## 3 Results and Discussion
### Effect of Antecedent Rainfall for an Instance of Extreme Rainfall of 84 mm/h  
The second scenario is an application of a historical extreme rainfall event. The extreme rainfall (84 mm/h) was applied to a model with an initial saturation degree of 50% for varying application conditions such as directly with no antecedent rainfall and with antecedent rainfalls of 2.5, 5, and 10 mm/h for varying durations. The primary objective is to assess the impact of antecedent rainfall, including its duration, in relation to the actual rainfall event that triggers the slope instability and to seek the time required for failure. Several analyses with different durations with three antecedent rainfall intensities were run for the extreme rainfall condition. The results are presented as the time (minutes) required for failure for each condition in Figure 7 for all cases. The times required for failure when there is no antecedent rainfall were found to be 52 and 80 min for the soils in the FLAC sample and this study, respectively. It is important to remember that the actual time for the recorded rainfall was 3 h at the actual location. For all soils, the slope failure would be achieved with the selected extreme rainfall. Figure 6: The saturation variations and after the application of (**a**) 2.5 mm/h, (**b**) 5 mm/h, and (**c**) 10 mm/h rainfalls when the initial saturation was 55%. When the successive rainfalls were considered, the antecedent rainfall directly affected the time for failure. The light intensity rainfall, 2.5 mm/h, may practically have a duration as long as a day, and, after 24 h, a storm may happen. When this condition was considered, the time required for failure for the 84 mm/h rainfall intensity was found to be 23 min for the FLAC sample and 26 min for this study's sample. In another point of view, the storm may happen after the 5 or 10 mm/h rainfalls eventually. In this instance, after an hour of the 5 mm/h and 10 mm/h rainfalls, the time required for failure for the 84 mm/h rainfall was found to be 48 and 44 min, respectively, for the FLAC sample. The time required for the soil of this study was found to be 59 and 53 min for the same condition. If there were a possibility of an extreme rainfall condition exceeding these durations according to the meteorological expectations, a warning may be called, or precautions can be carried out before the rainfall takes place. For each different duration of antecedent rainfalls, a zone appears in Figure 8a for each soil, and these zones were marked as dashed areas for the susceptible time for failure  
Figure 7: The time required for failure of the 84 mm/h rainfall for varying antecedent rainfall conditions for soils in (**a**) FLAC sample and (**b**) this study when the saturation was 50%. in Figure 8b. In Figure 8, three antecedent rainfalls were used, and the limitations of the zone were pointed out with lines where the upper limit belonged to the 2.5 mm/h rainfall and the lower limit to the 10 mm/h rainfall. For the other rainfall intensities between 2.5 and 10 mm/h, interpolations can easily be made. It is critical to remember that the initial saturation was 50% for the second scenario in this model. Such evaluations can be carried out for other possible initial saturation degrees. In real conditions, the saturation variations can be determined by in situ observations, and calculations can be carried out according to the in situ measurements. In this instance, the natural water content was measured around 7% of the soil sample of this study which corresponded to a saturation degree of 40%. Consequently, the failure time for 40% saturation degrees for the soil in this study was found to be 108 min, when there was no antecedent rainfall for the 84 mm/h rainfall. This type of graphical presentation may also be multiplied for other possible triggering rainfall conditions with site-specific investigations.