Seismic Design of Tunnels - Parsons Brinckerhoff

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Figure 3. Axial and Curvature Deformations (Source: Owen and Scholl, 1981) 28
Ovaling or Racking Deformations The ovaling or racking deformations of a tunnel structure may develop when waves propagate in a direction perpendicular or nearly perpendicular to the tunnel axis, resulting in a distortion of the cross-sectional shape of the tunnel lining. Design considerations for this type of deformation are in the transverse direction. Figure 4 shows the ovaling distortion and racking deformation associated with circular tunnels and rectangular tunnels, respectively. The general behavior of the lining may be simulated as a buried structure subject to ground deformations under a two-dimensional, plane-strain condition. Ovaling and racking deformations may be caused by vertically, horizontally or obliquely propagating seismic waves of any type. Many previous studies have suggested, however, that the vertically propagating shear wave is the predominant form of earthquake loading that governs the tunnel lining design against ovaling/racking. The following reasons are given: • Ground motion in the vertical direction is generally considered less severe than its horizontal component. Typically, vertical ground motion parameters are assumed to be 1/2 to 2/3 of the horizontal ones. (Note that a vertically propagating shear wave causes the ground to shake in the horizontal direction.) This relation is based on observation of California earthquakes, which are most commonly of the strike-slip variety in which horizontal motion predominates. For thrust faults, in which one rock block overrides another, vertical effects may equal or exceed the horizontal ones. The effects of thrust faulting are usually more localized, however, than those of the strike-slip faulting, and they are attenuated more rapidly with distance from the focus. • For tunnels embedded in soils or weak media, the horizontal motion associated with vertically propagating shear waves tends to be amplified. In contrast, the ground strains due to horizontally propagating waves are found to be strongly influenced by the ground strains in the rock beneath. Generally, the resulting strains are smaller than those calculated using the properties of the soils. 29
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: 3.0 RUNNING LINE TUNNEL DESIGN 3.1
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
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
Page 110 and 111:
Figure 25. Structure Deformations v
Page 112 and 113:
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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