# Triggering of Rain-Induced Landslides, with Applications in Southern Italy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Physical Models

_{s}), expressed as:

## 3. Hydrological Models

^{GA}SAKe (Genetic-Algorithms-Based release of the Self-Adaptive Kernel), Terranova et al. [17,131] adopted an approach based on filter functions that self-adapt to available information over time. By employing a black-box approach, the calibration is performed by means of genetic algorithms, GA [132]. At the beginning of any optimisation experiment, an initial population of Kernels (genotypes) are generated at random or by assuming a given pattern (e.g., decreasing triangular, increasing triangular, rectangular, etc.). The performance of each solution is evaluated by means of a fitness function ($\varphi $). At each iteration, best individuals are first selected by applying the selection operator, following an elitist approach. The random operator’s crossover and mutation are then employed to modify parents’ genes and obtain new populations (whose performances are again evaluated). The base time (t

_{b}) is also mutated, according to a random factor. Accordingly, better individuals, characterised by higher fitness values, can be progressively obtained over time by evolving the initial population of candidate solutions through a number of GA iterations. In such a way, a family of “optimal” Kernels that maximises the fitness can be determined. By means of a convolution between each Kernel and rainfall, a mobility function (phenotype) is obtained.

^{GA}SAKe provides multiple equivalent solutions, i.e., a family of “optimal” Kernels with the same fitness, but different in shape. The adoption of synthetic Kernels (i.e., obtained by averaging a set of optimal Kernels) permits the combination of the predictive power of a number of Kernels for practical applications. The model can be applied either to single landslides, characterised by several historical activations (to predict the timing of further mobilisations), or to a set of similar slope instabilities within a homogeneous geomorphological context (e.g., to predict new events of the triggering of shallow landslides). Once validated, the model can be applied within an early warning system to help estimating the timing of future activations in a given study area, based on measured or forecasted rainfall.

^{GA}SAKe could be easily applied also to other types of phenomena, i.e., to any kind of interaction between a controlling factor and its resulting effects. To date, it has been applied to investigate relationships between rainfall and landslide activations; however, it may similarly be used to explore relations between rainfall and depth of underground water table or water levels at a stream cross-section, etc. To this aim, experiments are in progress.

## 4. Coupled Hydrological and Physical Models

## 5. Some Model Applications

#### 5.1. Application of Physical Modelling

^{3}, c′ = 0 kPa, φ′ = 32°), in which most of the failure surface developed; as for its portion inside layer 2, it was assumed to be activated for the first time, and a friction angle slightly smaller than the peak value was assumed (γ = 18 kN/m

^{3}, c′ = 0 kPa, φ′ = 36°).

_{s}> 1.5) in the case of the summer pore-water pressure regime. Body 4 becomes unstable when the water table at S1 is 9 m below the ground, approximating the surface downslope; in the case of the further raising of the water table, retrogressive activations involve bodies 5 and 6 with the water table at S1 7 m and 6 m, respectively.; bodies one and two become unstable only for shallower depths, followed by body three. If the water table reaches a depth of 4 m at S1, all the considered bodies are unstable.

#### 5.2. Application of Hydrological Modelling

_{5,C}), with associated uncertainties (Figure 3):

_{5,TAR}) and Ionian (T

_{5,IAR}) alert regions (Figure 4):

_{5,EAR}threshold is steeper than T

_{5,WAR}. For D ≤ 12 h, a larger amount of cumulated rainfall is needed to trigger landslides in the WAR, whereas the opposite occurs for D > 12 h.

^{GA}SAKe model to different case studies in Southern Italy, in particular, to three rockslides in Calabria (at Acri-Serra di Buda, San Benedetto Ullano-San Rocco and San Fili-Uncino) and to 11 events of widespread soil-slip activations in the Sorrento Peninsula, in Campania (Figure 7). For each case study, the model was first optimised by considering a subset of calibration dates and then validated against the remaining dates of activation (cf. Table 1).

- For the Campanian shallow landslides of the Sorrento Peninsula, the obtained ${t}_{b}$ is quite short (28 days), about a half of those obtained for the Calabrian rock slides (ranging between 46 and 74 days), thus confirming the expected direct relationship between base time, on one side, and the extent of instability masses and groundwater paths on the other -cf. [9].
- The best performances were observed for the San Fili-Uncino (Figure 8) and for the San Benedetto Ullano-San Rocco case studies, with neither missing nor false alarms both in calibration and in validation (in fact, even for this latter case, the predicted activation anticipates “only few hours”, the alarm issued by the public authority of Civil Protection, hence
**Φ**_{v}is actually 100%). - Less satisfactory results were instead obtained for the Sorrento Peninsula study case. In general, concerning shallow landslides, worse modelling results are intrinsically expected due to a number of reasons: the differences in extent of the triggered landslides, heterogeneities in slope materials, inhomogeneous rainfall fields (especially in case of short-lasting, high-intensity storms) and poor quality of rain data due to low density of the rain-gauge network. Moreover, some dates of activation may even be missing, especially in remote areas. Anyhow, despite all such limitations,
**Φ**greater than 80% and 73% were obtained for calibration and validation in the Sorrento Peninsula, respectively. - For the Acri case study, the application of the model was evidently hampered by misleading geotechnical information (cf. e.g., [148]), reflecting in the unsatisfactory values of
**Φ**obtained both in calibration (ca. 83%) and especially in validation (ca. 62%). For this case study, some of the available dates of activation apparently refer to secondary portions of the main rockslide; historical archives did not permit an accurate understanding of the mobilised volumes, and then secondary movements (or even activations of different nearby phenomena) may have been incorrectly attributed to the investigated slope movement.

## 6. Conclusions and Some Research Perspectives

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**(

**a**) Contingency table showing the four possible outcomes of a binary classifier model. TP = True Positive, TN = True Negative, FP = False Positive, FN = False Negative. (

**b**) Receiver Operating Characteristic (ROC) space, with hypothetical model results. POD = Probability of Detection, POFD = Probability of False Detection (modified after [16]).

Skill Score | Formula | Range | Optimal Value |
---|---|---|---|

Probability of Detection | $POD=\frac{TP}{TP+FN}$ | [0, 1] | 1 |

Probability of False Detection | $POFD=\frac{FP}{FP+FN}$ | [0, 1] | 0 |

Probability of False Alarms | $POFA=\frac{FP}{TP+FP}$ | [0, 1] | 1 |

Hanssen and Kuipers | $HK=\left(\frac{TP}{TP+FN}\right)-\left(\frac{FP}{FP+TN}\right)$ | [−1, 1] | 1 |

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**Figure 1.**San Rocco landslide; (

**a**) the six hypothesised landslide bodies (in red), with geotechnical scheme and steady-state (summer) water table conditions; (

**b**) geotechnical scheme with worst (winter) water table conditions and approximated location of the boreholes; (

**c**) geomorphological scheme. In red: main fractures; green hatched area: inactive landslide; pink hatched area: portion of the landslide that showed the greatest evidence of mobilisation on both activations; yellow arrows: average directions of displacement; S1−5: boreholes (black dots); e1−10: extensometers; p0, p1: meteoric stations; black triangle: building; black square: water system tank (“v”); white dashed line) profile considered in the parametric analyses. A piezometer was installed in S1; S2−5 were equipped with inclinometers. The threatened area is evidenced in light-green and bordered with an orange dashed line. In green: fractures and directions of movement of other landslides. (

**d**) location maps. Layers 1–2 are distinguished by colours (yellow and orange, resp.), whereas the underlain bedrock is in brown, modified after [146].

**Figure 2.**San Rocco landslide: assumed water tables, mobilised bodies #4–6 (in red), and related safety factors. (

**a**) body #4: for water table at 9 m in S1, it is F

_{4}= 1.01; (

**b**) body #5: for water table at 7 m in S1, it is F

_{5}= 1.0; (

**c**) body #6: for water table at 6 m in S1, it is F

_{6}= 1.00; (

**d**) relationships between safety factor (F

_{i}) of the considered landslide bodies (#1–#6) and depth of ground water at S1 (modified after [146]). Colour of layers are the same as in Figure 1.

**Figure 3.**Rainfall duration vs. cumulated event rainfall (D, E) conditions that resulted in shallow landslides in Calabria (blue dots), and related E-D threshold at the 5% exceedance probability level. On top right, a location map of the study area is shown. On bottom right, the same threshold is shown in linear coordinates. The shaded marks threshold uncertainty (modified after [147]).

**Figure 4.**Rainfall duration vs. cumulated event rainfall (D, E) conditions that resulted in shallow landslides in Calabria in the Ionian alert region (orange dots) and in the Tyrrhenian alert region (red dots), and related E-D thresholds at the 5% exceedance probability levels (T

_{5,IAR}and T

_{5,TAR}). In the upper right, the Ionian and Tyrrhenian alert regions are shown, together with a location map of the study area. On bottom right, the same thresholds (T

_{5,IAR}and T

_{5,TAR}) are shown in linear coordinates. Shaded areas mark threshold uncertainties (modified after [147]).

**Figure 5.**Duration vs. cumulated event rainfall (D, E) conditions that resulted in shallow landslides in the Sicilian Eastern alert region (EAR) and Western alert region (WAR) and obtained E-D thresholds at the 5% exceedance probability level (T

_{5,EAR}and T

_{5,WAR}). In the upper right, a location map of the study area is provided. On bottom right, EAR and WAR are shown. Shaded areas mark threshold uncertainties (modified after [16]).

**Figure 6.**Mobility function obtained for the period January 1970–February 2010, with (on top) detailed view for the period December 2008–February 2010. The threshold value ${Y}_{cr}$ corresponds to the highest value of the mobility function not providing movements (modified after [117]).

**Figure 8.**San Fili-Uncino case study: (

**a**) optimal Kernel; (

**b**) mobility function obtained by applying the optimal Kernel to the entire set of available activation dates (modified after [17]).

**Table 1.**Model results for the considered case studies. For each case, the following details are listed: landslide type; number of activation dates employed for calibration and validation; base time, t

_{b}, of the optimal Kernel; maximum fitness obtained in calibration,

**Φ**, and in validation

_{c}**Φ**(cf. [17]). Best and worst fitness results are evidenced in bold and italics, resp. (*) the obtained fitness in validation for the San Rocco case study is actually 100% (cf. text).

_{v}Case Study | Landslide Type | Activation Date (Calibration + Validation) | t_{b}(Days) | Φ_{c}(%) | Φ_{v}(%) |
---|---|---|---|---|---|

Acri-Serra di Buda | Rockslide | 5 + 1 | 74 | 82.8 | 62.2 |

San Benedetto Ullano-San Rocco | Rockslide | 2 + 1 | 46 | 100 | 96.2 * |

San Fili-Uncino | Rockslide | 5 + 1 | 66 | 100 | 100 |

Sorrento Peninsula | Soil-slip | 10 + 1 | 28 | 80.6 | 73.3 |

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**MDPI and ACS Style**

D’Ippolito, A.; Lupiano, V.; Rago, V.; Terranova, O.G.; Iovine, G. Triggering of Rain-Induced Landslides, with Applications in Southern Italy. *Water* **2023**, *15*, 277.
https://doi.org/10.3390/w15020277

**AMA Style**

D’Ippolito A, Lupiano V, Rago V, Terranova OG, Iovine G. Triggering of Rain-Induced Landslides, with Applications in Southern Italy. *Water*. 2023; 15(2):277.
https://doi.org/10.3390/w15020277

**Chicago/Turabian Style**

D’Ippolito, Antonino, Valeria Lupiano, Valeria Rago, Oreste G. Terranova, and Giulio Iovine. 2023. "Triggering of Rain-Induced Landslides, with Applications in Southern Italy" *Water* 15, no. 2: 277.
https://doi.org/10.3390/w15020277