hydro-mechanical modelling of bentonite- based …massonr/momasmultiphasique2015/... · 2015. 10....

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



2) Very low permeability (~ 10−20 − 10−21 𝑚² in saturated conditions)

4

Motivations



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 …


8


behaviour

Mock-up test


Microstructure of compacted bentonite

Compaction of bentonite creates a double-porosity structure.

9

Lloret et al. (2003) Wang et al. (2013)


Compaction of bentonite creates a double-porosity structure.

10

8 – 10 nm 100 – 10 000 nm Lloret et al. (2003)


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


Clay layers are sensitive to water.

Hydration of bentonite-based materials yields important structural

changes !

12

Seiphoori et al. (2014)


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 !


14


behaviour

Mock-up test


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


17

ρd0 = 2.04 Mg/m³

Confined conditions

Unconfined conditions

𝑆𝑟 =𝑉𝑤

𝑉𝑣=

𝑒𝑤

𝑒

A unique relationship

cannot be defined !


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


25


behaviour

Mock-up test


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


32

Coupled modelling (HM)

𝐾𝑤 = 𝐾01−𝜙𝑀0

3

𝜙𝑀02

𝜙𝑀2

1−𝜙𝑀3 m²


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


34


behaviour

Mock-up test


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

hydro-mechanical modelling of bentonite- based …massonr/momasmultiphasique2015/... · 2015. 10....

Documents