Rôle de la zone endommagée sur la convergence des galeries de stockage, modélisation numérique d’expériences dans le laboratoire souterrain de Bure

Frédéric COLLIN, Université de Liege Robert CHARLIER, Université de Liege Benoît PARDOEN, Université de Louvain

Journée d’études SBGIMR sur le stockage géologique de déchets nucléaires

Rôle de la zone endommagée sur la convergence des galeries de stockage,

modélisation numérique d’expériences dans le laboratoire souterrain de Bure

Long-term management of radioactive wastes

Underground structures = network of galleries

1. Context

Deep geological disposal Repository in deep geological media with good confining properties

(Low permeability K<10-12 _m/s)

Disposal facility of Cigéo project in France (Labalette et al., 2013) Intermediate (long-lived) & high activity wastes

Callovo-Oxfordian claystone (COx)

Sedimentary clay rock (France).

- Underground research laboratory Feasibility of a safe repository

France (Meuse / Haute-Marne, Bure)

(Armand et al., 2014)

1. Context

Borehole core samples

Repository phases

Construction Excavation Maintenance Ventilation Repository Sealing Long term Corrosion, heat generation

Type C wastes (Andra, 2005)

1. Context

T

1. Context

T

Heat transfer

H

M

Mechanics

Water overpressure

Repository phases

Construction Excavation Maintenance Ventilation Repository Sealing Long term Corrosion, heat generation

Type C wastes (Andra, 2005)

1. Context

T

Excavation Damaged Zone (EDZ)

Fracturing & permeability increase (several orders of magnitude)

Opalinus clay in Switzerland

(Bossart et al., 2002)

1. Context

Mechanical fracturing Excavation ↓ Stress redistribution ↓ Damage / Fracturing ↓ Coupled processes HM property modifications ↓

Safety function alteration

Water transfer Galleries ventilation ↓ Air-rock interaction ↓ Drainage / desaturation ↓ Modification of the water transfer Construction Maintenance

- Fracturing

Anisotropies: - stress : σ_H> σ_h~ σ_v

- material : HM cross-anisotropy.

Galery // to σ_h

Galery // to σ_H

Issues : Prediction of the fracturing. Effect of anisotropies ?

Permeability evolution & relation to fractures ?

(Armand et al., 2014)

1.

Context

2.

Fracture modelling with shear bands

3.

Influence of mechanical anisotropy

4.

Permeability evolution and water transfer

5.

Conclusions and perspectives

Outline

1.

Context

2.

Fracture modelling with shear bands

3.

Influence of mechanical anisotropy

4.

Permeability evolution and water transfer

2.1. Material rupture

- Compression test on small sample

- Fracture modelling

Shear strain localisation (continuous approach) Shear bands are observed

in many geomaterials. COx : 75% of fractures

in mode II (shear).

2. Fracture modelling with shear bands

- Mechanisms of rock mass failure around gallery

(after Diederichs, 2003) Axial shortening, ΔH [mm] A x ial lo a d , F [N] F Fconf H

2.2. Constitutive models for COx

- Mechanical law - 1st gradient model

Isotropic elasto-plastic internal friction model

Non-associated plasticity, Van Eeckelen yield surface :

φ hardening / c softening

- Hydraulic law

Fluid mass flow (advection, Darcy) :

Water retention and permeability curves (Mualem - Van Genuchten’s model)

ˆ ' tan C c F II_ m I_



    _  _   3 0



0



0 ˆ ˆ p f eq p c eq c c c c B





   

Strain localisation

2. Fracture modelling with shear bands

, , , w ij r w w w i w w j w j k k p f g x







_    _  _   

2.3. Gallery excavation modelling

- Numerical model HM modelling in 2D plane strain state Gallery radius = 2.3 m

-Gallery in COx // σ_h

Effect of stress anisotropy Anisotropic stress state

p_w,0= 4.5 [MPa]

σ_x,0 = σ_H= 1.3 σ_v= 15.6 [MPa] σ_y,0 = σ_v= 12 [MPa]

σ_z,0 = σ_h= 12 [MPa]

- Excavation

2. Fracture modelling with shear bands

σ

_H

- Localisation zone

Incompressible solid grains, b=1

 For an isotropic mechanical behaviour, the appearance and shape of the strain localisation are mainly due to mechanical effects linked to the anisotropic stress state.

3 days σ_r/σ_r,0= 0.4 4 days σ_r/σ_r,0= 0.2 5 days σ_r/σ_r,0= 0.0 100 days σ/σ₀= 0.00 1000 days σ/σ₀= 0.00

Total deviatoric strain Plasticity

2. Fracture modelling with shear bands

0 0.06 4.6 m 0.5 m 2 ˆ ˆ ˆ 3 eq ij ij





 

End of excavation

- Gallery air ventilation :

Water phases equilibrium at gallery wall (Kelvin's law)

Compressibility of the solid grains: b=0.6

Ventilation p_w= -30.7 [MPa] No ventilation p_w= p_atm[MPa] Total deviatoric strain Plasticity No ventilation 100 days 1000 days 0 0.184 Ventilation 100 days 1000 days

2. Fracture modelling with shear bands

,0 v c v v w p p M RH exp p RT



    _ _   suction ↑ σ’ ↑  Elastic unloading  Inhibition of localisation  Restrain ε , r w w ij ij ij b S p







 



- Convergence:

Important during the excavation Anisotropic convergence

Influence of the ventilation

Experimental results (GED -Andra’s URL) No strain localisation

Calcul with large D or no loc SDZ? If large D ça rigidifie un peu Shear band position

Shear bands are necessary for anisotropy

2.5. Conclusions and outlooks

- Conclusions

 Reproduction of EDZ with shear bands.

 Shape and extent of EDZ governed by anisotropic stress state.

- Next steps…

X Mechanical rock behaviour.

 Material anisotropy, gallery // σ_H.

X HM coupling in EDZ.

 Influence of fracturing on hydraulic properties.

X Gallery air ventilation and water transfer (drainage / desaturation).

- Linear elasticity :

Cross-anisotropic (5 param.) + Biot’s coefficients

- Plasticity :

Cohesion anisotropy with fabric tensor

Cross-anisotropy / /, , / / / /, // , // E E_

 

_ G _

b b

_{/ /}

,

_ ' ' ' ' ' i i i ij i j i ij ij c a l l l







 

    12 22 23 0

3. Influence of mechanical anisotropy



/ / / /( ) / / / /( ) ...



4.5m

3.3. Gallery excavation modelling for anisotropic initial stress state

- Stress state

Major stress in the axial direction σx,0= σh= 12.40 MPa

Gallery // to σ_H σ_y,0= σ_v= 12.70 MPa

σ_z,0= σ_H= 1.3 x σ_h= 16.12 MPa

- Shear banding

Total deviatoric strain

 Shape modification due to σ_H

0 0.05 3m Horizontal Vertical - Convergence  Long-term deformation Experimental Numerical

3. Influence of mechanical anisotropy

- Creep deformation Permanent strain In the long term Under constant stress below the yield strength

- Viscosity

Time-dependent plastic strain

(Jia et al., 2008; Zhou et al. 2008)

Horizontal Vertical - Convergence  Viscosity effect σ₁ σ₃ ' ˆ ( ) vp vp vp vp c c I F II g R A C R  





    _  _    3 0 3 e p vp ij ij ij ij















3.4. Conclusions and outlooks

- Conclusions

 Reproduction of EDZ in both directions.  Shape and extent of EDZ governed by:

- anisotropic stress state.

- anisotropic mechanical behaviour.

 Long-term convergence with viscosity.

- Next steps…

X HM coupling in EDZ.

 Influence of fracturing on hydraulic properties.

X Gallery air ventilation and water transfer.

GED // σ_h

GCS // σ_H

4. Permeability evolution and water transfer

4.1. Large-scale experiment of gallery ventilation (SDZ)

Characterise the effect of gallery ventilation on the hydraulic transfer around it.

 drainage / desaturation  exchange at gallery wall

4.2. Permeability variation in fractured zone

HM coupling in the EDZ.

4.2.1. Saturated permeability in boreholes

Fracture and rock matrix permeabilities  Capture k_wevolution

 Relation to fractures

4.2.2. Evolution of intrinsic water permeability

Various approaches: deformation, damage, cracks…

- Relation to deformation

Volumetric effects = increase of porous space

()(

(Kozeny-Carman)

- Fracture permeability

Cubic law for parallel-plate approach

(Witherspoon 1980; Snow 1969, Olivella and Alonso 2008)

Poiseuille flow (laminar flow) equivalentDarcy’s media

- Empirical law

Related to strain localisation effect Permeability variation threshold

w b k B  3 12 cr w b k  2 12 n n bb₀B







₀









1 2 1 2 0 ,0 0 1 1 w w k k           





, n n w w k k ₀ 1 A







₀ 3 Localised deformation Fracture initiation

3

ii v











, , , ˆ thr w ij w ij per eq k k ₀ 1



YIYI



3 ˆ ˆ p II YI II   

4. Permeability evolution and water transfer

4.4. Modelling of excavation and SDZ experiment

4.4.1. HM coupling in EDZ

- Gallery excavation SDZ  GED gallery // σ_h Anisotropicσ_ij,0and material  Localisation zone dominated

by stress anisotropy

- Intrinsic permeability evolution

Cross-sections

Plastic strain and a part of the elastic one  EDZ extension + kwincrease

Plasticity Total deviatoric strain k_w,,ij/ k_w,ij,0 [-]

0.95

thr

YI







, , , ˆ w ij thr eq w ij k YI YI k  







3 0 1

Experimental Numerical - Drainage / p_wreproduction

Oblique 45° Horizontal

α_v= 10-3_m/s

- Desaturation EDZ / w reproduction

Horizontal boreholes

 Desaturation: overestimation in long term  Vapour transfer (α_v= 10-3_m/s)

 Good reproduction at gallery wall At gallery wall

4. Permeability evolution and water transfer

w s M w M 

Outline

1.

Context

2.

Fracture modelling with shear bands

3.

Influence of mechanical anisotropy

4.

Permeability evolution and water transfer

5. Conclusions and perspectives

Conclusions

Better understand, predict, and model the behaviour of the EDZ in partially

saturated clay rock, at large scale.

Contribution : Provide new elements for the prediction and understanding of the HM behaviour of the EDZ. Innovations : Fracturing process is predicted on a large scale with shear bands.

Strain localisation effects are taken into account in coupled processes (water flow). Fracture description

EDZ with strain localisation.

Constitutive models

Mechanics: anisotropy, viscosity. Coupled: fracture influence on

permeability.

Numerical modelling Shape, extent.

Influence of fracturing, permeability variation, anisotropy.

5 m

12 m

12 m

_{5 m}

R: 2.3 m

z

y

x

z

x

y

- Fracturation = 3D problem

Fractures pattern around a gallery in Boom clay

- Mesh:

Mechanical modelling in 3D state. Classical FE, no regularisation method.

I.

Gallery excavation in 3D

- Localisation zone:

Equivalent deformation ε_eqduring boring.

3.75 days 4 days 4.25 days

σ/σ0= 0.25 σ/σ0= 0.20 σ/σ0= 0.15

3 days 3.25 days 3.5 days

σ/σ0= 0.40 σ/σ0= 0.35 σ/σ0= 0.30 0 0.025

z

y

x

2 ˆ ˆ ˆ 3 eq ij ij





 

I.

Gallery excavation in 3D

- Localisation zone:

Equivalent deformation ε_eqduring boring.

z

y

3 days 3.25 days 3.5 days

σ/σ0= 0.40 σ/σ0= 0.35 σ/σ0= 0.30

3.75 days 4 days 4.25 days

σ/σ0= 0.25 σ/σ0= 0.20 σ/σ0= 0.15 0 0.025 2 ˆ ˆ ˆ 3 eq ij ij





 

- Localisation zone

Equivalent deformationε_eq- for 4.25 days of excavation (σ/σ₀= 0.15) :

z<0 : excavation zone z=0 : gallery front z>0 : rock mass

I.

Gallery excavation in 3D

z=-2.25m z=-1.25m z=-0.25m z=+0.25m z=+1.25m 0 0.025

x

y

0 0.184 Biot’s coefficient: b=0.6

Plasticity

Compressibility influence on shear banding

3 days σ_r/σ_r,0 = 0.4 4 days σ_r/σ_r,0= 0.2 5 days σ_r/σ_r,0= 0.0 100 days σ/σ₀= 0.00 1000 days σ/σ₀= 0.00 End of excavation

Total deviatoric strain Plasticity

b=0.6 b=1

4 days 5 days 4 days 5 days

,

r w w ij ij ij b S p

- Gallery air ventilation : Total deviatoric strain Plasticity 0 0.184 suction ↑ σ’ ↑ Elastic unloading Inhibition of localisation  Restrain ε , r w w ij ij ij b S p







 



Air ventilation influence on shear banding

Ventilation

- Spatial discretisation

Matricial form of balance equations:

vector of the unknown increments of nodal variables

- Element stiffness matrix

Unsaturated condition, S_r,w Soild phase compressibility, b

Permeability anisotropy and evolution, k_w,ij

Finite element formulation – 2d gradient model

1 2 1 2 1 *, 1 1 1 1 1 1 1 ( , ) ( , ) 1 2 3 T x x x x U E dU d            _ _            



1 2 1 (x x, ) dU     Unknown fields 7 d.o.f.

Second gradient mechanical law – Influence of the elastic modulus

Plasticity _{Total deviatoric strain} ˆ 2 ˆ ˆ

3

eq ij ij





 

D = 80 N D = 20 N D = 5 N - Second gradient mechanical law

Linear elastic law function Independent of p_w

Internal length scale D represents the physical microstructure

 D should be evaluated based on experimental measurements

 Better numerical precision if a few elements compose the shear band width  Large scale… ijk [ ] ij k D x



   

Cross-anisotropic elasticity

Linear elasticity (5 param.)

Biot’s coefficients

Micro-homogeneity and micro-isotropy assumptions (Cheng, 1997)

for which Ksis homogeneous and isotropic at grains scale.

Influence of mechanical anisotropy

/ / / / / / / / / / // // / / / / / / / / / / / / / / // / // / / / 1 - -1 - -1 - -1 2 1 2 1 2 e ijkl E E E E E E E E E G G G D               _       _{ }                   _             _                            ' e e ij ijkl kl d



 D d



E_{/ /},E_,

 

_{/ / / /}, _//,G_// 3 e ijkk ij ij s C b K



  / / / / ij b b b b             // / / / / E E



_



_   / / / / / / / / / / 2(1 ) E G



  / / / / / / / / / / / / / / / / 2 / / / / // // / / / / / / / / 1 1 3 1 2 2 1 3 s s b E E K b E E K



 







 

                 

Anisotropic plasticity with fabric tensor

Cohesion anisotropy with fabric tensor.

c0is the projection of the tensor on a generalised unit loading vector :

Deviatoric part:

Generalisation with higher order tensor:

Orthotropy: Cross-anisotropy: ' ' ' ' ' i i i ij i j i i ij ij c a l l l







l

 

    12 22 32  0 1

Influence of mechanical anisotropy

ˆ , ii ij ij ij a a a c



c  3











_{ij i j ij i j ij i j} ...



c₀ c 1A l l b A l l₁ 2b₂ A l l 3





















/ / / / / / / / / / / / / / / / ... ij i j A l l A l c c A l b A l b A l            2 2 2 3 2 2 2 3 2 0 2 1 2 2 2 1 3 1 1 3 1 3 1 3 ij ij i j A A A A l l A l A l A l A     _{ }         11 2 2 2 22 11 1 22 2 33 3 33 0 0 0 0 0 0 / / / / / / / / / / / / , ij i A A A A A A l                 0 0 0 0 0 0 2 1



ij i j



c c A l l  ₀  1 ˆ ˆ , ij ij ii ii a A A a c   0

Viscosity

Time-dependent plastic strain, delayed plastic deformation

Progressive evolution of the material microstructure or to mechanical properties degradation (damage)

Viscoplastic loading surface and potential surface:

Delayed viscoplastic hardening function:

' ˆ ( ) vp vp vp vp c c I F II g R A C R  





    _  _    3 0 3 e p vp ij ij ij ij















Viscosity





' ˆ ( ) vp vp vp vp c c I G II g R C R  







     _  _   3 0 3





eqvp vp vp vp vp vp eq B











    0 1 0 ' N vp vp vp ij c ij F G R







  

Permeability evolution and water transfer

- Reproduction at the end of excavation

(a) Volumetric strain

(b) Equivalent deviatoric total strain

(c) Equivalent deviatoric plastic strain

(d) Plastic strain and a part of the elastic one





, , , w ij w ij k k ₀ 1

 

3

2

ˆ

ˆ ˆ

3

eq ij ij

 





 

/ 3

v ii

 







2

ˆ

ˆ ˆ

3

p p p eq ij ij

 





 





, , , ˆ thr w ij w ij eq k k ₀ 1



YIYI



3  EDZ extension  k_wincrease 14

10





10

10





10

10





10

10

0.95

thr

YI







- Drainage / p_wreproduction Horizontal Oblique 45° Vertical Horizontal α_v= 10-3_m/s  Good matching  HM effect - k_w,h> kw,v

- Desaturation EDZ / w reproduction At gallery wall

 Low vertical drainage

 k_w,h> k_{w,v :} k_w,h/v= 4 10-20_{/ 1.33 10}-20 _[m²] Vertical kw,,ij/ kw,ij,0 [-] ,

1

w s r w s w

V

S

w

V

V

















- Convergence

Total deviatoric strain

Velocity norm Diametrical convergence || ||v  v_x2v_y2 σ_r/σ_r,0 = 0.04 t = 16.8 days σ_r/σ_r,0= 0.00 t = 21 days σ_r/σ_r,0= 0.08 t = 15.4 days

Mechanical anisotropy

Kinetics of drying process – Mixed boundary condition

- Non-classical mixed boundary condition

Progressive thermodynamic equilibrium by vapour transfer. Vapour transfer in a boundary layer.

- Non-classical mixed boundary condition Liquid water + water vapour

- Seepage flow :

- Evaporation flow :

(Nasrallah and Perre, 1988)

2

(

) if

and

0

pen air w atm w w w atm

S

K

p

p

p

p

p

p

S

otherwise

  

 















(

air

)

v v v

E



 







w

q

 

S

E

Evaporation and seepage flows at gallery wall for a constant air ventilation (Gerard et al., 2008).

Kinetics of drying process – Water vapour transfer

Drying test : saline solutions (control vapour phase & RH), or convective drying tests

Drying flux curve:

Thermo-hydraulic process and exchanges in a boundary layer. 1. Preheating

2. Constant flux : heat totally used for water evaporation, saturated boundary layer, external conditions (RH, T, v). 3. Decrease of the flow : internal resistances restrict the water outflow, desaturation of the boundary layer

Dry ing v a pour flux, E Water content, w S urfac e tempe ra tu re , T Time, t W a ter ma s s , Mw Time, t 1 _w d dM E A dt  





max 0, 0, 1 max ( ) ( ) air v v v w d v air h air a v v v v E dM A dt E T RH T                        

Gallery excavation modelling for anisotropic initial stress state

Gallery // to σ_h

Convergence and HM coupling

Close to gallery wall:

Strong effect of the localisation bands σΓ_{=cst, p}

w↑, σ’↓ , εpl↑ (on the yield surface)

Convergence keep increasing In the vertical: similar

- Displacements

Andra’s URL Mine-by experiment

Borehole– extensometers and pore pressure  Characterise the displacements in the rock mass

- Displacements

Viscosity based on creep tests

- Convergence Horizontal Vertical Horizontal Vertical

Mine-by experiment

- Displacements

Viscosity based on in situ measurements  Viscosity influence

- Convergence

Horizontal

Vertical

Viscosity allows to reproduce the increase of convergence in the long term.

Horizontal

Vertical

- Pore water pressure Mine-by test

After excavation: RH=100% , pw= 0 MPa in the gallery

Horizontal: