Uncertainty Analysis of Contaminant Transportation Through Ground Water Using Fuzzy-Stochastic Response Surface

Abstract

The process of contaminant transportation through ground water can be varied with different parameters such as soil characteristics, ground water flow velocity, longitudinal and transverse dispersion coefficients, self-degradation of contaminant etc. The precise definition of these parameters is very difficult due to various factors such as measurement error, sampling error, dependence of complex physical phenomena, etc. The analytical solution of transient advection–diffusion equation is being used to assess the ground water contamination due to the industrial discharge. The paper describes a methodology to estimate the hybrid uncertainty, i.e., combination of aleatory and epistemic using the fuzzy-stochastic system. Aleatory uncertainty due to random variation of input parameter is estimated using polynomial chaos expansion method. To take into account the effect of imprecise variation (i.e., epistemic uncertainty) of input parameter, a fuzzy $\alpha$-cut technique has been used. The large sample space of concentration reduction factor (CRF) have been generated using fuzzy-stochastic response surface to arrive the upper uncertainty bound corresponds to the 95th percentile value at a specified distance from the source and period of time. The methodology will be very useful to assess the safety margin or discharge limit from the industry.