Limiting Behavior of the Function Governing the Dynamic Earthquake Slip Process with the Interaction Among Heat, Fluid Pressure and Dilatancy

Abstract:

We have investigated the effect of the interaction among heat, fluid pressure and dilatancy on dynamic earthquake slip process. Our framework includes three nondimensional parameters, Su, Su’ and Ta. The parameter Su represents the relative dominance of the effect of inelastic pore creation on the fluid pressure change over that of shear heating, while Su’ is associated with the dominance of fluid flow effect over the effect of shear heating. The nondimensional parameter Ta describes the effect of the upper limit of inelastic porosity evolution. With the assumption Su’=0, two qualitatively different slip behaviors were found to occur: slip acceleration and spontaneous slip cessation. We have derived the analytical form of function G describing the boundary between the acceleration and spontaneous slip cessation domains on the space of the parameters Su and Ta. If G is positive (this means that the minimum slip velocity is positive), the acceleration occurs, while if G is negative, the slip ceases spontaneously. Physically important outcome here about the function G is that the boundary between the acceleration and spontaneous cessation domains is expressed by a straight line for Su>>1 and Ta>>1; the acceleration domain is above the straight line, whereas the spontaneous slip cassation domain is below the line. From the form of G, we obtain a result that the coefficient of the straight line is given by 1/v₀*, where v₀* is the normalized initial slip velocity. In addition, this outcome suggests that if φ_∞ is smaller than a critical value φ_c, spontaneous cessation will not occur for any values of Su (>>1) and Ta (>>1) because there exists a relationship Ta = φ_c/(φ_∞ v₀*) Su and the straight line describing this relationship and the boundary on the plane do not cross each other if the condition φ_∞ < φ_c is satisfied. For future slip behavior, comparison of φ_∞ with φ_c may give some implications whether the acceleration or cessation occurs.