4. Radial Stress Boundary Conditions
( )
4
1
2 3 1 2 2
1 1 1
1
1
3
3
3
r a
r r
r r i i i
r m b m m
r m b
r P
r r c c n
r c c n
r P c n
r P
K
1
1
1
1
2
2 1 1 2
2
1 2 1
2
1 2 1
1
3 1
i
m
n
r a
n
i i i i
n
m m m m
m
r a
r a n c r P
r r c c
r r c c
r b
b
5. Example (Pa = 0 and Pb=15 MPa)
5
0
2
4
6
8
10
12
14
16
18
20
1 10 100 1000
EffectiveStress(MPa)
r/a
One Segment Two Segments
Three Segments Four Segments
Number of
Creep-Law
Segments
Parameters Involved
Steady-State
Volumetric
Closure Rate
per Year
1 n1 and A1 0.010
2 n1, n2 and A1, A2 0.061
3 n1, n2, n3 and A1, A2, A3 0.085
4 n1, n2, n3, n4 and A1, A2, A3, A4 0.095
Compare Effective Stress at Cavern Wall
For High-Stress and Multi-Segmented Creep Laws
Multi-Segmented Creep Law Can Make
10 Times More Cavern Closure