Considering the effect of the separation between the supporting layer and the base layer of the ballastless railway caused by foundation settlement, a simplified method was proposed for calculating the rail deformation of the ballastless railway to tunnelling underneath. Firstly, the track slab and the supporting layer were supposed as a composite elastic beam, and a simplified equation for the deformation of ballastless railway composite beams induced by shield tunneling was proposed by ignoring the influence of fasteners on the composite beam deformation. Afterwards, the composite beam was divided into a void zone and a joint zone, and the analytical solutions for the deformations of the composite beams caused by tunnlling underneath were proposed based on the elastic foundation beam theory. Furthmore, the rail was regarded as an Euler beam connecting with the composite beam by the dispersed spring, and the equations for the rail deformation caused by the composite beam deformation were derived. Based on the above, compared with the numerical simulation and theoretical results in the existing literature, the proposed simplified method of the ballastless railway caused by tunneling underneath was validated. Finally, the influences of model parameters on the rail deformation to tunnelling underneath were discussed, including the tunnelling induced ground loss rate, the composite beam bending stiffness, the fastener stiffness, and the rail bending stiffness. The results indicate that the theoretical calculation results were overestimated by neglecting the local suspension effect of the supporting layer. Reducing the tunnelling induced ground loss rate, strengthening the composite beams and rails can control the rail deformation of the ballastless railway caused by tunnlling undercrossing, but strengthening the fasteners stiffness may increase the unevenness of rail deformation.
| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |