Analytical approach for circular-jointed shield tunnel lining based on the state space method

This paper presents a new analytical solution to the circular segmental tunnel lining subjected to overburden and surrounding earth pressures. The governing equations are derived by adopting the curved Euler beam theory and the principle of minimum potential energy. Based on the state space method, the displacements and the relevant energy-conjugated internal forces are treated as the fundamental unknown state vector and can be obtained by solving the state function. The inter-segment joints on the lining are modeled by a set of linear springs, including shear, compression, and rotation. The presented method allows for the arbitrary distribution of the segmented joints and loads along the circumferential direction. The most striking advantages of the proposed method include the rigid body displacement treatment, lining-displacement-dependent soil reaction, and internal force direction dependency of the joint stiffness. Using this method, the displacements and internal forces of the entire lining can be obtained conveniently and simultaneously under the arbitrary loading and joint distribution conditions. The verification of the analytical solutions is provided by several examples.