually constructed from pervious or semi-pervious materials, which provide the necessary weight and structural stability.
• Core: A central impervious zone made of clay or silt that acts as a water barrier to prevent excessive seepage through the dam.
• Filter Zones: Layers of graded sand and gravel placed between the core and the shell to prevent internal erosion (piping) by allowing water to drain while retaining soil particles.
• Upstream Slope Protection: Rip-rap or concrete blocks placed on the upstream face to protect against wave action and erosion.
• Downstream Slope Protection: Grass turfing or stone pitching to protect the downstream face from rain-cut erosion.
• Drainage System: Features like toe drains or chimney drains that collect and safely discharge seepage water to prevent saturation of the downstream slope.
• Crest: The top portion of the dam, which may serve as a roadway and must be wide enough to ensure the phreatic line remains within the dam body.

A typical cross-section consists of a central core, upstream and downstream shells, filter drains, and a toe drain. The upstream slope is generally flatter than the downstream slope to account for water pressure and saturation effects. The phreatic line (top flow line) must be kept well below the downstream face to ensure stability.

To determine the factor of safety (FOS) for a slope in saturated clay under undrained conditions (φ = 0), we use the method of slices or the stability number approach. Given the parameters: depth H = 8 m, slope angle β = 45° (1:1 slope), cohesion C_u = 70 kN/m², and unit weight γ = 15 kN/m³.

The factor of safety is defined as the ratio of the resisting moment to the driving moment. For a circular slip surface, the resisting moment is M_R = C_u × L × R, where L is the arc length and R is the radius. The driving moment is M_D = W × x, where W is the weight of the sliding mass and x is the horizontal distance from the center of rotation to the center of gravity of the sliding mass.

For a φ = 0 analysis, the stability number (S_n) is defined as:

Alternatively, using Taylor's stability charts for a 1:1 slope (β = 45°), the stability number S_n for a deep-seated failure is approximately 0.18. Rearranging the formula to solve for the factor of safety:

Substituting the given values:

This factor of safety indicates that the slope is stable under the given undrained conditions. Note that the exact value depends on the specific geometry of the trial slip circle provided in the diagram; if the circle is restricted (e.g., passing through the toe), the stability number might vary slightly based on the depth factor D.