Consider the gravity dam (Figure 2) whose concrete density is noted Pb. The vertical dam profile has a triangular shape (see notations in Figure 2). During a flood, the water (density p.) reaches the top of the structure (water height noted hb). A pressure due to water infiltration into the porous soil is applied on the horizontal tower face of the dam. We assume that this pressure varies linearly from B to O. in this exercise we consider only the risk of overturn of the dam about its downstream toe (Oy). Dam height hb = 30 m, dam width at the bottom (BO) = 44 m, dam length Lb = 25 m, a = 65°, B = 45°. 1) We assume a zero-water depth downstream of the dam (hav = 0 m). Determine the minimum value of the concrete density po to guarantee the equilibrium of the dam. 2) We assume that the water depth downstream of the dam is hav = 5 m. Determine the minimum value of the concrete density pb to guarantee the equilibrium of the dam. Comment the results. 3) A crack forms in the dam structure and water entering the crack will flow out it, which may jeopardize the stability of the dam. The thickness of the crack is denoted 2e and its length is assumed to be equal to that of the dam Lb (Figure 3). The axis of the crack is located in the middle of the dam (i.e. at a height h/2). It is assumed that the section of the crack is rectangular (2exLb). Determine the leakage flow rate for 2e= 0.40 mm.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Stability of a gravity dam

Transcribed Image Text:Consider the gravity dam (Figure 2) whose concrete density is noted pb. The vertical dam profile has a triangular shape (see notations in Figure 2). During a flood, the water (density p.) reaches the top of the structure (water height noted hb). A pressure due to water infiltration into the porous soil is applied on the horizontal tower face of the dam. We assume that this pressure varies linearly from B to O. in this exercise we consider only the risk of overturn of the dam about its downstream toe (Oy). Dam height hb = 30 m, dam width at the bottom (BO) = 44 m, dam length Lb = 25 m, α = 65°, B = 45°. 1) We assume a zero-water depth downstream of the dam (hav=0 m). Determine the minimum value of the concrete density po to guarantee the equilibrium of the dam. 2) We assume that the water depth downstream of the dam is hav = 5 m. Determine the minimum value of the concrete density po to guarantee the equilibrium of the dam. Comment the results. 3) A crack forms in the dam structure and water entering the crack will flow out it, which may jeopardize the stability of the dam. The thickness of the crack is denoted 2e and its length is assumed to be equal to that of the dam Lb (Figure 3). The axis of the crack is located in the middle of the dam (i.e. at a height h/2). It is assumed that the section of the crack is rectangular (2exLb). Determine the leakage flow rate for 2e= 0.40 mm.

a
Figure 2. Schematic view of the dam
B
crack
Figure 3. Schematic view of the crack
3
+0
Z
hav
F
2e

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