Measurement of safety state of cross-jointed segmental lining based on system performance index

The correlation between convergence deformation and the safety state of a cross-jointed segmental lining is investigated and clarified. The limitations of convergence deformation as a measuring scale is explored also. Firstly, an analytical algorithm (known as the relative stiffness method, RSM) is developed and verified for tracing the mechanical response of a cross-jointed segmental lining in failure history. Then, an explicit mapping relationship between convergence deformation and the causal factors is established using the RSM. Finally, the root causes of the limitations in using convergence deformation as a scale to evaluate tunnel safety state are discussed, and an alternative quantity, the system performance index (SPI), is proposed. It shows that: (1) The convergence deformation consists of three components induced by segment bending, elastic joint rotation, and joint stiffness attenuating, respectively. The deformation induced by attenuating joint stiffness is dependent on the failure index of segment joints and provides crucial information about the load-bearing state of the segment joints; (2) The components of elastic joint rotation and joint stiffness attenuating are significantly affected by the contact stiffness of the segment joint interface, including the physical and mechanical properties of the packing material. The magnitudes of convergence deformation and its components are not suitable for use as a quantitative scale to evaluate the safety state of the lining due to their inherent drawbacks; (3) The proposed dimensionless variable SPI can eliminate the influence of packing material on the safety state of the segment lining and reflect the comprehensive influence of the failure indexes of the segment joints.