Deformation behaviour of railway embankment ... - Liikennevirasto

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10 TABLE OF CONTENTS ABSTRACT ..................................................................................................................... 3 TIIVISTELMÄ................................................................................................................. 6 FOREWORD.................................................................................................................... 9 1 INTRODUCTION....................................................................................................... 13 1.1 Background............................................................................................................... 13 1.2 Objectives ................................................................................................................. 15 1.3 Content of research and structure of the literature review........................................ 15 2 INTRODUCTION TO THE MECHANICAL BEHAVIOUR OF GRANULAR MATERIALS ................................................................................................................. 17 2.1 Stresses in engineering materials.............................................................................. 17 2.2 Deformation characteristics of unbound granular materials..................................... 21 2.3 Interaction between water and granular materials.................................................... 27 3 BASIC APPROACHES IN MODELLING OF GRANULAR MATERIALS ........... 29 3.1 Introduction .............................................................................................................. 29 3.2 Models of continuum mechanics.............................................................................. 29 3.2.1 Principle of continuum mechanics modelling approach................................ 29 3.2.2 Linear elastic material models....................................................................... 30 3.2.3 Non-linear elastic material models................................................................ 35 3.3 Models of particulate mechanics .............................................................................. 36 4 FACTORS AFFECTING RESILIENT DEFORMATION......................................... 39 4.1 Introduction .............................................................................................................. 39 4.2 Stress level................................................................................................................ 39 4.3 Loading characteristics............................................................................................. 43 4.3.1 Stress history ................................................................................................. 43 4.3.2 Number of load cycles................................................................................... 44 4.3.3 Load duration and load frequency................................................................. 44 4.3.4 Load sequence ............................................................................................... 44 4.4 Strain level................................................................................................................ 44 4.5 Density...................................................................................................................... 46 4.6 Grading characteristics ............................................................................................. 49 4.6.1 Introduction ................................................................................................... 49 4.6.2 Grain size distribution ................................................................................... 49 4.6.3 Fines content.................................................................................................. 54 4.6.4 Maximum grain size ...................................................................................... 56 4.7 Moisture content....................................................................................................... 58 4.8 Particle characteristics .............................................................................................. 66 5 MODELLING OF RESILIENT DEFORMATION BEHAVIOUR ........................... 72 5.1 Introduction .............................................................................................................. 72 5.2 Models based on resilient modulus and Poisson’s ratio........................................... 73 5.2.1 Definition of resilient modulus and Poisson’s ratio ...................................... 73 5.2.2 Resilient modulus as a function of hydrostatic stress.................................... 74
11 5.2.3 Resilient modulus as a function of deviatoric stress...................................... 75 5.2.4 Influence of different factors on the equations parameters ........................... 79 5.2.5 Poisson’s ratio as a function of stress............................................................ 82 5.3 Resilient modulus using shear-volumetric approach................................................ 86 6 FACTORS AFFECTING PERMANENT DEFORMATION..................................... 94 6.1 Introduction .............................................................................................................. 94 6.2 Stress level................................................................................................................ 95 6.3 Stress history ............................................................................................................ 99 6.4 Number of load applications................................................................................... 102 6.5 Principal stress rotation .......................................................................................... 105 6.6 Moisture content..................................................................................................... 109 6.7 Density.................................................................................................................... 117 6.8 Fines content and grading....................................................................................... 121 6.8.1 Fines content................................................................................................ 121 6.8.2 Grading ........................................................................................................ 122 6.9 Physical properties of aggregate particles .............................................................. 125 6.9.1 Introduction ................................................................................................. 125 6.9.2 Grain type and shape ................................................................................... 125 6.9.3 Particle Surface Roughness ......................................................................... 126 6.9.4 Electro-chemical properties......................................................................... 126 6.10 Temperature.......................................................................................................... 126 7 MODELLING OF PERMANENT DEFORMATION BEHAVIOUR ..................... 128 7.1 Introduction ............................................................................................................ 128 7.2 Correlation between static and dynamic loading tests ........................................... 129 7.3 Correlation between resilient and plastic behaviour............................................... 130 7.4 Permanent deformation moduli .............................................................................. 131 7.5 Permanent strain and number of cycles.................................................................. 132 7.6 Permanent strain and its relationship to stresses .................................................... 137 7.7 The Shakedown Theory.......................................................................................... 141 8 REPEATED LOAD TRIAXIAL APPARATUS ...................................................... 151 8.1 Introduction ............................................................................................................ 151 8.2 Repeated load triaxial test: advantages and drawbacks.......................................... 151 8.3 Constant (CCP) and variable (VCP) confining pressure tests................................ 152 8.4 General guidelines on specimen size...................................................................... 153 8.5 General guidelines on instrumentation................................................................... 154 8.6 University of Nottingham’s repeated load triaxial apparatus................................. 154 8.6.1 Introduction ................................................................................................. 154 8.6.2 Repeated load triaxial tests by Lekarp (1997)............................................. 156 8.6.3 Repeated load triaxial tests by Werkmeister (2003).................................... 158 8.7 Stockholm Royal Institute of Technology’s repeated load triaxial apparatus........ 160 8.7.1 Introduction ................................................................................................. 160 8.7.2 Description of the repeated load triaxial apparatus used by Lekarp (1999) 161 8.7.3 Description of the test series performed by Lekarp (1999)......................... 169 8.8 Laboratoire des Ponts et Chaussées’ repeated load triaxial apparatus ................... 169 8.8.1 Introduction ................................................................................................. 169 8.8.2 Description of the repeated load triaxial test apparatus............................... 170 8.8.3 Description of the test procedure................................................................. 172
Page 1: A 5/2006 Deformation behaviour of r
Page 4 and 5: Finnish Rail Administration Publica
Page 6 and 7: 4 Past investigations have shown cl
Page 8 and 9: 6 Brecciaroli, Fabrizio - Kolisoja,
Page 10 and 11: 8 kuvataan jakamalla jännitykset j
Page 14 and 15: 12 8.9 Trondheim NTNU/SINTEF’s re
Page 16 and 17: 14 combination of resilient strains
Page 18 and 19: 16 Modelling is an important necess
Page 20 and 21: 18 Figure 2.1:2 Two-dimensional sta
Page 22 and 23: 20 σ xx − σ 3 2 det τ yx σ yy
Page 24 and 25: 22 stresses. As it can be seen from
Page 26 and 27: 24 grains. The resistance to partic
Page 28 and 29: 26 The reason was argued to be that
Page 30 and 31: 28 term matric suction implies the
Page 32 and 33: 30 Figure 3.2.1:1 Idealisation of t
Page 34 and 35: 32 ε ε 2 ν = , (Eq. 3.2.2:4) whe
Page 36 and 37: 34 where sij = σ −σ , (Eq. 3.2.
Page 38 and 39: 36 addition, when both the complexi
Page 40 and 41: 38 supplement continuum mechanics m
Page 42 and 43: 40 Figure 4.2:1 A typical variation
Page 44 and 45: 42 Figure 4.2:3 Modulus of resilien
Page 46 and 47: 44 provided that the applied stress
Page 48 and 49: 46 material (Uzan 1985). Dilation i
Page 50 and 51: 48 Figure 4.5:1 Resilient modulus o
Page 52 and 53: 50 The grain size distribution of g
Page 54 and 55: 52 The grain sizes that determine t
Page 56 and 57: 54 4.6.3 Fines content A simple cha
Page 58 and 59: 56 grained than for fine-grained ag
Page 60 and 61: 58 and the shape of the particles a
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60 Figure 4.7:1 Effect of the wetti
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62 Figure 4.7:3 Modulus of resilien
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64 Figure 4.7:6 Dry -density as a f
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66 Figure 4.7:7 Resilient response
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68 The form index can be measured u
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70 Hovinmoen are gravel materials.
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72 5 MODELLING OF RESILIENT DEFORMA
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74 5.2.2 Resilient modulus as a fun
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76 M r k2 k3 ⎛ θ ⎞ ⎛ q ⎞ =
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78 the model showed good representa
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80 discussed. However it can be exp
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82 et al. (2003) calculated the res
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84 p u = unit pressure (1 kPa), δp
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86 Figure 5.2.5:2 Vertical resilien
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88 2 1 ⎛ ⎞ = A q ε ν p ⎜1
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90 Figure 5.3:2 An example of the c
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92 by incorporating a coefficient o
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94 6 FACTORS AFFECTING PERMANENT DE
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96 cycles. He drew the general conc
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98 accumulated strain, ε p , is co
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100 Figure 6.3:1 Effect of loading
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102 load” is not equal to the fai
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104 Chan (1990) noticed, in his stu
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106 Youd (1972) studied the behavio
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108 Figure 6.5:2 Comparison of plas
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110 ample fine-grained fractions th
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112 of a dolomitic limestone with a
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114 Fuller curve (Equation 4.6.2:3)
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116 Figure 6.6:7 Elastic and plasti
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118 Figure 6.7:1 Dependence of the
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120 0,7 0,6 Elastic limit Failure s
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122 Figure 6.8.1:1 Influence of fin
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124 explain why the differences in
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126 was then argued that the variat
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128 7 MODELLING OF PERMANENT DEFORM
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130 Figure 7.2:1 Mohr-Coulomb repre
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132 where K p (N) = bulk modulus wi
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134 1993)) have reported that at le
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136 ε 1,p = accumulated permanent
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138 Barksdale (1972) conducted repe
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140 Figure 7.6:2 Relationship betwe
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142 also be employed for pavement d
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144 repeated loads, although adapta
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146 series of specimens (or in a mu
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148 Figure 7.7:5 S-N design models
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150 In conclusion, both Huurman (19
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152 aim to simulate as closely as p
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154 by the American Association of
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156 Confining pressure is applied t
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158 particles. During the test, the
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160 method takes the average value
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162 Figure 8.7.2:2 Schematic illust
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164 through each platen is provided
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166 measured for the 600 mm central
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168 displayed on the monitor in gra
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170 unbound granular materials. The
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172 Figure 8.8.2:2 Permanent axial
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174 performance-related (functional
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176 the six supports of the vertica
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178 under the same isotropic stress
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180 9 CONCLUSIONS 9.1 Resilient def
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182 − Permanent deformation resis
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184 Balay J., Gomes Correia A., Jou
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186 Cheung, L.W. (1994). Laboratory
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188 El abd, A., Hornych, P., Breyss
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190 Hoff, I., Nordal, S., and Norda
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192 Kolisoja, P. (1996b) Large Scal
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194 Mitry, F.G. (1964). Determinati
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196 Plaistow, N.C. (1994). Non-Line
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198 Tam, W.A. and Brown, S.F. (1988
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200 Wellner, F. (1996). Influence o
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Liite RHK:n julkaisuun A 5/2006 1 L
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RATAHALLINTOKESKUKSEN JULKAISUJA A-
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