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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
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