## 4 Case Study
As a point of view, when a slope is subjected to a thunderstorm, the effect of a thunderstorm triggering the initial movement considering the mechanical solicitation of the sound waves and/or wind-induced vibrations are also discussed [40]; yet, this is generally neglected in landslide studies, and this study, as well, only focuses on the saturation and rainfall antecedent conditions. In the modeling process, the initial saturation degree and pore pressures were established to reflect the conditions resulting from the light rainfall at the onset of the day during a period of precipitation. To achieve this, a pore water pressure of approximately \(-10\) kPa was targeted. This value was predicted as an expected piece of data in the field after light rainfall during the rainy period in the study of [PERSON] et al. [10]. For the application of the following rainfalls, regarding the station records and the data in [PERSON]'s study, to apply a rainfall intensity of 5 mm/h for 5 h followed by 3 h of 39 mm/h rainfall (a total of 142 mm) was considered as a representative case study. A total of 26 analyses were conducted with varying durations of three antecedent rainfall intensities (2.5, 5, and 10 mm/h) for a specific rainfall event of 39 mm/h. The time required for failure in relation to the antecedent rainfall durations is presented in Figure 12.  
The time required for failure for the 39 mm/h rainfall with no antecedent rainfall was found to be 3 h and 35 min. Regarding the actual rainfall duration, no failure would be expected when the rainfall was evaluated and analyzed individually. Yet, analogous to the real condition, when the 39 mm/h rainfall was applied after rainfall of 5 mm/h for 5 h, the time required for failure can be read as 145 min, which was indicated by the letter \"b\" in the chart. When compared to the actual rainfall duration, it is seen that the slope was found to fail as it was in real conditions. In practice, when evaluating the observed meteorological data for this case study, an alarm can be raised when the duration of the 39 mm/h rainfall exceeds 2 h. Nevertheless, it is recommended that potential extreme precipitation be modelled in advance, so that possible collapses could be identified and related precautions could be taken in accordance with the findings before the failure occurs. Figure 11: Observed rainfall conditions in September 1999 in Busan [39]. For different antecedent rainfalls, the time required for failure can be found from the chart as well. In instance, 110 min and 165 min for 10 mm/h and 2.5 mm/h, as indicated by the letters \"a\" and \"c\", can be read from the chart, respectively. Regarding the fact that the extreme rainfall was 3 h, it is reasonable to conclude that, when the antecedent rainfall was 2.5 mm/h instead of 5 mm/h for 5 h, then the failure would still be in consideration. The proposed procedure and the chart easily allow the tracking of many scenarios that occurred under different meteorological conditions for one expected main instance of extreme rainfall. The analysis of a slope triggered by rainfall is typically conducted using the cumulative rainfall over a specified duration. The cumulative rainfall for the eight-hour period was 142 mm in this study. The corresponding average hourly precipitation of 142 mm in 8 h is 17.75 mm. When the analysis was conducted using a rainfall of 17.75 mm/h, the slope was found to remain stable throughout its actual duration, showing that using the average or cumulative rainfall criteria is not adequate for this rainfall condition. Furthermore, the time required for failure for the average rainfall value was found to be more than 5 days. Even more, the time required for failure for an average rainfall of 200 mm in 3 days would be higher than that of 17.75 mm/h. The rainfall-induced slope failures were discussed in the study of [PERSON] et al.