Seismic Design of Tunnels - Parsons Brinckerhoff

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amplitude is relatively small. Using the given wavelength and the corresponding displacement amplitude, the calculated free-field ground strains would be significantly smaller than those calculated using the simplified equations shown in Table 1. This suggests that it may be overly conservative to use the simplified equations to estimate the axial and curvature strains caused by seismic waves travelling in soils for tunnel design. • With regard to the derivations of spring coefficients K a and K t , there is no consensus among design engineers. The derivations of these spring coefficients differ from those for the conventional beam on elastic foundation problems in that: -The spring coefficients should be representative of the dynamic modulus of the ground under seismic loads. -The derivations should consider the fact that loading felt by the surrounding soil (medium) is alternately positive and negative due to the assumed sinusoidal seismic wave. Limited information on this problem is available in the literature (SFBARTD 1960, St. John and Zahrah, 1987 and Owen and Scholl, 1981). For preliminary design, it appears that the expressions suggested by St. John and Zahrah (1987) should serve the purpose: K t = K a = 16pG m(1 - v m ) (3 - 4v m ) d L (Eq. 3-6) where G m = shear modulus of the medium (see Section 4.2 in Chapter 4) n m = Poisson’s radio of the medium d L = diameter (or equivalent diameter) of the tunnel = wavelength • A review of Equations 3-1, 3-3 and 3-4 reveals that increasing the stiffness of the structure (i.e., E c A c and E c I c ), although it may increase the strength capacity of the structure, will not result in reduced forces. In fact, the structure may attract more forces as a result. Therefore, the designer should realize that strengthening of an overstressed section by increasing its sectional dimensions (e.g., lining thickness) may not always provide an efficient solution for seismic design of tunnel structures. Sometimes, a more flexible configuration with adequate reinforcements to provide sufficient ductility is a more desirable measure. 42
Design Example 2: A Linear Tunnel in Soft Ground In this example, a tunnel lined with a cast-in-place circular concrete lining (e.g., a permanent second-pass support) is assumed to be built in a soft soil site. The geotechnical, structural and earthquake parameters are listed as follows: Geotechnical Parameters: - Effective shear wave velocity, C S =350 ft/sec. - Soil unit weight, g t =110 pcf =0.110 kcf. - Soil Poisson’s ratio, n m =0.5 (saturated soft clay). - Soil deposit thickness over rigid bedrock, H =100 ft. Structural Parameters: - Lining thickness, t =1 ft. - Lining diameter, d =20 ft. - Lining moment of inertia, I c = 0.5 x 3148 = 1574 ft 4 (one half of the full section moment of inertia to account for concrete cracking and nonlinearity during the MDE). - Lining cross section area, A c =62.8 ft 2 . - Concrete Young’s Modulus, E c =3600 ksi =518400 ksf. - Concrete yield strength, f c =4000 psi. - Allowable concrete compression strain under combined axial and bending compression, e allow = 0.003 (during the MDE) Earthquake Parameters (for the MDE): - Peak ground particle acceleration in soil, A s =0.6 g. - Peak ground particle velocity in soil, V s =3.2 ft/sec. 43
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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 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: - In the JSCE (Japanese Society of
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
Page 100 and 101: thrust that is approximately 1.5 to
Page 102 and 103: 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
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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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