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 mag- nitude 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 a/（b - a） when k = kcr 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 ct = 0.56 with （b - a）/a 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 α 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 k 〉 kcr（V,）, 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.

Frictional sliding of infilled planar granite fracture under oscillating normal stress

This paper investigates the frictional behavior of the infilled rock fracture under dynamic normal stress.A series of direct shear tests were conducted on saw-cut granite fractures infilled with quartz using a selfdeveloped dynamic shear apparatus,and the effects of normal load oscillation amplitude,normal load oscillation period and sliding velocity were studied.The test results reveal that the shear response can be divided into three stages over a whole loading-unloading process,characterized by different time spans and stress variations.Generally,a smaller oscillation amplitude,a longer oscillation period and a fast shear velocity promote the stability of the friction system,which is also confirmed by the Coulomb failure criterion calculated based on the observed periodic apparent friction coefficient.The dynamic strengthening/weakening phenomenon is dependent on the oscillation amplitude and product of sliding velocity and oscillation period(vT).Also,the rate and state friction law incorporating the parameter a that characterizes the normal stress variation is employed to describe the dynamic friction coefficient but exhibits an incompetent performance when handling intensive variation in normal stress.Finally,the potential seismicity induced by oscillating normal stress based on the observed stress drop is analyzed.This work helps us understand the sliding process and stability evolution of natural faults,and its benefits for relative hazard mitigation.