Post on 15-Feb-2020
B. Pardoen - S. Levasseur - F. Collin - D. Seyedi
Clay conference 2015 – Brussels, Belgium
Modelling the excavation damaged zone in Callovo-Oxfordian
claystone using shear strain localisation
In situ evidences (Andra) : Anisotropy: - stress : σH>σh~σv Galery // to σh
- material : cross-anisotropy
Galery // to σH Major issues : prediction of the extension, fracturing structure and properties modifications.
Study : - fractures modelling with shear strain localisation,
- influence of permeability variation
Excavation damaged zone
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 2
(Armand et al. 2014)
Outline
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 3
1. CONSTITUTIVE MODELS
2. FRACTURES MODELLING
- GALLERY // TO σh
- GALLERY // TO σH
3. PERMEABILITY EVOLUTION
1. Constitutive models
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 4
1.1 Strain localisation with regularization - Coupled 2d gradient model : (Chambon et al., 1998 and 2001)
The continuum is enriched with microstructure effects. The kinematics include the classical one
(macro) and the microkinematics (Toupin 1962, Mindlin 1964, Germain 1973).
Biphasic porous media : solid + fluid (Collin et al., 2006)
Balance equations for
biphasic porous media : Bishop’s effective stress : Double stress :
ij ij ij rw wb S p
*
* 2
*
*
* * *
* *
,
q
i i
ij ijk i i i i i i
j j
w w
k
w
i w w
i
u ud G u d t u T D
p
u dx x
Mp m d Q p d q p d
t
x
x
2 *
ijk , i
j k
uf B
x x
1.2 Mechanical model :
Linear elasticity : Cross-anisotropic (5 param.) + Biot’s coefficient
Plasticity :
Van Eeckelen yield surface Cohesion anisotropy :
Hardening/softening of φ/c :
1. Constitutive models
/ / / / / /
/ / / /
/ / / / / /
/ / / /
// //
/ / / /
/ / / /
/ /
//
//
1- -
1- -
1- -
1
1
2
1
2
eijkl
E E E
E E E
E E E
E
G
G
D
ˆ 'tan C
cF II m I
30
'e e
ij ijkl kld D d / / / / / / // //, , , ,E E G
' ' '
' '
( ) ( ) ...ij i j
i i ii
ij ij
c a l l c A l b A l
l
2 2 2 2
11 3 1 11 3
2 2 2
1 2 3
1 1 3 1 3
3
e
ijkk
ij ij
s
Cb
K
/ /
/ /ij
b
b b
b
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 5
1. Constitutive models
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 6
1.3 Flow model : Advection of liquid phase (Darcy’s flow) : Water retention and permeability curves (Van Genuchten’s model) :
,
,
ij r w ww i w
w j
k k pm
x
, max 1
mn
cr w res res
r
pS S S S
P
2
1/
, , ,1 1m
m
r w r w r wk S S
1E-25
1E-24
1E-23
1E-22
1E-21
1E-20
1E-19
0 0.2 0.4 0.6 0.8 1
Srw (-)
Kw
(m
²)
Pham 2006
Semete 2008
Boulin 2008
Hoxha 2005
Homand 2004
van Genuchten0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 10 100 1000
Succion (MPa)
Srw
(-)
LML - GL Gaz
Laego - GL Gaz
Yang 2008
Pham 2006
Boulin 2008
Zhang 2007
Hoxha 2004
van Genuchten - PGZ
2.1 Gallery // to σh : Anisotropic stress state, isotropic model Initial anisotropic stress state(Andra URL) :
pw,0 = 4.5 [MPa]
σv,0 = σh,0 = 12 [MPa]
σH,0 = 1.3 σv,0 = 15.6 [MPa] HM modelling in 2D plane strain state (LAGAMINE-Ulg) Excavation :
2. Fractures modelling
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 7
,0
,0
(1 )
(1 )
r r
w w wp p
2. Fractures modelling
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 8
Total
deviatoric
strain
σ/σ0=0.4 σ/σ0=0.2 σ/σ0=0.0
σ/σ0 = 0.40 σ/σ0 = 0.20 σ/σ0 = 0.00
End of
excavation
Plasticity
2ˆ ˆ
3eq ij ij
0 0.184
Fractures Total deviatoric strain Convergence
σ anisotropy is the predominant factor leading to strain
localisation and to the elliptical shape of the damaged zone.
2. Fractures modelling
0 0.184
0.5 m
4.6 m
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 9
2.2 Gallery // to σH :
Isotropic stress state (σ=12 MPa),
anisotropic model HM modelling in 2D plane
strain state
2. Fractures modelling
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 10
End of excavation
Cohesion evolution :
Anisotropy:
Initially : isotropic σij
Excavation : σr ↓ and σort ↑
2. Fractures modelling
' ' '
' '( ) ( ) ... i i i
ij i j i
ij ij
c a l l c A l b A l l
2 2 22 2 2 2 1 2 3
11 2 1 11 21 1 3 1 3
/ .c c l 2 3 3 0 58
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 11
Anisotropic stress state, anisotropic model σH,0 = 1.3 σv,0 > σv,0 = σh,0 = 12 [MPa]
Fractures Total deviatoric strain Convergence
Isotropic stress state in the gallery section does not lead to shear
strain localisation unless the material anisotropy is considered.
Material anisotropy seems to be the predominant factor leading
to strain localisation and to the elliptical shape of the damaged zone.
2. Fractures modelling
0 0.05
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 12
3.2 m
4 m
3.1 In situ evidences : Hydraulic properties are not homogeneous in the damaged zone. Influence of rock fracturing on intrinsic permeability. In situ permeability in Callovo-Oxfordian claystone (Armand et al. 2014, Cruchaudet et al. 2010b)
3.2 Permeability variation : Total deviatoric strain (if εeq > εeq
min ) End of Vertical Horizontal excavation y-axis x-axis α = 2 x 108 , β = 3
3. Permeability evolution
min
,0
1 ( )
2ˆ ˆ
3
ij
eq eq
ij
eq ij ij
k
k
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 13
3.3 Rock-atmosphere interaction (gallery air ventilation) : Water phases equilibrium at gallery wall, Kelvin's law : Air RH = 80%, pw = -30.7 [MPa] End of calculation Vertical y-axis Vertical y-axis
k(εeq) k(εeq) k = cst
3. Permeability evolution
,0
v c v
v w
p p MRH exp
p RT
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 14
Damaged zone strain localisation zone similar to in situ measurements modelling provide information about the rock structure and evolution within this
zone, as observed in situ.
rock anisotropy and properties modification
Conclusions
EDZ Constitutive models Fractures modelling Permeability evolution Conclusions 15