Seismic Design of Tunnels - Parsons Brinckerhoff

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Wave Type Longitudinal Strain (Axial) Curvature Shear Wave General Form Maximum Value e= Vs Cs sinq cosq e max = V s 2C s for q=45 Ê1 As Ër ˆ¯ = q Cs 2 cos3 Ê1 Ë ˆ¯max r = A s C s 2 for q=0 Rayleigh Wave General Form Maximum Value e= V R C R cos 2 q e max = V R C R for q=0 Ê1 Ë ˆ¯ r = A R 2 C cos2 q R Ê1 AR Ë = for q=0 ˆ¯max 2 r C R q = Angle of Incidence with respect to Tunnel Axis r = Radius of Curvature V S , V R = Peak Particle Velocity for Shear Wave and Rayleigh Wave, respectively C S , C R = Effective Propagation Velocity for Shear Wave and Rayleigh Wave, respectively A S , A R = Peak Particle Acceleration for Shear Wave and Rayleigh Wave, respectively Table 1. Free-Field Ground Strains 34
3.4 Design Conforming to Free-Field Axial and Curvature Deformations Background and Assumptions The free-field ground strain equations, originally developed by Newmark (Table 1), have been widely used in the seismic design of underground pipelines. This method has also been used successfully for seismic design of long, linear tunnel structures in several major transportation projects (Monsees, 1991; Kuesel, 1969). When these equations are used, it is assumed that the structures experience the same strains as the ground in the free-field. The presence of the structures and the disturbance due to the excavation are ignored. This simplified approach usually provides an upper-bound estimate of the strains that may be induced in the structures by the traveling waves. The greatest advantage of this approach is that it requires the least amount of input. Underground pipelines, for which this method of analysis was originally developed, are flexible because of their small diameters (i.e., small bending rigidity), making the freefield deformation method a simple and reasonable design tool. For large underground structures such as tunnels, the importance of structure stiffness sometimes cannot be overlooked. Some field data indicated that stiff tunnels in soft soils rarely experience strains that are equal to the soil strains (Nakamura, Katayama, and Kubo, 1981). A method to consider tunnel stiffness will be presented and discussed later in Section 3.5. Design Example 1: The Los Angeles Metro For the purpose of illustration, a design example modified from the seismic design criteria for the LA Metro project (SCRTD, 1984) is presented here. In this project, it was determined that a shear wave propagating at 45 degree (angle of incidence) to the tunnel axis would create the most critical axial strain within the tunnel structure. Although a P- wave (compressional wave) traveling along the tunnel axis might also produce a similar effect, it was not considered because: • Measurement of P-wave velocity can be highly misleading, particularly when a soil deposit is saturated with water (Monsees, 1991). • The magnitudes of soil strains produced by a nearly horizontally propagating P-wave are generally small and about the same as those produced in the underlying rock and, therefore, not as critical as the shear-wave generated axial strains (SFBART, 1960). This phenomenon was discussed previously in Section 3.3. 35
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 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: Simplified Equations for Axial Stra
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
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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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