Elastic–Plastic Solutions for Deformation Pressure on Deep‐Buried Circular Tunnels in Non‐Uniform Stress Field

ABSTRACT As the utilization of shallow and medium‐depth underground spaces approaches saturation, the future development of urban underground space will increasingly shift toward deeper strata. The geological composition of these underground spaces primarily consists of soil layers. The ground pressure acting on underground structures is closely related to ground deformation. However, traditional loosening earth pressure theory fails to account for the effect of ground deformation on ground pressure. This study presents an elastic–plastic solution for the deformation pressure of deep‐buried circular tunnels under non‐uniform stress fields. To derive the elastic–plastic solution, a new method is proposed for constructing the stress function. This method enables the determination of the elastic stress field of a tunnel in an infinite domain under gravity. The obtained elastic–plastic solution effectively captures the evolution of ground pressure during tunnel deformation. The validity of the elastic–plastic solution is verified through finite element analyses and model tests. In addition, the proposed method is compared with the loosening earth pressure theory. The results indicate that as the C / D ratio ( C and D denote the tunnel burial depth and diameter) increases, the ground pressure calculated by the loosening earth pressure theory decreases, whereas the pressure obtained from the proposed method increases. Under finite deformation conditions, the loosening earth pressure theory tends to underestimate the tunnel load.