*2.3. Reconstruction of the Physicallybased Thresholds*

The adopted procedure for the reconstruction of the physicallybased thresholds is composed of a series of consequent steps (Figure 5):

1. Identification of the representative testsite. Montuè was chosen as testsite exhibiting the typical geological and geomorphological settings prone to shallow landsliding in the study area (Figure 2a). The typical soil profile is shown in Figure 2b and described in detail in Bordoni et al. [24]. Test-site soils are low plastic clayey–sandy silts with a thickness mostly between 0.5 and 1.5 m. From the ground surface till 0.7 m, the upper soil layer (US) is characterized by a high content in carbonates (15%), as soft concretions, and unit weight in the order of 16.7–17.0 kN/m3. Below this level, the lower soil layer (LS), from 0.7 to 1.1 m from the ground level, is characterized by similar carbonate content with respect to the US, but it presents a higher unit weight, ranging around 18.6 kN/m3. Between 1.1 and 1.3 m from ground level, there is a layer (CAL) characterized by a significant increase in carbonate content, till 35.3%. The weathered bedrock (WB), which is composed of sand and poorly cemented conglomerates, is at 1.3 m from the ground surface. US and LS are characterized by similar values of friction angle, equal to 31◦ and 33◦, respectively, and by a nil effective cohesion. Instead, the CAL horizon has a lower value of friction angle (26◦), but a higher effective cohesion (29 kPa). Saturated hydraulic conductivity (Ks) is in the order of 10−5 m/s, except for CAL level that is characterized by a saturated hydraulic conductivity of 10−7 m/s. Soil water characteristic curves (SWCCs) of the soil layers, fitted through Van Genuchten's [46] model, are quite similar [47], with wetting paths having saturated (θs) and residual (θr) water contents of 0.37–0.40 and 0.01 m3/m3, respectively. λ and n fitted parameters of the model range between 0.011 and 0.017 kPa−1 and between 1.20 and 1.40, respectively.

From the geomorphological point of view, the testsite has steep slopes (steepness higher than 15◦ and mostly between 26◦ and 35◦) and is east-facing. The slope elevation ranges from 170 to 210 m a.s.l. The land use is mainly constituted by grass and shrubs passing to a woodland of black robust trees at the bottom of the slope. Shallow landslides occurred on this slope in response to two events: (i) on 27 and 28 April 2009, as a consequence of an extreme rainfall event characterized by 160 mm of cumulated rain in 62 h; (ii) between 28 February and 2 March 2014, as a consequence of an event of 68.9 mm in 42 h. The source areas of these shallow landslides have a slope angle higher than 25◦, especially between 30◦ and 35◦. The failure surfaces are located at a depth of around 1.0–1.2 m from ground level.

In the test-site slope, an integrated meteorological and hydrological monitoring station has been installed since 27 March 2012, and is still functioning [24]. The station allows meteorological parameters (rainfall depth, air temperature and humidity, air pressure, net solar radiation, wind speed and direction) to be measured, together with soil pore-water pressure, at depths of 0.2, 0.6, and 1.2 m from ground level, and soil water content, at depths of 0.2, 0.4, 0.6, 1.0, 1.2, and 1.4 m from ground level. Further details on this monitoring station are reported in Bordoni et al. [24,47].

2. Physicallybased model, to model the hydrological and the mechanical responses of the slope to different rainfall events. The well-established physicallybased methodology named TRIGRS [48] was used. It has been already applied successfully for modeling the occurrence of these phenomena [1,49–54]. This physicallybased model considers the method outlined by Srivastava and Yeh [55] and Iverson [56] to explain shallow landslide triggering in relation to rainwater infiltration both in saturated or unsaturated soil conditions, assuming an impermeable basal boundary at a finite depth and a simple runoff-routing scheme. The model assesses the pore-water pressure and the slope safety factor (Fs) during different moments of a rainfall event, due to rainwater infiltration.

A 5 × 5 m digital elevation model (DEM), realized through LiDAR data acquired in 2008 and 2010 by the Italian Ministry for Environment, Land, and Sea, provided the topographic basis for the study area and was used to derive the slope angle and the flow direction maps required by the model. Hydrological parameters required for the hydrological model of TRIGRS were Ks, θs, θr, and the ξ parameter, which represents the fitting parameter of Gardner's [57] SWCC equation. ξ was estimated based on the λ and n fitting parameters of Van Genuchten's model through the method proposed by Ghezzehei et al. [58] (Equation (3)):

$$
\xi = \lambda (1.3 \times \text{n}) \tag{3}
$$

Hydrological boundary condition of the model corresponded to the presence of a low permeable soil level, which limits the infiltration of the rainwater and causes the uprising of a perched-water table in correspondence of the most intense rainfall events. As demonstrated by Bordoni et al. [24], this can be assumed as the main triggering mechanism of shallow failures in the study area. This

water table developed in correspondence of the CAL layer, due to its lower permeability than the overlying soil levels, at about 1.1–1.2 m from ground level. The perched water table could rise up to 0.8–1.0 m from ground level, in LS layer, during the most intense rainfall events. TRIGRS modeled water table depth in the soil profile and the corresponding pore-water pressure profiles during a rainfall event, considering also the water table depth at the beginning of a modeled event, which was estimated through the most superficial measured pore-water pressure (in US soil layer; ρUS) [59] (Equation (4)):

$$\mathbf{d}\_{\rm W} = \rho\_{\rm US} / (\gamma\_{\rm W} \cos^2 \beta),\tag{4}$$

where γw is the water unit weight (9.8 kN/m3), and β is the slope angle.

In TRIGRS model, an infinite slope stability analysis is coupled with the hydrological model to compute the Fs at different time instants at different points and depths in the analyzed area (Fs(z, t)), considering its change over time during a rainfall event, due to change in pore-water pressure ρ(z, t) (Equation (5)):

$$\text{Fs}(\mathbf{z}, \mathbf{t}) = (\tan \varphi' / \tan \beta) + [(\mathbf{c'} - \varrho(\mathbf{z}, \mathbf{t}) \gamma\_W \tan \varphi') / (\gamma z \sin \beta \cos \beta)].\tag{5}$$

where ϕ' is the soil shear strength angle, c' is the effective cohesion, γ is the soil unit weight, and z is the soil depth.

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{n\_{\text{tot}}} \left(\rho\_{o,i} - \rho\_{m,i}\right)^2}{n\_{\text{tot}}}} \tag{6}$$

where ρ*o,i* is the observed pore-water pressure at the *i*th hour of the considered rainfall event, ρ*m,i* is the pore-water pressure estimated by the model at the same *i*th hour of the same event, and *ntot* is the number of observations, which corresponds to the duration of the rainfall event (in hours).

5. Modeling slope safety factor (Fs) for different rainfall events. Once both the implementation and validation had been completed, the physicallybased model was used to estimate Fs of the testsite for rainfall scenarios corresponding to the ones identified by CTRL-T algorithm during the phase of reconstruction of rainfall events. Furthermore, synthetic rainfalls characterized by average intensities of 50, 75, and 100 mm/h, for a duration ranging between 1 and 12 h, were also modeled. A modeled rainfall event represented a triggering moment for shallow landslides if Fs dropped below 1 (unstable conditions) in correspondence of the sectors of the testsite where typically shallow landslides source areas developed in the past, namely the sectors with a slope angle higher than 25◦. Instead, if Fs stayed higher than 1 (stable conditions) in all the testsite, the rainfall event was not considered to be a triggering event. Each event was modeled by considering different initial pore-water pressures representative of the typical antecedent conditions before

landslide triggering, particularly in correspondence of the depth where typically sliding surfaces developed in the testsite (1.0 m).

6. Reconstruction of the rainfall thresholds. The method used for the reconstruction of the physicallybased thresholds was the same applied for the assessment of the empirical ones. In this case, only rainfall scenarios leading to shallow-landslide triggering based on the model application were considered. As for empirical thresholds, the physicallybased ones had fitting parameters corresponding to the mean values of the different bootstrap thresholds, with their respective uncertainties. Different rainfallthresholds could be reconstructed, according to the different initial pore-water pressure conditions used in modeling the rainfall events.

**Table 2.** Soil input parameters of TRIGRS model. (Ks) saturated hydraulic conductivity; (θs) saturated water content; (θr) residual water content; (ξ) Gardner's model fitting parameter; (ϕ') soil friction angle; (c') soil cohesion; and (γ) soil unit weight; (z) soil depth.

**Figure 5.** Flowchart of the methodology adopted for the reconstruction of the physicallybased thresholds.