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