Stability analysis of slip of a one-body spring-slider model in the presence of thermal pressurization

Abstract

This study is focused on stability of slip in a one-body spring-slider system, with stiffness k of the slider, in the presence of thermal pressurizationfor two end-member models of thermal pressurization, i.e., the adiabatic-undrained- deformation (AUD) model and slip-on-a-plane (SOP) model. Analytic studies based on the functions of frictional stress, t_f, versus slip, d, of the two models show that k_cr=|dt_f/dd| at d=0 is the critical stiffness of the system. k_cr is a finite positive value for the AUD model and infinity for the SOP model. Slip is stable when k>k_cr and unstable when k<k_cr. Analytic stability conditions of slip from the equations of motions of a one-body spring-slider model with the t_f–d function of the ADU model are also those from |dt_f/dd| at d=0. Under ADU thermal pressurization, modeled final slip and maximum velocity for k=5 to 31 MPa/m, with k_cr=30 MPa/m, both decrease with increasing k. The motions become very weak when k≥k_cr, thus being unable to result in unstable motions. The phase portraits of v versus d for k<30 MPa/m show the existence of a non-zero unstable fixed point.