PSI - Issue 84

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

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represents the fraction of rainfall that effectively infiltrates the soil, reduced as a function of vegetation cover or surface slope. h j is the rainfall depth recorded at time t j , and the summation in Eq. (1a) accounts for the contribution of rainfall over a generic time t . All geotechnical parameters required by the model must be calibrated using documented landslide events or assigned on the basis of well-established parameter ranges derived from previous analyses. Further details on the SLIP model formulation and its applications can be found in the literature (Montrasio 2000; Montrasio et al. 2023). 2.2. Method for the assessment of potential triggering: synthetic rainfall for SLIP analyses To assess the potential triggering of soil slips, the proposed method involves the application of the SLIP model and the computation of the factor of safety (FS) using synthetic rainfall distributed over a 30-day period. For simplicity, the triggering rainfall is assumed to occur on the 30th day, while precipitation during the preceding 29 days is considered predisposing. The latter must realistically represent the typical rainfall conditions of the study area and are hereafter referred to as “background noise”, to be calibrated both in terms of cumulative rainfall and temporal distribution pattern. During calibration against past events, the rainfall peak on the 30th day ( P30 ) is assumed to coincide with the rainfall that triggered the landslide. Predisposing rainfall is therefore generated starting from an average daily rainfall value h̅ , distributed according to three different patterns over the preceding 29 days. Three equivalent distribution patterns are considered: (i) uniform, with h j = h̅ ; (ii) triangular, with h j = h̅ ∙ 2 29 ∙ j; and (iii) parabolic, with h j = h̅ ∙ 3 29 2 ∙ j 2 . For each pattern, h̅ can be calibrated so that, when combined with P30 , it results in FS =1 on the day of the event. To relate this value to local rainfall conditions and to make the method applicable to other areas, h̅ is compared with three different statistical distributions of daily rainfall: • Distribution 1 (D1): distribution of daily rainfall observed over a reference period (10–20 years); • Distribution 2 (D2): average daily rainfall for each calendar month, obtained by cumulating the monthly rainfall from D1 and dividing by the number of rainy days in the month; • Distribution 3 (D3): distribution of average daily rainfall computed over moving windows. For each day in D1, a 30-day moving window is considered, within which rainfall amounts are cumulated and divided by the number of rainy days. For each distribution, the percentile is identified such that the mean of non-zero rainfall values below that percentile coincides with h̅ . The distribution yielding the lowest percentile is adopted as the reference, interpreting the background noise as a non-exceptional pluviometric condition. Figures 1, 2, and 3 illustrate exemplary distributions and the application of the proposed procedure.

Fig. 1. Example of the D1 daily rainfall distribution showing two selected percentiles.