1. Rock rheology – time dependence of dilation and stress around a tunnel P. Ván HAS, Institute of Particle and Nuclear Physics and Montavid Research Group, Hungary Z. Szarka University of Miskolc, Institute of Mathematics and Montavid Research Group, Hungary – Poynting-Thomson: not one of the many – Unloading – rod – Unloading – circular tunnel – Conclusions EuRock’06, Liège

2. Rock rheology – the Poynting-Thomson modell balance of momentum Helmholtz free energy Universal – independent of microstructure

3. Entropy production Ideal elastic Small deformation Isotropic

4. Poynting-Thomson = Hooke+Kelvin-Voigt

5. Opening of 1D tunnel – released rod F l Three stages: primary: equilibrium is linear elastic Opening: new initial condition secondary: processes after the opening

6. A) Released rod – primary stage Elastic equilibrium F l p=F/A

7. B) Released rod – opening F l p=F/A Fast, “quasielastic” Finally:

8. V=(0.1,0.2,0.5,1,3,100) V=0.5 jump: t ε F l

9. B) Released rod – secondary Initial condition Finally: F l

10. Opening of a circular tunnel Three stages: primary: equilibrium is linear elastic opening: new initial condition secondary: processes after the opening p R r

11. Cylindrical symmetry

12. Initial conditions: Asymptotic condition:

13. Time dependent radial displacement: Time dependent deformation fields:

14. Radial displacement : G=10000MPa, K=30000MPa, p=1, R=1m, η=400000 MPah t=10h, α=9h β = 11h PT – jump PT – no jump Ideal elastic

15. Time dependent stress field:

16. jump Remark to the presentation of F. Sandrone, J.P. Dudt, V. Laiouse and F. Dexcoeudres Convergence (m) t (day)

17. Conclusions –Poynting-Thomson is not just one of them –Separate timescales: initial jump –Analytical solution can be generalized: elliptical, lining, etc. –Measurements of the material parameters – Numerics mesh: gradient generalization (thermodynamics!) – Practice: stops and starts in tunnel excavations swelling? F l

18. Thank you for your attention!