rsfmodel.plot¶

rsfmodel.rsf¶

exception rsfmodel.rsf.IncompleteModelError¶

Bases: exceptions.Exception

Special error case for trying to run the model with inadequate information.

class rsfmodel.rsf.LoadingSystem¶

Bases: object

Contains attributes relating to the external loading system.

Attributes

k	(float) System stiffness in units of fricton/displacement.
time	(list) List of time values at which the system will be solved.
loadpoint_velocity	(list) List of the imposed loadpoint velocities at the corresponding time value. Must be same length as time.
v	(float) Slider velocity
mu	(float) The current friciton value of the system.

Methods

friction_evolution(loadpoint_vel)¶

velocity_evolution()¶

class rsfmodel.rsf.Model¶

Bases: rsfmodel.rsf.LoadingSystem

Houses the model coefficients and does the integration.

Attributes

mu0	(float) Reference friction value at vref.
a	(float) Rate and state constitutive parameter.
vref	(float) System reference velocity at which the reference friction is measured.
state_relations	(list) List of state relations to be used when calculating the model.
results	(namedtuple) Stores all model outputs.

Methods

readyCheck()¶

Determines if all necessary parameters are set to run the model. Will raise appropriate error as necessary.

solve(threshold=2, **kwargs)¶

Runs the integrator to actually solve the model and returns a named tuple of results.

Parameters:	threshold : float Threshold used to determine when integration care should be taken. This threshold is in terms of maximum load-point acceleration before time step is marked.
Returns:	results : named tuple Results of the model

rsfmodel.staterelations¶

class rsfmodel.staterelations.DieterichState¶

Bases: rsfmodel.staterelations.StateRelation

The slowness or Dieterich state relation as proposed by [1].

Notes

\[\frac{d\theta}{dt} = 1 - \frac{V_\text{slider} \theta}{D_c}\]

[1]	Dieterich, J. “Modeling of rock friction: 1. Experimental results and constitutive equations.” Journal of Geophysical Research: Solid Earth (19782012) 84.B5 (1979): 2161-2168.

Methods

evolve_state(system)¶

set_steady_state(system)¶

class rsfmodel.staterelations.NagataState¶

Bases: rsfmodel.staterelations.StateRelation

The Nagata state relation as proposed by [2]:

Notes

\[\frac{d\theta}{dt} = 1 - \frac{V_\text{slider} \theta}{D_c} - \frac{c}{b}\theta\frac{d\mu}{dt}\]

[2]	Nagata, K., Nakatani, M., Yoshida, S., “A revised rate-and-state -dependent friction law obtained by constraining constitutive and evolution laws separately with laboratory data,” Journal of Geophysical Research: Solid Earth, vol 117, 2012.

Methods

evolve_state(system)¶

set_steady_state(system)¶

class rsfmodel.staterelations.PrzState¶

Bases: rsfmodel.staterelations.StateRelation

The PRZ state relation as proposed by [3]:

Notes

\[\frac{d\theta}{dt} = 1 - \left(\frac{V_\text{slider} \theta}{2D_c}\right) ^2\]

[3]	Perrin, G., Rice, J., and Zheng, G. “Self-healing slip pulse on a frictional surface.” Journal of the Mechanics and Physics of Solids 43.9 (1995): 1461-1495.

Methods

evolve_state(system)¶

set_steady_state(system)¶

velocity_component(system)¶

Perrin-Rice velocity contribution

\[V_\text{contribution} = b \text{ln}\left(V_{\text{prz}0} \theta\right)\]

class rsfmodel.staterelations.RuinaState¶

Bases: rsfmodel.staterelations.StateRelation

The slip or Ruina state relation as proposed by [4].

Notes

\[\frac{d heta}{dt} = -\frac{V_\text{slider} \theta}{D_c} \text{ln}\left(\frac{V_\text{slider} \theta}{D_c}\right)\]

[4]	Ruina, Andy. “Slip instability and state variable friction laws.” J. geophys. Res 88.10 (1983): 359-10.

Methods

evolve_state(system)¶

set_steady_state(system)¶

class rsfmodel.staterelations.StateRelation¶

Bases: object

Abstract state relation object that contains the generally used atributes in state relations (b,Dc).

Attributes

b	(float) Rate and state empirical parameter b.
Dc	(float) Critical slip distance.
state	(float) State variable.

Methods

velocity_component(system)¶

General velocity contribution from a given state variable

Notes

\[V_\text{contribution} = b \text{ln}\left(\frac{V_0 \theta}{D_c}\right)\]