Analytical analyses of the effect of filled karst cavern on tunnel lining structure under complex geological conditions

In this study, based on the elastic foundation beam theory, a local elastic foundation model has been developed. Using the model, the mechanical characteristics of the effect of tunnel-filled karst on the lining structure has been investigated. Incorporating the characteristic of the karst area, the formulas for the displacement, bending moment, and shear force of an equivalent beam have been derived. By applying the formulas to a beam under different working conditions, such as different cavern sizes and different compression modulus ratios of the filling media, analyses of the mechanical states have been carried out. The results show that if the compression modulus ratio of different filling media is close to unity, the effect of the cave on the lining structure is very small. On the other hand, if the ratio is much less than unity, the effect is more significant. The effect on the stability of the lining structure is greater for the larger caves, and smaller for the smaller caves. For the tunnel bottom equivalent beam, its bending point is at the point where the cave is in contact with the surrounding rock. Further, the maximum shear force is at the contact surface. For a beam that is closer to the karst, the displacement is larger. Under this situation, the beam section is in an adverse force state and prone to cracks. The results from this study can be used as a significant guide for the design, maintenance and construction of a tunnel which has a cavern at the base of the tunnel.