PSI - Issue 84

Michele Placido Antonio Gatto et al. / Procedia Structural Integrity 84 (2026) 111–118

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Table 1. Parameters adopted for the Sondrio (1994) and Casargo (2019) case studies. The triggering rainfall P30 and its corresponding percentile within the D1 distribution are also reported.

Analyzed case

Geological class

φ′ (°) n (–) A (kPa) Sr0 (%) k t (s⁻¹)

P30 (mm) P30 percentile in D1

Sondrio

Gravels, sands, and silts 30 0.46 60

60 2.5·10 -6

72.2 139.8

99.51 99.82

Casargo (LC)

Paragneiss

25 0.46 80

60

1·10 -6

The P30 percentile value for the Casargo event is particularly high. With the k t value adopted during calibration, the thickness of the equivalent saturated layer induced by rainfall on the day of the event m 30 exceeds the critical value m crit , i.e., the threshold beyond which FS falls below 1. This implies that any rainfall distribution over the preceding 29 days would have been sufficient to trigger instability. Therefore, the methodology for selecting the most representative rainfall pattern was developed based on the Sondrio event and subsequently applied to the Casargo case, as described below. In the Sondrio case (where m 30 < m crit ), once k t and P30 were fixed, Eq. (1a) was evaluated on day 29. Considering the three possible patterns of rainfall distribution, the mean daily background rainfall ( h̅ ) was estimated and compared with the distributions derived using the three methods. Specifically, for each distribution, the percentile was identified such that the mean of the values below this threshold coincided with h̅ . The results are reported in Table 2. It is observed that, under the parabolic pattern, the background noise can be represented by the mean rainfall below the 50th percentile of the D2 and D3 distributions. The D2 distribution was adopted as the reference, as it is simpler to construct.

Table 2. Comparison of the three predisposing rainfall distribution patterns for the Sondrio and Casargo case studies. Sondrio Casargo

Percentile

P30 (mm/day)

P30 percentile (D1)

Daily background rainfall h̅ (mm/day)

Pattern

D1

D2

D3

Uniform Triangular Parabolic

10.22 5.99 4.60

99.93 93.66 86.94

99.50 73.79 49.05

99.88 74.30 48.37

58.05 32.02 16.53

96.2 88.5 74.7

In the Casargo case, the mean daily background rainfall h̅ was found to be equal to 6.516 mm/day. To assess which rainfall pattern was the most representative, the corresponding P30 value was calculated for each case and compared with the D1 distribution in order to identify the associated percentile. Consistently with the literature, rainfall peaks associated with landslide triggering are frequently located at the upper tail of local precipitation distributions, often exceeding the 90th–95th percentile (Caine 1980; Guzzetti et al. 2008). As reported in Table 2, for the Casargo case the uniform pattern proves to be the most suitable: a peak of 58.05 mm on day 30 is already sufficient to predict potential soil slip triggering. Finally, Figure 6 shows FS maps computed using X-SLIP for day 29 and day 30 (the event day), adopting the rainfall distributions described above.