3.2. Gravity Dams

 Gravity Dams: Detailed Explanation

A gravity dam is a massive structure designed to hold back water using its weight. These dams are constructed from concrete or stone masonry and rely on gravity to resist the horizontal pressure exerted by the water behind them. The shape of gravity dams is typically triangular or trapezoidal in cross-section, with the base being broader than the top.

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1. Introduction to Gravity Dams

Definition:
A gravity dam is a type of dam that resists the force of water by using the weight of the material (concrete or masonry) to resist the horizontal pressure. These dams are generally constructed on rocky foundations where their immense weight can be effectively supported.

Uses:

• Water storage for irrigation and domestic use
• Flood control
• Hydroelectric power generation
• Recreational purposes
• Navigation

Examples of Gravity Dams:

• Hoover Dam, USA
• Bhakra Dam, India
• Grand Coulee Dam, USA

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2. Forces Acting on a Gravity Dam

Understanding the forces acting on a gravity dam is crucial for its design and stability. The primary forces that act on a gravity dam include:

1. Water Pressure (Hydrostatic Pressure):

   • Description: The most significant force acting on a gravity dam. It is the horizontal pressure exerted by the water stored in the reservoir.
   • Direction: Acts horizontally and increases with depth (maximum at the bottom).
   • Calculation: $$P = \frac{1}{2} \gamma w H^2$$Where:
     • $P$ = Total hydrostatic pressure
     • $\gamma$ = Unit weight of water (typically 9.81 kN/m³)
     • $H$ = Height of water behind the dam

2. Self-weight of the Dam:

   • Description: The vertical force due to the weight of the dam itself, which provides stability against overturning.
   • Direction: Acts vertically downwards through the center of gravity of the dam.
   • Calculation: $$W = A \times \gamma_c$$ Where:
     • $W$ = Weight of the dam
     • $A$ = Cross-sectional area of the dam
     • ${\gamma }_c$ = Unit weight of concrete (typically 24 kN/m³)

3. Uplift Pressure:

   • Description: Pressure exerted by water that seeps underneath the dam. It reduces the effective weight of the dam.
   • Direction: Acts vertically upward, from the base of the dam.
   • Calculation:
     Uplift pressure is generally assumed to vary linearly from the upstream to the downstream face. $$U = \frac{1}{2} \gamma w H^2 \times \text{Base Length}$$

4. Silt Pressure:

   • Description: The pressure exerted by silt deposited against the upstream face of the dam. It adds to the water pressure.
   • Direction: Acts horizontally, similar to water pressure.
   • Calculation: $$P_s = \frac{1}{2} \gamma_s h^2$$ Where:
     • $P_s$ = Silt pressure
     • ${\gamma }_s$ = Unit weight of silt
     • $h$ = Height of silt deposited

5. Earthquake Forces:

   • Description: Additional forces induced during seismic activities. They can significantly impact the stability of the dam.
   • Direction: Can act both horizontally and vertically.
   • Calculation:
     The earthquake force is considered using pseudo-static analysis, represented as a fraction of the weight of the water and the dam.
     Horizontal seismic force, $H_s$: $$H_s=k_h\times W$$ Where $k_h$ is the horizontal seismic coefficient.

6. Wave Pressure:

   • Description: Pressure exerted by wind-generated waves on the upstream face of the dam.
   • Direction: Acts horizontally on the upper portion of the dam.
   • Calculation: $$P_w = 2.4 \times \gamma_w \times H_w$$ Where $H_w$ is the wave height.

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3. Design of Gravity Dams

The design of gravity dams involves ensuring that the structure can withstand all applied forces and remain stable. The following steps and considerations are essential in the design process:

A. Structural Stability Requirements

1. Stability Against Overturning:

   • Objective: To ensure that the dam does not overturn due to water pressure and other forces.
   • Condition:
     The overturning moment (caused by horizontal forces) should be less than the resisting moment (caused by the dam's weight). $$M_{resisting}>M_{overturning}$$
     • Calculated by taking moments about the toe (downstream edge) of the dam.

2. Stability Against Sliding:

   • Objective: To prevent the dam from sliding along its base due to horizontal forces.
   • Condition:
     The resisting forces (friction and shear strength at the base) should be greater than the driving forces (horizontal water pressure). $$F_{resisting} > F_{driving}$$ Where:
     • $F_{resisting} = \mu \times W + c \times A$
     • $\mu$ = Coefficient of friction
     • $c$ = Cohesion
     • $A$ = Area of base

3. Stability Against Bearing Capacity Failure:

   • Objective: To ensure that the stresses on the foundation do not exceed the bearing capacity of the foundation material.
   • Condition:
     The maximum pressure on the foundation should be less than the allowable bearing capacity.

B. Design Procedures

1. Preliminary Dimensions:

   • Set the dam height based on water storage requirements and topographical surveys.
   • Determine the base width using empirical formulas or guidelines, typically around $\frac{3H}{5}$ (where $H$ is the height of the dam).

2. Hydraulic Design:

   • Design spillways to handle maximum flood discharge safely.
   • Design outlet works for controlled water release.

3. Structural Analysis:

   • Use finite element methods (FEM) or other structural analysis techniques to model the dam and analyze stress distribution.
   • Ensure that the dam can withstand normal, flood, and seismic loading conditions.

4. Uplift Control Measures:

   • Provide drainage galleries and relief wells to control uplift pressure.
   • Use cut-off walls or grouting to reduce seepage.

5. Material Selection:

   • Choose appropriate materials (concrete, masonry) based on availability, cost, and environmental conditions.
   • Ensure that the material properties meet the strength and durability requirements.

6. Seismic Considerations:

   • Incorporate seismic design criteria based on regional seismicity.
   • Use damping devices or base isolators if necessary to reduce seismic forces.

C. Safety Factors

• Use safety factors in design to account for uncertainties in loadings, material properties, and construction quality.
• Typical safety factors:
  • Overturning: ≥ 1.5
  • Sliding: ≥ 1.5 (1.75 in seismic regions)
  • Bearing Capacity: ≥ 2.0

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4. Case Study: Hoover Dam, USA

Background:

• Location: Colorado River, USA
• Height: 221.4 m
• Length: 379 m
• Material: Concrete
• Purpose: Hydroelectric power, water supply, flood control.

Design Features:

• Base Width: 200 m (approximately half the height, ensuring stability).
• Upstream and Downstream Faces: The upstream face is vertical, while the downstream face slopes to reduce water pressure and resist overturning.
• Spillways: Designed to handle large floods; Hoover Dam has two spillways, one on each side.
• Cooling Pipes: Embedded pipes used to control the temperature of the concrete during curing to prevent cracking.
• Drainage Galleries: Installed to reduce uplift pressure by draining seepage water.

  

Forces Considered:

• Hydrostatic Pressure: Calculated based on the maximum water level.
• Self-weight: Ensured to be sufficient to counteract overturning and sliding.
• Uplift Pressure: Mitigated using drainage galleries.
• Earthquake Forces: Considered due to the dam’s location in a seismic region; designed to withstand significant seismic forces.

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5. Conclusion

Gravity dams are essential structures in water management and energy production. Their design requires a thorough understanding of the forces acting on the dam and careful planning to ensure stability and safety. By optimizing the shape, size, and materials used, engineers can construct gravity dams that efficiently serve their purpose while maintaining long-term stability and durability.

Understanding the principles of gravity dam design helps civil engineers develop safe and effective water storage solutions, ensuring a balance between engineering needs and environmental considerations.