Chapter 2: Total Hydrostatic Force on Surfaces Principles of Hydrostatics Chapter 2: Total Hydrostatic Force on Surfaces Chapter 3: Hydrostatic Force on Surfaces

Analysis Of Gravity Dams Purpose of a dam: Dams are built for (1) Irrigation and drinking water (2) Power Supply (hydroelectric) (3) Navigation (4) Flood Control (5) Multi Purpose

Types of Dams: (1) Gravity Dams (2) Embankment Dams (3) Arch Dams (4) Buttress Dams

Example 1: In the figure shown, find the width b of the concrete dam necessary to prevent the dam from sliding. The specific gravity of concrete is 2.4 and the coefficient of friction between the base of the dam and the foundation is 0.4. Use 1.5 as the factor of safety against sliding. Is the dam also safe from overturning? Drawing P3-28 Page 124

Example 2: A dam is triangular in cross-section with the upstream face vertical. Water is flushed with the top. The dam is 8m high and 6m wide at the base and weighs 2.4 tons per cubic meter. The coefficient of friction between the base and the foundation is 0.8. Determine (a) the maximum and minimum unit pressure on the foundation, and the (b) factors of safety against overturning and against sliding. Drawing P3-29 Page 125

Example 3: A gravity dam of trapezoidal cross-section with one face vertical and horizontal base is 22 m high and has a thickness of 4 m at the top. Water upstream stands 2 m below the crest of the dam. The specific gravity of masonry is 2.4. A. Neglecting hydrostatic uplift 1. Find the base width B of the dam so that the resultant force will cut the extreme edge of the middle third near the toe. 2. Compute the factors of safety against sliding and overturning. Use µ = 0.5 Drawing P3-30 Page 126

Example 3: A gravity dam of trapezoidal cross-section with one face vertical and horizontal base is 22 m high and has a thickness of 4 m at the top. Water upstream stands 2 m below the crest of the dam. The specific gravity of masonry is 2.4. B. Considering hydrostatic uplift to vary uniformly from full hydrostatic pressure at the heel to zero at the toe; 1. Find the base width B of the dam so that the resultant force will act at the extremity of the middle third near the toe. 2. Compute the maximum and minimum compressive stresses acting against the base of the dam. Drawing P3-30 Page 126

Example 4: The section of a concrete gravity dam is shown in the figure. The depth of water at the upstream side is 6m. Neglecting hydrostatic uplift and us unit weight of concrete equal to 23.5 kN/m3. Coefficient of friction between the base of the dam and the foundation is 0.6. Determine the following: (a) Factor of safety against sliding, (b) the factor of safety against overturning, and (c) the overturning moment acting against the dam in kN-m. Drawing P3-31 Page 130

Example 5: The section of a gravity dam is shown in the figure. Assume hydrostatic uplift to vary uniformly from full hydrostatic uplift from the heel to zero at the toe. Determine the total reaction per unit length at the base of the dam. Use specific gravity of concrete = 2.4. Drawing P3-32 Page 132

Example 6: A section of the masonry dam is shown. The specific weight of the water is 9.81 kN/m3 and that of concrete is 23.54 kN/m3. Assuming uplift pressure varies linearly from maximum hydrostatic pressure at the heel to zero at the location of the drain, determine the (a) location of the resultant force, (b) factor of safety against sliding if coefficient of friction is 0.75, (c) factor of safety against overturning, (d) the stress at the heel and at the toe, and (e) the unit horizontal shearing stress at the base. Drawing P 3-33 Page 133

Example 7: The section of a concrete gravity dam is shown in the figure. The depth of water at the upstream side is 6m. Neglecting hydrostatic uplift and us unit weight of concrete equal to 23.5 kN/m3. Coefficient of friction between the base of the dam and the foundation is 0.6. Determine the following: (a) Factor of safety against sliding, (b) the factor of safety against overturning, and (c) the overturning moment acting against the dam in kN-m. Drawing P3-31 Page 130