Gravity Dam

For our Honors Engineering class, we were challenged with a design problem: how can you design a gravity dam that uses the least amount of concrete while remaining stable?

Special thanks to my teammates, Anthony, Liam, and Yauheni for their collaboration on this project.

The Design Challenge

Our task was to design a 100-meter-long gravity dam that could safely hold back a 20-meter hydraulic head (the height difference between the water level upstream and downstream). The key goal was to minimize the amount of concrete required.

If a dam uses more material than necessary, it becomes inefficient and expensive. But it has to use enough so it doesn't fail. The critical failure mode we studied is called overturning, which occurs when water pressure pushes hard enough to tip the dam over its downstream edge (called the toe). To prevent overturning, the gravity moment of the dam (caused by its own weight) must exceed the overturning moment caused by the water.

Understanding Hydrostatic Pressure

We started with some basics of hydrostatics. The pressure from water increases with depth, following the equation:

P = ρ g h

Where:

ρ (rho) is the density of water (1000 kg/m³),

g is the acceleration due to gravity (9.81 m/s²),

h is the depth of the water.

At the bottom of the 20-meter head, the hydrostatic pressure is:

P = (1000)(9.81)(20) ≈ 196,000 Pa (Pascals)

This pressure acts across the dam face as a triangular distributed load, with zero pressure at the surface and maximum at the bottom.

We calculated that the total hydrostatic force acting on the dam is about 196,000,000 N, and its overturning moment around the toe is approximately 1.31 × 10⁹ Nm. This became our benchmark: our dam’s weight and geometry must resist at least this much overturning force.

Rectangular Dam as Baseline

We first tested a simple rectangular dam design (5 m wide, 20 m tall). It turned out this shape wasn’t wide enough—the overturning moment from the water exceeded the stabilizing gravity moment. After optimization, we found a rectangular dam would need to be 11.1 m wide to resist overturning safely. That design would use about 22,200 m³ of concrete.

Exploring Alternative Geometries

For each geometry below, we optimized the design parameters so the dam achieves the required gravity moment (1.31 × 10⁹ Nm) to prevent overturning, while using the smallest possible cross-sectional area (and therefore the least concrete). We also confirmed that each design is stable, since the dam’s center of gravity lies between the heel and toe.

Key Takeaways

This project gave us insight into how engineers optimize structures not just for strength, but also for efficiency and cost-effectiveness. By analyzing the relationship between hydrostatic pressure, dam weight, and geometry, we were able to reduce the required concrete volume by over 84% compared to the naive rectangular design.