D2011 Project

CEA-IRSN Results

Alain MILLARD, Frédéric DELERUYELLE

Wakkanai, Japan, October 20-23, 2008

Task A - STEPS 0/1

Contents

• Introduction• Step 0

– Theoretical model and hypothesis– Material parameters– Drying test – Model setup– Results

• Step 1– Hypothesis– Preliminary results

• Conclusion

Introduction

• Step 0 : Preparation to VE calculation– Analysis of supplied reports– Simple laboratory experiment : Drying test– Use of Floria et al’s report for modelling

• Step 1 : Calculation of VE : phases 0 and 1– Preliminary analysis – Same model and material properties

Theoretical model and Hypothesis

Water mass balance :

- vapour mass negligible compared to liquid water

- ρl constant

- liquid water flux given by Darcy’s law: FpgradkK

q llll

rl

l

=>

FpgradkK

div

qdivSt

ll

l

lrl

lll

- Isothermal unsaturated poroelastic model

- pores filled by liquid water and gaz ( air + vapor)

- gaz pressure assumed constant ( Richard’s model)

Theoretical model and Hypothesis

Capillary pressure curve (Munoz et al, 2003) : modified Van genuchten’s law :

P

p

P

pS

s

ccs

l 111

1

0,1

1

10

100

1000

0 0,2 0,4 0,6 0,8 1

Sl

Pg

-Pl

(MP

a)

model

Munoz1

Munoz2

Zhang

Vilar1

Gens

Fit on drying paths

λ = 0.128

Ps = 700 MPa

λs = 0.273

Theoretical model and Hypothesis

Water relative permeability (Munoz et al, 2003) : Van genuchten’s law :

SSk llrl

'1

'

11

2

Intrinsic permeability (Munoz et al, 2003) :

0

03

2

2

3

0

1

1

KK

Proposed parameters :

φ0 = 0.16 K0 = 2. 10-20 m2

λ’ = 0.68

Theoretical model and Hypothesis

Momentum balance :

Behavior law :

0 f

lls S )1(

ldpBdCd

Isotropic case: 1S lbB

Material parameters Parameters Value Unit Reference

Van Genuchten’s parameters λ P λs

Ps

λ’

0.1283.902.737000.68

-MPa

-MPa

-

Munoz et al (2003)

initial porosity, φ0 0.160 - Floria et al (2002)

intrinsic permeability, K0 2.10-20 m2 “

grain density ρs 2710 Kg/m3 Bock (2001)

water density ρl 1000 Kg/m3 “

isotropic Young’s modulus 6000.0 MPa “

isotropic Poisson’s ratio 0.27

transverse isotropicYoung’s moduli in bedding plane, E1 = E2

perpendicular to bedding plane E3

10000.04000.0

MPaMPa

“

Poisson’s ratio, ν12, ν23 0.24, 0.33 - “

shear modulus, G12 1200.0 MPa “

Biot’s coefficient b 0.75 - -

Drying test

• 3 samples of Opalinus clay : MA, MB, MC

• Drying in a chamber with controlled T and Hr

• Continuous measure of weight loss• Water content profiles at 21, 99 and 142 days• Cylindrical samples φ=101 mm, h=280 mm • Bedding planes parallel to samples axis• Drying from upper face• Unconstrained lateral displacements

Drying test

Drying test

Drying test

Model setup

• H behaviour is ~ 1D => axisymetric model• Isotropic properties• Refined mesh close to drying boundary• Constant temperature T=30°C

• Hr either constant (33%) or linearly variable ( from 25% to 45%)

• Different permeabilities considered• Computer code : Cast3M (CEA)

Initial and boundary conditions

T(0) = T(t) = 30°C

W(0) = 7%

φ (0) = 0.16

Pl= Patm + (ρl R T /Mv) ln Hr

Hr = 33% or Hr(t)

Φl . n = 0

ResultsK0 = 2.0 10-20 m2, Hr = 33%

Water content profiles

Change in mass with time

Results K0 = 1.96 10-20 m2, Hr = 33%

Water content profilesChange in mass with time

Results K0 = 1.96 10-20 m2, Hr = Hr(t)

Water content profilesChange in mass with time

Step 1 – VE Experiment Phases 0,1

0102030405060708090

100

RH

[%

]

Applied RH

Mean of the RH of tunnelsensorsRH of outcoming air

Section SA3

In flow

RH-out

Water pan 1SA1

SB1 SC1SA2 SD1 SE

SC2 SB2SD2 SA4

SA3

Rear doors

Out flow

RH-outRH-in RH-1 RH-2

Water Pan 2

RH-in

Instrum ented section:SA : M in i P ie zo m e tersSB : H um id ity se ns orsSC : T D RsSD : Exten so m e te rsSE : G e oe le ctric

Forward doors

Legend :

R H-n : hyg ro m e te rRH-rRH-l

10 m

7 m

1,50 m

1,00 m

0,65 m

0,65 m

0,60 m

0,60 m

0,60 m

0,60 m

1,00 m

0,65 m

0,65 m

1,50 m

Phase 1

Step 1 – Hypothesis

• 2D plane strain model• Isotropic properties• Isotropic in-situ stresses• Constant temperature T=15°C

• Prescribed Pl from Hr at tunnel wall

• Same material properties as for Step 0• Phases 0 and 1 : calculation over 2123 days

Mesh

130 m

Initial and boundary conditions

σ = -3.2MPa, Pl = 1.21MPa

Pl = Hr (t)

U . n = 0

Φl . n = 0

σ (0) and Pl (0)

affine in z

Sl (0) = 1

φ (0) = 0.16

Pore pressure from 65 cm to 69 cm

Hr from 65 cm to 69 cm

Relative humidity

50556065707580859095

100

18-0

7-02

26-1

0-02

03-0

2-03

14-0

5-03

22-0

8-03

30-1

1-03

RH

[%

]HC-SB1/Sur (0.67 m)

HC-B71 (0.9 m)

HC-B64 (1 m)

HC-B75 (1.15 m)

HC-B66 (1.4 m)

HC-B69 (1.65 m)

HC-B73 (1.9 m)

HC-B77 (2.15 m)

Section B1

100 %

40 %

70 %

1,40 m

0,90 m1,00 m

0,67 m

1,90 m

Relative displacement

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2R

ela

tiv

e d

isp

lac

em

en

t [m

m]

0

10

20

30

40

50

60

70

80

90

100

RH

[%

]

46 (vert) 47 (hor) 48 (vert) 49 (hor)

Compression

Expansion

0.2 mm

-1.5 mm

0.

Initial water pressure

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

0.65 1.15 1.65 2.15 2.65

Distance from MT center [m]

pw

[k

Pa

]28/07/2002 (horizontal)

28/07/2002 (45º)

28/07/2002 (vertical)

2 MPa

-12 MPa

0.

Water pressure

0

100

200

300

400

500

600

700

800

900

18-07-02 26-10-02 03-02-03 14-05-03 22-08-03 30-11-03

Pre

ss

ure

[k

Pa

]

0

10

20

30

40

50

60

70

80

90

100P-B55/2.11 P-B56/2.11

P-B57/1.80 P-B58/1.10

P-B59/2.12 P-B60/1.50

P-B61/1.80 P-B62/2.13

Applied RH

Section A2

2000 KPa

-1500 KPa

0.

1,70 m

2.10 m

2.40 m

2.80 m

Conclusion

• Step 0 :– H behaviour dominates– Fair H predictions using parameters proposed

– Hr = constant is a reasonnable hypothesis

– Possible improvement: evaporation condition

• Step 1 : – Preliminary results– Improvements : Phase 0 and boundary condition in

tunnel