Seismic Design of Tunnels - Parsons Brinckerhoff

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1.2 Scope of this Study The work performed to achieve these goals consisted of: • A summary of observed earthquake effects on underground structures. • A comparison of seismic design philosophies for underground structures and other civil engineering facilities. Based on this comparison, seismic design criteria were developed for underground tunnels. • A quantitative description of ground behavior during traveling seismic waves. Various modes of ground deformations and their engineering implications for tunnel design are discussed. • A review of current seismic design methodology for both circular mined tunnels and cut-and-cover rectangular tunnels. Examples were used to study the applicability of these conventionally used methods of analysis. • The development of a refined (yet simple) method for evaluating the earthquake ovaling effect on circular linings. This method considers the soil-structure interaction effects and is built from a theory that is familiar to most mining/underground engineers. To ease the design process, a series of design charts was developed, and these theoretical results were further validated through a series of numerical analyses. • The development of a simplified frame analysis model for evaluating the earthquake racking effect on cut-and-cover rectangular tunnels. During the process of this development, an extensive study using dynamic finite-element, soil-structure interaction analyses was conducted to cover a wide range of structural, geotechnical and ground motion parameters. The purpose of these complex and time consuming analyses was not to show the elegance of the mathematical computations. Rather, these analyses were used to generate design data that could be readily incorporated into the recommended simplified frame analysis model. 1.3 Background Importance of Seismic Design One of the significant aspects of the 1989 Loma Prieta earthquake in the San Francisco area was its severe impact on the aboveground transportation system: 4
• The collapse of the I-880 viaduct claimed more than 40 lives. • The direct damage costs to the transportation facilities alone totalled nearly $2 billion (Werner and Taylor, 1990). • The indirect losses were several times greater as a result of major disruptions of transportation, particularly on the San Francisco-Oakland Bay Bridge and several major segments of the Bay area highway system. The San Francisco Bay Area Rapid Transit (BART) subway system was found to be one of the safest places during the event, and it became the only direct public transportation link between Oakland and San Francisco after the earthquake. Had BART been damaged and rendered inoperative, the consequences and impact on the Bay area would have been unthinkable. The 60-mile BART system was unscathed by the earthquake because PB engineers had the foresight 30 years ago to incorporate state-of-the-art seismic design criteria in their plans for the subway tunnels (SFBARTD, 1960; Kuesel, 1969; and Douglas and Warshaw, 1971). The Loma Prieta earthquake proved the worth of their pioneering efforts. Seismic Design Before the ‘90s Based on the performance record, it is undoubtedly fair to say that underground structures are less vulnerable to earthquakes than surface structures (Dowding and Rozen, 1978; Rowe, 1992). Interestingly, some tunnels and shafts built without special earthquake provisions have survived relatively strong earthquakes in the past — for example, the Mexico City subway during the 1985 Mexico City earthquake. On the other hand, some underground structures have been damaged severely in other events (see Section 1.5). Limited progress has been made in seismic design methodology for underground tunnels since the work for BART, possibly because of favorable performance data, and limited research work has been done toward a practical solution. The lack of a rational methodology for engineers and the nonexistence of applicable codes has led to widely varied measures taken by different engineers. For example: • Some ignore seismic effects and fail to check the resistance of the structures to earthquakes, even in highly seismic areas. • Others conduct their seismic design for underground structures using the same methodology developed for aboveground structures, without recognizing that underground structures are constrained by the surrounding medium. 5
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 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 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
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Figure 7. Free-Field Shear Distorti
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Figure 8. Free-Field Shear Distorti
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R = radius of the tunnel lining t =
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Lining Properties Soil Properties R
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The expressions of these lining res
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Figure 11. Lining Response Coeffici
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Thrust Response Coefficient, K 2 Fi
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Thrust Response Coefficient, K 2 Fi
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Figure 15. Normalized Lining Deflec
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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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