State Relations¶
rsfmodel.staterelations¶
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class
rsfmodel.staterelations.DieterichState¶ Bases:
rsfmodel.staterelations.StateRelationThe 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
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evolve_state(system)¶
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set_steady_state(system)¶
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class
rsfmodel.staterelations.NagataState¶ Bases:
rsfmodel.staterelations.StateRelationThe 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
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evolve_state(system)¶
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set_steady_state(system)¶
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class
rsfmodel.staterelations.PrzState¶ Bases:
rsfmodel.staterelations.StateRelationThe 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
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evolve_state(system)¶
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set_steady_state(system)¶
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velocity_component(system)¶ Perrin-Rice velocity contribution
\[V_\text{contribution} = b \text{ln}\left(V_{\text{prz}0} \theta\right)\]
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class
rsfmodel.staterelations.RuinaState¶ Bases:
rsfmodel.staterelations.StateRelationThe 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
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evolve_state(system)¶
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set_steady_state(system)¶
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class
rsfmodel.staterelations.StateRelation¶ Bases:
objectAbstract 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
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velocity_component(system)¶ General velocity contribution from a given state variable
Notes
\[V_\text{contribution} = b \text{ln}\left(\frac{V_0 \theta}{D_c}\right)\]
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