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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)
Motivations
In most concepts, bentonite-based materials will be used for sealing and
backfilling of the excavated shafts, galleries and boreholes.
2
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
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
3
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
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)
4
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
5
Motivations
Objectives of the PhD : develop a hydromechanical model for the behaviour
of compacted bentonite-based materials under in situ conditions
6
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.
Outline of the presentation
7
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
Outline of the presentation
8
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
Microstructure of compacted bentonite
Compaction of bentonite creates a double-porosity structure.
9
Lloret et al. (2003) Wang et al. (2013)
Microstructure of compacted bentonite
Compaction of bentonite creates a double-porosity structure.
10
8 – 10 nm 100 – 10 000 nm Lloret et al. (2003)
Microstructure of compacted bentonite
Clay aggregates are clusters of clay particles. It is at this scale that swelling
occurs !
11
Montmorillonite layers are
electronegative
The natural tendency is to
ensure electroneutrality
Hydrated cations and water
molecules are attracted in the
interlayer
Microstructure of compacted bentonite
Clay layers are sensitive to water.
Hydration of bentonite-based materials yields important structural
changes !
12
Seiphoori et al. (2014)
Microstructure of compacted bentonite
We want to quantify these processes to include information from the
microstructure in constitutive models !
13
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 !
Outline of the presentation
14
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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
15
Experimental observations
16
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
Experimental observations
17
ρd0 = 2.04 Mg/m³
Confined conditions
Unconfined conditions
𝑆𝑟 =𝑉𝑤
𝑉𝑣=
𝑒𝑤
𝑒
A unique relationship
cannot be defined !
Experimental observations
18
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
Water retention model
19
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
Water retention model
20
« 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)
Model validation
21
Hydration under confined conditions of bentonite compacted to different
dry densities
Model validation
22
Hydration under unconfined conditions of high-density compacted
bentonite
Model validation
23
Microstructure evolution under confined and unconfined conditions
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
24
Outline of the presentation
25
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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
26
Multiphase flow model
27
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)
Numerical results (uncoupled)
28
Uncoupled modelling (H)
𝑘𝑟𝑤 = 𝑆𝑟3.4
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
29
Mechanical model
Barcelona Basic Model (Alonso et al. 1990)
Calibration on controlled-suction oedometer tests (Wang et al. 2013)
30
Numerical results (coupled)
31
Coupled modelling (HM)
𝐾𝑤 = 1.3 10−20 m²
Numerical results (coupled)
32
Coupled modelling (HM)
𝐾𝑤 = 𝐾01−𝜙𝑀0
3
𝜙𝑀02
𝜙𝑀2
1−𝜙𝑀3 m²
Numerical results (coupled)
33
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
Outline of the presentation
34
Microstructure Water retention
behaviour
Mock-up test
Towards larger scales …
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.
35
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.
36
Thank you for your attention !
… Questions ? Comments ?
37
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