A Comparison of Numerical Methods and Analytical Methods

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

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

Tunnel �A tunnel is an underground passageway, used for access, ventilation etc, completely enclosed except 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. 3

Room and Pillar Tunnel and Underground Mining Cut and Fill Sublevel Caving Tunnel Block Caving Shrinkage Sublevel Stoping Longwall 4

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. 5

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 stresses around the tunnel. �Analysis of tunnels’ roof and walls stability and determination of displacement in these regions, can help to design optimum support system. 6

Case study: Parvade Underground Coal Mine � The Parvade coal field lies approximately 85 km south of the city of Tabas in 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 4 m by 4 m. 7

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. 8

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. 9

The Input Parameters Used in Numerical Modeling 10

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

Extracted Results from Phase 2 Horizontal Displacement Deformation Vectors 12

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

Analytical Method �For the analytical modeling, the Duncan Fama Method 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. 14

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 displacement is 164 mm. 15

Ground Reaction Curve 16

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

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. 18

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 19

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. 20

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. 21

Thank you for your attention 22