A plastic analysis of radial displacements at tunnel crown based on the non-associated flow rule

This paper considers the non-associated flow rule to propose an analytical solution to calculate the ground reaction curve at the crown of a circular tunnel. This solution is based on the Mohr-Coulomb failure criterion and the dilation angle has been considered as a function of two factors of rock mass quality and confining stress. The results show that if the radial displacements are not controlled, a loosening zone is produced in the tunnel crown (cohesion=0.2 MPa and friction angle=25°). Moreover, based on the trend of the ground reaction curve at the tunnel crown, three new concepts “minimum required support pressure”, “maximum allowable strain”, and “safety factor based on the maximum allowable strain” was presented. Considering the interaction between the support characteristics curve and ground reaction curves, the efficiency of the associated flow rule to the non-associated flow rule was investigated. Results state that the use of the associated flow rule causes some sort of computational errors in determining the maximum allowable strain (too high) and consequently, the design accuracy of the support system is very low. Moreover, taking into account the associated flow and non-associated flow rules at the sidewall and tunnel crown, the interaction between the support characteristics curve and ground reaction curve was investigated. Based on the results, it was suggested that to design an optimal support system, it is necessary to calculate the safety factor based on the maximum allowable strain by considering the interaction between the support characteristics curve and the ground reaction curve at the tunnel crown. Finally, a procedure was presented for the design of the support system.