An arch dam transfers loads to the abutments and foundations both by cantilever action and through horizontal arches, and a method of distribution was developed by Stucky in Switzerland and the USBoR.
The assumptions made are not strictly true so the effect of each must be understood before accepting the design.
- The concrete in the dam and the rock foundations are homogeneous and isotropic;
- Stresses within the elastic limit for both concrete and the rock formations and that stress will be proportional to strain;
- That plane sections before bending remain plane after bending;
- That direct stresses vary linearly between the upstream and downstream faces, in both arch and cantilever elements;
- That the modulus of elasticity of concrete and the modulus of deformation of the foundation are the same in tension as in compression;
- That temperature stresses and strains are proportional to temperature changes;
- That water load on the reservoir walls does not cause differential movements at the damsite;
- That foundation deformations are independent of the shape of the foundation;
- That tensions are relieved by cracking so that all loads are carried by compression and shear in the uncracked portions;
- That the dam acts as a monlith, i.e. that contraction joints or slots have been tightly grouted and that all shrinkage of the concrete has taken place before this.
The parameters controlling design, other than actual geometry include:
- The loads on the dam; Loading and Factor of Safety
- The degree of fixity to foundation and abutments;
- The properties of the component materials of the dam and the foundations.
Steel reinforcement can reduce the thickness of the dam but at a cost. If reinforcement was not used then cracking in the faces of an arch dam may result from:
Definition of different arch dams based on base thickness (h is height of the dam):
- Excessive tensile stress due to dam geometry;
- Secondary tension resulting from high compressive forces in thin members;
- Secondary tensile stresses at the arch haunches and parallel to the abutments;
- 'Hang up' of concrete adjacent to a near vertical abutment;
- Temperature effects - either due to hydration of the cement or climatic conditions.
|Medium arch||0.2h - 0.3h|
Reinforcement is not generally required in arch-gravity dams or thick arch dams. Its use in thin arch dams is favoured, however for a 90m high dam the cost of reinforcement will be many millions of dollars, which could mitigate the adoption of such a dam.
Uplift - is not usually of importance in thin arch dams, but in thick arch dams provision is made for internal drainage, as for gravity dams. If the design assumes that the concrete will crack if tensions exceed say 0.4MPa, then it is consistent to assume that full hydrostatic pressure can act in such cracks.
Tensile stresses - the aim of the designer is to eliminate tensile stresses, although this is not always possible since an irregular cross-section can generate local stress concentrations, and necessary excavation of abutments beyond the design limits will alter the geometry of the dam, and possibly affect the degree of fixity.