1. 2 3 Generally, support system for a tunnel is designed by some analytical calculation + experience Designs are often suitable but not optimum In this.

1

Selection of Tunnel Support System by Using Multi Criteria Decision-Making ToolsKazem Oraee, Navid Hosseini, Mehran Gholinejad

29th International Conference onGround Control in Mining

2

Support system selection and effective parameters

Support System

Selection

Technical

EconomicalPerformance

3

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

4

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

5

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

6

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

7

Numerical modeling – FLAC3D Software

3D grid model and stresses contours in X, Y, and Z direction

8

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

9

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

10

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

11

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

12

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

13

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

14

A typical simple decision tree

a

b

c

d

Pay – off(Goal)

1

2

2

1

EMV

EMV

AlternativesCriterion

Decision Point

15

Hierarchy of optimum support system selection

16

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.

17

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

18

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.

19

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

20

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.

21

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

22

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

23

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

24

Positive and negative distance / Relative closeness and ranking

Support system

Positive distance

Negative distance

Relative closeness

Ranking Rank 3 4 2 1

25

3) Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE)

The PROMETHEE is a multi-criteria decision making methodology

The PROMETHEE determines preference between alternatives

26

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

27

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

28

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

29

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

30

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

31

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

32

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.

33

for kind attention