A New Close-Form Solution for Elastoplastic Seepage-Induced Stresses to Circular Tunnel with Considering Intermediate Principal Stress

Based on the DP (Drucker–Prager) yield criterion, a new semi-analytical method for hydraulic–mechanical coupling in circular tunnels is proposed which takes into account the evolution of the permeability coefficient by incorporating it into the seepage equation. The definite condition is supplemented through the method of equal flow at the elastic–plastic junction. Constitutive equation and yield criterion are expressed by effective stress. When the pore water pressure drops to zero, the solution presented in this paper can degenerate into the classical Lamé solution in elastic region, and the solution obtained after yielding is consistent with the Drucker–Prage’s solution. The numerical simulation method is used to verify the proposed solution, and then, the sensitivity of the strength parameters is discussed. The results show that the radius of the plastic zone decreases with increasing cohesion C and internal friction angle φ°, and the decreasing tendency is more sensitive at lower cohesion and internal friction angle. Higher initial yield stresses are easily obtained by increasing the values of these two parameters appropriately. The solution presented in this paper is not applicable when the internal friction angle is greater than 40°. Considering the intermediate principal stress, the solution presented in this paper shows a higher initial yield in-situ stress than that of MC (Mohr–Coulomb) and Hoek–Brown (HB) materials. Compared with the solution of DP criterion, the solution in the current work has a larger range of plastic region, and is more obvious in high in-situ stress area. In addition, the initial yield stress also increases linearly with the head loss.