This manuscript established an innovative approach for recognizing deformation patterns of a built tunnel, which benefits for diagnosing possible causes for lining anomalies. Demonstrating with a circular tunnel, the deformation of a tunnel lining is first assumed to be composition of specific deformation patterns. These patterns are numerically approved as linearly independent to each other with sufficient degrees of freedom, and are thus regarded as characteristic modes which can assemble all deformation situations by multiplying various constants. Several simple examples with load variation on boundaries are introduced to demonstrate the proposed method. Lining displacements in each example are decomposed as linear combination of characteristic modes. Diagrammatic illustrations indicate these deformation patterns posing different physical meaning including translation, rotation, and several types of deformation for tunnel lining.


Instrumentation in underground structures after the completion of construction is used to check the overall behavior of the excavation during operation (Hoek & Brown, 2002). Early detection of lining anomalies is the first step for operational tunnel maintenance. Diagnosing possible causes accounting for anomalies and implementing necessary repairing measures in time accordingly are of importance for tunnel managements and infrastructure sustainable developments (Wang et al., 2007). Although it is imperative to know to what is leading the tunnel into instability, diverse causes and complex feature of anomalies for operational tunnels make it extremely difficult to interpret the monitoring results. Without awareness of deformation mechanism, the rehabilitation and reinforcement strategy may not be appropriate and the degradation of tunnel remains.

Contemporary researches on deformation analysis of operational tunnels can roughly be categorized into two types (Japan Society of Civil Engineers, 2003). One of them determines tunnel deformation by considering rock mass deformation, such as long-term effects caused by the visco-elasto-plastic behavior of a rock mass (Cristescu, 1988; Cristescu et al., 1987) and stiffness deterioration (Ladanyi, 1974; Shimamoto et al., 2009). The other solely takes account of timedependent variation of engineering characteristics for tunnel lining. He et al. (2009) conducted physical model experiments for concrete tunnels subjected to concentrated loads acting from various directions and induced three dominant failure modes. Chiu et al. (2012) made uses of numerical simulation for relating various types of loading increments with tunnel deformation patterns and named them after characteristic deformation curves. Wang (2010) characterized the spatial distribution patterns of lining cracks induced by slope instability. Stiros and Kontogianni (2009), Obara et al. (2011) fit the deformed shape of a circular tunnel with an ellipse to determine the directions of principal stresses. For uniform deformation cases like Figure 1, most of the aforementioned methods give satisfactory approximation. However, the deformation patterns of operational tunnels are generally far more complicated than that in Figure 1, new approaches to analyze deformation patterns for tunnels in operation are still needed.

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