Seismic Design of Tunnels - Parsons Brinckerhoff

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LIST OF FIGURES Figure Title Page 1 Ground Response to Seismic Waves 6 2 Damage Statistics 11 3 Axial and Curvature Deformations 28 4 Ovaling and Racking Deformations 30 5 Geometry of a Sinusoidal Shear Wave Oblique to Axis of Tunnel 32 6 Sectional Forces Due to Curvature and Axial Deformations 39 7 Free-Field Shear Distortions of Ground Under Vertically Propagating Shear Waves 57 8 Free-Field Shear Distortion of Ground (Non-Perforated Medium) 59 9 Shear Distortion of Perforated Ground (Cavity In-Place) 59 10 Lining Response Coefficient, K 1 (Full-Slip Interface) 66 11 Lining Response Coefficient, K 1 (Full-Slip Interface) 67 12 Lining Response (Thrust) Coefficient, K 2 (No-Slip Interface) 69 13 Lining Response (Thrust) Coefficient, K 2 (No-Slip Interface) 70 14 Lining Response (Thrust) Coefficient, K 2 (No-Slip Interface) 71 15 Normalized Lining Deflection (Full-Slip Interface) 73 16 Normalized Lining Deflection (Full-Slip Interface) 74 17 Finite Difference Mesh (Pure Shear Condition) 75 18 Influence of Interface Condition on Bending Moment 78 19 Influence of Interface Condition on Lining Deflection 80 iv
Figure Title Page 20 Typical Free-Field Racking Deformation Imposed on a Buried Rectangular Frame 89 21 Structure Stability for Buried Rectangular Frames 91 22 Soil-Structure System Analyzed in Example 93 23 Subsurface Shear Velocity Profiles 95 24 Free-Field Shear Deformations (from Free-Field Site Response Analysis, SHAKE) 97 25 Structure Deformations vs. Free-Field Deformations, Case I (from Soil/Structure Interaction Analysis, FLUSH) 98 26 Structure Deformations vs. Free-Field Deformations, Case ll (from Soil/Structure Interaction Analysis, FLUSH) 99 27 Typical Finite Element Model (for Structure Type 2) 103 28 Earthquake Accelerograms on Rock West Coast 104 Northeast 105 29 Design Response Spectra on Rock (West Coast Earthquake vs. Northeast Earthquake) 106 30 Types of Structure Geometry Used in the Study 107 31 Relative Stiffness Between Soil and a Rectangular Frame 108 32 Determination of Racking Stiffness 111 33 Normalized Racking Deflections (for Cases 1 through 25) 115 34 Normalized Structure Deflections 116 35 Normalized Structure Deflections 117 v
Page 1 and 2: 1991 William Barclay Parsons Fellow
Page 3 and 4: CONTENTS Foreword ix 1.0 Introducti
Page 5: Mononobe-Okabe Method 87 Wood Metho
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 and 50: Applicability of the Free-Field Def
Page 51 and 52: Figure 6. Sectional Forces Due to C
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
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10. Calculate the allowable shear s
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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
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Figure 7. Free-Field Shear Distorti
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Figure 8. Free-Field Shear Distorti
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R = radius of the tunnel lining t =
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Lining Properties Soil Properties R
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The expressions of these lining res
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Figure 11. Lining Response Coeffici
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Thrust Response Coefficient, K 2 Fi
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Thrust Response Coefficient, K 2 Fi
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Figure 15. Normalized Lining Deflec
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Figure 17. Finite Difference Mesh (
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Table 2. Cases Analyzed by Finite D
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maximum bending moment than the no-
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Table 3. Influence of Interface Con
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5.0 RACKING EFFECT ON RECTANGULAR T
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Third, typically soil is backfilled
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thrust that is approximately 1.5 to
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San Francisco BART In his pioneerin
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general, flexibility can be achieve
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• 254 ft/sec for case I • 415 f
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locations of roof and invert are ap
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Figure 25. Structure Deformations v
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Factors Contributing to the Soil-St
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As Figures 28A and 28B show, earthq
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Figure 28A. West Coast Earthquake A
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Figure 29. Design Response Spectra
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Figure 31. Relative Stiffness Betwe
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developed for a one-barrel frame wi
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• For flexibility ratios less tha
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where g s = angular distortion of t
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Structure Deformation Free-Field De
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Because the Poisson’s Ratios of t
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Table 5. Cases Analyzed to Study th
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In comparison with the results show
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Structure Deformation Free-Field De
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• Pseudo-Concentrated Force Model
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deformations result. Section 2.4 in
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Figure 40. Moments at Invert-Wall C
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Figure 42. Moments at Invert-Wall C
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Table 7. Seismic Racking Design App
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136
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• The more frequently occurring e
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Use of this method will lead to a c
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142
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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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