PyLith_custom_friction

Custom friction (failure) laws implemented for PyLith v2 used in:

E. Bolotskaya, B.H. Hager, and J-P. Ampuero; Effects of failure parameterization on pre- and co-seismic earthquake rupture (in review with GJI)

Friction laws

Double slip-weakening (DSW) model:

$$ \mu = \begin{cases} \mu_s - (\mu_s-\mu_t)\frac{D}{D_{w1}} & D < D_{w1}\\ \mu_t - (\mu_t-\mu_d)\frac{D-D_{w1}}{D_{w2}-D_{w1}} & D_{w1} \le D \le D_{w2}\\ \mu_d & D > D_{w2}\\ \end{cases} , \qquad \qquad \qquad \qquad (1) $$

where $\mu_s$, $\mu_t$, and $\mu_d$ are the static, transitional, and dynamic friction coefficients, $D_{w1}$ is the transition slip distance and $D_{w2}$ is the final slip distannce. The last segment of the failure law is horizontal with $\mu=\mu_d$.

Exponential cohesive zone (ECZ):

$$ \mu = \mu_d + (\mu_s-\mu_d)\frac{D+D_1}{D_2} e^{1-\frac{D+D_1}{D_2}} , \qquad \qquad \qquad \qquad \qquad \qquad (2) $$

where $\mu$ is the friction coefficient, $\mu_s$ and $\mu_d$ are the static and dynamic friction coefficients, and $D_1$ and $D_2$ are the two slip distances which we call "slip-shift" and "slip-stretch" respectively.

Parabolic cohesive zone (PCZ):

$$ \mu = \begin{cases} \mu_s - (\mu_s-\mu_d) \left( \frac{D-D_1}{D_2} \right) ^2 & D \le D_1+D_2\\ \mu_d & D > D_1+D_2\\ \end{cases} , \qquad \qquad \qquad \qquad (3) $$

where $\mu$ is the friction coefficient, $\mu_s$ and $\mu_d$ are the static and dynamic friction coefficients, $D_1$ and $D_2$ are the slip-strengthening (or "slip-shift") and slip-weakening (or "slip-stretch") distances respectively.

Repository contents

• friction/ directory
• spatialdb_examples/ directory
• README.md
• LICENSE

friction/

Contains all the files needed to implement custom friction laws in PyLith v2. The directory contains the original ViscousFriction example files and the 3 new friction model files:

• DoubleSlipWeakeningFrictionNoHeal*
• ExponentialCohesiveZoneNoHeal*
• ParabolicCohesiveZoneNoHeal*

* Healing is not implemented in these laws. If you're interested in implementing it, refer to the SlipWeakening friction in original PyLith and the forceHealing flag for guidance.

To use: substitute the contents of pylith/templates/friction with the contents of friction/ directory here and build/install as described in friction/README

Here are the energy curves (shear stress vs. slip) recovered from PyLith dynamic rupture simulations with these custom friction laws (color - node position along the fault). Slip-weakening friction (SW) is also shown.

spatialdb_examples/

Contains 3 example spatialdb files for the new friction laws.

Use in .cfg file (DSW):

[pylithapp.timedependent.interfaces.fault]
# Use DSW friction.
friction = pylith.friction.contrib.DoubleSlipWeakeningFrictionNoHeal
friction.label = DoubleSlipWeakeningFrictionNoHeal

# Set the friction model parameters.
friction.db_properties = spatialdata.spatialdb.SimpleDB
friction.db_properties.label = DoubleSlipWeakeningFrictionNoHeal_properties
friction.db_properties.iohandler.filename = spatialdb/1_friction_DSW.spatialdb.spatialdb

Use in .cfg file (ECZ):

[pylithapp.timedependent.interfaces.fault]
# Use ECZ friction.
friction = pylith.friction.contrib.ExponentialCohesiveZoneNoHeal
friction.label = ExponentialCohesiveZoneNoHeal

# Set the friction model parameters.
friction.db_properties = spatialdata.spatialdb.SimpleDB
friction.db_properties.label = ExponentialCohesiveZoneNoHeal_properties
friction.db_properties.iohandler.filename = spatialdb/2_friction_EXP.spatialdb

Use in .cfg file (PCZ):

[pylithapp.timedependent.interfaces.fault]
# Use PCZ friction.
friction = pylith.friction.contrib.ParabolicCohesiveZoneNoHeal
friction.label = ParabolicCohesiveZoneNoHeal

# Set the friction model parameters.
friction.db_properties = spatialdata.spatialdb.SimpleDB
friction.db_properties.label = ParabolicCohesiveZoneNoHeal_properties
friction.db_properties.iohandler.filename = spatialdb/3_friction_PAR.spatialdb

Reference

The results obtained using these failure laws are part of my Thesis: Bolotskaya, E., 2023. Effects of fault failure parameterization and bulk rheology on earthquake rupture (Doctoral dissertation, Massachusetts Institute of Technology)

and a publication submitted to GJI: E. Bolotskaya, B.H. Hager, and J-P. Ampuero, "Effects of failure parameterization on pre- and co-seismic earthquake rupture"

Please contact me if you use these custom friction laws for your research and would like a citation before the publication is out.

Release on Zenodo: