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3. 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. 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 4

5. 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 5

6. 6 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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8. No.Support system explanationIndex 1Supporting by B40 shotcrete 5 cm in thicknessA 2Supporting by B40 shotcrete 8 cm in thicknessB 3Supporting by B40 shotcrete 8 cm in thickness together with rock boltsC 4Application of roof piping together with cement injectionD 5Application of rock bolts to the gallery, roof and sidesE 6Application of steel arches with 1m spacingF 7Application of steel arches with 0.5 m spacingG 8Supporting by B50 shotcrete, 5 cm in thicknessH 9Supporting by B50 shotcrete, 8 cm in thicknessI 10Application of steel arches with 1 m spacing together with rock boltsJ 8

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11. Model index Displacement at point (cm) The maximum stress on tunnel circumference (MPa) Safety factor 1234 A11.5126.8212.254.0336.441.04 B8.9224.0011.032.0829.931.47 C1.893.721.330.5024.752.32 D2.103.921.020.4323.732.44 E10.3023.368.195.1129.471.15 F4.146.354.123.1922.821.79 G2.813.631.300.6125.702.13 H10.6225.1111.833.2935.611.25 I8.1323.9110.092.0130.041.59 J3.504.012.610.8225.112.28 11

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14. 14ab c d 1 2 2 1 EMV EMV

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17. 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 17

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19. Alternatives Criteria Goal 19 Support SystemCDGJ Weight0.2010.1460.2020.451 The overall inconsistency < 0.1 is acceptable

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22. CDGJ C10.04770.02520.01170.0045 C20.00840.02100.03360.0756 C30.05460.01680.02940.1092 C40.05740.02460.09840.2296 C50.00440.02160.01200.0020 C60.02030.03780.00350.0084 C70.00360.00210.01620.0081 Criteria Support Systems with safety factor > 2 22

23. A*A* A-A- C10.04770.0045 C20.07560.0084 C30.10920.0168 C40.22960.0246 C50.02160.0020 C60.03780.0035 C70.01620.0021 positive ideal solutionnegative ideal solution 23

24. Support system Positive distance Negative distance Relative closeness 24

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26. Step 1: deviation matrixStep 2: preference functionsStep 3: preference index and matrixStep 4: outgoing flowsStep 5: entering flowsStep 6: ranking 26

27. C1C2C3C4C5C6C7 C-D:0.25-0.090.180.08-0.43-0.250.05 C-G:0.40-0.180.12-0.10-0.190.24-0.42 C-J:0.48-0.48-0.26-0.420.060.17-0.15 D-C:-0.250.09-0.18-0.080.430.25-0.05 D-G:0.15-0.09-0.06-0.180.240.49-0.47 D-J:0.23-0.39-0.44-0.500.490.42-0.20 G-C:-0.400.18-0.120.100.19-0.240.42 G-D:-0.150.090.060.18-0.24-0.490.47 G-J:0.08-0.30-0.38-0.320.25-0.070.27 J-C:-0.480.480.260.42-0.06-0.170.15 J-D:-0.230.390.440.50-0.49-0.420.20 J-G:-0.080.300.380.32-0.250.07-0.27 support systems Criteria 27

28. CriteriaC1C2C3C4C5C6C7 Threshold0.2650.2550.2400.2670.2770.2730.260 C1C2C3C4C5C6C7 P(C,D)0.3590.0000.2450.0440.000 0.018 P(C,G)0.6800.0000.1180.000 0.3200.000 P(C,J)0.8060.000 0.0230.1760.000 P(D,C)0.0000.0600.000 0.7010.3420.000 P(D,G)0.1480.000 0.3140.7990.000 P(D,J)0.3140.000 0.7920.6930.000 P(G,C)0.0000.2210.0000.0680.2100.0000.729 P(G,D)0.0000.0600.0310.2040.000 0.805 P(G,J)0.0450.000 0.3350.0000.417 P(J,C)0.0000.8300.4440.7110.000 0.153 P(J,D)0.0000.6890.8140.8280.000 0.256 P(J,G)0.0000.4990.7140.5130.0000.0320.000 Preference function 28

29. CDGJ C00.1020.1080.086 D0.06000.0820.108 G0.0890.12300.030 J0.5050.6140.4330 support system 29 Matrix of preference indexes Preferenceindex Preference index Preference function Weight of the ith attribute

30. CDGJ Outgoing flow0.09880.08360.08050.5175 Entering flow0.21830.27980.20760.0747 Net flow-0.1195-0.1962-0.12710.4428 support system 30 Outgoing flow Entering flow Net flow

31. Preference1234 AHPJGCD TOPSISJGCD PROMETHEEJCGD J: Application of steel arches with 1 m spacing together with rock boltsG: Application of steel arches with 0.5 m spacingC: Supporting by B40 shotcrete 8 cm in thickness together with rock boltsD: Application of roof piping together with cement injection 31

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