Reliability-based optimum design of hydraulic water retaining structure constructed on heterogeneous porous media: utilizing stochastic ensemble surrogate model-based linked simulation optimization model

Abstract

AbstractSeepage characteristics under hydraulic water retaining structures (HWRSs) significantly affect the hydraulic serviceability and stability of such structures. The expected hydraulic conductivity value and its spatial and directional variation substantially influence seepage characteristics. Furthermore, the uniform and homogenous hydraulic conductive is rarely seen in the real field. To study the effects of uncertainty and variation in hydraulic conductivity, a random field concept was used to generate different realizations of heterogeneous hydraulic conductivity with constant mean and varied standard deviation. Consequently, the seepage characteristics stochastically varied, creating uncertainty in seepage characteristics which influenced the HWRS design. Therefore, the objective of this paper was to integrate the reliability concept in the linked simulation optimization (S-O) model to address the uncertainty of hydraulic conductivity. Hence, the safest and most cost-effective HWRS design could be attained considering the effects of the uncertainty of hydraulic conductivity. The reliability-based optimum design (RBOD) concept was implemented utilizing the multiple realization optimization technique based on stochastic ensemble surrogate models. The reliability degree of each candidate design was measured based on the number of stochastic constraints satisfying the design requirements to the total number of constraints. The S-O model-based RBOD was formulated to find the most cost-effective HWRS design satisfying a beforehand desired degree of reliability. Each surrogate model was trained utilizing several (input–output) data sets simulated using numerical seepage modeling code (SEEPW). The Gaussian process regression machine learning technique was used to train several surrogate models to imitate the responses of the numerical seepage modeling. Each single input data set was solved (4\u2009×\u20095) times to simulate four different realizations of spatial variation resulting from one of the five different standard deviation values (0.85, 1.55, 2.25, 2.95, 3.65\xa0m/day) with constant mean (2\xa0m/day). Each group of data for single standard deviation was utilized to train a single surrogate model. The genetic algorithm-based S-O model was utilized as an efficient optimization solver for such complex optimization task. The results of this study demonstrated that the reliability significantly influenced the design of HWRS. Further, the deterministic optimum design of HWRS was insufficient to be considered a reliable design, especially when a high degree of uncertainty due to the hydraulic conductivity estimation is included. Hence, RBOD for such problem is essential and helps the designer make a decision.\n