Robert Flory, JP Renaud

1
Robert Flory, JP Renaud

• Computer modelling update
• 15 December 2005, Newcastle

2
Overview

• Modelling options
• Introduction to FLAC two phase flow module
• Theoretical Explanation
• Comparison with SHETRAN
• Initial BIONICS Fully coupled Slope modelling
• Future Plans

3
Modelling options

• Two main options considered for the modelling
• Running a hydrology model separately to a slope
  mechanics model by exchanging data when necessary
• solving the hydrology and mechanical equations
  simultaneously within one model (fully coupled
  modelling)

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Advantages of using FLAC

• TPflow and fully coupled modelling
• FLAC has enabled the possibility of fully coupled
  modelling using the two-phase flow option
  (tpflow) which allows the modelling of flow
  through partially saturated soils
• FISH
• FLAC has an inbuilt programming language (FISH)
• user defined functions and variables (vegetation
  components and input of climate data)
• user defined constitutive models (constitutive
  modelling of unsaturated soils)

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Overview of Two Phase Flow module in FLAC

• Model of flow of two immiscible fluids through
  porous media
• Pore space is entirely filled by two fluids one
  wetting more than the other
• The capillary pressure and relative permeability
  laws are built-in functions of the van Genuchten
  form.
• Darcys law is used to describe the flow of each
  fluid

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Mechanical Coupling

• The tpflow model can be coupled with any
  constitutive model
• Features included in FLAC tpflow
• Effective stress changes cause volumetric changes
• This deformation causes fluid pressure changes
  and saturation changes
• Bishop effective stress is used in the detection
  of yield in constitutive models
• Not included
• Volumetric deformations induce changes in
  porosity, permeability and the capillary pressure
  curve. But could be included using FISH

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Tp-flow formulation boundary conditions

• Boundary conditions available (for the flow)
• Imposed pressure (water and air)
• Imposed fluid flux (water and air)
• Seepage

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Aims and objectives of modelling with FLAC tpflow

• Build a sound method of modelling unsaturated
  flow through the embankment using FLAC
• Compare flow model with other more recognised
  hydrology packages such as SHETRAN and ESTEL
• Build some vegetation package to enable
  infiltrations to be calculated from Climate data
• Turn on mechanical calculations for fully coupled
  model

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Tp-flow formulation

• Two phases
• Water (wetting fluid) Pressure Pw, Saturation
  Sw
• Air (non wetting) Pressure Pg, Saturation Sg
• Interactions between the two phases
• Saturation
• Capillary Pressure

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Tp-flow formulation

• Capillary pressure
• related to normal van Genuchten parameters as
  follows

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Tp-flow formulation

• Momentum conservation Darcys law

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Tp-flow formulation

• Fluid constitutive laws

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SHETRAN- FLAC Comparison

• Using the BIONICS embankment dimensions
• Boundary and initial conditions
• Hydrostatic pore pressure
• W.T. 2m below ground level
• Flux boundary condition on top 0.1 mm/hr
• 2.7778 m/s
• Pore pressure fixed as hydrostatic on side
  boundary
• SHETRAN uses richards equation
• No air phase
• Non wetting fluid pore pressure 0
• Incompressible wetting fluid
• Kw set to 100 times pressure differential

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FLAC and SHETRAN grid
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SHETRAN- FLAC Comparison initial conditions
pore pressure conditions
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SHETRAN- FLAC Comparison

• Material Properties
• Porosity 0.5
• Permeability 0.173m/day 2e-6 m/s
• Residual saturation 0.15
• a 0.01 cm-1
• Po9810
• n1.2
• Van Genuchten a 0.16667

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Initial Saturation Conditions
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Comparison results
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SHETRAN rainfall infiltration
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Rainfall infiltration results
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FLAC SHETRAN conclusions

• ESTEL was also used and was found to produce
  results closer to SHETRAN than FLAC (both use
  Richards equation)
• FLAC steady state conditions identical
• Response to infiltration is slower
• Difference maybe due to relative permeabilities

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Initial fully coupled models - 10 years rainfall
data

• Material Properties
• Porosity 0.5
• Permeability 2e-9 m/day
• Residual saturation 0.15
• a 0.01 cm-1 - Po9810
• n1.2
• Van Genuchten a 0.16667
• c 7 kPa
• F 20o
• K 4e6 Pa
• G 3e6 Pa

Infiltration (m/s)
Time in s (total 10 yrs)
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Fully coupled model results
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Fully coupled model results
Shear strain contours
Mid-slope displacement
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Future work

• Simple vegetation components added and compared
  with SHETRAN
• Canopy interception
• Evapotranspiration
• Overland flow
• Run model using climate data entirely without
  SHETRAN
• Mechanical calculations to be switched on for
  fully coupled model
• Appropriate constitutive model for embankment to
  be explored
• Unsaturated Constitutive Modelling investigated
  by F. Ciavaglia, A. Russell from Bristol Uni.
  and M. Rouainia from Newcastle Uni
• Model the construction phase of the embankment
  for initial stress conditions
• Include changes in porosity and permeability due
  to volumetric strain

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Conclusions

• FLAC tpflow (two phase flow) module used for
  modelling unsaturated flow through embankment
• This will enable a fully coupled model to be done
  with a user defined unsaturated constitutive
  model
• Comparisons with current unsaturated models give
  identical results for steady state but a slower
  response to infiltration
• Next step will be the development of vegetation
  components