--- title: "Overturning and sliding check with shear strength" subject: "Hydro Power" chapter: 4 key: "semester_6/hydro_power:gravity-dam-overturning-sliding" source: https://www.bctengineer.com/q/semester_6/hydro_power/gravity-dam-overturning-sliding site: BCT Engineering --- # Overturning and sliding check with shear strength Hydro Power · Chapter 4: Dam Engineering - Asked in: 2075 Bhadra, 8 marks - Video: [Design of Gravity dam numerical || stability check of gravity dam numerical](https://www.youtube.com/watch?v=A0W93k5bjvs) — CIVIL ZONE - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/hydro_power/gravity-dam-overturning-sliding - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-4 ## Question Check the stability of concrete gravity dam against overturning and sliding. Consider μ = 0.7, γconcrete = 24 kN/m³, average shear strength of material at the horizontal section (q) = 1400 kN/m. [Figure: gravity dam with vertical upstream face and top width 6 m; the downstream face is vertical for the top 13 m and then slopes over a further 20 m height to the toe, giving a base of 6 m + 15 m = 21 m; upstream water depth is 30 m.] ## Short answer With full uplift: overturning FS 1.39, friction FS 0.83, but shear friction factor 7.49 confirms sliding safety. Without uplift FS improves. Provide drainage to reduce uplift. ## Answer #### Geometry and assumptions (per metre length) - Dam height $= 13 + 20 = 33$ m; water depth $h = 30$ m; no tailwater. - Top width 6 m; downstream face vertical for 13 m, then slopes 15 m horizontally over 20 m height; base $B = 21$ m. - $\gamma_w = 9.81$ kN/m³, $\gamma_c = 24$ kN/m³, μ = 0.7, shear strength $q = 1400$ kN/m² (taken per m² of base). - Uplift is taken as full (C = 1), varying from $\gamma_w h$ at heel to zero at toe. ```text 6 m +----+ | | 13 m 30 | W1 + m | \ W2 20 m -> | \ heel+-------\ toe <6>|<-15-> B = 21 m ``` #### Forces and moments about the toe | Force | Value (kN) | Arm (m) | Moment (kN·m) | |---|---|---|---| | W1 = 6×33×24 | 4,752 ↓ | 18.0 | +85,536 | | W2 = ½×15×20×24 | 3,600 ↓ | 10.0 | +36,000 | | P = ½×9.81×30² | 4,414.5 → | 10.0 | −44,145 | | U = ½×9.81×30×21 | 3,090.2 ↑ | 14.0 | −43,262 | $$ \begin{aligned} \sum V &= 4{,}752 + 3{,}600 - 3{,}090.2 = 5{,}261.9\ \text{kN} \\ \sum M_R &= 121{,}536, \quad \sum M_O = 44{,}145 + 43{,}262 = 87{,}407\ \text{kN·m} \end{aligned} $$ #### Overturning $$ FS_o = \frac{121{,}536}{87{,}407} = 1.39 $$ #### Sliding $$ \begin{aligned} FS_s &= \frac{\mu\sum V}{\sum H} = \frac{0.7 \times 5{,}261.9}{4{,}414.5} = 0.83 \\ SFF &= \frac{\mu\sum V + Bq}{\sum H} = \frac{3{,}683.3 + 21 \times 1400}{4{,}414.5} = 7.49 \end{aligned} $$ #### Results | Check | With uplift | Without uplift | Required | |---|---|---|---| | FS overturning | 1.39 | 2.75 | ≥ 1.5 | | FS sliding (friction) | 0.83 | 1.32 | ≥ 1.0 | | Shear friction factor | 7.49 | 7.98 | ≥ 3–5 | (Without uplift: $\sum V = 8{,}352$ kN, $\sum M_O = 44{,}145$ kN·m.) **Answer: With full uplift, FS overturning = 1.39 (slightly below 1.5) and friction FS = 0.83, but the shear friction factor = 7.49 > 5, so the dam is safe against sliding when the shear strength of the joint is counted. Without uplift, FS overturning = 2.75 and SFF = 7.98 (safe).** To improve overturning safety, drainage holes should be provided to reduce uplift. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What uplift assumption is used here? A. Full uplift (C = 1), from gamma_w h at heel to zero at toe B. No uplift C. Uplift of 0.5 gamma_w h at the heel D. Uplift constant over the base Answer: A. The solution takes C = 1 with triangular variation and no tailwater. (Key point: Full uplift) 2. FS by friction alone = 0.7 x 5,261.9 / 4,414.5. What is it and what does it show? A. 0.83 > 1 safe B. 0.83 < 1, friction alone is insufficient C. 7.49, safe D. 1.39, safe Answer: B. FS_s = 0.83 is below 1, so friction alone does not resist the thrust. (Key point: Friction sliding) 3. What is the shear friction factor? A. mu sum V / sum H B. q / sum H C. (mu sum V + B q) / sum H = 7.49 D. sum M_R / sum M_O Answer: C. SFF counts the shear strength of the joint, giving 7.49 > 5, so the dam is safe in sliding. (Key point: Shear friction factor) 4. FS overturning with uplift is 1.39 (< 1.5). What is the suggested remedy? A. Remove the tailwater B. Reduce the top width C. Raise the reservoir level D. Provide drainage holes to reduce uplift Answer: D. Without uplift FS_o is 2.75, so reducing uplift by drains helps. 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