Seismic Design of Tunnels - Parsons Brinckerhoff

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This rule of thumb procedure may present some design problems in the real world too. These problems arise when a very stiff structure is surrounded by a very soft soil. A typical example would be to construct a very stiff immersed tube in a soft lake or river bed. In this case the flexibility ratio is very low, and the tunnel-ground interaction must be considered to achieve a more efficient design. In the following section a refined procedure, equally simple, if not simpler, will be presented. This refined procedure considers the tunnel-ground interaction effect and provides a more accurate assessment of the seismic effect upon a circular lining. 4.5 Lining-Ground Interaction Closed Form Solutions Closed form solutions for estimating ground-structure interaction for circular tunnels have been proposed by many investigators. These solutions are commonly used for static design of tunnel lining. They are generally based on the assumptions that: • The ground is an infinite, elastic, homogeneous, isotropic medium. • The circular lining is generally an elastic, thin walled tube under plane strain conditions. The models used in these previous studies vary in the following two major assumptions, the effects of which have been addressed by Mohraz et al. (1975) and Einstein et al. (1979): • Full-slip or no-slip conditions exist along the interface between the ground and the lining. • Loading conditions are to be simulated as external loading (overpressure loading) or excavation loading. Most of the recent developments in these models fall into the category of excavation loading conditions, as they represent a more realistic simulation of actual tunnel excavation (Duddeck and Erdmann, 1982). To evaluate the effect of seismic loading, however, the solutions for external loading should be used. Peck, Hendron, and Mohraz (1972), based on the work by Burns and Richard (1964) and Hoeg (1968), proposed closed form solutions in terms of thrusts, bending moments and displacements under external loading conditions. 64
The expressions of these lining responses are functions of flexibility ratio and compressibility ratio as presented previously in Equations 4-5 and 4-6. The solutions also depend on the in-situ overburden pressure, g t H, and the at rest coefficient of earth pressure, K o . To be adapted to the loading caused by seismic shear waves, it is necessary to replace the in-situ overburden pressure with free-field shear stress, t, and assign K o =–1, to simulate the simple shear condition in the field. The shear stress, t, can be expressed as a function of shear strain, g. With some mathematical manipulations, the resulting expressions for maximum thrust, T max , bending moment, M max , and diametric strain, DD/D, can be presented in the following forms: T max =± 1 6 K 1 E m (1 + v m ) Rg max (Eq. 4-8) E m M max =± 1 6 K1 (1 + v m ) R2 g max (Eq. 4-9) DD D =±1 3 K 1Fg max (Eq. 4-10) where K 1 = 12(1 - vm ) (Eq. 4-11) 2F + 5 - 6v m 65 where Em, n m = modulus of elasticity and Poisson’s Ratio of medium R = radius of the tunnel lining g max = maximum free-field shear strain F = flexibility ratio K 1 is defined herein as lining response coefficient. The earthquake loading parameter is represented by the maximum shear strain, g max , which may be obtained through a simplified approach (such as Equation 4-1), or by performing a site-response analysis. To ease the design process, Figures 10 and 11 show the lining response coefficient, K 1 , as a function of flexibility ratio and Poisson’s Ratio of the ground. It should be noted that the solutions provided here are based on the full-slip interface assumption.
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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
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
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: Lining Properties Soil Properties R
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 112 and 113: Factors Contributing to the Soil-St
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
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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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