A novel characteristic matrix approach for analyzing displacement patterns of tunnels in operation

Analyzing tunnel displacements is a conventional and the most effective approach for diagnosing possible causes of structural anomalies, which is essential to maintaining operational rock tunnels. To analyze the in-plane 2D displacements of a tunnel with a circular profile, this work applies a novel characteristic matrix approach. The characteristic matrix is a collection of the characteristic displacement modes, which are deduced from the normalized displacements along a tunnel wall caused by a unit force at various degrees of freedom, and has unit column vectors that are mutually orthogonal. Measured tunnel displacements can be decomposed analytically into characteristic displacement modes using the characteristic matrix. The characteristic displacement modes can be described by a series of trigonometric functions with distinct periods; thus, the physical meaning of each mode is clear. The proposed approach is compared with the reported characteristic deformation curve method, and is applied to decompose measured displacements of an operational tunnel into deformation modes to demonstrate its application.