Modeling the Effects of a Normal-Stress-Dependent State Variable, Within the Rate- and State-Dependent Friction Framework, at Stepovers and Dip-Slip Faults

The development of the rate- and state-dependent friction framework (Dieterich Appl Geophys 116:790–806, 1978 ; J Geophys Res 84, 2161–2168, 1979 ; Ruina Friction laws and instabilities: a quasistatic analysis of some dry friction behavior, Ph.D. Thesis, Brown Univ., Providence, R.I., 1980 ; J Geophys Res 88:10359–10370, 1983 ) includes the dependence of friction coefficient on normal stress (Linker and Dieterich J Geophys Res 97:4923–4940, 1992 ); however, a direct dependence of the friction law on time-varying normal stress in dynamic stepover and dip-slip fault models has not yet been extensively explored. Using rate- and state-dependent friction laws and a 2-D dynamic finite element code (Barall J Int 178, 845–859, 2009 ), we investigate the effect of the Linker–Dieterich dependence of state variable on normal stress at stepovers and dip-slip faults, where normal stress should not be constant with time (e.g., Harris and Day J Geophys Res 98:4461–4472, 1993 ; Nielsen Geophys Res Lett 25:125–128, 1998 ). Specifically, we use the relation d ψ /d t = −( α / σ )(d σ /d t ) from Linker and Dieterich (J Geophys Res 97:4923–4940, 1992 ), in which a change in normal stress leads to a change in state variable of the opposite sign. We investigate a range of values for alpha, which scales the impact of the normal stress change on state, from 0 to 0.5 (laboratory values range from 0.2 to 0.56). For stepovers, we find that adding normal-stress dependence to the state variable delays or stops re-nucleation on the secondary fault segment when compared to normal-stress-independent state evolution. This inhibition of jumping rupture is due to the fact that re-nucleation along the secondary segment occurs in areas of decreased normal stress in both compressional and dilational stepovers. However, the magnitude of such an effect differs between dilational and compressional systems. Additionally, it is well known that the asymmetric geometry of reverse and normal faults can lead to greater slip and a greater peak slip rate on reverse faults than on normal faults, given the same initial conditions for each (Nielsen Geophys Res Lett 25:125–128, 1998 ; Oglesby et al. Science 280:1055–1059, 1998 ; Oglesby and Archuleta J Geophys Res 105:13643–13653, 2000 ; Oglesby et al. Bull Seismol Soc Am 90:616–628, 2000 ). For dip-slip models, we find that adding the Linker–Dieterich normal stress dependence to the state variable serves to mitigate differences in peak slip rate between re