Summary
Highlights
Dams are barriers that restrict water flow, used for various purposes like irrigation and hydropower. Earth dams are constructed using soil and rock, and while highly adaptable, they face the challenge of seepage, where water flows through the soil. This can lead to piping, a major cause of dam failure where water displaces soil particles, creating pipe-like openings.
Earth dams are categorized into three types based on the availability and use of soil. Homogeneous dams are built entirely from fine-grained, relatively impervious soil, with a horizontal blanket drain to manage seepage. Dams with an impervious core use a concentrated impervious soil core for water retention, supported by pervious outer shells. Zoned dams utilize different soil types in specific zones for optimal performance, with impervious soil in the interior and pervious soil in the exterior.
Essential components of an earth dam include the core (fine-grained soil to control seepage), the shell (coarse-grained material for stability), a cut-off barrier to prevent foundation seepage, and transition filters between different soil zones to prevent particle migration. Internal drains, made of sand and gravel, are crucial for intercepting and safely channeling seepage water out of the dam.
Protective layers on both upstream and downstream slopes prevent erosion from wave action and heavy rain, respectively, using materials like boulders or vegetation. Toe drainage, typically made of cobbles, manages the exiting seepage water at the dam's base, which is usually wet.
Since zero seepage is impractical, it must be kept within acceptable limits. The video explains how to estimate seepage losses in a homogeneous earth dam with a horizontal filter using a flow net. This involves starting with known boundary conditions and then determining the unknown upper boundary, called the phreatic line or seepage line.
Casagrande observed that the seepage line in dams closely follows a parabolic shape for most of its length. He proposed treating it as a basic parabola and making manual corrections at the upstream and downstream faces. The starting point 'h' of this parabola on the upstream face is determined by a specific calculation related to the upstream face's horizontal projection.
The video explains the properties of a parabola (locus of points equidistant from focus and directrix) and derives its equation. It then applies this to the seepage line, defining the focus and vertex of the parabola within the dam structure to facilitate its construction based on known points.
The method of constructing the seepage parabola is demonstrated. By utilizing the property that every point on the parabola is equidistant from its focus and directrix, additional points can be plotted. Once the parabola is drawn, it's manually adjusted at the upstream face to conform to flow net conditions, establishing the final unknown boundary for a complete flow net construction.
After establishing the flow net, the video details how to calculate the approximate seepage quantity using Darcy's law. By considering a section of the flow and substituting the hydraulic gradient derived from the parabola equation, a simplified expression for the discharge through the dam per unit length is obtained. The value 's' in the formula is determined using the coordinates of the parabola's starting point and the reservoir's water height.