--- title: "Khosla: barrage HGL and floor thickness" subject: "Irrigation and Drainage Engineering" chapter: 5 key: "semester_6/irrigation_and_drainage_engineering:khosla-barrage-hgl-thickness-pond1135" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-barrage-hgl-thickness-pond1135 site: BCT Engineering --- # Khosla: barrage HGL and floor thickness Irrigation and Drainage Engineering · Chapter 5: Diversion Headworks - Asked in: 2080 Chaitra, 5+3+1 marks - Video: [Safe Exit Gradient (Khosla's Theory)](https://www.youtube.com/watch?v=e5PnIfAn6rE) — RD STUDY - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/khosla-barrage-hgl-thickness-pond1135 - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-5 ## Question A barrage weir profile with an upstream pond level of 1135.0 m and downstream tailwater level of 1126.5 m is given below. Assume 1.0 m initial thickness of the floor throughout the length and the sheet pile is 0.5 m inside from the edge of the floor. Draw the hydraulic gradient line (HGL) and compute the designed thickness of the floor for no flow condition. Check the profile for piping failure. The safe exit gradient for the soil on which the weir is standing is 1:5. [Figure: weir section; pond level 1135.0 m, crest 1127.0 m, upstream floor level 1126.5 m, upstream pile bottom 1120.5 m, downstream floor level 1123.75 m, downstream tailwater 1126.5 m, downstream pile bottom 1118.5 m; upstream glacis 1:3 and downstream 1:3 slopes; horizontal dimensions 13.5 m, 0.5 m, 6.25 m, 9.75 m and 40 m; end points E1, C1 (upstream) and E2, C2 (downstream)] ## Short answer No‑flow head 11.25 m; required floor thickness up to 3.7 m exceeds provided 1.0 m; exit gradient 0.327 >0.200 (1/5) – unsafe against uplift and piping. ## Answer #### Data and assumptions - Pond level 1135.0 m. For the no-flow condition the d/s water level is taken at the d/s floor level 1123.75 m, so the head is $H = 1135.0 - 1123.75 = 11.25$ m. - The u/s sheet pile (bottom 1120.5 m) is 6.0 m deep below the u/s floor (1126.5 m). The d/s pile (bottom 1118.5 m) is 5.25 m deep below the d/s floor (1123.75 m). Floor length between the piles $b = 40$ m. - Floor thickness 1.0 m throughout (given); specific gravity of concrete $G = 2.4$. - Slope correction for a 1:3 slope $= 4.5\%$, multiplied by (slope length / $b$): u/s slope length $1.5$ m (up the slope, subtracted at $C_1$); d/s glacis length $9.75$ m (down the slope, added at $E_2$). #### Khosla's constants $\alpha = b/d$, $\lambda = \dfrac{1+\sqrt{1+\alpha^2}}{2}$, $\phi_E = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda-2}{\lambda}$, $\phi_D = \dfrac{1}{\pi}\cos^{-1}\dfrac{\lambda-1}{\lambda}$ (in percent), total floor length $b = 40$ m. For the u/s pile, $\phi_{D1} = 100-\phi_D$ and $\phi_{C1} = 100-\phi_E$. | Pile | d (m) | α | λ | φE (%) | φD (%) | |---|---|---|---|---|---| | U/s pile | 6.00 | 6.667 | 3.871 | 33.94 | 23.40 | | D/s pile | 5.25 | 7.619 | 4.342 | 31.86 | 22.04 | #### Pressures at the key points Pressure is expressed as a percentage of the head $H = 11.25$ m (no flow). | Point | Simple φ (%) | Corrections (%) | Corrected φ (%) | Pressure head (m) | |---|---|---|---|---| | E1 (top of u/s pile) | 100.00 | 0 | 100.00 | 11.25 | | D1 | 76.60 | - | 76.60 | 8.62 | | C1 | 66.06 | thk +1.76, int +2.97, slope -0.17 | 70.62 | 7.94 | | E2 | 31.86 | thk -1.87, int -1.15, slope +1.10 | 29.94 | 3.37 | | D2 | 22.04 | - | 22.04 | 2.48 | | C2 (d/s end) | 0 | 0 | 0 | 0 | Corrections: thk = floor thickness, $+\dfrac{\phi_D-\phi_C}{d}t$ at C and $-\dfrac{\phi_E-\phi_D}{d}t$ at E; int = mutual interference, $19\sqrt{D/b'}\,\dfrac{d+D}{b}$ (at $C_1$: $D = 1126.5-1118.5 = 8.0$ m, $d = 6$ m; at $E_2$: $D = 1123.75-1120.5 = 3.25$ m, $d = 5.25$ m; $b' = 40$ m), positive at $C_1$ and negative at $E_2$; slope = slope correction. The D points are not corrected. #### Floor thickness Unbalanced head $h$ = hydraulic-gradient level at the floor $-$ floor top level; required thickness $t = \dfrac{h}{G-1}$ with $G = 2.40$ (the HGL is taken as a straight line from $C_1$ to $E_2$ along the floor). | Location | x (m) | φ (%) | HG level (m) | Floor top (m) | Unbalanced head (m) | Required t (m) | Provided t (m) | Check | |---|---|---|---|---|---|---|---|---| | C1 (u/s pile junction) | 0 | 70.62 | 1131.69 | 1126.50 | 5.19 | 3.71 | 1.00 | not safe | | Toe of d/s glacis | 23.75 | 46.47 | 1128.98 | 1123.75 | 5.23 | 3.73 | 1.00 | not safe | | E2 (d/s pile junction) | 40 | 29.94 | 1127.12 | 1123.75 | 3.37 | 2.41 | 1.00 | not safe | #### Exit gradient $$ G_E = \frac{H}{d}\cdot\frac{1}{\pi\sqrt{\lambda}} = \frac{11.25}{5.25}\times\frac{1}{\pi\sqrt{4.342}} = 0.3273\ (\approx 1/3.1) $$ Permissible $= 1/5 = 0.2000$. Not safe against piping; deepen the d/s pile or lengthen the floor. #### Hydraulic gradient line Bars show the corrected pressure (each # is 2.5%): ```text E1 100.0% |######################################## D1 76.6% |############################### C1 70.6% |############################ E2 29.9% |############ D2 22.0% |######### C2 0.0% | ``` The hydraulic gradient line (HGL) drops vertically across each pile (from E to D to C) and runs as a straight line along the floor between the pile junctions ($C_1$ to $E_2$). **Conclusion:** For no flow, the floor needs about 3.7 m thickness at the u/s junction and at the toe of the glacis, reducing to about 2.4 m at the d/s pile. The 1.0 m provided is not enough anywhere, so the floor must be thickened (or the u/s floor lengthened and the u/s pile deepened to reduce the uplift). The exit gradient (1/3.1) exceeds the safe value of 1/5, so the profile is also unsafe against piping; the d/s pile must be deepened. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For the no-flow condition the head is: A. 1135.0 - 1123.75 = 11.25 m (d/s water at floor level) B. 1135 - 1126.5 = 8.5 m C. 1135 - 1118.5 D. 1127 - 1123.75 Answer: A. With no flow, the d/s water is at the d/s floor level, so H = 11.25 m. (Key point: No-flow head) 2. The hydraulic gradient line: A. Drops across each pile E-D-C and is straight between pile junctions along the floor B. Is a single straight line from pond to tail C. Is horizontal under the floor D. Rises downstream Answer: A. Pressure drops at piles; between C of one pile and E of the next it is taken straight. (Key point: HGL shape) 3. Floor thickness is checked using: A. t = h/(G-1), h unbalanced head, G = 2.4 B. t = h x 2.4 C. t = H/5 D. t = G/h Answer: A. The submerged weight of the floor balances the unbalanced head. (Key point: Thickness) 4. Which sign applies to the slope correction on a d/s glacis (down slope)? A. Positive, added at E2 B. Negative C. Zero D. Added at C1 Answer: A. Down slopes in the flow direction add; up slopes subtract. (Key point: Corrections applied) 5. Exit gradient 0.327 vs safe 1/5 = 0.2 means: A. Unsafe; increase d/s pile or lengthen floor B. Safe C. Safe if floor thickened D. Check not required Answer: A. The computed gradient exceeds the permissible value, so piping can occur. (Key point: Piping check) ## Related in Irrigation and Drainage Engineering - [Khosla: HGL and d/s floor thickness, three piles](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akhosla-corrected-phi-three-piles-hgl) — Irrigation and Drainage Engineering, chapter 5 - [Khosla: residual pressures and HGL, pond 260 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akhosla-weir-profile-pond260) — Irrigation and Drainage Engineering, chapter 5 - [Khosla: cistern floor thickness from corrected phi](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akhosla-corrected-phi-barrage-cistern) — Irrigation and Drainage Engineering, chapter 5 - [Khosla: HGL and exit gradient, pond 102.50](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akhosla-hgl-weir-profile-pond1025) — Irrigation and Drainage Engineering, chapter 5 - [Uplift at inside corners, 50 m floor weir](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Aweir-uplift-two-inside-corners-50m) — Irrigation and Drainage Engineering, chapter 5, asked 2× - [Khosla (analytical): uplift and d/s floor thickness](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akhosla-analytical-head-regulator-floor-thickness) — Irrigation and Drainage Engineering, chapter 5 ## Related in other subjects - [Resistance of alloy sheet along length and thickness](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aresistivity-alloy-sheet-resistance) — Basic Electrical Engineering, chapter 1 - [Anchored sheet pile, free earth, with anchor pull](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aanchored-sheet-pile-embedment) — Foundation Engineering, chapter 5 - [Slope change 1/120 to 1/1500, jump and profile length](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Awide-channel-slope-break-jump-two-steps) — Hydraulics, chapter 8 - [Sheet pile seepage quantity numerical](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asheet-pile-seepage-quantity-numerical) — Soil Mechanics, chapter 7