Seismic Design of Tunnels - Parsons Brinckerhoff

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1987). In general, the tunnel-ground system is simulated as an elastic beam on an elastic foundation, with the theory of wave propagating in an infinite, homogeneous, isotropic medium. When subjected to the axial and curvature deformations caused by the traveling waves in the ground, the tunnel will experience the following sectional forces (see Figure 6): • Axial forces, Q, on the cross-section due to the axial deformation • Bending moments, M, and shear forces, V, on the cross-section due to the curvature deformation Simplified Interaction Equations Maximum Axial Force: Qmax. Through theoretical derivations, the resulting maximum sectional axial forces caused by a shear wave with 45 degree angle of incidence can be obtained: K a L Q max = 2p K 1 + 2 Ê a ˆÊ L ˆ ËE c A c ¯Ë2p ¯ 2 D (Eq. 3-1) Where L = wavelength of an ideal sinusoidal shear wave K a =longitudinal spring coefficient of medium (in force per unit deformation per unit length of tunnel) D = free-field displacement response amplitude of an ideal sinusoidal shear wave E c = modulus of elasticity of tunnel lining A c = cross-section area of tunnel lining The calculated maximum axial force, Q max , shall not exceed an upper limit defined by the ultimate soil drag resistance in the longitudinal direction. This upper limit is expressed as: Q limit = fL 4 (Eq. 3-2) where f = ultimate friction force (per unit length of tunnel) between the tunnel and the surrounding medium 38
Figure 6. Sectional Forces Due to Curvature and Axial Deformations (Source: Owen and Scholl, 1981) 39
Page 1 and 2: 1991 William Barclay Parsons Fellow
Page 3 and 4: CONTENTS Foreword ix 1.0 Introducti
Page 5 and 6: Mononobe-Okabe Method 87 Wood Metho
Page 7 and 8: Figure Title Page 20 Typical Free-F
Page 9 and 10: LIST OF TABLES Table Title Page 1 F
Page 11 and 12: FOREWORD For more than a century, P
Page 13: 1.0 INTRODUCTION 1
Page 16 and 17: 1.2 Scope of this Study The work pe
Page 18 and 19: Figure 1. Ground Response to Seismi
Page 20 and 21: Ground Failure Ground failure broad
Page 22 and 23: - Formation of plastic hinges at th
Page 24 and 25: • The effects of overburden depth
Page 27 and 28: 2.0 SEISMIC DESIGN PHILOSOPHY FOR T
Page 29 and 30: 2.3 Seismic Design Philosophies for
Page 31 and 32: 2.4 Proposed Seismic Design Philoso
Page 33 and 34: expressed in terms of internal mome
Page 35: Comments on Loading Combinations fo
Page 39 and 40: 3.0 RUNNING LINE TUNNEL DESIGN 3.1
Page 41 and 42: Ovaling or Racking Deformations The
Page 43 and 44: 3.3 Free-Field Axial and Curvature
Page 45 and 46: Simplified Equations for Axial Stra
Page 47 and 48: 3.4 Design Conforming to Free-Field
Page 49: Applicability of the Free-Field Def
Page 53 and 54: - In the JSCE (Japanese Society of
Page 55 and 56: Design Example 2: A Linear Tunnel i
Page 57 and 58: 5. Derive the ground displacement a
Page 59 and 60: 10. Calculate the allowable shear s
Page 61 and 62: It is believed that the only transp
Page 63: Based on Equations 3-7 and 3-8, the
Page 67 and 68: 4.0 OVALING EFFECT ON CIRCULAR TUNN
Page 69 and 70: Figure 7. Free-Field Shear Distorti
Page 71 and 72: Figure 8. Free-Field Shear Distorti
Page 73 and 74: R = radius of the tunnel lining t =
Page 75 and 76: Lining Properties Soil Properties R
Page 77 and 78: The expressions of these lining res
Page 79 and 80: Figure 11. Lining Response Coeffici
Page 81 and 82: Thrust Response Coefficient, K 2 Fi
Page 83 and 84: Thrust Response Coefficient, K 2 Fi
Page 85 and 86: Figure 15. Normalized Lining Deflec
Page 87 and 88: Figure 17. Finite Difference Mesh (
Page 89 and 90: Table 2. Cases Analyzed by Finite D
Page 91 and 92: maximum bending moment than the no-
Page 93 and 94: Table 3. Influence of Interface Con
Page 95: 5.0 RACKING EFFECT ON RECTANGULAR T
Page 98 and 99: Third, typically soil is backfilled
Page 100 and 101:
thrust that is approximately 1.5 to
Page 102 and 103:
San Francisco BART In his pioneerin
Page 104 and 105:
general, flexibility can be achieve
Page 106 and 107:
• 254 ft/sec for case I • 415 f
Page 108 and 109:
locations of roof and invert are ap
Page 110 and 111:
Figure 25. Structure Deformations v
Page 112 and 113:
Factors Contributing to the Soil-St
Page 114 and 115:
As Figures 28A and 28B show, earthq
Page 116 and 117:
Figure 28A. West Coast Earthquake A
Page 118 and 119:
Figure 29. Design Response Spectra
Page 120 and 121:
Figure 31. Relative Stiffness Betwe
Page 122 and 123:
developed for a one-barrel frame wi
Page 124 and 125:
• For flexibility ratios less tha
Page 126 and 127:
where g s = angular distortion of t
Page 128 and 129:
Structure Deformation Free-Field De
Page 130 and 131:
Because the Poisson’s Ratios of t
Page 132 and 133:
Table 5. Cases Analyzed to Study th
Page 134 and 135:
In comparison with the results show
Page 136 and 137:
Structure Deformation Free-Field De
Page 138 and 139:
• Pseudo-Concentrated Force Model
Page 140 and 141:
deformations result. Section 2.4 in
Page 142 and 143:
Figure 40. Moments at Invert-Wall C
Page 144 and 145:
Figure 42. Moments at Invert-Wall C
Page 146 and 147:
Table 7. Seismic Racking Design App
Page 148 and 149:
136
Page 150 and 151:
• The more frequently occurring e
Page 152 and 153:
Use of this method will lead to a c
Page 154 and 155:
142
Page 156 and 157:
Duddeck, H. and Erdman, J., “Stru
Page 158 and 159:
Tunnels, Report No. UMTA-MA-06-0100
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Seismic Design of Tunnels - Parsons Brinckerhoff

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