Probabilistic structural reliability study of concrete gravity dam

The safety and/or probability of failure of an existing concrete gravity dam subjected to normal static and dynamic loads is evaluated. The study describes a probabilistic generalized methodology of quantifying the uncertainties of input random variables. The application demonstrated that the performance of gravity dams can be assessed more realistically than through deterministic methods.

Statistical parametric studies are performed on structural data measurements of the dam covering a period of approximately twenty-five-years. Expressions for uplift pressure distribution at the base of the dam is derived by the principle of least squares curve fitting. Comparison of the derived uplift forces to Tennessee Valley Authority's uplift design equation indicates close agreement. A suite of thirty-nine actual earthquake acceleration time history records was normalized to 0.15g horizontal and O.lOg vertical. A total of twenty- six directional components was input to a program that performs a dynamic earthquake finite element analysis of the dam. Two water elevations of the reservoir were considered, a mean of 1656.0 feet and a maximum flood of 1710.0 feet. Statistical analyses were performed on the structural responses of the dam for each reservoir level. The mean annual temperature distribution of the dam was verified by a statistical study of temperature readings taken at thermometers and growth meters located across the dam. Thermal stress analysis was performed using GTSRUDL Finite Element Program linear elastic plane strain element capability. Comparison of the thermal stresses with that of other load effects indicates significant thermal stress levels across the dam. However, these critical stresses occur at elements not significantly affected by both static and earthquake loadings.

Three modes of failure were considered, namely, sliding, overturning, and overstressing. These modes of failure define the structural stability of the dam. Ten limit states or performance functions were investigated, five for each reservoir level. The corresponding reliability indices and probabilities of failure were calculated using the first order second moment (FOSM) and second order reliability method (SORM). These probabilistic methods indicated that the dam has an extremely low probability of failure for the static loading combinations. However, when the dynamic inertia forces were included, the overturning and overstressing probability of failures become critical. The calculated factor of safety closely confirms the stability of the dam. The joint conditional probability of failure was calculated by taking the product of the critical probability of failure, the probability of a maximum credible earthquake occurrence, and the probability of occurrence of maximum flood.