2007-02-22

SP2 SupportWP 2.1 Track bed quality assessmentTask 2.1.10 Numerical modelling of poor quality sites

First phase report on the modelling of poor quality sites

CZECH TECHNICAL UNIVERSITY IN PRAGUE

2008-02-21

2007-02-22

Numerical modelling: list of FE models

List of the studied models:

1. axisymmetric FE model of the experimental box

2. 3-D FE model of the experimental box

3. axisymmetric FE model of the in-situ conditions

4. 3-D FE model with reinforcing geogrid

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2007-02-22

FE modelling of laboratory experiments

1. Why? To reduce number of experiments needed to evaluate all possible situations

2. Variable parameters (material properties, construction layer thickness, contact behaviour)

3. To assess the importance of each variable observed (sensitivity analysis)

4. Result: nomograms (e.g. layer thickness vs. bearing capacity required)

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2007-02-22

5 strain gauge rosettes

from principal strains

using correlation method

with FE model calculate

the vertical

displacements

very precise assessment

of the deformation area

validation of the

numerical model

Settlement of the rubber (soil) measured by strain gauges

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Results for 22.5 tons 25.0 tons and 27.5 tons loading

temperature compensation included

good correspondence with theory

deformation known in all points

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FEM model of the experimental box with sleeper

experimental box modelled

vertical displacement in good

correlation with the measured values

known strains and stresses

relationship between vertical

displacement and principal strains

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2007-02-22

Results - vertical displacements calculated vs. measured

- for all cases: B35/SB20/E20, B35/SB20/E20, B45/SB20/E20

- good correspondence with the experimental results for all

cases (average standard deviation is 16.7 %), except for

the case of ballast thickness 350 mm

- discrepancy caused by an error in measurement of the

sleeper deflections

- calculated displacements at the ballast sub-ballast

interface in good agreement with experimental values

even in the case of ballast thickness 350 mm (average

standard deviation less than 15.6 %)

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Design graphs for single layer construction

axisymmetrical, fully parametric FE

models

results in terms of design graphs

horizontal axis = modulus of

deformation of the existing subgrade

vertical axis = sub-ballast thickness

required to achieve specified modulus

of deformation on the top

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Example of the design graphs

Required modulus

of deformation

<20 MPa,80 MPa>

Steps in 5 MPa

increments

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Design graphs for two layer construction

again axisymmetrical, fully parametric

FE models

results in terms of design graphs

thickness of the top layer held

constant,

design graphs for required modulus of

deformation in <50MPa, 90MPa>

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Design graphs for construction with geosynthetics

again axisymmetrical, fully parametric

FE models

material properties of geosynthetics

important

proper modelling of the contact

studied

calibrated with the experimental

measurements from the box

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2007-02-22

Extension of our parametric FE models to rail track

plain strain and 3-D models

quadratic elements used

high quality of elements required

proper contact modelling studied

evaluation of design criteria

assessed using parametric modelling

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results as design graphs

On-going work :: reinforcing effect of cement layer

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2007-02-22

Geogrids and geotextilies modelling in 3D

• 2-D and 3-D models

• importance of proper geogrid modelling

• proper contact behaviour modelling

• significance of different size of mesh

• contact behaviour and increase of

bearing capacity verified by physical

modelling in the experimental box

2007-02-22

Probabilistic approach

• scatter of input parameters (material properties)

described by e.g. Gaussian distribution with

standard deviation of ±3 – 5%

• how large is the scatter of the output parameters

(settlement, stress, etc)?

• which input variables contribute the most to the

scatter of an output parameter and to the failure

probability?

• what are the sensitivities of the output parameter

with respect to the input variables?

• Monte-Carlo, Latin hypercube, ...

2008-02-21