Effect of varying normal stress on stability and dynamic motion of a spring-slider system with rate- and state-dependent friction

Incorporating rate and state friction laws, stability of linearly stable (i.e., with stiffness greater than the critical value) spring-slider systems subjected to triggering perturbations was analyzed under variable normal stress condition, and comparison was made between our results and that of fixed normal stress cases revealed in previous studies. For systems associated with the slip law, the critical magnitude of rate steps for triggering unstable slips are found to have a similar pattern to the fixed normal stress case, and the critical velocity steps scale with <i<a</i</(<i<b</i< - <i<a</i<) when <i<k</i< = <i<k</i<<sub<cr</sub< for both cases. The rate-step boundaries for the variable normal stress cases are revealed to be lower than the fixed normal stress case by 7 %–16 % for a relatively large <i<α</i< = 0.56 with (<i<b</i< - <i<a</i<)/<i<a</i< ranging from 0.25 to 1, indicating easier triggering under the variable normal stress condition with rate steps. The difference between fixed and variable normal stress cases decreases when the <i<α</i< value is smaller. In the same slip-law-type systems, critical displacements to trigger instability are revealed to be little affected by the variable normal stress condition. When <i<k</i< ≥ <i<k</i<<sub<cr</sub<(<i<V</i<<sub<*</sub<), a spring-slider system with the slowness law is much more stable than with the slip law, suggesting that the slowness law fits experimental data better when a single state variable is adopted. In stick-slip motions, the variable normal stress case has larger stress drops than the constant normal stress case. The variable normal stress has little effect on the range of slip velocity in systems associated with the slowness law, whereas systems associated with the slip law have a slowest slip velocity immensely smaller than the fixed normal stress case, by ~10 orders of magnitude.