Fig.1-1. Intersection of KJ Tunnel 17

Fig.1-2. Intersection of SN-YJ Subway 18

Fig.1-3. Intersection of SBD Subway (1) 18

Fig.1-4. Intersection of SBD Subway (2) 18

Fig.1-5. Influence from superposition of vibration due to two trains 19

Fig.1-6. Schematic and objectives for research 20

Fig.2-1. Terminologies of vibration wave 25

Fig.2-2. Displacement, velocity, acceleration for a simple harmonic motion 26

Fig.2-3. Definition of simple harmonic motion 27

Fig.2-4. Raw signal data 29

Fig.2-5. RMS velocity (㏈(V)) 29

Fig.2-6. Superposition of waves propagating in two opposite directions 31

Fig.2-7. Constructive Interference (Daniel A. Russell, 2004) 32

Fig.2-8. Two sine waves with different frequence : Beats 33

Fig.2-9. Superposition of wave propagating on adjacent two tunnels 34

Fig.2-10. Cases of numerical analysis 35

Fig.2-11. Sine waves loads 35

Fig.2-12. Vertical acceleration of tunnel crown(A) 36

Fig.2-13. Vertical acceleration of ground surface 37

Fig.2-14. Vertical acceleration of tunnel crown(B) 37

Fig.2-15. Vertical acceleration of ground surface 38

Fig.2-16. Vertical acceleration of tunnel crown(A) 38

Fig.2-17. Vertical acceleration of tunnel crown(B) 39

Fig.2-18. Vertical acceleration of ground surface 39

Fig.2-19. Vertical acceleration of tunnel crown(A) 40

Fig.2-20. Vertical acceleration of tunnel crown(B) 40

Fig.2-21. Vertical acceleration of ground surface 40

Fig.2-22. Acceleration of each CASES 41

Fig.3-1. Outline of laboratory model test 43

Fig.3-2. The laboratory model tester installation process 44

Fig.3-3. Vibration generating device(1) 44

Fig.3-4. Vibration generating(1) 45

Fig.3-5. Vibration generating device(2) 45

Fig.3-6. Vibration generating device(2) 46

Fig.3-7. Wireless instrumentation system 46

Fig.3-8. Picture of laboratory dynamic test 47

Fig.3-9. Location of measuring point 48

Fig.3-10. Result of CASE 1 49

Fig.3-11. Result of CASE 2 50

Fig.3-12. Result of CASE 3(Ground surface) 50

Fig.3-13. Acceleration history in phase difference case 51

Fig.3-14. Result of CASE 4(Ground surface) 51

Fig.3-15. Model for laboratory dynamic test 52

Fig.3-16. Dynamic load 53

Fig.3-17. Modelling for numerical analysis 53

Fig.3-18. Acceleration at A point (CASE 1) 54

Fig.3-19. Acceleration at A point (CASE 2) 55

Fig.3-20. Acceleration at A point (CASE 3) 55

Fig.3-21. Acceleration and FFT graph at upper tunnel(B) 57

Fig.3-22. Acceleration and FFT graph at lower tunnel(C) 57

Fig.3-23. Ground surface acceleration (CASE 1) 58

Fig.3-24. Ground surface acceleration (CASE 2) 58

Fig.3-25. Ground surface acceleration (CASE 3) 58

Fig.3-26. Acceleration and FFT graph at upper tunnel(B) 59

Fig.3-27. Acceleration and FFT graph at lower tunnel(C) 59

Fig.3-28. Ground surface acceleration (CASE 1) 60

Fig.3-29. Ground surface acceleration (CASE 2) 60

Fig.3-30. Ground surface acceleration (CASE 3) 60

Fig.3-31. Acceleration and FFT graph at upper tunnel(B) 61

Fig.3-32. Acceleration and FFT graph at lower tunnel(C) 61

Fig.3-33. Ground surface acceleration (CASE 1) 62

Fig.3-34. Ground surface acceleration (CASE 2) 62

Fig.3-35. Ground surface acceleration (CASE 3) 62

Fig.3-36. Ground surface acceleration on frequency disagreement 63

Fig.3-37. Ground surface acceleration on frequency agreement 63

Fig.4-1. Flow Diagram for Analysis 65

Fig.4-2. Characteristic of ground vibrations due to trains 71

Fig.4-3. General tendency of attenuation in distance 73

Fig.4-4. Field instrumentation of SINKANSEN in JAPAN 74

Fig.4-5. Application of Time function EL-18 (Max speed 110㎞/hr) 75

Fig.4-6. Field measuring data from the building near Subway 76

Fig.4-7. Frequency response function curve for estimating train loads 76

Fig.4-8. Modeling for validation of field instrumentation data 78

Fig.4-9. Filed instrumentation data 78

Fig.4-10. Output data 78

Fig.4-11. General relation of strength-strain 79

Fig.4-12. Relation of shear modulus-shear strain 79

Fig.4-13. Stress-Strain curves for a system with hysteresis damping 81

Fig.4-14. Dynamic modulus of elasticity 83

Fig.4-15. Dynamic poisson's ratio 83

Fig.4-16. Influencing ranges for different intersection angles 84

Fig.4-17. Load loading method in 3D model 85

Fig.4-18. 3D Modeling 86

Fig.4-19. 2D modeling 87

Fig.4-20. Vertical acceleration comparison 2D with 3D in upper tunnel 88

Fig.4-21. Vertical acceleration comparison 2D with 3D in lower tunnel 89

Fig.4-22. Acceleration comparison 2D with 3D at upper tunnel 90

Fig.4-23. Acceleration comparison 2D with 3D at lower tunnel 91

Fig.5-1. Cases of numerical analysis 92

Fig.5-2. Model for interaction between same shape tunnels 93

Fig.5-3. Model for interaction between different shape tunnels 94

Fig.5-4. Cases of same loads 96

Fig.5-5. Measuring point of numerical analysis result 96

Fig.5-6. Acceleration at vertical direction (SS-TY1) 97

Fig.5-7. Acceleration at horizontal direction (SS-TY1) 98

Fig.5-8. Ground displacement (SS-TY1) 99

Fig.5-9. Velocity (SS-TY1) 100

Fig.5-10. Acceleration (SS-TY1) 101

Fig.5-11. Acceleration at vertical direction (SS-TY2) 102

Fig.5-12. Acceleration at horizontal direction (SS-TY2) 103

Fig.5-13. Ground displacement (SS-TY2) 104

Fig.5-14. Velocity (SS-TY2) 105

Fig.5-15. Acceleration (SS-TY2) 106

Fig.5-16. Acceleration at vertical direction (SS-TY3) 107

Fig.5-17. Acceleration at horizontal direction (SS-TY3) 108

Fig.5-18. Ground displacement (SS-TY3) 109

Fig.5-19. Velocity (SS-TY3) 110

Fig.5-20. Acceleration (SS-TY3) 111

Fig.5-21. Comparison with acceleration at ground surface 114

Fig.5-22. Maximum vertical acceleration contour line 116

Fig.5-23. Cases of different Loads 117

Fig.5-24. Comparison upper tunnel SS-TY2 with SS-TY4 118

Fig.5-25. Comparison lower tunnel SS-TY2 with SS-TY4 119

Fig.5-26. Comparison with vertical acceleration at ground surface 121

Fig.5-27. Comparison with maximum vertical acceleration contour line 122

Fig.5-28. Cases of Typical cross section 123

Fig.5-29. Measuring point of numerical analysis result 123

Fig.5-30. Acceleration at vertical direction (DS-TY1) 124

Fig.5-31. Acceleration at vertical direction (DS-TY2) 125

Fig.5-32. Acceleration at vertical direction (DS-TY3) 126

Fig.5-33. Acceleration at horizontal direction (DS-TY1) 127

Fig.5-34. Acceleration at horizontal direction (DS-TY2) 128

Fig.5-35. Acceleration at horizontal direction (DS-TY3) 129

Fig.5-36. Comparison with acceleration at ground surface 131

Fig.5-37. Maximum vertical acceleration contour line 132

Fig.5-38. Cases of superposition of separative distance 133

Fig.5-39. amax vs vertical distance with respect to lateral distance(이미지참조) 135

Fig.5-40. amax vs lateral distance with respect to vertical distance(이미지참조) 135

Fig.5-41. amax vs vertical distance with respect to lateral distance(이미지참조) 137

Fig.5-42. amax vs lateral distance with respect to vertical distance(이미지참조) 137

Fig.5-43. Factor of vibration superposition 138

Fig.5-44. Surface measuring point with distance between tunnels 138

Fig.5-45. Acceleration with horizontal distance between tunnels at point No.3 139

Fig.5-46. Acceleration with horizontal distance between tunnels at point No.4 140

Fig.5-47. Acceleration with horizontal distance between tunnels at point No.5 140

Fig.5-48. Acceleration with horizontal distance between tunnels at point No.6 140

Fig.5-49. Maximum vertical acceleration contour lines (Each CASE) 141

Fig.5-50. Cases of changing overburden 142

Fig.5-51. Maximum vertical acceleration of upper tunnel according to overburden 143

Fig.5-52. Maximum vertical acceleration of lower tunnel according to overburden 143

Fig.5-53. Maximum vertical acceleration of surface according to overburden 144

Fig.5-54. Maximum vertical acceleration contour line 146

Fig.5-55. Acceleration of upper tunnel according to geotechnical property 148

Fig.5-56. Acceleration of lower tunnel according to geotechnical property 148

Fig.5-57. Maximum vertical acceleration of surface according to geotechnical property 149

Fig.5-58. Maximum vertical acceleration contour line 151

Fig.5-59. Influence zone of ground-borne-vibration due to two Tunnels 154

Fig.6-1. Generalized Ground Surface Vibration Curves (FTA, 2006) 156

Fig.6-2. Assumption for ground vibration assessment 160

Fig.6-3. Determination of ground surface vibration 161

Fig.6-4. Simplification of intersection of two tunnels 164

Fig.6-5. The rate of increase in vertical acceleration at No.3 165

Fig.6-6. Ground vibration assessment considering superposition effect 167

Fig.6-7. The relationship of α, β and vertical distance 169