--- title: "Forces acting on gravity dam" subject: "Hydro Power" chapter: 4 key: "semester_6/hydro_power:gravity-dam-forces-sketch" source: https://www.bctengineer.com/q/semester_6/hydro_power/gravity-dam-forces-sketch site: BCT Engineering --- # Forces acting on gravity dam Hydro Power · Chapter 4: Dam Engineering - Asked in: 2070 Magh, 6 marks - Video: [Line Academy | Civil Engineering Loksewa | Hydropower | Forces Acting on Concrete Gravity Dam I](https://www.youtube.com/watch?v=k7wcLcv9GS8) — 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-sketch - Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-4 ## Question Discuss with neat sketch the force acting on a gravity dam. ## Short answer Self weight, upstream and tailwater pressure, uplift, silt, wave, and earthquake forces act. These demand stability checks for overturning, sliding, no tension (e≤B/6) and no crushing. ## Answer A gravity dam stays in place by its own weight. The forces acting on it are grouped into stabilising forces (self weight, tailwater) and destabilising forces (water pressure, uplift, silt, waves, earthquake). ```text crest ~~~~~ +---+ <- wave pressure Pw | | |\ Pi -> | | \ <- wind | | W | \ W = self weight P1 -> | | \ (+ EQ: aW horizontal) | | | W2 \ Ps -> | | \ ~~~~ tailwater (silt) | | \ <- P2 +---+-------+ toe heel ^ ^ ^ ^ ^ U (uplift) ``` #### 1. Self weight (W) Main resisting force. $W = \gamma_c \times$ cross-sectional area (per metre length), acting through the centroid. The section is split into rectangles and triangles. #### 2. Water pressure - Upstream: $P_1 = \frac{1}{2}\gamma_w h_1^2$, horizontal, at $h_1/3$ above the base. If the upstream face is sloping, the weight of water above the slope acts vertically downward. - Tailwater: $P_2 = \frac{1}{2}\gamma_w h_2^2$ acting upstream, and the weight of water on the downstream slope. #### 3. Uplift pressure (U) Seepage water under the base and in the joints acts upward and reduces the effective weight. It varies linearly from $C\gamma_w h_1$ at the heel to $\gamma_w h_2$ at the toe; drains reduce it. #### 4. Silt (sediment) pressure $P_s = \frac{1}{2}\gamma_{sub}h_s^2 K_a$, where $K_a = (1-\sin\phi)/(1+\sin\phi)$, acting at $h_s/3$ from the base. #### 5. Wave pressure Wind waves strike the top of the dam. $P_w = 2\gamma_w h_w^2$ acting at $3h_w/8$ above the reservoir level; wave height from Molitor's formula. #### 6. Earthquake forces - Horizontal inertia force on the dam $\alpha_h W$ (and vertical $\alpha_v W$). - Hydrodynamic pressure of the reservoir water (Westergaard/Zanger method), acting at about $4h/(3\pi)$ above the base. #### 7. Ice and wind pressure Ice thrust (cold regions) about 250 kN/m² on the ice thickness; wind pressure is small and usually neglected. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which grouping is correct? A. Self weight and tailwater stabilise; water pressure, uplift, silt, waves, earthquake destabilise B. Silt stabilises C. All forces destabilise D. Uplift stabilises; self weight destabilises Answer: A. Self weight and tailwater help stability while the others push or lift the dam. (Key point: Stabilising vs destabilising) 2. Where does wave pressure act and what is its value? A. alpha_h W at centroid B. P_w = 2 gamma_w h_w^2 at 3h_w/8 above reservoir level C. gamma_w h^2/2 at h/3 D. gamma_w h_w at base Answer: B. Wave pressure acts near the top, 3h_w/8 above still water. (Key point: Wave pressure) 3. What are the earthquake effects? A. Only vertical weight B. Ice thrust C. Inertia force alpha_h W on the dam and hydrodynamic pressure of the reservoir D. Only uplift Answer: C. Both inertia and hydrodynamic water pressure are considered. 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