Irazábal González Oñate 2017a - Revision history

Scipediacontent at 11:05, 14 January 2019

2019-01-14T11:05:04Z

Scipediacontent at 10:56, 14 January 2019

2019-01-14T10:56:56Z

Scipediacontent at 10:54, 14 January 2019

2019-01-14T10:54:47Z

Scipediacontent at 10:53, 14 January 2019

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Scipediacontent at 10:51, 14 January 2019

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Scipediacontent at 09:04, 14 January 2019

2019-01-14T09:04:25Z

Scipediacontent at 08:57, 14 January 2019

2019-01-14T08:57:54Z

Scipediacontent at 08:56, 14 January 2019

2019-01-14T08:56:28Z

Scipediacontent at 08:39, 14 January 2019

2019-01-14T08:39:46Z

Scipediacontent at 12:45, 14 December 2018

2018-12-14T12:45:48Z

@@ Line 5,403: / Line 5,403: @@
 Unlike the large scale direct shear test where the particles were sphere clusters, in this case the Young modulus is supposed to be between the values proposed by Ahmed et al. for potential particles due to the similarities between their contact mechanism and that of spherical particles (the Young modulus is lower for clusters due to the higher number of contacts due to spheres overlaps, see Section [[#6.3 Large-scale direct shear test|6.3]]).
-The sleeper and the boundary surfaces are considered completely rigid, they can not be deformed. However, the contact stiffness between ballast and those surfaces depends on their material properties (see equation [[#eq-4.1.a|4.1.a]]). Concrete surfaces are characterised by a Young modulus <math display="inline">E = 30 \hbox{ GPa}</math> and a Poisson ratio <math display="inline">\nu = 0.2</math>, while the properties of the boundary lateral walls are taken from the characteristics of the bulk ballast layer with a Young modulus <math display="inline">E = 0.2 \hbox{ GPa}</math> and a Poisson ratio <math display="inline">\nu = 0.2</math> <span id='citeF-133'></span>[[#cite-133|[133]]].
+The sleeper and the boundary surfaces are considered completely rigid, they can not be deformed. However, the contact stiffness between ballast and those surfaces depends on their material properties (see equation [[#eq-4.1|4.1]]). Concrete surfaces are characterised by a Young modulus <math display="inline">E = 30 \hbox{ GPa}</math> and a Poisson ratio <math display="inline">\nu = 0.2</math>, while the properties of the boundary lateral walls are taken from the characteristics of the bulk ballast layer with a Young modulus <math display="inline">E = 0.2 \hbox{ GPa}</math> and a Poisson ratio <math display="inline">\nu = 0.2</math> <span id='citeF-133'></span>[[#cite-133|[133]]].
 <span style="text-align: center; font-size: 75%;">

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 Leading to the following equivalent contact properties:
 <div id='eq-4.1.a'></div>
 <div id='eq-4.1.b'></div>

@@ Line 1,648: / Line 1,648: @@
 <div id='eq-4.1.c'></div>
 <div id='eq-4.1.d'></div>
-<div id='eq-4.1'></div>
+<div id='eq-4.1.e'></div>
 {| class="formulaSCP" style="width: 100%; text-align: left;"
 |-

@@ Line 1,648: / Line 1,648: @@
 <div id='eq-4.1.c'></div>
 <div id='eq-4.1.d'></div>
-<div id='eq-4.1.e'></div>
+<div id='eq-4.1'></div>
 {| class="formulaSCP" style="width: 100%; text-align: left;"
 |-

@@ Line 4,803: / Line 4,803: @@
 The material properties of the ballast in the pre-calculation are the same as for the numerical calculation of the angle of repose defined in Table [[#table-16|16]].
-Regarding the rigid boundary walls, the value of the Young modulus and the Poisson ratio is the same as for ballast, while friction between them and the granular material is set to <math display="inline">0</math> in order to allow a better particle arrangement. It may be thought that it is not congruent to assign a value of the Young modulus and Poisson ratio to a rigid wall, however, this parameters are necessary in order to define the normal and tangential stiffness of their contact with the DEs (see equation [[#eq-4.1.a|4.1.a]]).
+Regarding the rigid boundary walls, the value of the Young modulus and the Poisson ratio is the same as for ballast, while friction between them and the granular material is set to <math display="inline">0</math> in order to allow a better particle arrangement. It may be thought that it is not congruent to assign a value of the Young modulus and Poisson ratio to a rigid wall, however, this parameters are necessary in order to define the normal and tangential stiffness of their contact with the DEs (see equation [[#eq-4.1|4.1]]).
 Figure [[#img-104|104]] presents the pre-calculation process. As the void ratio of the assembly is 0.82, the total volume of the ballast stones is <math display="inline">V = 0.0096525 \hbox{ m}^3</math>, so, a ballast sample with the specified granulometry and a volume close to <math display="inline">V</math> is created using the cluster mesher. However, the cluster mesher can not generate compacted assemblies and the particles are separated from one another, occupying a space larger than the box. The initial configuration of the pre-calculation is shown in Figure [[#img-104a|104a]]. The pre-calculation starts and the ballast stones fall freely placing themselves in an equilibrium position (Figure [[#img-104b|104b]]). Finally, the loading plate is moved down to the proper position (Figure [[#img-104c|104c]]) and the calculation continues during <math display="inline">0.5 \hbox{ s}</math> to ensure that all the particles are at rest (Figure [[#img-104d|104d]]).

@@ Line 2,978: / Line 2,978: @@
 |}
-Eq. [[#5.2.1 Bounded Rolling Friction (BROF) Model|5.2.1]] highlights the differences in the computation of the rolling resistance torque between the classical model A and the BROF model.
+Eq. [[#eq-5.6.a|5.6.a]] highlights the differences in the computation of the rolling resistance torque between the classical model A and the BROF model.
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@@ Line 5,720: / Line 5,720: @@
 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math>
+| style="text-align: center;" | <math>L = \sqrt[3]{\frac{8EI}{K}}</math>
-−
-L = \sqrt=3
-−
 </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7.3)
@@ Line 5,762: / Line 5,758: @@
 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math>
+| style="text-align: center;" | <math>u = \sqrt[3]{\frac{K^4}{64EI}}</math>
-−
-u = \sqrt=3
-−
 </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7.5)