Determination of Safety Factors for Design of Temporary Support System in Tunnels Using Reliability Analysis

In this paper, reliability analysis is achieved for composite supports consisting of steel sets and shotcrete in tunnels. Appropriate distribution functions for spacing between steel frames and shotcrete thicknesses in tunnels are obtained from the statistical data collected from a recent tunnel project in north of Iran. The distribution functions are then utilized for reliability analysis of the supports using Monte Carlo technique to simulate shotcrete thickness and steel set intervals. The results indicates that effect of imperfections and deviations of shotcrete thickness should be considered in the determination of safety factor for design of temporary composite supports. Construction of tunnels has been increasing in recent years due to development of infrastructures such as highways, underground, railways and passive defense facilities. In order to excavate tunnels, both traditional drilling and blasting methods, as well as modern techniques such as TBMs (tunnel boring machines) might be used. After excavation, support systems need to be employed to make the tunnel stable. There are several approaches to support tunnels. Steel frames combined with shotcrete are usually utilized as primary support system in loose ground conditions that is the case studied in this research. Quick installations of steel frames and rough boundaries of the tunnel due to excavation circumstances lead to different shotcrete thicknesses and different spacings between steel sets. As a result, the thickness of shotcrete and spacing between steel sets can be considered as random variables. Therefore, in this paper, different failure probability is derived for different safety factors, which are used for design of steel sets and shotcrete composite support system.  For this study, different distribution functions have been utilized to fit the data. Each function is evaluated by three well known methods called Chi-squared, Kolmogorov-Smirnov and Anderson-Darling methods. According to the results obtained from all the three methods, the generalized extreme value (GEV) distribution function is recommended for the thickness of shotcrete and the Wakeby distribution function is suggested for the spacing between the steel sets. The selected distribution functions are then utilized to simulate the thickness of shotcrete and the spacings between steel sets. The Monte Carlo technique is used to evaluate the possibility of failure for various circumstances of different shotcrete thicknesses and steel sets intervals.  The results indicates that effect of deviations in shotcrete thickness should be considered to determine safety factor for design of composite sections of steel sets and shotcrete. Therefore, in this paper, safety factors are determined to reach several certain amounts of failure probabilities.