HYDRO-MECHANICAL MODELLING OF BENTONITE- BASED …massonr/MOMASMultiphasique2015/... · 2015. 10....
Transcript of HYDRO-MECHANICAL MODELLING OF BENTONITE- BASED …massonr/MOMASMultiphasique2015/... · 2015. 10....
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HYDRO-MECHANICAL MODELLING OF BENTONITE-
BASED MATERIALS
Journées MOMAS Multiphasiques 2015 – Nice – October 6, 2015
Anne-Catherine Dieudonné1,2
Frédéric Collin1
Robert Charlier1
1 University of Liege (Belgium)
2 F.R.I.A., FRS-FNRS (Belgium)
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Motivations
In most concepts, bentonite-based materials will be used for sealing and
backfilling of the excavated shafts, galleries and boreholes.
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Bentonite seal
Concrete plug
Concrete plug
Linking drift
French Design (CIGEO concept) Bentonite is a natural material which
primarily consists of montmorillonite
(clay mineral).
Objectives:
Limit water flow around the
excavated galleries
Delay the release of
radionuclides to the biosphere
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Motivations
Bentonite-based materials are used because of their:
1) Significant swelling upon hydration = swelling capacity
2) Very low permeability
3) Important radionuclides retardation capacities
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Swelling potential = relative
change of volume experienced
upon wetting under unconfined
conditions
∆𝑉
𝑉0=
𝑉 − 𝑉0
𝑉0
Swelling pressure = pressure
developed upon wetting under
confined conditions
𝑆𝑝
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Motivations
Bentonite-based materials are used because of their:
1) Significant swelling upon hydration = swelling capacity
2) Very low permeability (~ 10−20 − 10−21 𝑚² in saturated conditions)
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Motivations
Bentonite-based materials are used because of their:
1) Significant swelling upon hydration = swelling capacity
2) Very low permeability (~ 10−20 − 10−21 𝑚² in saturated conditions)
3) Important radionuclides retardation capacities
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Motivations
Objectives of the PhD : develop a hydromechanical model for the behaviour
of compacted bentonite-based materials under in situ conditions
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Buffer hydration
Buffer swelling
Desaturation of the host rock ?
Technological gap closure
Host formation
recompression
Swelling conditions
evolve from free
swelling to constrained
volume.
These processes are modelled using the finite element code LAGAMINE.
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Outline of the presentation
7
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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Outline of the presentation
8
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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Microstructure of compacted bentonite
Compaction of bentonite creates a double-porosity structure.
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Lloret et al. (2003) Wang et al. (2013)
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Microstructure of compacted bentonite
Compaction of bentonite creates a double-porosity structure.
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8 – 10 nm 100 – 10 000 nm Lloret et al. (2003)
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Microstructure of compacted bentonite
Clay aggregates are clusters of clay particles. It is at this scale that swelling
occurs !
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Montmorillonite layers are
electronegative
The natural tendency is to
ensure electroneutrality
Hydrated cations and water
molecules are attracted in the
interlayer
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Microstructure of compacted bentonite
Clay layers are sensitive to water.
Hydration of bentonite-based materials yields important structural
changes !
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Seiphoori et al. (2014)
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Microstructure of compacted bentonite
We want to quantify these processes to include information from the
microstructure in constitutive models !
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Interpretation of a large
number of pore-size
distribution curves
Micro-void ratio
𝑒𝑚 =𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑚𝑖𝑐𝑟𝑜𝑝𝑜𝑟𝑒𝑠
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑𝑠
is only a function of the
water content !
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Outline of the presentation
14
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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Definitions
The water retention curve: amount of water stored = f(suction…)
(generally a unique relationship !)
Degree of saturation
𝑆𝑟𝑤 =𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑣𝑜𝑖𝑑𝑠
Water content
𝑤 =𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑𝑠
Water ratio
𝑒𝑤 =𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑𝑠
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Experimental observations
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Inter-aggregate governing suction
Intra-aggregate governing suction ρd = 1.69 Mg/m³
ρd = 2.03 Mg/m³
ρd0 = 2.04 Mg/m³
ρd0 = 1.71 Mg/m³
Gatabin et al. (2006), Wang et al. (2013)
𝑤 =𝑀𝑤
𝑀𝑆
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Experimental observations
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ρd0 = 2.04 Mg/m³
Confined conditions
Unconfined conditions
𝑆𝑟 =𝑉𝑤
𝑉𝑣=
𝑒𝑤
𝑒
A unique relationship
cannot be defined !
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Experimental observations
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Competing effects of
Water uptake
Swelling
𝑆𝑟 =𝑉𝑤
𝑉𝑣=
𝑒𝑤
𝑒
Need for a WR model
capable of interpreting these
data within a unified
framework
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Water retention model
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𝑒𝑤𝑚 𝑠, 𝑒𝑚 = 𝑒𝑚 exp − 𝐶𝑎𝑑𝑠𝑠 𝑛𝑎𝑑𝑠
𝑒𝑤 = 𝑆𝑟 . 𝑒 = 𝑒𝑤𝑚 + 𝑒𝑤𝑀
𝑒𝑤𝑀 𝑠, 𝑒, 𝑒𝑚 = 𝑒 − 𝑒𝑚 1 +𝑠
𝑎
𝑛 −𝑚
« Van-Genuchten » model
Dubinin model
Number of parameters:
Microstructure: 3 (2)
Microstructure WR model: 2
Macrostructure WR model: 3 (1)
Equilibrium of suction is
assumed between the
structural levels
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Water retention model
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« van Genuchten » model: 𝑒𝑤𝑀 𝑠, 𝑒, 𝑒𝑚 = 𝑒 − 𝑒𝑚 1 +𝑠
𝑎
𝑛 −𝑚
𝑎 =𝐴
𝑒 − 𝑒𝑚
The water retention curve is
density-dependent
The effect of density is
included in the parameter a
(« air-entry » value)
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Model validation
21
Hydration under confined conditions of bentonite compacted to different
dry densities
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Model validation
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Hydration under unconfined conditions of high-density compacted
bentonite
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Model validation
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Microstructure evolution under confined and unconfined conditions
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Implementation in LAGAMINE
The equations to solve are
𝑒𝑤 = 𝑒𝑤 𝑠, 𝑒, 𝑒𝑚
and
𝑒𝑚 = 𝑒𝑚 𝑒𝑤
Suction s and void ratio e are given as input of the routine (pore
pressure and total deformations)
A bisection method is used to solve the system of non-linear equations
𝑒𝑤 ∈ 0, 𝑒 ≡ 𝑆𝑟 ∈ 0,1
Severe convergence criterion required to achieve good convergence of
large and strongly coupled problems BUT the time spent in to solve the
model <<<<<< time required to solve the global problem
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Outline of the presentation
25
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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Infiltration test
Infiltration column test (Wang et al. 2013)
H = 250 mm
D = 50 mm
Initial conditions:
w = 11%
ρd = 1.67 Mg/m³
Hydration from bottom at patm
Relative humidity (RH) monitoring
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Multiphase flow model
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Water in liquid and vapour phases
𝒇𝒘 = 𝜌𝑤𝒒𝒍 + 𝒊𝒘𝒈
Liquid advection: Generalized Darcy’s law:
𝒒𝒍 = −𝑘𝑟𝑤𝐾𝑤
𝜇𝑤𝛻𝑢𝑤 + 𝜌𝑤𝑔
Vapour diffusion: Fick’s law
𝒊𝒘𝒈
= −𝜙 1 − 𝑆𝑟 𝜏𝐷𝑤𝑔
𝜌𝑔𝛻𝜌𝑣
𝜌𝑎
𝑘𝑟𝑤 = 𝑆𝑟𝑛
n = fitting parameter
1.3 10−20 m²
(Gatabin et al. 2006)
0.007
(estimated from effective gas diffusion coefficient)
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Numerical results (uncoupled)
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Uncoupled modelling (H)
𝑘𝑟𝑤 = 𝑆𝑟3.4
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Mechanical model
Barcelona Basic Model (Alonso et al. 1990)
𝒅𝜺𝒗𝒆 𝒔 =
𝜿𝒔
𝟏 + 𝒆
𝒅𝒔
𝒔 + 𝒑𝒂𝒕
𝒒𝟐 + 𝑴𝟐 (𝒑 + 𝒑𝒔(𝒔)) 𝒑 − 𝒑𝟎(𝒔) = 𝟎
𝒅𝜺𝒗𝒆 𝒑 =
𝜿
𝟏 + 𝒆
𝒅𝒑
𝒑
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Mechanical model
Barcelona Basic Model (Alonso et al. 1990)
Calibration on controlled-suction oedometer tests (Wang et al. 2013)
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Numerical results (coupled)
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Coupled modelling (HM)
𝐾𝑤 = 1.3 10−20 m²
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Numerical results (coupled)
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Coupled modelling (HM)
𝐾𝑤 = 𝐾01−𝜙𝑀0
3
𝜙𝑀02
𝜙𝑀2
1−𝜙𝑀3 m²
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Numerical results (coupled)
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0
50
100
150
200
250
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250 300 350 400
Wat
er
volu
me
(cm
³)
Swe
llin
g p
ress
ure
(M
Pa)
Time (days)
Modeled swelling pressure
Measured swelling pressure
Modeled injected water volume
Measured injected water volume
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Outline of the presentation
34
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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Conclusions
Bentonite-based materials are characterized by a double-porosity
structure. This structure evolves upon hydraulic and mechanical
wetting.
In this work, the microstructure is characterized by the volume of
micropores.
A water retention model (saturation – suction) is developed accounting
for
The different water retention mechanisms
The evolution of the microstructure.
This model is used to model the hydromechanical behaviour of
bentonite under laboratory (and repository) conditions.
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Perspectives
For high-density compacted bentonite, the microstructure development
upon hydration is limited by the volume constraints.
In this case, mechanical stress may also affect the micropore volume.
Non-equilibrium between the structural levels may further improve the
modelling.
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Thank you for your attention !
… Questions ? Comments ?
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