Introduction

2. Introduction • Finite element analysis of a pre-cast arch cut and cover rail tunnel • Reasons for the study • Increased collision design loads • Increasing use of arch cut and cover tunnels • Comparatively thin section thickness • Lack of guidance in codes • Analyses Compared • Simple analysis with equivalent static loads • Nin-linear analysis with equivalent static loads • Non-linear “push-over” analysis

3. Rail Collision Design Loads • Current Austroads Bridge Design Code – 1992 Longitudinal: 2000 kN Transverse: 1000 kN • Draft Australian Standard Bridge Design Code - 2000 Longitudinal: 3000 kN Transverse: 2000 kN • Loads applied simultaneously at a height of 2 metres above rail level – Ultimate Limit State Load

4. Analysis Procedure • 2D plane strain finite element analysis • The fill was modelled as a mohr-coulomb elasto-plastic material • Non-cohesive fill between pile caps • Arch modelled using beam elements including moment-curvature behaviour • Friction elements allowed slip between the arch and the soil • Varying fill properties • Material and geometric non-linearity included • Effects of fill stiffness and strength and concrete section strength and ductility assessed

5. Arch Cross Section

6. Detail of Finite Element Model

7. Analysis runs considered • Simplified model: All materials linear elastic; no friction elements • Non-linear soil, linear elastic beam elements • Moment-curvature behaviour of beams added • Friction elements added • Non-linear geometry added • Model 5 with varying soil and concrete section parameters

8. Run No. Fill Concrete Elastic Modulus, MPa Poisson’s Ratio Strength Tensile Reinf. Density % Ultimate Curvature, m-1 6A 10 0.3 40 0.76 0.30 6B 30 0.3 40 0.76 0.30 6C 60 0.3 40 0.76 0.30 6D 30 0.3 40 1.72 0.087 Parameters for run series 6

9. Moment Curvature Diagram

10. Bending Moments; Linear elastic concrete

11. Shear Forces; Linear elastic concrete

12. Bending Moments; Non-linear concrete

13. Shear Forces; Non-linear concrete

14. Deflections; Non-linear concrete

15. Beam curvature; Non-linear concrete

16. Summary, Runs 2-5

17. Push over analysis animation

18. Push over analysis animation

19. Bending moments; push over analysis

20. Shear Forces; push over analysis

21. Curvature; push over analysis

22. Applied Force; push over analysis

23. Summary, Runs 6

24. Summary, Runs 6

25. Conclusions • Linear elastic analysis overestimates the bending moments and shear forces in the structure • A typical arch section had adequate ductility for rail impact loading, When the moment-curvature behaviour of the arch section was included in the analysis • Slip at the soil/concrete interface, and geometric non-linearity effects have a significant effect on the arch forces and deflections • Increasing the amount of tensile reinforcement reduced the ductility of the section, and is not recommended. • The provision of confinement reinforcement had only limited effect on the section ductility.

26. Conclusions • The fill stiffness is important. With low stiffness (10 MPa) fill, the ductility of the section used in this paper was only just adequate. • Three dimensional distribution of the impact pressures through the fill, and the dynamic stiffness of the fill provide an additional level of safety. • Provide an alternative load path to maintain the stability of the structure, in the event of the failure of one precast panel.

27. Recommendations • 2D finite element analysis of the impact load. • Distribute the load across one precast panel • Include the fill and foundations within the zone of influence of the structure • Allow for slip between the structure and the soil • Allow for both material and geometric non-linearity • Model moment-curvature behaviour of the reinforced concrete • Include the required stiffness of the fill material in the project specification. • Provide an alternative load path to maintain the stability of the structure, in the event of the failure of one precast panel