Seismic Design of Tunnels - Parsons Brinckerhoff

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Loading Criteria Maximum Design Earthquake (MDE). Given the performance goals of the MDE (i.e., public safety), the recommended seismic loading combinations using the load factor design method are as follows: For Cut-and-Cover Tunnel Structures U = D + L + E1+ E2 + EQ (Eq. 2-1) Where U = required structural strength capacity D = effects due to dead loads of structural components L = effects due to live loads E1 = effects due to vertical loads of earth and water E2 = effects due to horizontal loads of earth and water EQ = effects due to design earthquake (MDE) For Mined (Circular) Tunnel Lining U = D + L + EX + H + EQ (Eq. 2-2) where U, D, L, and EQ are as defined in Equation 2-1 EX = effects of static loads due to excavation (e.g., O’Rourke, 1984) H = effects due to hydrostatic water pressure Comments on Loading Combinations for MDE • The structure should first be designed with adequate strength capacity under static loading conditions. • The structure should then be checked in terms of ductility as well as strength when earthquake effects, EQ, are considered. The “EQ” term for conventional surface structure design reflects primarily the inertial effect on the structures. For tunnel structures, the earthquake effect is governed by the displacements/deformations imposed on the tunnels by the ground. • In checking the strength capacity, the effects of earthquake loading should be 20
expressed in terms of internal moments and forces, which can be calculated according to the lining deformations (distortions) imposed by the surrounding ground. If the “strength” criteria expressed by Equation 2-1 or 2-2 can be satisfied based on elastic structural analysis, no further provisions under the MDE are required. Generally the strength criteria can easily be met when the earthquake loading intensity is low (i.e., in low seismic risk areas) and/or the ground is very stiff. • If the flexural strength of the tunnel lining, using elastic analysis and Equation 2-1 or 2- 2, is found to be exceeded (e.g., at certain joints of a cut-and-cover tunnel frame), one of the following two design procedures should be followed: (1) Provide sufficient ductility (using proper detailing procedure) at the critical locations of the lining to accommodate the deformations imposed by the ground in addition to those caused by other loading effects (see Equations 2-1 and 2-2). The intent is to ensure that the structural strength does not degrade as a result of inelastic deformations and the damage can be controlled at an acceptable level. In general the more ductility is provided, the more reduction in earthquake forces (the “EQ” term) can be made in evaluating the required strength, U. As a rule of thumb, the force reduction factor can be assumed equal to the ductility provided. This reduction factor is similar by definition to the response modification factor used in bridge design code (AASHTO). Note, however, that since an inelastic “shear” deformation may result in strength degradation, it should always be prevented by providing sufficient shear strengths in structure members, particularly in the cut-and-cover rectangular frame. (2) Re-analyze the structure response by assuming the formation of plastic hinges at the joints that are strained into inelastic action. Based on the plastic-hinge analysis, a redistribution of moments and internal forces will result. If new plastic hinges are developed based on the results, the analysis is re-run by incorporating the new hinges (i.e., an iterative procedure) until all potential plastic hinges are properly accounted for. Proper detailing at the hinges is then carried out to provide adequate ductility. The structural design in terms of required strength (Equations 2-1 and 2-2) can then be based on the results from the plastic-hinge analysis. As discussed earlier, the overall stability of tunnel structures during and after the MDE has to be maintained. Realizing that the structures also must have sufficient capacity (besides the earthquake effect) to carry static loads (e.g., D, L, E1, E2 and H terms), the potential modes of instability due to the development of plastic 21
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: 2.4 Proposed Seismic Design Philoso
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 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 (
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Table 2. Cases Analyzed by Finite D
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maximum bending moment than the no-
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Table 3. Influence of Interface Con
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5.0 RACKING EFFECT ON RECTANGULAR T
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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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