“dynamic simulation of shear rupture in planar faults
TRANSCRIPT
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