Guarantee Rate Statistics and Product-Moment Correlation Analysis of the Optimal Deformation Allowance for Loess Tunnel in China

Abstract

The relevant value standards for reserved deformation of tunnels with different types of loess soil are not yet perfect. Through mathematical statistics, literature research, and other methods, 148 monitoring sections of loess tunnels with different soil types were investigated. Pearson, Kendall, and Spearman correlation coefficients were used to analyze the influence of surrounding rock grade, moisture content, and burial depth on the deformation law of tunnels, providing reference for the value of reserved deformation for loess tunnels. The research results indicate that: (1) The correlation between soil type and convergence around the tunnel is strong, followed by excavation span, and the correlation between moisture content and burial depth is weak. Therefore, the design of reserved deformation should focus on considering the soil type and excavation span. (2) For loess tunnel sections with class IV surrounding rock, the deformation allowance for cohesive loess and silty loess tunnel sections can be set within 15 cm, and for sandy loess, it can be set within 15–20 cm. (3) For the loess tunnel section with V-grade surrounding rock, the deformation margin can be determined as follows: viscous loess within 15–20 cm, silty loess within 15 cm, and sandy loess within 35–47.5 cm. (4) The moisture content is mainly distributed between 11% and 23%. It is worth noting that in sandy loess sections, the influence of moisture content on tunnel arch settlement is more significant compared to cohesive loess and silty loess sections. (5) The settlement of the arch crown is affected by changes in coverage depth and has discreteness. When the deformation margin is set to 16 cm, the assurance rate can reach 84.6%. Finally, the rationality of the proposed reserved deformation amount was verified through engineering practice. The research results can provide reference for related similar projects.