1. D2011 Project CEA-IRSN Results Alain MILLARD, Frédéric DELERUYELLE Wakkanai, Japan, October 20-23, 2008 Task A - STEPS 0/1

2. Contents Introduction Step 0 –Theoretical model and hypothesis –Material parameters –Drying test –Model setup –Results Step 1 –Hypothesis –Preliminary results Conclusion

3. 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

4. Theoretical model and Hypothesis Water mass balance : - vapour mass negligible compared to liquid water - ρ l constant - liquid water flux given by Darcy’s law: => - Isothermal unsaturated poroelastic model - pores filled by liquid water and gaz ( air + vapor) - gaz pressure assumed constant ( Richard’s model)

5. Theoretical model and Hypothesis Capillary pressure curve (Munoz et al, 2003) : modified Van genuchten’s law : Fit on drying paths λ = 0.128 P s = 700 MPa λ s = 0.273

6. Theoretical model and Hypothesis Water relative permeability (Munoz et al, 2003) : Van genuchten’s law : Intrinsic permeability (Munoz et al, 2003) : Proposed parameters : φ 0 = 0.16 K 0 = 2. 10 -20 m 2 λ ’ = 0.68

7. Theoretical model and Hypothesis Momentum balance : Behavior law : Isotropic case:

8. Material parameters ParametersValueUnitReference Van Genuchten’s parameters λ P λ s P s λ ’ 0.128 3.90 2.73 700 0.68 - MPa - MPa - Munoz et al (2003) initial porosity, φ 0 0.160-Floria et al (2002) intrinsic permeability, K 0 2.10 -20 m2m2 “ grain density ρ s 2710Kg/m 3 Bock (2001) water density ρ l 1000Kg/m 3 “ isotropic Young’s modulus6000.0MPa“ isotropic Poisson’s ratio0.27 transverse isotropicYoung’s moduli in bedding plane, E 1 = E 2 perpendicular to bedding plane E 3 10000.0 4000.0 MPa “ Poisson’s ratio, ν 12, ν 23 0.24, 0.33-“ shear modulus, G 12 1200.0MPa“ Biot’s coefficient b0.75--

9. Drying test 3 samples of Opalinus clay : MA, MB, MC Drying in a chamber with controlled T and H r 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

10. Drying test

13. Model setup H behaviour is ~ 1D => axisymetric model Isotropic properties Refined mesh close to drying boundary Constant temperature T=30°C H r either constant (33%) or linearly variable ( from 25% to 45%) Different permeabilities considered Computer code : Cast3M (CEA)

14. Initial and boundary conditions T(0) = T(t) = 30°C W(0) = 7% φ (0) = 0.16 P l = P atm + (ρ l R T /M v ) ln H r H r = 33% or H r (t) Φ l. n = 0

15. Results K 0 = 2.0 10 -20 m 2, H r = 33% Water content profilesChange in mass with time

16. Results K 0 = 1.96 10 -20 m 2, H r = 33% Water content profilesChange in mass with time

17. Results K 0 = 1.96 10 -20 m 2, H r = H r (t) Water content profiles Change in mass with time

18. Step 1 – VE Experiment Phases 0,1 Phase 1

19. Step 1 – Hypothesis 2D plane strain model Isotropic properties Isotropic in-situ stresses Constant temperature T=15°C Prescribed P l from H r at tunnel wall Same material properties as for Step 0 Phases 0 and 1 : calculation over 2123 days

20. Mesh 130 m

21. Initial and boundary conditions σ = -3.2MPa, P l = 1.21MPa P l = Hr (t) U. n = 0 Φ l. n = 0 σ (0) and P l (0) affine in z S l (0) = 1 φ (0) = 0.16

22. Pore pressure from 65 cm to 69 cm

23. H r from 65 cm to 69 cm

24. Relative humidity 100 % 40 % 70 % 1,40 m 0,90 m 1,00 m 0,67 m 1,90 m

25. Relative displacement 0.2 mm -1.5 mm 0.

26. Initial water pressure 2 MPa -12 MPa 0.

27. Water pressure 2000 KPa -1500 KPa 0. 1,70 m 2.10 m 2.40 m 2.80 m

28. Conclusion Step 0 : –H behaviour dominates –Fair H predictions using parameters proposed –H r = constant is a reasonnable hypothesis –Possible improvement: evaporation condition Step 1 : –Preliminary results –Improvements : Phase 0 and boundary condition in tunnel