# Nucleation Mechanism and Rupture Dynamics of Laboratory Earthquakes at Different Loading Rates
## 3 Results
### Effect of Loading Rate on Earthquake Nucleation Process  
#### 3.3.1 Basic Characteristics of Earthquake Nucleation  
The high-speed photography and strain rosette are used to simultaneously monitor the full-field displacement field and the shear stress at multiple locations along the fault at different loading rates. Figure 10 collectively presents the spatiotemporal evolution of the fault slip and the history of the shear stress along the fault from the quasi-static nucleation to the dynamic coseismic rupture. Figure 11 shows the detailed spatiotemporal progression of the rupture fronts at a 0.5 \(\upmu\)m/s loading rate. The red line represents a linear fit of the rupture points, with its slope indicating the inverse of the rupture propagation speed. It highlights the contrast between the fast dynamic propagation at 1908 m/s and the notably slower quasi-static progression within the critical length (\(\mathbf{L_{C}}\)), moving at an approximate 11 m/s--well under the S-wave velocity. In this stage, the shear stress in the nucleation zone is partially released, which may be due to the development of localized pre-slip [4,7]. Dynamic rupture occurs when the size nucleation zone attains a critical length (\(\mathbf{L_{C}}\)). In the dynamic rupture stage, ruptures always propagate bilaterally at a velocity approaching or  
Figure 8: Static friction versus recurrence interval. At a fixed loading rate, static friction rises logarithmically with recurrence intervals, consistent with the previous findings [41,42].  
Figure 9: (**a**) Stress drop and (**b**) friction drop as functions of loading rate. The light color symbols represent the actual values. The highlight color symbols are the mean values with a 95% confidence interval. The dotted line is the fitting curve based on the mean values at different loading rates.  
even exceeding the S-wave velocity. The abrupt increase in the fault slip corresponds to the abrupt drop in the shear stress, indicating that both the displacement and the shear stress monitoring can disclose the transient rupture process. Previous studies clearly showed that the rupture process can be divided into three stages: quasi-static growth, acceleration, and dynamic rupture [7,14]. Our observations are generally consistent with previous studies.  
In addition, we found that the nucleation phase is controlled by the loading rate. As the loading rate increases, the nucleation size gradually decreases. When the loading rate reaches 3.0 \(\upmu\)m/s, the nucleation region cannot be observed in the observation system mentioned in this paper. The direct shear experiment based on meter-scale rocks found that the nucleation phase exists at slow (0.01 mm/s) and intermediate (0.1 mm/s) loading rates, while it disappears at a fast loading rate (1 mm/s) [33]. In addition, the relationship between the nucleation length and the loading rate through double shear experiments are studied using high-speed photography and strain rosette [35]. It was found that when the loading rate increased from 0.01 MPa/s to 6 MPa/s, the nucleation length was nearly  
Figure 10: Evolution process of displacement field and strain during fault nucleation and rupture at loading rates of (**a**) 0.5 \(\upmu\)m/s, (**b**) 1.0 \(\upmu\)m/s, (**c**) 1.5 \(\upmu\)m/s, (**d**) 2.0 \(\upmu\)m/s, and (**e**) 2.5 \(\upmu\)m/s. The nephogram is the location–time view of fault slip evolution; the purple curve represents the shear strain at the corresponding position. Time 0 means the trigger time of displacement and strain monitoring system.  
three times shorter. It is considered that the loading rate affects the nucleation length by modifying the dimensionless variable \(V\theta/d_{c}\) in the framework of the rate-and-state constitutive friction law. The minimum nucleation length observed in the experiment is 0.8 cm.