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Practical stochastic response surface method (SRSM) using ordinary high-order polynomials with mixed terms to approximate the true limit state function (LSF) is proposed to analyze the reliability of bypass seepage stability of earth-rockfill dam. Firstly, the orders of random variable are determined with a univariate fitting. Secondly, nonessential variables are excluded to identify possible mixed terms. Thirdly, orthogonal table is used to arrange additional samples, and stepwise regression is conducted to achieve a specific high-order response surface polynomial (RSP). Fourthly, Monte Carlo simulation (MCS) is used to calculate the failure probability, and RSP is updated by arranging several additional samplings around the design point. At last, the Bantou complex reinforced earth-rockfill dam was taken as an example. There are 6 random variables, that is, the upper water level and 5 hydraulic conductivities (HCs). The result shows that a third-order RSP can ensure good precision, and the failure probability of bypass seepage stability is within an acceptable risk range. The HC of concrete cut-off wall and the HC of rockfill are unimportant random variables. Maximum failure probability at the bank slope has positive correlation with the HC of curtain and the upper water level, negative correlation with the HC of alluvial deposits, and less significance with the HC of filled soil. With the increase of coefficient of variation (Cov) of the HC of curtain, the bypass seepage failure probability increases dramatically. Practical SRSM adopts a nonintrusive form. The reliability analysis and the bypass seepage analysis were conducted separately; therefore, it has a high computational efficiency. Compared with the existing SRSM, the RSP of practical SRSM is simpler and the procedure of the reliability analysis is easier. This paper provides a further evidence for readily application of the high-order practical SRSM to engineering.

mathematical problems in engineering

Reliability Analysis for Bypass Seepage Stability of Complex Reinforced Earth-Rockfill Dam with High-Order Practical Stochastic Response Surface Method