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A Comparison of Numerical Methods and Analytical Methods in Determination of

Tunnel Walls DisplacementBehdeen Oraee-Mirzamani

Imperial College London, UK

Saeed ZandiAzad University, Iran

Professor Kazem OraeeUniversity of Stirling, UK

32th International Conference on Ground Control in Mining

Morgantown, WV

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Structure of presentation

Background and introduction

Tunnels in underground mining

Case study

Analytical methods

Numerical methods

Summary

Conclusion

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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.

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Tunnel and Underground Mining

Tunnel

Room and Pillar

Sublevel Caving

Block Caving

LongwallSublevel Stoping

Shrinkage

Cut and Fill

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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.

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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.

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Case study: Parvade Underground Coal MineThe Parvade coal field lies approximately 85km 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 4m by 4m.

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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.

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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.

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The Input Parameters Used in Numerical Modeling

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Created Model in Phase 2

According to in-situ stresses and material properties,

this finite element model was created.

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Extracted Results from Phase 2

Horizontal Displacement Deformation Vectors

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Horizontal Displacement

According to the extracted results from Phase 2, the

maximum tunnel walls displacement is 20mm.

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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.

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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 164mm.

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Ground Reaction Curve

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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.

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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.

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ConclusionsAnalytical 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

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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.

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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.

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Thank you for your attention