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Diversion Headworks: Sub-Surface Flow Analysis and Khosla’s Theory

 Diversion headworks divert river water into main canals while preventing sediment entry. Seepage beneath weir floors built on permeable foundations induces dangerous uplift pressure and piping. Early empirical models like Bligh’s Creep Theory and Lane’s Weighted Creep Theory assumed uniform head loss along the wetted perimeter. However, Khosla’s Theory solved the governing Laplace equation $(\frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial z^2} = 0)$ using conformal transformation to determine exact uplift pressures at key floor profile points $(\phi_E, \phi_D, \phi_C).$ The exit hydraulic gradient at the downstream end is evaluated as:

$$G_E = \frac{H}{d} \cdot \frac{1}{\pi \sqrt{\lambda}}$$

​Where $H$ is head, $d$ is depth of downstream sheet pile, and $\lambda = \frac{1 + \sqrt{1 + \alpha^2}}{2}$ with floor length-to-depth ratio $\alpha = \frac{b}{d}.$

​Barrages built on soft alluvial beds of major North Indian rivers (e.g., Ganga, Yamuna) face severe subsurface erosion risks under high differential heads during non-monsoon operation.

​Contemporary barrage engineering utilizes sheet-pile arrays driven by high-frequency vibratory hammers combined with downstream concrete block launching aprons. Modern finite element seepage software (such as GeoStudio SEEP/W) models complex 3D anisotropy and non-homogeneous foundation strata, enabling precise design of floor thicknesses and cut-off depths to maintain safety margins against piping failure.

​Note: This technical content was curated and structured with AI assistance to support technical education.

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