Analytical Inversion of the Equivalent Horizontal Load on Shield Tunnel Linings from a Single-Point Rotation Measurement

External loads acting on shield tunnel linings in service are difficult to determine, while existing back analysis methods often require multiple monitoring quantities and repeated numerical calculations. This study develops an analytical method for identifying the equivalent horizontal load and lateral pressure coefficient from a single rotation measurement. The lining is modelled as a continuous Euler–Bernoulli curved beam on a radial Winkler foundation, with circumferential compression and bending considered. The radial components of the vertical and horizontal loads are decomposed into uniform and second-order terms. Closed-form solutions are obtained for displacement, rotation, and internal forces, followed by an explicit inverse relation between rotation at one circumferential position and the load difference. The analytical responses agree closely with an independent plane-frame finite element model. Prescribed horizontal loads and lateral pressure coefficients are also recovered accurately from finite element rotations. A FLAC3D model of the complete ring with continuous elastic ground further shows that the circumferential response pattern is retained and that the equivalent horizontal load can still be estimated when the Winkler ground representation is relaxed. The method identifies the load difference from one rotation measurement, and when the vertical load is independently estimated, determines the equivalent horizontal load. It provides a basis for assessing lining ovalization, bending response, and abnormal loading states.