Abstract: The high pressure and water-bearing caverns close to the face of karst tunnels are liable to induce geological hazard of water inrush and mud outburst, therefore, the determination of appropriate rock wall thickness is a pivotal problem which needs to be solved immediately in tunnel construction. Two procedures, one with linear Mohr-Coulomb criterion and the other for the case of nonlinear Hoek-Brown failure criterion are proposed to compute the rock wall thickness based on upper bound theorem of limit analysis theory. According to the three-dimensional failure pattern established here, the specific procedures are deduced to derive the expressions of rock wall thickness with these two methods. The linear Mohr-Coulomb method is adopted to calculate the rock wall thickness under the surrounding rock ranging from levelⅠto Ⅴ. The results indicate that with the decrease of surrounding rock level, namely a lower values of cohesion and internal frictional angle, the thickness increases continuously. As to the nonlinear Hoek-Brown approach, the effect of each parameter on rock wall thickness is analyzed, and the failure shape and scope of rock wall are plotted based on the calculation results. Meanwhile，the suggested values of constant A, B in Hoek-Brown criterion are given. Namely, the surrounding rock changes from the level Ⅰ to Ⅵ, the lithologic condition ranging from good to bad，it is suggested to give A for 0.5~0.3 and B for 0.7~0.9. The rock wall thicknesses of Yunwushan tunnel and Yesanguan tunnel are calculated with two methods, respectively, and the results are in good agreement with engineering practice, which verifies the validity of the methods in this literature. The two methods could provide reference for the design and construction of tunnels in high-risk karst regions.

Key words: karst tunnels, rock wall thickness, limit analysis theory, water inrush and mud outburst, linear Mohr-Coulomb criterion, nonlinear Hoek-Brown criterion