1. Concrete 2003 Brisbane July 2003 Design Of Pre-cast Buried Structures For Internal Impact Loading

2. Introduction Finite element analysis of a pre-cast arch cut and cover rail tunnel Reasons for the study o Increased collision design loads o Increasing use of arch cut and cover tunnels o Comparatively thin section thickness o Lack of guidance in codes Analyses Compared o Simple analysis with equivalent static loads o Nin-linear analysis with equivalent static loads o 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 1.Simplified model: All materials linear elastic; no friction elements 2.Non-linear soil, linear elastic beam elements 3.Moment-curvature behaviour of beams added 4.Friction elements added 5.Non-linear geometry added 6.Model 5 with varying soil and concrete section parameters

8. Parameters for run series 6 Run No. FillConcrete Elastic Modulus, MPa Poisson’ s Ratio StrengthTensile Reinf. Density % Ultimate Curvature, m -1 6A100.3400.760.30 6B300.3400.760.30 6C600.3400.760.30 6D300.3401.720.087

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

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