Probabilistic assessment of seismic risk for nuclear power plants

Abstract Probabilistic approaches to the design, siting, and safety analysis of nuclear power plants have been proposed by Farmer, Wall, and Garrick. Farmer and Wall established a limit line which delineates between acceptable and unacceptable risks. To implement the method, all accidental chains are systematically analyzed to determine their probability and associated fission product release magnitude; the combination is compared to the limit line. For proper implementation, the seismic risk should be evaluated in a quantified manner. Conceptually, this evaluation is made in two stages: the probability of an earthquake occurrence as a function of its intensity and, given a seismic intensity, the conditional probability of damage. This paper reports on an initial study into the latter aspect. The effect of uncertainty in several parameters which determine the response of a nuclear reactor building to earthquake forces is assessed. Probability distributions for material properties were determined from site measurements and these distributions were utilized for determining the building response and the damage criterion. A subjective probability density function for damping was assigned from the available information and the judgment of experienced engineers. Four accelerograms, El Centro NS 1940, and three artificial earthquakes were used to represent the variability in the forcing functions. The uncertainty in the model idealization was assessed by evaluating three alternate models. A versatile computer program was developed to compute the response of the mathematical model to the forcing functions using matrix formulation and modal method of analysis. An exact solution, rather than numerical integration, was used to obtain the dynamic response of the system in generalized coordinates. The stresses within the reactor building are similar for different earthquakes considered in this study when they are normalized to ground acceleration, indicating that the shape of the accelerogram and its frequency content are less significant than the magnitude of the maximum ground acceleration for the reactor building. The variation in modulus of elasticity for concrete had a significant effect on the building response. Damping, in general, reduced the response, but in cases where the duration of an earthquake is short the effect was not very significant. A simple failure criteria for ultimate shear stress in shear walls, τ ult = 4.75 √ƒ′ c , where ƒ′ c is the ultimate compressive strength of concrete, is used to estimate the initiation of cracking in the walls. The normal design of the reactor building is deterministic and is based on a 0.2 g design basis earthquake. Using the results obtained by the parametric study on the variation of response, the probability of damage was estimated by a Monte Carlo analysis. It was estimated that, given the occurrence of a design basis earthquake, there is less than approximately 10−3 probability of cracking in the shear walls of the reactor building. The initiation of cracking in the concrete should not lead to a significant release of contained fission products.