Seismic Design of Tunnels - Parsons Brinckerhoff

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Generally, the solutions to these interface problems are to provide either of the following: • A movable joint, such as the one used at the connection between the Trans-Bay Tube and the ventilation building (Warshaw, 1968) • A rigid connection with adequate strength and ductility At these critical interfaces, structures are subjected to potential differential movements due to the difference in stiffness of two adjoining structures or geological media. Estimates of these differential movements generally require a dynamic analysis taking into account the soil-structure interaction effect (e.g., SFBARTD, 1991). There are cases where, with some assumptions, a simple free-field site response analysis will suffice. The calculated differential movements provide necessary data for further evaluations to determine whether special seismic joints are needed. Once the differential movements are given, there are some simple procedures that may provide approximate solutions to this problem. For example, a linear tunnel entering a large station may experience a transverse differential deflection between the junction and the far field due to the large shear rigidity provided by the end wall of the station structure. If a conventional design using a rigid connection at the interface is proposed, additional bending and shearing stresses will develop near the interface. These stress concentrations can be evaluated by assuming a semi-infinite beam supported on an elastic foundation, with a fixed end at the connection. According to Yeh (1974) and Hetenyi (1976), the induced moment, M(x), and shear, V(x), due to the differential transverse deflection, d, can be estimated as: M(x) = Kt 2l 2 de -lx (sinlx - coslx) (Eq. 3-7) V(x) = K t l de Ê Kt l= ˆ Ë4E c I c ¯ -lx cos 1 4 lx (Eq. 3-8) where x I c = distance from the connection = moment of inertia of the tunnel cross section E c = Young’s modulus of the tunnel lining K t = transverse spring coefficient of ground (in force per unit deformation per unit length of tunnel) 50
Based on Equations 3-7 and 3-8, the maximum bending moment and shear force occur at x=0 (i.e., at the connection). If it is concluded that an adequate design cannot be achieved by using the rigid connection scheme, then special seismic (movable) joints should be considered. 51
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1991 William Barclay Parsons Fellow
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CONTENTS Foreword ix 1.0 Introducti
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Mononobe-Okabe Method 87 Wood Metho
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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
Page 57 and 58: 5. Derive the ground displacement a
Page 59 and 60: 10. Calculate the allowable shear s
Page 61: It is believed that the only transp
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
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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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