Seismic Design of Tunnels - Parsons Brinckerhoff

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3.3 Free-Field Axial and Curvature Deformations 31 Background 31 A Practical Approach to Describing Ground Behavior 31 Simplified Equations for Axial Strains and Curvature 33 3.4 Design Conforming to Free-Field Axial and Curvature Deformations 35 Background and Assumptions 35 Design Example 1: The Los Angeles Metro 35 Applicability of the Free-Field Deformation Approach 37 3.5 Tunnel-Ground Interaction 37 Simplified Interaction Equations 38 Design Example 2: A Linear Tunnel in Soft Ground 43 3.6 Special Considerations 48 Unstable Ground 48 Faulting 48 Abrupt Changes in Structural Stiffness or Ground Conditions 49 4.0 Ovaling Effect on Circular Tunnels 53 4.1 Ovaling Effect 55 4.2 Free-Field Shear Deformations 55 Simplified Equation for Shear Deformations 56 4.3 Lining Conforming to Free-Field Shear Deformations 58 4.4 Importance of Lining Stiffness 60 Compressibility and Flexibility Ratios 60 Example 1 61 Example 2 62 Summary and Conclusions 63 4.5 Lining-Ground Interaction 64 Closed Form Solutions 64 Numerical Analysis 76 Results and Recommendations 76 5.0 Racking Effect on Rectangular Tunnels 83 5.1 General 85 5.2 Racking Effect 86 5.3 Dynamic Earth Pressure Methods 87 ii
Mononobe-Okabe Method 87 Wood Method 87 Implications for Design 88 5.4 Free-Field Racking Deformation Method 88 San Francisco BART 90 Los Angeles Metro 90 Flexibility vs. Stiffness 90 Applicability of the Free-Field Racking Method 92 Examples 92 5.5 Tunnel-Ground Interaction Analysis 96 Factors Contributing to the Soil-Structure Interaction Effect 100 Method of Analysis 100 Flexibility Ratio for Rectangular Tunnels 102 Results of Analysis 112 5.6 Recommended Procedure: Simplified Frame Analysis Models 122 Step-by-Step Design Procedure 122 Verification of the Simplified Frame Models 128 5.7 Summary of Racking Design Approaches 133 6.0 Summary 135 Vulnerability of Tunnel Structures 137 Seismic Design Philosophy 137 Running Line Tunnel Design 138 Ovaling Effect on Circular Tunnels 139 Racking Effect on Rectangular Tunnels 139 References 141 iii
Page 1 and 2: 1991 William Barclay Parsons Fellow
Page 3: CONTENTS Foreword ix 1.0 Introducti
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 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
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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
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Based on Equations 3-7 and 3-8, the
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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
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Tunnels, Report No. UMTA-MA-06-0100
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Seismic Design of Tunnels - Parsons Brinckerhoff

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