Arch Dam Calculator: Water Pressure, Hoop Thrust, Compressive Stress and Thickness Needed
A first estimate of the forces and the stress in a thin arch dam or a curved wall that holds back water.
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How this calculator works
Enter the water depth, the radius of the arch, the angle it spans at its centre, the thickness at the base and the allowable compressive stress of the concrete.
The calculator gives the arc length L = R theta, the chord C = 2R sin(theta/2), the water pressure p = gamma h, the force P = one half gamma h squared for each metre and the total water force on the projected area.
It then finds the thrust carried round the arch, H = pR, the average compressive stress H over t, the thickness needed for the allowable stress, and the thrust at each abutment, with a check that the two abutments balance the water force.
Formulas used
- L = R\theta,\quad C = 2R\sin\frac{\theta}{2}
- p = \gamma_w h,\quad P = \tfrac12\gamma_w h^2
- H \approx pR
- \sigma_c = \frac{H}{t\times1}\le f_{allow}
Worked example
With the default numbers in the calculator above:
- Length of the arc along the dam: 104.72 m
- Chord: the straight distance between the springing points: 91.93 m
- Rise of the arch above the chord: 21.43 m
- Water pressure at the base: 294.30 kPa
- Water force for each metre of width, and where it acts: 4414.50 kN per metre, acting 10.00 m above the base (one third of the depth)
- Total water force on the dam (pressure on the projected area, which is the chord times the depth): 405.80 MN (405804.38 kN)
- Thrust carried round the arch at the base, for each metre of height (thin arch): 17658.00 kN per metre of height
- Average compressive stress in the arch at the base: 2.94 MPa
- Thickness needed at the base for the allowable stress: 3.53 m
- Total thrust delivered to each abutment (the thrust added up over the whole depth): 264.87 MN along the tangent of the arch at the springing
- Direction of that thrust: the tangent at the springing makes this angle with the chord: 50.00 degrees
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
How does an arch dam carry the water?
By arch action. The water pushes the curved wall against the rock at the two ends, so the concrete is in compression, which it is good at.
Why is the dam thicker at the base?
The pressure rises with depth, and so does the thrust, so the base has to be thicker to keep the stress about the same.
Is this enough to design a dam?
No. It is the simplified thin-arch estimate. A real design needs a three-dimensional analysis, the foundation and the abutments, uplift, temperature, earthquake and the load combinations required by the codes.
What are the main design checks?
Abutment stability, sliding, overturning, uplift, temperature effects and the stress in the foundation.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: USBR, Design of Arch Dams; ANCOLD Guidelines on Design Criteria for Concrete Gravity Dams; Novak et al, Hydraulic Structures.
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