Seismic Design of Tunnels - Parsons Brinckerhoff

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First, try the simplified equation as used in Design Example 1. The combined maximum axial strain and curvature strain is calculated as: emax = ± Vs ± AsR 2C cos 3 q=± 3.2 . 0.6x32.2x10 ± cos Cs 2 s 2x350 3 45 o ( 350) 2 =±0.0046 ± 0.0006 =±0.0052 The calculated maximum compression strain exceeds the allowable compression strain of concrete (i.e., e max > e allow = 0.003). Now use the tunnel-ground interaction procedure. 1. Estimate the predominant natural period of the soil deposit (Dobry, et al, 1976). T = 4H C s = 4x100' 350 = 1.14 sec. 2. Estimate the idealized wavelength (Equation 3-5): L = TxC s = 4H = 400 ft 3. Estimate the shear modulus of soil: G m =rC s 2 = 0.110kcf 32.2 x350 2 = 418.5ksf 4. Derive the equivalent spring coefficients of the soil (Equation 3-6): K = K = 16pG m (1 -n m ) d a t (3- 4n m ) L 16px418.5 (1 - 0.5) = (3 - 4 x0.5) = 526 kips/ft x 20 400 44
5. Derive the ground displacement amplitude, D: As discussed before, the ground displacement amplitude is generally a function of the wavelength, L. A reasonable estimate of the displacement amplitude must consider the site-specific subsurface conditions as well as the characteristics of the input ground motion. In this design example, however, the ground displacement amplitudes are calculated in such a manner that the ground strains as a result of these displacement amplitudes are comparable to the ground strains used in the calculations based on the simplified free-field equations. The purpose of this assumption is to allow a direct and clear evaluation of the effect of tunnel-ground interaction. Thus, by assuming a sinusoidal wave with a displacement amplitude D and a wavelength L, we can obtain: For free-field axial strain: V s = 2pD 2C s L fi D = Da = 0.291ft 45 For free-field bending curvature: A s cos 3 45 o = 4p2 D fi D = D b = 0.226 ft 2 C s L 2 6. Calculate the maximum axial force (Equation 3-1) and the corresponding axial strain of the tunnel lining: K a L Q max = 2p K 1 + 2Ê a ˆÊ L ËE c A c ¯Ë ˆ¯ D 2 a 2p 526x400 = 2p 526 1+2Ê ˆÊ400ˆ x 0.291 2 Ë518400x62.8¯Ë 2p ¯ = 8619kips e axial = Q max 8619 = E c A c 518400x62.8 = 0.00026 45
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1991 William Barclay Parsons Fellow
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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 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: Design Example 2: A Linear Tunnel i
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
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
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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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