Reliability Analysis of Tunnel Face in Broken Soft Rocks Using Improved Response Surface Method

Abstract

An improved response surface method (RSM) is presented for reliability analysis of a tunnel face in broken soft rocks. To fully consider the variation of the slip surface caused by the random variables in the process of reliability analysis, the method uses an implicit performance function, and it is adjustable according to each possible combination of the random variables. The improved RSM and the traditional method, which is based on a deterministic performance function (a fixed slip surface), are compared. In practical projects, random variables are often correlated, and normal distributions are not advisable under some circumstances. To satisfy the practical requirements, the proposed method was extended into the space of nonnormal correlated random variables. Sensitivity analysis was performed by examining different combinations of the coefficient of variation (COV) of random variables. Results show the following: (1) A significant improvement was observed in the reliability analysis using the proposed method, especially when a large uniform force was applied to the tunnel face. (2) Beta distributions are suggested in lieu of normal distributions to exclude the negative values that probably occur as random data. (3) The stability of the tunnel face tended to be underestimated without consideration of negative correlation of random variables. (4) The stability of the tunnel face was more sensitive to the internal friction angle than to the cohesion, and the sensitivity was intensified when the negative correlation was considered. In summary, the improved RSM adequately considers the uncertainties in engineering and leads to a more reliable stability assessment of the tunnel face.