Arch Dam

How an arch dam carries the lake

Stand a curved wall across a canyon and fill the upstream side with water. Pressure on each square meter of the dam is hydrostatic: p = ρ·g·h, growing linearly with depth h. Near the surface a few kPa; at the base of a 250 m dam, 2.45 MPa — about 25 atmospheres pushing on every square meter.

An arch dam handles that load as a horizontal arch at every elevation. Each thin slice acts like a Roman arch laid on its side: water pushes it downstream, but the curve forces the load to travel as compression around the curve, exiting as horizontal thrust into the canyon wall. Sound rock absorbs the thrust the way the ground absorbs the spring of a real arch.

The hoop stress in a thin slice follows the pressure-vessel formula:

σ_hoop = p · R / t

where p is water pressure at that depth, R is radius of curvature, and t is thickness. Designers tune R and t at every elevation to keep σ below the allowable compression of mass concrete (typically 6–10 MPa working, 30–40 MPa ultimate).

In a double-curvature dam the structure also bends vertically. Each vertical strip becomes a cantilever rooted in the foundation, splitting load between arch and cantilever paths. The "trial-load" method, developed by the U.S. Bureau of Reclamation in the 1930s for Hoover, allocates the load between the two systems by enforcing equal deflection at every grid point. Modern 3D finite-element models supersede trial-load but verify the same equilibrium.

Cross-section, drawn

Looking from above (plan view) and from the side (section), a double-curvature arch dam looks like this:

PLAN (looking down):
                 reservoir
                    ││
                    ││
                    ││ ← water pressure
        rock        ▽▽▽▽▽         rock
        █████        ___        █████
        █████      ／    ＼      █████
        █████    ／        ＼    █████
        █████──／            ＼──█████
        █████        dam        █████
        █████ ← thrust       thrust → █████
         abutment              abutment
                    │
                    ▽
              downstream (dry)

SECTION (looking from canyon side):
                    crown
                      ↓
                    ┌─┐ ← thin (4–8 m)
                    │ │
              water │ │ air
                    │ │
                    │ │
                    │ │
                  ┌─┘ │
                ┌─┘   │  ← wider near base (10–20 m)
              ┌─┘     │
            ┌─┘       │
       ────┘  base    │  ← seated in bedrock
       █████ rock █████

Two key proportions: the chord-to-height ratio (canyon width / dam height) and the slenderness ratio (base thickness / dam height). Arch dams thrive at chord/height under 4 and slenderness under 0.3. Anything wider and the geometry can't hoop the load; anything stockier and you've just built a gravity dam in disguise.

Arch dam vs other dam types

Dam type	Load path	Concrete volume	Best canyon	Foundation	Examples
Double-curvature arch	Hoop + cantilever	Low (slimmest)	Narrow, V-shaped	Sound rock, both sides	Vajont (262 m), Mauvoisin (250 m), Inguri (271 m)
Single-curvature arch	Hoop only	Low–medium	Narrow, U-shaped	Sound rock, both sides	Salanfe, Big Dalton
Gravity	Self-weight friction	Very high	Wide or narrow	Rock or stiff soil	Hoover (221 m, hybrid), Grand Coulee (168 m), Three Gorges (181 m)
Buttress	Reinforced piers + facing	Medium	Wide, flat	Stiff rock or bedrock	Daniel-Johnson (214 m), Roselend (150 m)
Embankment (earth/rock fill)	Mass + impervious core	None (fill only)	Any	Soil or rock	Nurek (300 m), Tarbela (143 m), Aswan High (111 m)
Concrete-faced rockfill	Fill with watertight face	Low (face only)	Any	Soil or rock	Shuibuya (233 m), Bakun (205 m)
Arch-gravity (hybrid)	Both, combined	Medium	Moderately narrow	Rock	Hoover (Boulder Canyon), Glen Canyon

Site geology, almost always, makes the choice. A wide flat valley with deep alluvium permits only embankment construction; a narrow gorge in granite with no flood-routing constraint is an arch dam waiting to happen.

Real-world arch dams

• Hoover Dam (USA, 1936): 221 m, gravity-arch hybrid. The trial-load method that designed it solved 60 simultaneous equations by hand over months.
• Vajont (Italy, 1959): 262 m, tallest double-curvature arch ever built. Survived 1963 landslide overtopping intact — the dam still stands — but 1917 lives were lost downstream.
• Mauvoisin (Switzerland, 1957): 250 m double-curvature arch holding 211 million m³ for hydropower, raised 13 m in 1991.
• Jinping-I (China, 2013): 305 m, tallest arch dam in service. Abutment grouting alone consumed 800,000 m of drilled holes.
• Inguri (Georgia, 1987): 271 m, fifth tallest arch dam, supplies 60% of Georgia's electricity.
• Hoover (gravity-arch, 200 m thick at base) vs Vajont (arch, 27 m thick at base): same height class, an order-of-magnitude less concrete in the pure arch — when the canyon allows it.

Variants

• Single-curvature vs double-curvature. Single-curvature dams are cylinders — curved in plan, vertical in section. Cheaper to form, work in wider canyons, but less efficient. Double-curvature dams curve in both directions and reduce concrete by 30–50 % at the cost of more complex formwork and stricter geometry.
• Constant radius vs constant angle. A constant-radius arch keeps R fixed at every elevation; the central angle changes with depth. A constant-angle arch keeps the central angle (typically 100–140°) and varies R. Constant-angle is more efficient because each elevation tunes its own R for the local p.
• Arch-gravity hybrid. Wide enough to count on self-weight, curved enough to share load through hoop action. Hoover is the canonical example. Useful when the canyon doesn't quite qualify as "arch territory" but you still want some material savings.
• Multiple-arch. A series of small arches spanning between buttresses — each arch is short, so the hoop stress is small. Daniel-Johnson Dam in Quebec is the world's largest example, with 13 arches and 14 buttresses. Cuts material further but multiplies abutment problems.
• Roller-compacted concrete (RCC) arch. Modern construction technique using stiff zero-slump concrete placed and compacted with rollers. Slashes construction time and cost but limits the dam to thicker, less aggressive arch shapes.

Failure modes

• Abutment thrust failure (Vajont, 1963). The dam itself doesn't crack — the rock it pushes into shears or slides. At Vajont a 270 Mm³ landslide on the reservoir rim slid into the lake. Malpasset (France, 1959) failed when foundation rock fractured along unmapped joints under thrust, killing 423.
• Foundation uplift. Water leaks under the dam through fissures and lifts it off its base. Drainage galleries with relief wells are mandatory; Hoover has a 1.6 km gallery network.
• Crack propagation through cold joints. Mass concrete cures slowly with enormous heat. Without staged cooling, temperature gradients crack the dam along lift sequences. Hoover used embedded refrigeration pipes during construction.
• Alkali-silica reaction (ASR). Reactive aggregates plus alkalis plus moisture form an expansive gel that pries the concrete apart. Chambon Dam suffered ASR-driven swelling that pushed the crest 1 m upstream over decades.
• Earthquake response. Reservoir inertia (Westergaard added mass) doubles or triples effective load in a quake. Koyna Dam (1967) cracked horizontally in a 6.5-magnitude reservoir-induced earthquake.
• Overtopping. Floods that exceed spillway capacity erode the downstream toe. Most dam-failure deaths historically come from overtopping erosion, not from collapse of the dam itself.

When the arch is the right choice

• Narrow canyon (chord/height under 4) with sound rock both sides.
• High dam height (over 100 m) where material savings dominate.
• Limited spillway requirement — arch crests are too thin for huge spillways.
• Low seismicity, or sound geology that survives seismic loading.
• Engineering and inspection capacity to manage 100-year design life with monitoring.
• Project economics that justify the upfront geological investigation cost.