“Dynamic Simulation of Shear Rupture in Planar Faults ...
Transcript of “Dynamic Simulation of Shear Rupture in Planar Faults ...
School of Civil Engineering High Performance Computing Laboratory
“Dynamic Simulation of Shear Rupture in Planar Faults Using XFEM” by : M. Parchei, S. Mohammadi, and H. Zafarani
Anti-plane Shear (Mode III) In plane Shear (Mode I/II)
Out of plane mesh deformation In plane mesh deformation
Com
puta
tion
of a
nti-p
lane
rup
ture
par
amet
ers
Com
puta
tion
of in
pla
ne r
uptu
re p
aram
eter
s
Numerical calculation of SV wave front evolution by XFEM (using C elements) 0
Lr =
32.
1875
L
r = 2
4.18
75
Lr =
16.
1875
L
r = 8
.187
5
u z τ yz
Snapshots of SH wave propagation at different rupture lengths (L ) r
u x τ xy σ xx
Lr =
24.
1875
L
r = 1
6.18
75
Lr =
8.1
875
Lr =
4.1
875
Snapshots of coupled P-SV wave propagation at different rupture lengths (L ) r
Schematic of LATIN method for imposing non-linear contact boundary conditions
E AI
E IA
S A 0
S A n S A
n+1
S I 0
S I n
S AI A
I
A : Linear Equation of Motion I : Non-linear Boundary Conditions
X X X
time time
0.4
6.8
13.2
19.6
26
32.4
38.8
45.2
51.6
58
64.4
-1
0
1
2
3
4
5
6
-35.
0-3
2.2
-29.
4-2
6.6
-23.
8-2
1.0
-18 .
2-1
5.4
-12.
6-9
.8-7
.0
-4.2
-1.4
1.0
3.8
6.6
9.4
12.2
15.0
17.8
20.6
23.4
26.2
29.0
31.8
34.6
timeX
Shea
r Str
ess
X
time
Shea
r str
ess
0.4
6.8
13.2
19.6
26
32.4
38.8
45.2
51.6
58
64.4
0
5
10
15
20
25
30
35
40
45
-35.
0-3
2.2
-29.
4-2
6.6
-23.
8-2
1.0
-18.
2-1
5.4
-12.
6-9
.8-7
.0
-4.2
-1.4
1.0
3.8
6.6
9.4
12.2
15.0
17.8
20.6
23.4
26.2
29.0
31.8
34.6
timeX
Shea
r Str
ess
X time
Slip
0.4
6.8
13.2
19.6
26
32.4
38.8
45.2
51.6
58
64.4
0
2
4
6
8
10
12
-35.
0-3
2.2
-29.
4-2
6.6
-23.
8-2
1.0
-18.
2-1
5.4
-12.
6-9
.8-7
.0
-4.2
-1.4
1.0
3.8
6.6
9.4
12.2
15.0
17.8
20.6
23.4
26.2
29.0
31.8
34.6
timeX
Shea
r Str
ess
X time
Slip
Rat
e
Slip
Rat
e
A
Detailed view of A: Shear Deformation of a Split Element in a LATIN-based Contact Model
0.4
6.8
13.2
19.6
26
32.4
38.8
45.2
51.6
58
64.4
0
2
4
6
8
10
12
14
16
-35.
37-3
2.57
-29.
77-2
6.97
-24.
17-2
1.37
-18.
57-1
5.77
-12.
97-1
0.17
-7.3
7
-4.5
7
-1.7
7
0.57
3.37
6.17
8.97
11.7
7
14.5
7
17.3
7
20.1
7
22.9
7
25.7
7
28.5
7
31.3
7
34.1
7
timeX
Slip
Rat
eSl
ip R
ate
X
time
0.4
6.8
13.2
19.6
26
32.4
38.8
45.2
51.6
58
64.4
-1
4
9
14
19
24
29
34
39
44
49
-35.
37-3
2.57
-29.
77-2
6.97
-24.
17-2
1.37
-18.
57-1
5.77
-12.
97-1
0.17
-7.3
7
-4.5
7
-1.7
7
0.57
3.37
6.17
8.97
11.7
7
14.5
7
17.3
7
20.1
7
22.9
7
25.7
7
28.5
7
31.3
7
34.1
7
timeX
Slip
Slip
X time
0.4
6.8
13.2
19.6
26
32.4
38.8
45.2
51.6
58
64.4
-1
-0.5
0
0.5
1
1.5
2
2.5
-35.
4-3
2.6
-29.
8-2
7.0
-24.
2-2
1.4
-18.
6-1
5.8
-13.
0-1
0.2
-7.4
-4.6
-1.8
0.6
3.4
6.2
9.0
11.8
14.6
17.4
20.2
23.0
25.8
28.6
31.4
34.2
timeX
Shea
r Str
ess
Shea
r str
ess
X time
-1.5
-1
-0.5
0
0.5
1
-36 -27 -18 -9 0 9 18 27 36
Shea
r Str
ess
x
t = 16
-1.5
-1
-0.5
0
0.5
1
1.5
-36 -27 -18 -9 0 9 18 27 36
Shea
r Str
ess
x
t = 32
-1.5
-1
-0.5
0
0.5
1
1.5
-36 -27 -18 -9 0 9 18 27 36
Shea
r Str
ess
x
t = 48
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-36 -27 -18 -9 0 9 18 27 36Shea
r Str
ess
x
t = 64
0
2
4
6
8
10
12
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 16
0
5
10
15
20
25
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 32
0
5
10
15
20
25
30
35
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 48
0
5
10
15
20
25
30
35
40
45
50
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 64
0
1
2
3
4
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 16
0
1
2
3
4
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 32
0
1
2
3
4
5
6
7
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 48
0
2
4
6
8
10
12
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 64
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 10 20 30 40 50 60 70
Shea
r Str
ess
Time
Analytical (Kastrov 1964)
XFEM without Artificial Damping
XFEM with Artificial Damping
x = 10 x = 20 x = 30
-1.5
-1
-0.5
0
0.5
1
-36 -27 -18 -9 0 9 18 27 36
She
ar S
tres
s
x
t = 12
-1.5
-1
-0.5
0
0.5
1
-36 -27 -18 -9 0 9 18 27 36
She
ar S
tres
s
x
t = 24
-1.5
-1
-0.5
0
0.5
1
-36 -27 -18 -9 0 9 18 27 36
She
ar S
tres
s
x
t = 36
-1.5
-1
-0.5
0
0.5
1
-36 -27 -18 -9 0 9 18 27 36
She
ar S
tres
s
x
t = 48
0
0.5
1
1.5
2
2.5
3
3.5
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 12
0
0.5
1
1.5
2
2.5
3
3.5
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 24
0
0.5
1
1.5
2
2.5
3
3.5
4
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 36
0
0.5
1
1.5
2
2.5
3
3.5
4
-36 -27 -18 -9 0 9 18 27 36
Slip
Rat
e
x
t = 48
0
1
2
3
4
5
6
7
8
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 12
0
2
4
6
8
10
12
14
16
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 24
0
2
4
6
8
10
12
14
16
18
20
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 36
0
5
10
15
20
25
30
-36 -27 -18 -9 0 9 18 27 36
Slip
x
t = 48