8.3.1 Stress and Rupture Dynamics

8.3.1 Stress and Rupture Dynamics

We examine the anatomy of the shear stress on the fault near the rupture front shown in figure 8.4 to find the relationship between its features and the dynamics of the rupture. From fracture mechanics,¹² we know that ahead of the rupture front the shear stresses increase and becomes nearly singular just ahead of the leading edge of the rupture. At the leading edge of the rupture where slip begins, the shear stresses decrease dramatically, and then, depending on the friction model, may or may not recover as the slip rate decreases. Of course, in the earth and our finite-element models failure occurs at a finite value which prevents the formation of a true singularity.

Figure 8.4: Diagrams of the concentration of shear stress near the rupture front as a function of space (left diagram) and as a function of time (right diagram).

The friction model controls the decrease in friction stress as slip progresses, and therefore, the dynamic stress drop. The rate of the dynamic stress drop governs the slip rate with faster decreases in shear stress leading to faster increases in slip. The dynamic stress drop and the distance from failure (the difference between the failure stress and the initial shear stress) determine the nature of the concentration of stress ahead of the leading edge of the rupture. A larger distance from failure magnifies the stress concentration, and a larger dynamic stress drop increases the rate of the decay of the stress concentration. The increase in shear stress associated with the stress concentration dictates when slip occurs at each point and, as a result, the rupture speed. Thus, the slip rate and rupture speed are related through the dynamic stress drop.

8.3.1 Stress and Rupture Dynamics