Deformation behaviour of railway embankment ... - Liikennevirasto

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36 addition, when both the complexity of the model and the number of parameters increase, the physical meaning of a single parameter is more difficult to conceive. It may also happen that the model describes very accurately the behaviour of the material in the loading condition of a certain laboratory test, but the applicability of the model to other loading conditions cannot always be guaranteed. Finally, it is not usually known how the changes in the quality and physical state of the material affect the model parameters. Instead, the changes must be investigated separately for all different conditions. Non-linear elastic models for resilient deformation are described in detail in Chapter 5. 3.3 Models of particulate mechanics The counterpart of the continuum mechanics based modelling of the mechanical behaviour of granular materials is the so-called particulate mechanics modelling, where interactions between the distinct particles are explicitly investigated. The basic idea of the approach is that, when the number of particles is sufficiently large, the behaviour of the group of particles can be extended to describe the macroscopic behaviour of the actual material. The approaches for modelling the mechanical behaviour of the granular materials starting from the particle level can be divided into two groups, namely, numerical simulation models and analytical models (Kolisoja 1997). A natural way to implement a model describing the behaviour of materials composed of discrete particles is to use computer simulation. In the simulation model the material is modelled by means of a particulate system where the location and the surfaces of each particle are mathematically defined. Moreover, each contact point between the particles is individually modelled along with the forces at the contact point. A mechanical model of a contact point can be, for example, as illustrated in Figure 3.3:1.
37 Figure 3.3:1 An example of a mechanical model of a contact point between two particles used in numerical simulations (Ting et al. 1989). Another method, together with numerical simulation, for modelling the mechanical behaviour of the granular materials starting from the particle level is based on the analytical study of the particulate system. The constitutive equations that describe the macroscopic behaviour of the material can be derived by modelling the structure of the particulate system and the micro-level interactions between the particles. Both the numerical and analytical modelling methods have still many restrictions when it comes to analysing real soil materials, real coarse grained aggregates, and general three dimensional stress states. In particular, continuous grain size distribution and variations in particle size and grain shape are very difficult to model correctly using particulate mechanics. One more impediment to the straightforward application of the particulate mechanics modelling is that initial modelling data, such as elastic and surface properties of the particles, are in most cases inadequately known. The application possibilities of the numerical simulation models in particular are, however, steadily improving due to the sharp increase in the capacity of computers. Despite its shortcomings and limitations, the particulate mechanics modelling approach offers a physically well-justified point of view to the mechanical modelling of the aggregates and other soil materials. It can be used, for example, to support and
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 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 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
Page 68 and 69: 66 Figure 4.7:7 Resilient response
Page 70 and 71: 68 The form index can be measured u
Page 72 and 73: 70 Hovinmoen are gravel materials.
Page 74 and 75: 72 5 MODELLING OF RESILIENT DEFORMA
Page 76 and 77: 74 5.2.2 Resilient modulus as a fun
Page 78 and 79: 76 M r k2 k3 ⎛ θ ⎞ ⎛ q ⎞ =
Page 80 and 81: 78 the model showed good representa
Page 82 and 83: 80 discussed. However it can be exp
Page 84 and 85: 82 et al. (2003) calculated the res
Page 86 and 87: 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)
Page 118 and 119:
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
Page 124 and 125:
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
Page 150 and 151:
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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Liite RHK:n julkaisuun A 5/2006 3 2
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Liite RHK:n julkaisuun A 5/2006 5 R
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RATAHALLINTOKESKUKSEN JULKAISUJA A-
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