Evaluation of Uncertainty Associated With Spatially Variable Properties

Uncertainties associated with spatially variable properties of geologic characteristics are especially important. However, these uncertainties cannot be specified in a deterministic manner because the process of formation or evolution of host rock is random and because the limited number of data is available for the statistic evaluation of this random process. We develop the hybrid model of fuzzy geostatistics for the appropriate treatment of uncertainties associated with spatially variable properties. For the application of the above method, we prepared the virtual field with heterogeneous hydraulic conductivity for the simulation of site characterization. In this simulation, we consider the situation that the limited number of boring data is available. The conventional method can determine only one variogram. In this case, uncertainties due to the ignorance are not appropriately handled and the degree of belief for the determined variogram is not specified. For the appropriate treatment of ignorance, we define the possible range of variogram in terms of fuzzy membership functions on the level of conservatism. A large number of heterogeneous hydraulic conductivity fields are realized by using corresponding variograms that sampled from the possible range of variogram. For each realized field, we compute the groundwater flow model and estimate the average flow velocity. Resulting many average flow velocities are processed by fuzzy rule to obtain the membership function of estimated average flow velocity. This can be used as the input data for the hybrid probabilistic and possibilistic safety assessment. Comparing with the previous work, the process of defining the membership function of average flow velocity becomes transparent and the reliability of safety assessment is enhanced.