--- title: "Forces on gravity dam and stability requirements" subject: "Hydro Power" chapter: 4 key: "semester_6/hydro_power:gravity-dam-forces-stability" source: https://www.bctengineer.com/q/semester_6/hydro_power/gravity-dam-forces-stability site: BCT Engineering --- # Forces on gravity dam and stability requirements Hydro Power · Chapter 4: Dam Engineering - Asked in: 2072 Asoj, 9 marks - Video: [Line Academy | Civil Engineering Loksewa | Hydropower | Forces Acting on Concrete Gravity Dam II](https://www.youtube.com/watch?v=LiSjFm4zdn0) — line academy - 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-forces-stability - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-4 ## Question Describe the forces that possibly acted to the gravity dam. Show them in neat and clean sketch. Describe the stability requirements of gravity dam. ## Short answer Forces include self weight, water pressure, uplift, silt, wave, earthquake, ice and wind. Stability requires: overturning FS≥1.5, sliding FS≥1 or shear friction factor 3–5, resultant within middle third (e≤B/6), and allowable compressive stress. ## Answer A **gravity dam** is a solid concrete or masonry dam that resists all external forces by its own weight. The forces acting on it are: ```text crest ~~~~~ +---+ <- wave pressure Pw | | |\ Pi -> | | \ <- wind | | W | \ W = self weight P1 -> | | \ (+ EQ: aW horizontal) | | | W2 \ Ps -> | | \ ~~~~ tailwater (silt) | | \ <- P2 +---+-------+ toe heel ^ ^ ^ ^ ^ U (uplift) ``` #### Forces acting on a gravity dam 1. **Self weight (W):** the main stabilising force; $W = \gamma_c \times$ area per metre length, acting at the centroid. Divided into rectangles and triangles for calculation. 2. **Water pressure:** - Upstream horizontal: $P_1 = \frac{1}{2}\gamma_w h_1^2$ at $h_1/3$ above base. - Vertical weight of water on a sloping upstream face (if any). - Tailwater: $P_2 = \frac{1}{2}\gamma_w h_2^2$ acting upstream, plus weight of water on the downstream slope. 3. **Uplift pressure (U):** water seeping through the foundation and joints pushes upward. It varies from $C\gamma_w h_1$ at heel to $\gamma_w h_2$ at toe; drainage galleries reduce it (head at drains $= h_2 + \frac{1}{3}(h_1 - h_2)$). 4. **Silt pressure (Ps):** silt deposited against the upstream face: $P_s = \frac{1}{2}\gamma_{sub} h_s^2 K_a$, $K_a = \frac{1-\sin\phi}{1+\sin\phi}$, at $h_s/3$. 5. **Wave pressure (Pw):** due to wind waves; wave height $h_w = 0.032\sqrt{VF} + 0.763 - 0.271F^{1/4}$ for fetch $F < 32$ km; $P_w = 2\gamma_w h_w^2$, acting $3h_w/8$ above still water level. 6. **Earthquake forces:** - Inertia force on the dam $= \alpha_h W$ horizontally (and $\alpha_v W$ vertically) at the centroid. - Hydrodynamic pressure of water: Westergaard/Zanger, e.g. $P_e = 0.726\,p_e\,h$ with $p_e = C_m\alpha_h\gamma_w h$. 7. **Ice pressure:** in cold regions, about 250 kN/m² over the ice thickness. 8. **Wind pressure:** small; usually neglected. #### Stability requirements The dam must be safe for all load combinations (empty reservoir, full reservoir, flood, earthquake): | Requirement | Criterion | |---|---| | No overturning | $FS_o = \sum M_R / \sum M_O \geq 1.5$ (2–3 normal) | | No sliding | $FS_s = \mu\sum V/\sum H \geq 1$; shear friction factor $(\mu\sum V + Bq)/\sum H \geq 3$–5 | | No tension | Resultant within middle third: $e \leq B/6$ | | No crushing | $p_{max} = \frac{\sum V}{B}(1 + \frac{6e}{B})$ and principal stress $\leq$ allowable | Also, the foundation must be safe in bearing and the dam must have adequate freeboard to avoid overtopping. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the main stabilising force of a gravity dam? A. Self weight B. Uplift C. Wave pressure D. Silt pressure Answer: A. A gravity dam resists loads by its own weight. (Key point: Main stabilising force) 2. How does uplift vary and what reduces it? A. Equal to tailwater pressure everywhere B. C gamma_w h1 at heel to gamma_w h2 at toe; drainage galleries reduce it C. Zero at heel and maximum at toe D. Constant over the base; grouting increases it Answer: B. Uplift varies linearly and drains cut it. (Key point: Uplift variation) 3. Which expression gives silt pressure? A. alpha_h W B. 2 gamma_w h_w^2 C. 1/2 gamma_sub h_s^2 K_a with K_a = (1 - sin phi)/(1 + sin phi) D. gamma_w h Answer: C. Silt pressure uses the submerged weight and Rankine active coefficient. (Key point: Silt pressure) 4. Which set of requirements is correct? A. Only sliding must be checked B. FS_o <= 1, e >= B/6 C. Tension allowed at heel D. FS_o >= 1.5, FS_s >= 1, e <= B/6, stress <= allowable Answer: D. The four requirements are overturning, sliding, tension and crushing. 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