Seismic Design of Tunnels - Parsons Brinckerhoff

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Factors Contributing to the Soil-Structure Interaction Effect Many factors contribute to the soil-structure interaction effect. In this study, the main factors that may potentially affect the dynamic racking response of rectangular tunnel structures are investigated. These factors are: • Relative Stiffness between Soil and Structure. Based on results derived for circular tunnels (see Chapter 4), it is anticipated that the relative stiffness between soil and structure is the dominating factor governing the soil/structure interaction. Therefore, a series of analyses using ground profiles with varying properties and structures with varying racking stiffness was conducted for parametric study purpose. A special case where a tunnel structure is resting directly on stiff foundation materials (e.g., rock) was also investigated. • Structure Geometry. Five different types of rectangular structure geometry were studied, including one-barrel, one-over-one two-barrel, and one-by-one twin-barrel tunnel structures. • Input Earthquake Motions. Two distinctly different time-history accelerograms were used as input earthquake excitations. • Tunnel Embedment Depth. Most cut-and-cover tunnels are built at shallow depths. To study the effect of the depth factor, analyses were performed with varying soil cover thickness. A total number of 36 dynamic finite element analyses were carried out to account for the variables discussed above. Method of Analysis Computer Program. The dynamic finite element analyses were performed using the computer code FLUSH (1975), a two-dimensional, plane strain, finite element program in frequency domain. Besides calculating the internal forces in the structure members, FLUSH analysis: • Produces data in the form of maximum relative movements between any two locations within the soil/structure system being analyzed • Allows a simultaneous free-field response analysis and compares the relative movement between any two locations in the soil/structure system and in the free field 100
These features are ideal for this study because design of the tunnel structures is based on the “deformation method.” A detailed description of this program can be found in Lysmer, et al. (1975). Soil-Structure Model. Figure 27 shows the typical soil-structure finite element model used. The assumptions related to the model were as follows: • The structure members are modeled by continuous flexural beam elements of linear elasticity. Structural frames with rigid connections are considered. • A rigid base underlies the soil (medium) deposit. • The soil overburden generally consists of a soft layer overlying a stiffer layer. Except for 7 cases where the top of the stiffer layer is raised to the invert elevation (to study the effect of stiff foundation), all cases assume the stiffer layer is below the base of the structure by a vertical distance of at least one time the full height of the structure. Materials of both layers are linearly elastic. • No-slip condition along the soil/structure interface is assumed. • Taking advantage of the anti-symmetric loading condition, only one half the entire soil/structure system is analyzed. Horizontal rollers are provided at planes of antisymmetry. • To minimize the boundary effect on the geometric dissipation of seismic energy, an energy absorbing boundary is placed at the far side of the mesh (i.e., transmitting boundary). Earthquake Accelerograms. The two digitized ground motion accelerograms employed in the analyses (see Figures 28A and 28B) were generated synthetically from the two sets of design response spectra presented in Figure 29. The following should be noted: • The “W. EQ” spectra and the corresponding accelerogram represent the rock outcrop ground motions that are typical in the western states of the United States. They were obtained from the San Francisco BART extension project. • The “N.E. EQ” spectra and the corresponding accelerogram represent rock outcrop earthquake motions in the northeastern part of the country. They are taken from the Seismic Design Criteria of Underground Structures for the Boston Central Artery and Third Harbor Tunnel project (1990). • Horizontal earthquake accelerograms are input at the rigid base to simulate the vertically propagating shear waves. 101
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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
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Figure Title Page 20 Typical Free-F
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LIST OF TABLES Table Title Page 1 F
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FOREWORD For more than a century, P
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1.0 INTRODUCTION 1
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1.2 Scope of this Study The work pe
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Figure 1. Ground Response to Seismi
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Ground Failure Ground failure broad
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- Formation of plastic hinges at th
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• The effects of overburden depth
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2.0 SEISMIC DESIGN PHILOSOPHY FOR T
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2.3 Seismic Design Philosophies for
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2.4 Proposed Seismic Design Philoso
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expressed in terms of internal mome
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Comments on Loading Combinations fo
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3.0 RUNNING LINE TUNNEL DESIGN 3.1
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Ovaling or Racking Deformations The
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3.3 Free-Field Axial and Curvature
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Simplified Equations for Axial Stra
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3.4 Design Conforming to Free-Field
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Applicability of the Free-Field Def
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Figure 6. Sectional Forces Due to C
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- In the JSCE (Japanese Society of
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Design Example 2: A Linear Tunnel i
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5. Derive the ground displacement a
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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
Page 106 and 107: • 254 ft/sec for case I • 415 f
Page 108 and 109: locations of roof and invert are ap
Page 110 and 111: Figure 25. Structure Deformations v
Page 114 and 115: As Figures 28A and 28B show, earthq
Page 116 and 117: Figure 28A. West Coast Earthquake A
Page 118 and 119: Figure 29. Design Response Spectra
Page 120 and 121: Figure 31. Relative Stiffness Betwe
Page 122 and 123: developed for a one-barrel frame wi
Page 124 and 125: • For flexibility ratios less tha
Page 126 and 127: where g s = angular distortion of t
Page 128 and 129: Structure Deformation Free-Field De
Page 130 and 131: Because the Poisson’s Ratios of t
Page 132 and 133: Table 5. Cases Analyzed to Study th
Page 134 and 135: In comparison with the results show
Page 136 and 137: Structure Deformation Free-Field De
Page 138 and 139: • Pseudo-Concentrated Force Model
Page 140 and 141: deformations result. Section 2.4 in
Page 142 and 143: Figure 40. Moments at Invert-Wall C
Page 144 and 145: Figure 42. Moments at Invert-Wall C
Page 146 and 147: Table 7. Seismic Racking Design App
Page 148 and 149: 136
Page 150 and 151: • The more frequently occurring e
Page 152 and 153: Use of this method will lead to a c
Page 154 and 155: 142
Page 156 and 157: Duddeck, H. and Erdman, J., “Stru
Page 158 and 159: Tunnels, Report No. UMTA-MA-06-0100
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Seismic Design of Tunnels - Parsons Brinckerhoff

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