Seismic Design of Tunnels - Parsons Brinckerhoff

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7. Calculate the maximum bending moment (Equation 3-3) and the corresponding bending strain of the tunnel lining: Ê L 2 K ˆ t Ë M max = 2p ¯ 1 + Ê K t ˆÊ L ËE c I c ¯Ë ˆ¯ D b 4 2p Ê 526 400 2 ˆ Ë = 2p ¯ Ê 526 1 + ˆÊ 400ˆ x0.226 4 Ë518400x1574¯Ë 2p ¯ = 41539 k - ft e bending = M max R E c I c = 41539x10 518400x1574 = 0.00051 8. Compare the combined axial and bending compression strains to the allowable: e max =e axial +e bending = 0.00026 + 0.00051 = 0.00077
10. Calculate the allowable shear strength of concrete during the MDE: fV c = 0.85x2 fc A shear where f = shear strength reduction factor (0.85) f c = yield strength of concrete (4000 psi) A shear = effective shear area = A c /2 Note: Use of f = 0.85 for earthquake design may be very conservative. A shear fi fVc = 0.85x2 4000 x 62.8 2 x 144 1000 = 486 kips 11. Compare the induced maximum shear force with the allowable shear resistance: V max = 625 kips > fVc = 486 kips Although calculations indicate that the induced maximum shear force exceeds the available shear resistance provided by the plain concrete, this problem may not be of major concern in actual design because: • The nominal reinforcements generally required for other purposes may provide additional shear resistance during earthquakes. • The ground displacement amplitudes, D, used in this example are very conservative. Generally the spatial variations of ground displacements along a horizontal axis are much smaller than those used in this example, provided that there is no abrupt change in subsurface profiles. 47
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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
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
Page 57: 5. Derive the ground displacement a
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
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
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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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