Discussions of the Correctness of the Classical Analytical Solution to Real Concrete Dams

The classical analytical elastic solution for concrete dam is assumed that the bottom extends to infinitely far. However, real dam in nature is not that high. This paper intends to investigate whether this classical analytical solution could be applied to an idealized concrete dam where the dam foundation elasticity is infinite or can say extremely rigid. Results indicate that when adjacent to the bottom boundary line of the dam superstructure, the analytical solution and FEM solution deviate with each other. The analytical solution and FEM solution agree well with each other when the studied point is very far away from the bottom boundary line. All the results indicate that Saint-Venant’s Principle applied to the bottom boundary line of concrete dam for the analytical solution. The dam superstructure bottom boundary stress condition is not known when to obtain the classical analytical solution in the past. However in fact, the dam superstructure bottom boundary stress condition must affect the stress distribution in the dam superstructure. But the resultant forces of the stresses on the dam superstructure bottom boundary from the classical analytical solution satisfy the equilibrium equation of the dam superstructure under all external forces. This is just the merit and defect of the Saint-Venant’s Principle which loosens the boundary stress condition to obtain an approximate solution which is almost correct when the studied point is far away from the loosened boundary and always wrong when the studied point is near the loosened boundary. It means that only when the studied point is very far away from the bottom boundary line of a dam, the obtained stress distribution results from the classical analytical elastic solution are acceptable.