Behdeen Oraee-Mirzamani Imperial College London, UK Saeed Zandi Azad University, Iran

1. A Comparison of Numerical Methods and Analytical Methods in Determination of Tunnel Walls Displacement Behdeen Oraee-Mirzamani Imperial College London, UK SaeedZandi Azad University, Iran Professor Kazem Oraee University of Stirling, UK 32th International Conference on Ground Control in Mining Morgantown, WV

2. Structure of presentation • Background and introduction • Tunnels in underground mining • Case study • Analytical methods • Numerical methods • Summary • Conclusion

3. Tunnel • A tunnel is an underground passageway, used for access, ventilation etc, completely enclosedexcept commonly at both ends. • Tunnels are dug in different types of materials varying from soft clay to hard rock. • A tunnel may be used for foot, rail or vehicular road traffic.

4. Tunnel and Underground Mining

5. Tunnels in Underground Mining • Tunnels are important parts in underground mines and have a significant role in ore production and transportation. In some methods such as room and pillar mining, they represent an integral part of the mining process. • Tunnels’ stability can affect production and productivity in underground coal mines. • Tunnels’ instability or collapse can also cause safety hazards and economic damages since it can disrupt or stop production and ore transportation.

6. Therefore • Suitable and correct design and implementation of support systems is necessary in order to prevent collapse in tunnels. • In order to design a suitable support system for a tunnel, it is necessary to know the different types of stressesaround the tunnel. • Analysis of tunnels’ roof and walls stability and determination of displacement in these regions, can help to design optimum support system.

7. Case study: Parvade Underground Coal Mine • The Parvade coal field lies approximately 85km south of the city of Tabasin Iran. • The total probable anthracite reserve in the region is approximately 1.2 billion tons. • The minable reserve suitable for underground production is 28 million tons in mine 1. • In this study, displacement fields in the roof and walls of the tunnels have been studied. • The tunnel’s dimensions are 4m by 4m.

8. Analysis Methods • There are various methods for analysis of tunnel stability and determination of tunnels’ walls displacement. Two of the main methods are: Analytical Methods Numerical Methods • These methods have been used widely in order to analyze the stability of tunnels during the design process of underground mines.

9. Numerical Method • For numerical modeling, Phase 2 software is used • Phase 2 is based on Finite Element Method (FEM) • It is a 2-dimensional program that calculates stresses and displacements around underground openings. • It can be used in a wide range of mining and civil engineering problems.

10. The Input Parameters Used in Numerical Modeling

11. Created Model in Phase 2 • According to in-situ stresses and material properties, this finite element model was created.

12. Extracted Results from Phase 2 Horizontal Displacement Deformation Vectors

13. Horizontal Displacement • According to the extracted results from Phase 2, the maximum tunnel walls displacement is 20mm.

14. Analytical Method • For the analytical modeling, the Duncan FamaMethod is used. • This analytical method requires parameters such as: Modulus of elasticity (MPa), Poisson’s ratio, Internal angle of friction and Rock mass compressive strength. • This method has been used for drawing the Ground Reaction Curve in order to determine the tunnel walls displacement.

15. Ground Reaction Curve • The Ground Reaction Curve can be defined as a curve that describes the decreasing of the inner pressure and the increasing of radial displacement of the tunnel’s wall. • As evident from the Ground Reaction Curve obtained using the Duncan Fama method, the maximum tunnel walls displacementis 164mm.

16. Ground Reaction Curve

17. Summary • The displacement of tunnel walls was calculated using both numerical and analytical methods. • The maximum displacement of tunnel walls calculated using the numerical method was 20mm. • The maximum displacement of tunnel walls calculated using the analytical method was 164mm. • The comparison of these methods show a noteworthy difference in the tunnel walls displacement.

18. Summary • The reason for this difference is due to the difference in the assumptions and limitations within the two methods. • After this comparison, based on these results and mining conditions, the suitable method for stability analysis of tunnels can be chosen.

19. Conclusions • Analytical solutions often have limited application because they must be used within the range of assumptions.These assumption usually include: • Elastic behavior • Isotropic and homogeneous material • Time independent behavior • Quasi-static loading • The ratio of horizontal stress to vertical stress being constant

20. Conclusions • One of the other limiting assumptions in analytical methods is the need for the cross section of the tunnel to be circular. • Rocks may not be isotropic or homogeneous and the loading may not be static. Additionally the geometry of the problem may be complex. • In these cases,solutions can only be obtained numerically.

21. Conclusions • Numerical methods can be widely used to perform stability analysis in all underground excavations with different shapes and dimensions. • Comparing analytical and numerical methods, it seems that numerical methods (Phase 2) are more suitable for stability analysis of tunnels in underground coal mines.

22. Thank you for your attention