1. PhD Degree in Transportation Systems
Tiago Moço Ferreira
DESIGN OF RAILWAY TRACK SUBSTRUCTURE MODELLING THE LONG TERM THERMO-HYDRO-MECHANICAL BEHAVIOUR DUE TO TRAFFIC AND ENVIRONMENTAL ACTIONS
Supervisor:
Doctor Paulo Fonseca Teixeira
25th June 2015
with support of
Universidade de Lisboa Instituto Superior Técnico

2. Contents Research global objective2
Contents
Research global objective
The mechanical behaviour of the railway track substructure
Design of railway track substructure with modelling of environmental actions and traffic loading
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils
Conclusions and future research

3. Contents Research global objective3
Contents
Research global objective
The mechanical behaviour of the railway track substructure
Design of railway track substructure with modelling of environmental actions and traffic loading
Apresentação dividida em 5 blocos…
objectivo geral(e não objectivos)
Estado da arte sobre o comportamento mecanico
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils
Conclusions and future research

4. Cyclic traffic loading Environmental actions4
Research global objective
Railway substructure design
Cyclic traffic loading
Environmental actions
Atmospheric actions
Hydro-geological conditions
Contribuir para melhorar dimensionamento para tomar decisões mais racionais do ponto de vista do desing
---- …t
Objective: Improve substructure design accounting for its thermo-hydro-mechanical ………………behaviour due to traffic and environmental actions

5. Contents Research objectives5
Contents
Research objectives
The mechanical behaviour of the railway track substructure
Design of railway track substructure with modelling of environmental actions and traffic loading
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils
Conclusions and future research

6. Railway track structural design
The mechanical behaviour of the railway track substructure 6
Railway track structural design
Numerical modelling
Constitutive framework:
Linear elasticity
Non-linear elasticity (Boyce, 𝑘−𝜃)
Elastoplasticity (Drucker-Prager)
Foi feito estado da arte olhando para as metodologias de dimensionamento ferroviário e tambem os avanços feitos no campo da geotecnia
A evolução dos modelos em ferrovia veio desde modelos elásticos lineares (anos 70)
Progredindo p modelos constitutivos não lineares (80 anos)
E posteriormente para modelos elastoplasticos com criterios como o drucker-prager
Numerical methods:
Finite Element Method (FEM)
Finite Differences Method (FDM)
Multi-layered systems

7. Substructure modelling must account for the presence of water!
The mechanical behaviour of the railway track substructure 7
Railway track structural design
Permanent behaviour
Analytical Models
Visco-plastic Equivalent Models
Shakedown Models
Plasticity Theory based Models
(não fazer enquadramento ferroviario/geotecnico)
Utilizados também no ambito ferroviário, existem outros modelos q tentam ter em conta a acumulação de deformação permanente que se podem classificar em…
Analitical, etc…
O problema comum a todos eles é que não têm em conta a presença de água e por isso não são capazes de modelar o comportamento de solos não saturados.
Substructure modelling must account for the presence of water!

8. How environmental actions are considered in railway trackbed design?
The mechanical behaviour of the railway track substructure 8
Influence of water on the mechanical behaviour of the substructure
Reduction of the Resilient modulus (Mr)
Increase of permanent deformation with cyclic loading
(passar rápido)
….A água provoca redução do modulo resilente… 𝜎 𝜀
Edry
Ewet
How environmental actions are considered in railway trackbed design? ?

9. Constitutive modelling of unsaturated soils
The mechanical behaviour of the railway track substructure 9
Constitutive modelling of unsaturated soils
Barcelona Basic Model
BBM main modelling features:
Soil swelling and collapse upon wetting
Increase of soil stiffness with suction

10. Contents Research global objective10
Contents
Research global objective
The mechanical behaviour of the railway track substructure
Design of railway track substructure with modelling of environmental actions and traffic loading
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils
Conclusions and future research

11. ? Background Possible interest of using bituminous subballast
Design of railway track substructure with modelling
of environmental actions and traffic loading 11
Background
Possible interest of using bituminous subballast
Reduction of the overall track settlement
Homogenization of vertical stiffness variations
Increase of subgrade life cycle
Expected advantages: ?
passar
How to assess the potential benefits of using bituminous layers?

12. Modelling substructure THM behaviour due to environmental actions
Design of railway track substructure with modelling
of environmental actions and traffic loading 12
Modelling substructure THM behaviour due to environmental actions
Fully coupled Thermo-Hydro-Mechanical FE model
Evolution of track deformation and stress state (eventual collapsible/expansible behaviour)
Infiltration and run-off of rainwater and its collection in drainage ditches
Groundwater table variations
Evapo-transpiration of water from the subgrade
Evolution of temperature and saturation degree …….distribution in trackbed layers
Trazer resultados da tese de mestrado
Meter menos features
Fully coupled…

13. Modelling substructure THM behaviour due to environmental actions
Design of railway track substructure with modelling
of environmental actions and traffic loading 13
Modelling substructure THM behaviour due to environmental actions
Thermo-Hydro-Mechanical FE model
Modelling run-off of rainwater
Run-off of rainwater is modelled using a very permeable layer at the soil-atmosphere interface
Collection of rainwater is done at drainage ditches ( 𝑃 𝑙 ≥ 𝑃 𝑎𝑡𝑚 → Outflow)

14. Modelling substructure THM behaviour due to environmental actions
Design of railway track substructure with modelling
of environmental actions and traffic loading 14
Modelling substructure THM behaviour due to environmental actions
Atmospheric actions
Barcelona, 2010
O modelo foi desenvolvido p poder ter em conta intervalo de tempo de 30 min
Esta resolução é importante principalmente quando se quer modelar a ocorrência de eventos extremos!!!
Atmospheric variables:
Precipitation
Temperature
Relative humidity
Wind
Atmospheric data with 30 minutes temporal resolution
Multi-year simulations performed with data from 2010

15. Vertical displacements
Design of railway track substructure with modelling
of environmental actions and traffic loading 15
Modelling substructure THM behaviour due to environmental actions
Results - Construction phase
Vertical displacements
Pore water pressure

16. Modelling substructure THM behaviour due to environmental actions
Design of railway track substructure with modelling
of environmental actions and traffic loading 16
Modelling substructure THM behaviour due to environmental actions
Results - Initial 3 years after construction
Vertical displacements

17. Applications of the developed THM FE model to railway track design
Design of railway track substructure with modelling
of environmental actions and traffic loading 17
Applications of the developed THM FE model to railway track design
Possible modelling applications and scenarios
Track structural solutions
Extreme rainfall events
Extreme temperature variations
Track geometric layout
Rise of groundwater table
Mal-functioning of drainage components

18. Extreme Rainfall Scenarios
Design of railway track substructure with modelling
of environmental actions and traffic loading 18
Applications of the developed THM FE model to railway track design
Extreme rainfall events
Duration (min)
Intensity (mm/h)
IDF curves
Intensity-Duration-Frequency of rainfall events
Mediterranean Climate
(Barcelona)
Falar sobre as aplicações…vários tipos de aplicações
(pode meter-se uma figura c os vários exemplos!)
Dimensionamentode elementos de drenagem
Extreme Rainfall Scenarios

19. Applications of the developed THM FE model to railway track design
Design of railway track substructure with modelling
of environmental actions and traffic loading 19
Applications of the developed THM FE model to railway track design
Extreme rainfall events
Run-off and collection of rainwater ( 𝑃 𝑙 ≥ 𝑃 𝑎𝑡𝑚 → Outflow)

20. Applications of the developed THM FE model to railway track design
Design of railway track substructure with modelling
of environmental actions and traffic loading 20
Applications of the developed THM FE model to railway track design
Alternative track design solutions: Bituminous subballast
Evolution of saturation degree for granular and bituminous subballast solutions
Saturation degree (%)
P1A•
•P1A
P1B•
•P1B
Spatial distribution of saturation degree for granular and bituminous subballast solutions after a rainfall event

21. Sleeper-ballast interface
Design of railway track substructure with modelling
of environmental actions and traffic loading 21
Hydro-mechanical response of the substructure to cyclic traffic loading
Mechanical 3D FE model of the railway track (CESAR-LCPC)
Sleeper-ballast interface
Sleeper-ballast interface
Referir que no code_Bright
Não falar no drucker-prager
Quasi-static load
Drucker-Prager without hardening

22. Design of railway track substructure with modelling
of environmental actions and traffic loading 22
Hydro-mechanical response of the substructure to cyclic traffic loading
Application of cyclic loading to the coupled THM FE model (CODE_BRIGHT)
𝝄 𝒚 (𝑪𝑬𝑺𝑨𝑹−𝑳𝑪𝑷𝑪)
Unloaded stage
Loaded stage

23. Hydro-mechanical analysis
Design of railway track substructure with modelling
of environmental actions and traffic loading 23
Hydro-mechanical analysis
Last loading cycle
(N = 100)
Elastic Domain
Elastic Domain

24. Design of railway track substructure with modelling
of environmental actions and traffic loading 24
THM modelling of the railway substructure
Environmental conditions 
Soils unsaturated behaviour (BBM)
Run-off of rainwater
Atmospheric actions
Hydro-geological conditions
Elastic Domain
Cyclic traffic loading 
Accumulation of small strain after each loading cycle
Need for a constitutive model which allows for the accumulation of small strains in unsaturated soils due to cyclic loading

25. Contents Research global objective25
Contents
Research global objective
The mechanical behaviour of the railway track substructure
Design of railway track substructure with modelling of environmental actions and traffic loading
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils
Conclusions and future research

26. Unsaturated behaviour
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 26
The Bubble model and the Barcelona Basic Model
Bubble model
Barcelona Basic Model
Kinematic hardening
Isotropic hardening
Refeir q o modelo se chama BBBM
Modelling of plastic strains inside the yield
Accumulation of plastic strains due to cyclic loading
Accounting for stress history
Soil swelling and collapse upon wetting
Increase of soil stiffness with suction
Cyclic loading
Unsaturated behaviour
Formulation of a constitutive model with kinematic hardening for unsaturated soils
― Bubble-BBM model ―

27. Formulation of the Bubble-BBM kinematic hardening model
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 27
Formulation of the Bubble-BBM kinematic hardening model
Bubble-BBM model
Elastic law
𝑑 𝜀 𝑣 𝑒 =𝑑 𝜀 𝑣,𝑝 𝑒 +𝑑 𝜀 𝑣,𝑠 𝑒 = 𝜅 1+𝑒 𝑑𝑝 𝑝 + 𝜅 𝑠 1+𝑒 𝑑𝑠 (𝑠+ 𝑝 𝑎𝑡𝑚 )
𝑑 𝜀 𝑞 𝑒 = 𝑑𝑞 3𝐺
Bounding surface
Net stress:
𝝈 ′ =𝛔−𝑚𝑎𝑥 𝑃 𝑔 , 𝑃 𝑙 𝑰
𝐹= 𝑝− 𝑝 0 − 𝑝 𝑠 𝑀 2 𝒔 :𝒔− 𝑝 0 + 𝑝 𝑠 =0
Suction:
𝑠=𝑚𝑎𝑥 𝑃 𝑔 − 𝑃 𝑙 ,0
Desenvolvimento matemático da formulação
Referir q primeiro foi feito em tensões pricipais e q dps se passou para as tensões gerais
𝐺= 𝑝− 𝑝 0 − 𝑝 𝑠 𝛼 2 𝑀 2 𝒔 :𝒔− 𝑝 0 + 𝑝 𝑠 =0
𝛼= 𝑀 𝑀−9 𝑀−3 9 6−𝑀 1− 𝑘 𝜆
Non-associated flow rule
Yield surface (bubble)
𝑓= 𝑝− 𝑝 𝛼 𝑀 2 𝒔− 𝒔 𝜶 : 𝒔− 𝒔 𝜶 − 𝑅 2 𝑝 0 + 𝑝 𝑠 =0
𝑔= 𝑝− 𝑝 𝛼 𝛼 2 𝑀 2 𝒔− 𝒔 𝜶 : 𝒔− 𝒔 𝜶 − 𝑅 2 𝑝 0 + 𝑝 𝑠 =0

28. Kinematic hardening modulus
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 28
Formulation of the Bubble-BBM kinematic hardening model
Bubble-BBM model
Isotropic hardening law
𝑑𝑝 0 ∗ = 1+𝑒 𝜆 0 −𝜅 𝑝 0 ∗ 𝑑 𝜀 𝑣 𝑝
Kinematic hardening law
𝑑 𝝈 𝜶 = 𝑑 𝑝 0 𝑝 0 + 𝑝 𝑠 𝝈 𝜶 + 𝝈 𝒔𝟎 +𝑊𝜷
𝑊= 𝐻 ′ 𝑑𝜆 𝜕𝑓 𝜕𝝈 𝑇 𝜷
where
𝐻 ′ =4𝐵 1+𝑒 𝜆 𝑠 −𝜅 𝑝 0 𝑝 0 + 𝑝 𝑠 1 𝛼 𝑝 0 + 𝑝 𝑠 𝑏 𝑏 𝑚𝑎𝑥 𝜓
Kinematic hardening modulus
𝜓= 𝜓 𝜎 + 𝜓 𝜎 − 𝜓 𝑠 𝑑𝑠 𝑑𝝈 + 𝑑𝑠 𝑛

29. Numerical implementation of the Bubble-BBM model
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 29
Numerical implementation of the Bubble-BBM model
Viscoplastic approach
Reduce numerical instability due to collapse
Elasticity + viscoplasticity
𝜺 = 𝜺 𝑒 + 𝜺 𝑣𝑝
𝜺 𝑣𝑝 =Γ 𝜙 𝑓 𝜕𝑔 𝜕𝝈 ,
𝜙 𝑓 = 𝑓 𝑓 0 𝑁
Perzyna model
where
Γ :
Viscosity parameter
Γ∆𝑡→∞
Plastic model
Fully implicit integration scheme
Γ→0
Elastic model
𝑑 𝝈 ′𝑖 = 𝑫 ∗ 𝑫 𝑒 𝑩𝑑 𝒖 𝑖 − 𝑫 𝑒 𝑰 𝑎 𝑠 +∆𝑡𝜃 𝜕 𝜺 𝑣𝑝 𝜕𝑠 𝑑 𝑠 𝑖 − 𝒉 𝑘+1,𝑖
𝑫 ∗ = 𝑰+ 𝑫 𝑒 ∆𝑡𝜃 𝜕 𝜺 𝑣𝑝 𝜕𝝈 ′ −1 ; 𝑫 𝑡𝑎𝑛 = 𝑫 ∗ 𝑫 𝑒
where
𝜕 𝜺 𝑣𝑝 𝜕𝝈 ′ = 𝜕 𝜕𝝈 ′ Γ𝜙 𝑓 𝜕𝑔 𝜕𝝈 ′ =Γ 𝜕𝜙 𝑓 𝜕𝝈 ′ 𝜕𝑔 𝜕𝝈 ′ 𝑇 𝑇 +𝜙 𝑓 𝜕 2 𝑔 𝜕 𝝈 ′ 2
𝜕 𝜺 𝑣𝑝 𝜕𝑠 = 𝜕 𝜕𝑠 Γ𝜙 𝑓 𝜕𝑔 𝜕𝝈 ′ =Γ 𝜕𝜙 𝑓 𝜕𝑠 𝜕𝑔 𝜕𝝈 ′ +𝜙 𝑓 𝜕 2 𝑔 𝜕𝝈 ′ 𝜕𝑠

30. Numerical implementation of the Bubble-BBM model into CODE_BRIGHT
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 30
Numerical implementation of the Bubble-BBM model into CODE_BRIGHT

31. Isotropic compression cyclic tests (𝑠=0)
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 31
Validation of the Bubble-BBM model
Cyclic loading tests from Al-Tabbaa
Isotropic compression cyclic tests (𝑠=0)

32. Isotropic compression cyclic tests (𝑠=0;s=50 kPa)
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 32
Validation of the Bubble-BBM model
Extension for unsaturated conditions
Isotropic compression cyclic tests (𝑠=0;s=50 kPa)

33. Validation of the Bubble-BBM model
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 33
Validation of the Bubble-BBM model
Extension for unsaturated conditions
Isotropic compression with suction decrease
𝜓= 𝜓 𝜎 + 𝜓 𝜎 − 𝜓 𝑠 𝑑𝑠 𝑑𝝈 + 𝑑𝑠 𝑛

34. Validation of the Bubble-BBM model
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils 34
Validation of the Bubble-BBM model
Performance of the kinematic law
Undrained stress path after compression
Results using the Bubble model
Dizer o q é buble e o q é BBBM
Escrever “Developed model: Buble-BBM”
Results using the developed Bubble-BBM model
(Modified translation rule)

35. Contents Research global objective35
Contents
Research global objective
The mechanical behaviour of the railway track substructure
Design of railway track substructure with modelling of environmental actions and traffic loading
Development of an elastic-viscoplastic model with kinematic hardening for unsaturated soils
Conclusions and future research

36. Main conclusions Railway track THM FE modelling
Conclusions and future research 36
Main conclusions
Railway track THM FE modelling
An adequate design of the substructure must account for the unsaturated behaviour of trackbed layers
Modelling the run-off and collection of rainwater is mandatory to accurately model the total amount of water infiltrating the subgrade (use of properly temporal resolution)
Surface and deep drainage systems must be correctly designed and maintained (rainwater and groundwater must be diverted from the substructure)
Extreme rainfall events with low intensity and long duration may generate greater track settlements than the ones with high intensity and short duration
The compaction process and the height of the embankment are design parameters which strongly influence the susceptibility for soil collapse under extreme rainfall events

37. Main conclusions Bubble-BBM constitutive model
Conclusions and future research 37
Main conclusions
Bubble-BBM constitutive model
The use of the developed elastic-viscoplastic constitutive model with kinematic hardening adequately describes the behaviour of the soil due to cyclic loading
The increase in soil stiffness due to suction increase (drying) is properly modelled by the Bubble-BBM model
The analytical expression proposed for the stiffness interpolation parameter (𝜓) properly accounts for different hardening modulus (H’) depending on the amount of Δ𝜎 and Δ𝑠
The use of the Bubble-BBM model in the developed railway track THM FE model will allow to calculate in an integrated manner the response of the substructure due to environmental and traffic actions

38. Future research Railway track THM FE modelling
Conclusions and future research 38
Future research
Railway track THM FE modelling
Integration of the Bubble-BBM constitutive model in the railway track THM FE model
Creation of a special linear boundary FE for simulation of rainwater run-off
3D THM modelling of the railway track
Extension/Modification of the Bubble-BBM model to account for:
Anisotropy (initial state of the substructure due to compaction process)
Viscoplastic equivalent approach (𝜕 𝜀 𝑝 /𝜕𝑡→𝜕 𝜀 𝑝 /𝜕𝑁)
(…)

39. Thank you for your kind attention Obrigado. Gracias!39
Acknowledgements
Thank you for your kind attention
Obrigado. Gracias!
Tiago Moço Ferreira