1. 2 3 generally, support system for a tunnel is designed by some analytical calculation +...
TRANSCRIPT
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Selection of Tunnel Support System by Using Multi Criteria Decision-Making ToolsKazem Oraee, Navid Hosseini, Mehran Gholinejad
29th International Conference onGround Control in Mining
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Support system selection and effective parameters
Support System
Selection
Technical
EconomicalPerformance
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Generally, support system for a tunnel is designed by some analytical calculation + experience
Designs are often suitable but not optimum
In this paper selection is optimised and ranked
Selection process is assumed to be a multi-criteria decision making problem
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Three methods are used:AHP, TOPSIS, PROMETHEE
Optimum support system is chosen for C1 tunnel of Tabas coal mine of Iran
C1 is the main entry of the mine → Long life → Support system is important
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Geomechanical parameters of the rock mass and in-situ stresses
Uni-axial compressive strength: 10.7 MPa
Tensile strength based on Brazilian test: 1.3 MPa
Young’s modulus: 4385 MPa
Poisson’s ratio: 0.25
Friction angle: 35 degrees
Cohesion: 5 MPa
Vertical and horizontal in-situ stresses: 12.50, and 4.71MPa
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For modeling, the FLAC3D software is used. In FLAC3D:
Therefore: the potential support systems based on technical view points are selected
The geometry of tunnel is defined
Geomechanical parameters of the surrounding rock mass were input to the model
Potential values for failure and displacement parameters are calculated
Various support systems are applied in the model and the stability of the tunnel after application of each support system is determined
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Numerical modeling – FLAC3D Software
3D grid model and stresses contours in X, Y, and Z direction
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The studied support systems
No. Support system explanation Index
1 Supporting by B40 shotcrete 5 cm in thickness A
2 Supporting by B40 shotcrete 8 cm in thickness B
3 Supporting by B40 shotcrete 8 cm in thickness together with rock bolts C
4 Application of roof piping together with cement injection D
5 Application of rock bolts to the gallery, roof and sides E
6 Application of steel arches with 1m spacing F
7 Application of steel arches with 0.5 m spacing G
8 Supporting by B50 shotcrete, 5 cm in thickness H
9 Supporting by B50 shotcrete, 8 cm in thickness I
10 Application of steel arches with 1 m spacing together with rock bolts J
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Selected critical points in the tunnel
Point 1 is on the tunnel roof
Point 2 is on the floor
Point 3 is located on the intersection of the wall and floor, horizontal direction
Point 4 is located on the intersection of the wall and floor, vertical direction
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Numerical modeling and factor of safety
The 10 support systems are applied in the numerical model described
The minimum acceptable factor
of safety is decided to be 2
For each support system, the displacements and stresses are measured in points 1, 2, 3, and 4 to calculate the factor of safety
Support systems with factor of safety > 2 are acceptable
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Results of numerical model
Model index
Displacement at point (cm) The maximum stress ontunnel circumference
(MPa)
Safety factor
1 2 3 4
A 11.51 26.82 12.25 4.03 36.44 1.04
B 8.92 24.00 11.03 2.08 29.93 1.47
C 1.89 3.72 1.33 0.50 24.75 2.32D 2.10 3.92 1.02 0.43 23.73 2.44E 10.30 23.36 8.19 5.11 29.47 1.15
F 4.14 6.35 4.12 3.19 22.82 1.79
G 2.81 3.63 1.30 0.61 25.70 2.13H 10.62 25.11 11.83 3.29 35.61 1.25
I 8.13 23.91 10.09 2.01 30.04 1.59
J 3.50 4.01 2.61 0.82 25.11 2.28
From technical point of view (safety factor), the C, D, G, and J support systems are acceptable
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The support system with factor of safety of more than 2
C: Supporting by B40 shotcrete 8 cm in thickness together with
rock bolts
D: Application of roof piping together with cement injection
G: Application of steel arches with 0.5 m spacing
J: Application of steel arches with 1 m spacing together with
rock bolts
We now seek to devise a preference table between the
support systems
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Decision criteria for choosing the optimum support system
No. Criterions explanation Index
1 The vertical displacement at point 1 C1
2 The vertical displacement at point 2 C2
3 The horizontal displacement at point 3 C3
4 The vertical displacement at point 4 C4
5 The support system costs C5
6 The support system performance C6
7 Safety factor C7
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A typical simple decision tree
a
b
c
d
Pay – off(Goal)
1
2
2
1
EMV
EMV
AlternativesCriterion
Decision Point
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Hierarchy of optimum support system selection
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1) Analytical Hierarchy Processing (AHP) method
AHP is a structured technique for dealing with complex decisions.
Rather than prescribing a "correct" decision, the AHP helps decision maker to find the one that best suits his needs and provides conception of the problem.
AHP provides a comprehensive and rational framework for structuring a decision problem, for representing and quantifying its elements, relating those elements to overall goals and evaluating alternative solutions.
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The implementation steps of the AHP
Step 1:Hierarchy
Tree
Step 2:Decision Making Matrix
Step 3:Pair-wise
Comparison Matrix
Step 4:Normalized
Matrix
Step 5:Relative Weights
Step 6:Attributes Weights Vector
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AHP method and Expert Choice software
To select the support system based on AHP, the Expert Choice software is used. In Expert Choice:
1. Decision making tree is constructed.
2. The pair-wise comparison matrix of alternatives based on each criterion (C1 to C7) are generated.
3. The pair-wise comparison matrix of criteria is generated.
After data entry, the Expert Choice ranks the alternatives based on the AHP method.
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The ranking of support systems based on the AHP method – Expert Choice software
Alternatives
Criteria
Goal
Support System C D G J
Weight 0.201 0.146 0.202 0.451
Rank 3 4 2 1
The overall inconsistency < 0.1 is acceptable
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2) Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)
TOPSIS is a multi-criteria method to identify the solutions from a finite set of alternatives.
The concept of TOPSIS is that the chosen alternative should have the shortest distance from the ideal solution and the furthest distance from the negative-ideal solution.
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The implementation steps of TOPSIS
Step 1
• Construction of Weighted Normalized Matrix
Step 2
• Determination of Positive-Ideal and Negative-Ideal Solutions
Step 3
• Determination of the distance of the alternatives from positive and negative ideals
Step 4
• Determination of the relative closeness of each alternative to the ideal solution
Step 5
• Ranking
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Weighted normalized matrix
C D G J
C1 0.0477 0.0252 0.0117 0.0045
C2 0.0084 0.0210 0.0336 0.0756
C3 0.0546 0.0168 0.0294 0.1092
C4 0.0574 0.0246 0.0984 0.2296
C5 0.0044 0.0216 0.0120 0.0020
C6 0.0203 0.0378 0.0035 0.0084
C7 0.0036 0.0021 0.0162 0.0081
Criteria
Support Systems with safety factor > 2
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Positive and negative ideal solutions
A* A-
C1 0.0477 0.0045
C2 0.0756 0.0084
C3 0.1092 0.0168
C4 0.2296 0.0246
C5 0.0216 0.0020
C6 0.0378 0.0035
C7 0.0162 0.0021
positive ideal solution negative ideal solution
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Positive and negative distance / Relative closeness and ranking
Support system
Positive distance
Negative distance
Relative closeness
Ranking Rank 3 4 2 1
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3) Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE)
The PROMETHEE is a multi-criteria decision making methodology
The PROMETHEE determines preference between alternatives
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The implementation steps of the PROMETHEE
Step 1: deviation matrix
Step 2: preference functions
Step 3: preference index and matrix
Step 4: outgoing flows
Step 5: entering flows
Step 6: ranking
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Matrix of deviation amplitude for normalized values
C1 C2 C3 C4 C5 C6 C7
C-D: 0.25 -0.09 0.18 0.08 -0.43 -0.25 0.05
C-G: 0.40 -0.18 0.12 -0.10 -0.19 0.24 -0.42
C-J: 0.48 -0.48 -0.26 -0.42 0.06 0.17 -0.15
D-C: -0.25 0.09 -0.18 -0.08 0.43 0.25 -0.05
D-G: 0.15 -0.09 -0.06 -0.18 0.24 0.49 -0.47
D-J: 0.23 -0.39 -0.44 -0.50 0.49 0.42 -0.20
G-C: -0.40 0.18 -0.12 0.10 0.19 -0.24 0.42
G-D: -0.15 0.09 0.06 0.18 -0.24 -0.49 0.47
G-J: 0.08 -0.30 -0.38 -0.32 0.25 -0.07 0.27
J-C: -0.48 0.48 0.26 0.42 -0.06 -0.17 0.15
J-D: -0.23 0.39 0.44 0.50 -0.49 -0.42 0.20
J-G: -0.08 0.30 0.38 0.32 -0.25 0.07 -0.27
support systems
Criteria
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Values of threshold & Preference function
Criteria C1 C2 C3 C4 C5 C6 C7
Threshold 0.265 0.255 0.240 0.267 0.277 0.273 0.260
C1 C2 C3 C4 C5 C6 C7
P(C,D) 0.359 0.000 0.245 0.044 0.000 0.000 0.018
P(C,G) 0.680 0.000 0.118 0.000 0.000 0.320 0.000
P(C,J) 0.806 0.000 0.000 0.000 0.023 0.176 0.000
P(D,C) 0.000 0.060 0.000 0.000 0.701 0.342 0.000
P(D,G) 0.148 0.000 0.000 0.000 0.314 0.799 0.000
P(D,J) 0.314 0.000 0.000 0.000 0.792 0.693 0.000
P(G,C) 0.000 0.221 0.000 0.068 0.210 0.000 0.729
P(G,D) 0.000 0.060 0.031 0.204 0.000 0.000 0.805
P(G,J) 0.045 0.000 0.000 0.000 0.335 0.000 0.417
P(J,C) 0.000 0.830 0.444 0.711 0.000 0.000 0.153
P(J,D) 0.000 0.689 0.814 0.828 0.000 0.000 0.256
P(J,G) 0.000 0.499 0.714 0.513 0.000 0.032 0.000
Preference function
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Matrix of preference indexes
C D G J
C 0 0.102 0.108 0.086
D 0.060 0 0.082 0.108
G 0.089 0.123 0 0.030
J 0.505 0.614 0.433 0
support system
Matrix of preference indexes
Preference index
Preference function
Weight of the ith attribute
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All flows and ranking of alternatives – PROMETHEE method
C D G J
Outgoing flow 0.0988 0.0836 0.0805 0.5175
Entering flow 0.2183 0.2798 0.2076 0.0747
Net flow -0.1195 -0.1962 -0.1271 0.4428
Rank 2 4 3 1
support system
Outgoing flow
Entering flow
Net flow
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Ranking of support systems for this tunnel
Preference 1 2 3 4
AHP J G C D
TOPSIS J G C D
PROMETHEE J C G D
J: Application of steel arches with 1 m spacing together with rock bolts
G: Application of steel arches with 0.5 m spacing
C: Supporting by B40 shotcrete 8 cm in thickness together with rock bolts
D: Application of roof piping together with cement injection
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Conclusion
Multi criteria decision making techniques can be useful tools in selection of optimum support systems.
AHP and TOPSIS techniques have given identical results namely “application of steel arches with 1m spacing together with rock bolts” being the best.
PROMETHEE gives similar result with only 2nd and 3rd alternatives being different.
These methods can be applied in all similar situation.
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for kind attention