Deformation behaviour of railway embankment ... - Liikennevirasto

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16 Modelling is an important necessity for an analytical approach in describing material performance. Many researchers have outlined different procedures for predicting the resilient and permanent strain responses of granular materials. Chapter 5 and Chapter 7 give an overview of the models that have been used so far to model the resilient and permanent deformation behaviour of unbound granular materials respectively. Chapter 8 deals with the different repeated load triaxial test apparati used around the world to study the response of unbound granular material under cyclic, traffic-type loads.
17 2 INTRODUCTION TO THE MECHANICAL BEHAVIOUR OF GRANULAR MATERIALS 2.1 Stresses in engineering materials The stress state acting on a given infinitesimal cubic soil element can be defined by its normal and shear stress components oriented according to a cartesian reference system, as illustrated in Figure 2.1:1. Figure 2.1:1 Stress components on a cubic soil element. The stress components are often given in a matrix form. Stress is a tensor which can be represented by a matrix in Cartesian coordinates: σ τ xx yx zx τ τ xy yy zy τ σ xz σ = τ σ τ . (Eq. 2.1:1) yz zz The indices refer to the coordinate system x, y, z. The first index specifies the direction in which the stress component acts, and the second identifies the orientation of the surface upon which it is acting. We can use equilibrium of moments to study the relationship between τ xy and τ yx . Assuming a unit thickness, the horizontal and vertical faces are of area dx and dy respectively (Figure 2.1:2).
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 12 and 13: 10 TABLE OF CONTENTS ABSTRACT .....
Page 14 and 15: 12 8.9 Trondheim NTNU/SINTEF’s re
Page 16 and 17: 14 combination of resilient strains
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
Page 62 and 63: 60 Figure 4.7:1 Effect of the wetti
Page 64 and 65: 62 Figure 4.7:3 Modulus of resilien
Page 66 and 67: 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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