Excavation and design of the support parameters of circular hydraulic tunnel under non-uniform stress field

Diversion tunnel is one of the most important underground structures in agriculture, water conservancy and engineering fields. Optimal parameters are critical to ensure the safety of tunnel construction. In this study, the complex function was used to determine support parameters of a circular hydraulic tunnel, considering the influence of excavation unloading and the interaction between surrounding rock and lining. An analytical solution was also derived for the stress and displacement under the condition of immediate support after excavation in the non-uniform stress field with smooth contact between the lining and surrounding rock. The correctness of the solution was verified to compare with the classic Kirsch solution. Finally, the objective function of parameters optimization was established for the tunnel construction using the maximum principal stress criterion. Two cases were selected to design the excavation size of the tunnel and the elastic modulus of lining, namely, the horizontal ground stress less or greater than vertical ground stress. The results show that the stress concentration caused along the excavation boundary of surrounding rock, and the stress distribution inside the lining were all related to the size of the tunnel, the internal water pressure, the horizontal lateral pressure coefficient, the physical and mechanical parameters of surrounding rock and the lining. The excavation radius was optimized, when the horizontal lateral pressure coefficient was less than 1.00 in example 1 (design of excavation size of surrounding rock). It was also found that the maximum principal stress appeared at 0° of the inner wall, where 24.999 478 MPa was for the optimized excavation radius of 3.67 m, and about 28.29 MPa for the excavation radius of 4.00 m. When the excavation radius is 3.67 m, the resistance of lining material is satisfied, while when the excavation radius is 4.00 m, the strength limit of lining material is exceeded, and the tensile stress appeared. The maximum principal stress in the lining increased, with the increase of excavation size. The optimal size of tunnel excavation was beneficial to reduce the cost of lining support. The principal stress changed in the radial and circumferential directions, and even the tensile stress appeared near the 0° and 90° of the inner wall of the lining, with the further expansion of excavation size. Correspondingly, the reinforcement ratio for the inner wall of lining increased appropriately in the support design to enhance the tensile strength. The elastic modulus of lining was optimized, when the horizontal lateral pressure coefficient was greater than 1.00 in example 2 (design of elastic modulus of lining material). Comparing the optimized elastic modulus 14.71 GPa with the elastic modulus 15.00 GPa, it was found that the maximum principal stress appeared at 90° of the inner wall, where the former was about 24.999 968 MPa, which meets the resistance of the lining material, and the latter was about 25.26 MPa, which exceeds the strength limit of the lining material. The maximum principal stress value in the lining increased, with the increase of the elastic modulus of lining material. Consequently, a high-strength and low-modulus concrete ratio can be expected to design for the better bearing capacity of the lining. The findings can provide a sound theoretical reference for the tunnel excavation and support parameter design in modern projects.