Seismic Design of Tunnels - Parsons Brinckerhoff

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Axis of Tunnel Axial Displacement of Soil Transverse Displacement of Soil Figure 5. Geometry of a Sinusoidal Shear Wave Oblique to Axis of Tunnel (Source: SFBARTD, 1960) 32
Simplified Equations for Axial Strains and Curvature Using the simplified approach, the free-field axial strains and curvature due to shear waves and Rayleigh waves (surface waves) can be expressed as a function of angle of incidence, as shown in Table 1. The most critical angle of incidence and the maximum values of the strains are also included in the table. Equations caused by compressional P-waves are also available, but it is generally considered that they would not control the design. It is difficult to determine which type of wave will dominate due to the complex nature of the characteristics associated with different wave types. Generally, strains produced by Rayleigh waves may govern only when the site is at a large distance from the earthquake source and the structure is built at shallow depth. Application of the strain equations presented in Table 1 requires knowledge of: • The effective wave propagation velocity • The peak ground particle velocity • The peak ground particle acceleration The peak velocity and acceleration can be established through empirical methods, field measurements, or site-specific seismic exposure studies. The effective wave propagation velocity in rock can be determined with reasonable confidence from in-situ and laboratory tests. Estimating the effective wave propagation velocity in soil overburden presents the major difficulty. Previous studies have shown that, except possibly for vertically propagating shear waves, the use of soil properties in deriving the wave velocity in soil overburden may be overly conservative. It has been suggested that for horizontally or obliquely propagating waves the propagation velocities in soil overburden are affected significantly by the velocities in the underlying rock. That is to say, the actual velocity values in the soils may be much higher than those calculated based on the soil properties alone (Hadjian and Hadley, 1981). This phenomenon is attributable to the problem of deformation compatibility. The motion of a soil particle due to a horizontally propagating wave above the rock cannot differ greatly from the motion of the rock, unless the soil slides on top of the rock (a very unlikely occurrence) or the soil liquifies. For a very deep (thick) soil stratum, however, the top of the soil stratum is less coupled to the rock and is more free to follow a motion that is determined by its own physical properties. 33
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: 3.3 Free-Field Axial and Curvature
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
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
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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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