Rock%20rheology%20

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

EuRock06, Liège
2
Rock rheology the Poynting-Thomson modell
balance of momentum
Helmholtz free energy
Universal independent of microstructure
3
Ideal elastic
Small deformation
Isotropic
Entropy production
4
Poynting-Thomson HookeKelvin-Voigt
5
Opening of 1D tunnel released rod
Three stages primary equilibrium is linear
elastic Opening new initial condition secondar
y processes after the opening
6
A) Released rod primary stage
pF/A
Elastic equilibrium
7
B) Released rod opening
F
l
pF/A
Fast, quasielastic
Finally
8
e
V0.5
V(0.1,0.2,0.5,1,3,100)
t
9
B) Released rod secondary
Initial condition
Finally
10
Opening of a circular tunnel
Three stages primary equilibrium is linear
elastic opening new initial condition secondar
y processes after the opening
11
Cylindrical symmetry
12
Initial conditions
Asymptotic condition
13
Time dependent radial displacement
Time dependent deformation fields
14
Radial displacement
PT jump PT no jump Ideal elastic
G10000MPa, K30000MPa, p1, R1m, ?400000
MPah t10h, a9h ß 11h
15
Time dependent stress field
16
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?

18
Thank you for your attention!