# Incorporating the Effects of Complex Soil Layering and Thickness Local Variability into Distributed Landslide Susceptibility Assessments

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview of the Testing Area

#### 2.1. Geological and Stratigraphic Settings

_{basal}soil horizon; SM) is always present on the underlying carbonate bedrock (R). The thinning of the pyroclastic soil mantle, occurring on slope angles greater than 28° up to its disappearance on slope angles greater than 50°, was recognized as having a strong influence also on stratigraphic settings of the volcaniclastic series along the slopes. The variation of ash-fall pyroclastic soil thickness was linked to the local slope angle by an empirical model [49,61,62,64], which was used in this research. The reduction of the total thickness was recognized determining the downslope pinch out of the pyroclastic horizons (both C and Bb). Moreover, a further reduction of the total thickness was observed leading to the direct overlying of the B horizon on the Bb

_{basal}horizon [48,61].

#### 2.2. Flow-Type Landslides Involving Ash-Fall Pyroclastic Coverings

## 3. Data and Methods

#### 3.1. Overview of TRIGRS

^{2}δ − (I

_{ZLT}/K

_{S}) where: K

_{S}is the saturated hydraulic conductivity in the Z direction; I

_{ZLT}is the steady (initial) surface flux that can usually be approximated by the average precipitation in recent weeks or months that is needed to maintain the initial conditions; I

_{nZ}is the surface flux of a given intensity for the nth interval (i.e., model timestep); and D

_{1}= D

_{0}/cos

^{2}δ where D

_{0}is the saturated hydraulic diffusivity (D

_{0}= K

_{S}/S

_{S}; S

_{S}is the specific storage); N is the total number of time intervals for the defined duration of the simulation; H(t–t

_{n}) is the Heaviside step function; and t

_{n}is the time at the nth time interval in the rainfall sequence. The function ierfc is of the form ierfc (η) = $1/\surd \mathsf{\pi}$exp (−η

^{2}) − ηerfc(η), where erfc(η) is the complementary error function.

_{r}), saturated water content (θ

_{s}), inverse of capillary fringe (α), and hydraulic conductivity (K

_{sat}) to approximate the Soil Water Retention Curve-SWRC [100] and thus the one-dimensional infiltration flux [101], with no lateral flow/throughflow. In this case, the vertical water pressure head changes in the unsaturated zone are thus computed:

_{1}= α cos2δ; Ψ

_{0}is the pressure head at the water table (Ψ

_{0}= 0) or at the top of the capillary fringe (Ψ

_{0}= −1/α); and K(Z,t) is the hydraulic conductivity as a function of time and depth in the unsaturated zone [90,101,102].

_{W}= Z − d is the vertical depth below the initial water table; Ψ

_{hn}= β

_{hn}is the pressure head applied after the accumulation of water above the initial water table; and d

_{LZw}is the vertical height of the saturated layer (d

_{LZw}= d

_{LZ}− d).

_{w}is unit weight of water; and γ

_{s}is unit weight of soil. Ψ (Z, t) is the transient pressure head at depth Z and time t obtained from either Equations (1), (2) or (3) depending on the particular conditions modeled. Regarding the unsaturated zone, TRIGRS computes the FoS above the water table multiplying the matric suction Ψ(Z, t)γ

_{w}by χ = (θ − θ

_{r})/(θ

_{s}− θ

_{r}) [4].

#### 3.2. Parameterizing TRIGRS

^{2}), a 5-m resolution Digital Elevation Model (DEM) of the area obtained by LIDAR data made available from the Italian Environment Minister was used for TRIGRS modeling. This high-resolution DEM allowed the reconstruction of a new map of the distribution of ash-fall pyroclastic soil thickness according to the empirical model linking ash-fall pyroclastic soil thickness and local slope angle, which replicates observations that slope is inversely proportional to deposit thickness [59,61,62,64]. Furthermore, the same elevation data were used to calculate inputs required for TRIGRS simulations, including flow direction and slope angle maps.

## 4. Results

#### 4.1. TRIGRS Model Calibration

#### 4.2. Slope Stability Maps for Initial Landslides

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Geological setting of the peri–Vesuvian area: (1) alluvial deposits; (2) travertine deposits; (3) debris and slope talus deposits; (4) incoherent ash-fall deposits (Recent Pyroclastic Complex); (5) mainly coherent ash-fall deposits (Ancient Pyroclastic Complex); (6) lavas; (7) Miocene flysch; (8) Middle Jurassic–Upper Cretaceous limestones; (9) Lower Triassic–Middle Jurassic dolomites and calcareous limestones; (10) outcropping and buried faults; (11) total isopachs line (in m) of ash-fall pyroclastic deposits erupted by the Plinian Somma–Vesuvius’ eruptions (WGS84/UTM 33N) (modified from [57,60,62]).

**Figure 2.**Sample areas considered for the Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability (TRIGRS) analysis: (

**A**) site-specific scale area, located on southwestern slope of Mt. Pizzo D’Alvano, in which the scarp of the initial slide area (cell 1) of one May 1998 landslide events (red contour) and location of the monitoring station (L4 test site; cells 2 and 3) are shown; (

**B**) slope scale area coinciding with Sarno Mountains ridge and where the other three studied sample areas (L1, L2 and L3), corresponding to source areas of initial landslides occurred in May 1998, are shown (WGS84/UTM 33N).

**Figure 3.**Main hydro-mechanical properties of soil horizons characterizing ash-fall pyroclastic soil coverings of Sarno and Lattari Mountains. Data were obtained by in situ and laboratory tests [59,75]. Key to symbols: SWRCs = soil water retention curves; HFCs = hydraulic conductivity functions; $\mathsf{\varphi}$’ = effective friction angle; c’ = effective cohesion.

**Figure 4.**Results of hydrological modeling with Variably Saturated Two Dimensional (VS2D version 1.3) for a representative slope [77] showing the antecedent conditions (

**a**) and variation soil-water pressure head (PH) distribution with formation of near saturated/saturated zones closely upslope of morphological discontinuities (

**c**). Corresponding results of TRIGRS simulation showing the rise in the hypothetical water table through time (

**b**,

**d**). Both modeling results show the influence of reduction in ash-fall pyroclastic soil cover thickness on hydrologic response to rainfall.

**Figure 5.**Simplification of a multilayered slope model, reconstructed by field surveys and used for VS2D modeling (

**a**) [58,76,104] into a single-layered model with non–uniform thickness for each TRIGRS’ 5-m cell (

**b**). Cells considered for TRIGRS model calibration (1, 2, 3) are also indicated (

**b**) and summarized in Table 1.

**Figure 6.**Example of modeled Pressure Head (PH;

**a**,

**c**,

**e**) and Factor of Safety (FoS;

**b**,

**d**,

**f**) time series at different depths for each sample cell (1, 2, 3 in Figure 5). Results shown are related to 2.5 mm/h of rainfall intensity condition.

**Figure 7.**Comparison between deterministic rainfall thresholds obtained by TRIGRS (L4 site) and those obtained by coupled hydrological and stability modelling [77] of representative slopes (L1, L2 and L3 sites).

**Figure 8.**Distributed slope stability maps, at site-specific (

**A**) and slope distributed (

**B**) scales, resulting from a constant rainfall intensity of 2.5 mm/h with a duration of 96 h. Unstable and likely unstable cells were compared within sample areas (

**C**) L1, L2, L3 [77], L4 and the entire Sarno Mountains landslide inventory comprising the May 1998 Sarno landslide event. Monitoring station cells used for local scale modeling and L4 threshold definition are also shown (

**C**) (WGS84/UTM 33N).

**Figure 9.**Distributed slope stability maps, at site–specific (

**A**) and slope distributed (

**B**) scales, resulting from a constant rainfall intensity of 5.0 mm/h with a duration of 48 h. Unstable and likely unstable cells were compared within sample areas (

**C**) L1, L2, L3 [77], L4 and the entire Sarno Mountains landslide inventory comprising the May 1998 Sarno landslide event. Monitoring station cells used for local scale modeling and L4 threshold definition are also shown (

**C**) (WGS84/UTM 33N).

**Figure 10.**Distributed slope stability maps, at site–specific (

**A**) and the slope (

**B**) scales, resulting from a modeled constant rainfall intensity of 10.0 mm/h for 24 h. Unstable and likely unstable cells were compared within sample areas (

**C**) L1, L2, L3 [77], L4 and the entire Sarno Mountains landslide inventory comprising the May 1998 Sarno landslide event. Monitoring station cells used for local scale modeling and L4 threshold definition are also shown (

**C**) (WGS84/UTM 33N).

**Figure 11.**Distributed slope stability maps, at site–specific (

**A**) and the slope (

**B**) scales, resulting from a modeled constant rainfall intensity of 20 and 40 mm/h for 18 h, which are the same since the higher rainfall intensities exceed the infiltrain capacity of the model. Unstable and likely unstable cells were compared within sample areas (

**C**) L1, L2, L3 [77], L4 and the entire Sarno Mountains landslide inventory comprising the May 1998 Sarno landslide event. Monitoring station cells used for local scale modeling and L4 threshold definition are also shown (

**C**) (WGS84/UTM 33N).

**Figure 12.**Comparison between frequency curves of initial slides (related to May 1998 landslide event) depending on rainfall intensity considered and duration at the slope failure modelled. Deterministic rainfall thresholds by Napolitano et al. [77] are also shown.

**Table 1.**

**(a)**Unsaturated and saturated hydraulic and geotechnical soil properties determined for principal ash-fall pyroclastic soil horizons [76,77];

**(b)**Unsaturated/saturated hydraulic and geotechnical soil properties used for setting TRIGRS model and derived as median value of weighted harmonic means (WHM), estimated for 12 representative soil columns of four test sites (L1, L2, L3, L4) [76,77]. Keys to symbols: (K

_{sat}) saturated hydraulic conductivity; (θ

_{s}) saturated volumetric water content; (θ

_{r}) residual volumetric water content; (α and n) van Genuchten’s fitting parameters of soil water retention curve; ($\mathsf{\varphi}$’) = effective friction angle; (c’) = effective cohesion.

(a) | Hydro–Mechanical Properties | ||||||||

K_{sat} (m/s) | θ_{s} (ad.) | θ_{r} (ad.) | α (cm^{−1}) | n (ad.) | $\mathsf{\varphi}$’ (°) | c′ (kPa) | |||

Soil horizons (USDA) | B | 4.82 × 10^{−5} | 0.505 | 0.083 | 0.884 | 1.307 | 32.0 | 4.500 | |

C | 2.82 × 10^{−3} | 0.500 | 0.001 | 20.39 | 1.081 | 37.0 | 0.000 | ||

Bb | 6.00 × 10^{−6} | 0.663 | 0.001 | 0.884 | 1.307 | 34.0 | 1.800 | ||

Bb_{basal} | 2.48 × 10^{−7} | 0.505 | 0.083 | 0.884 | 1.307 | 35.0 | 8.100 | ||

(b) Test site | Soil column and thickness (m) | Weighted Harmonic Mean | |||||||

K_{sat} (m/s) | θ_{s} (ad.) | θ_{r} (ad.) | α (cm^{−1}) | n (ad.) | $\mathsf{\varphi}$’(°) | c′ (kPa) | |||

L1 | 1a | 4.85 | 8.53 × 10^{−6} | 0.590 | 0.132 | 3.059 | 1.294 | 34.0 | 3.820 |

1b | 4.34 | 4.78 × 10^{−6} | 0.581 | 0.111 | 3.851 | 1.316 | 33.8 | 4.350 | |

1c | 1.62 | 1.68 × 10^{−6} | 0.584 | 0.118 | 3.590 | 1.307 | 33.9 | 4.186 | |

L2 | 2a | 3.23 | 5.68 × 10^{−6} | 0.589 | 0.143 | 2.689 | 1.299 | 34.0 | 3.493 |

2b | 3.13 | 5.30 × 10^{−6} | 0.565 | 0.122 | 3.618 | 1.372 | 33.5 | 3.884 | |

2c | 1.75 | 2.06 × 10^{−6} | 0.567 | 0.099 | 4.384 | 1.356 | 33.5 | 4.585 | |

L3 | 3a | 3.99 | 2.65 × 10^{−6} | 0.580 | 0.073 | 5.174 | 1.302 | 33.8 | 5.496 |

3b | 3.35 | 3.34 × 10^{−6} | 0.573 | 0.098 | 4.347 | 1.335 | 33.7 | 4.659 | |

3c | 2.43 | 5.20 × 10^{−6} | 0.557 | 0.122 | 3.689 | 1.399 | 33.3 | 3.806 | |

L4 | 4a | 3.21 | 2.88 × 10^{−6} | 0.574 | 0.089 | 4.673 | 1.328 | 33.7 | 4.959 |

4b | 3.09 | 3.78 × 10^{−6} | 0.556 | 0.080 | 5.109 | 1.385 | 33.3 | 5.027 | |

4c | 1.47 | 7.16 × 10^{−6} | 0.558 | 0.097 | 4.512 | 1.386 | 33.3 | 4.539 | |

TRIGRS model | 4.28 × 10^{−6} | 0.574 | 0.105 | 4.099 | 1.332 | 33.7 | 4.445 |

**Table 2.**Duration of rainfall with constant intensity leading to slope failure [77] and durations to slope failure for given frequencies of May 1998 source areas, obtained by TRIGRS modelling.

Rainfall Intensity (mm/h) | 2.5 | 5.0 | 10 | 20 | 40 | |

Winter Threshold [77] | Duration (hours) | 77 | 47 | 22 | 11 | 6 |

Frequency of May 1998 source areas, unstable under TRIGRS modelling | 1% | 90 | 47 | 22 | 14 | 14 |

5% | 92 | 49 | 23 | 15 | 15 | |

50% | 109 | 55 | 33 | 27 | 27 | |

95% | 170 | 120 | 77 | 49 | 34 |

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**MDPI and ACS Style**

Fusco, F.; Mirus, B.B.; Baum, R.L.; Calcaterra, D.; De Vita, P.
Incorporating the Effects of Complex Soil Layering and Thickness Local Variability into Distributed Landslide Susceptibility Assessments. *Water* **2021**, *13*, 713.
https://doi.org/10.3390/w13050713

**AMA Style**

Fusco F, Mirus BB, Baum RL, Calcaterra D, De Vita P.
Incorporating the Effects of Complex Soil Layering and Thickness Local Variability into Distributed Landslide Susceptibility Assessments. *Water*. 2021; 13(5):713.
https://doi.org/10.3390/w13050713

**Chicago/Turabian Style**

Fusco, Francesco, Benjamin B. Mirus, Rex L. Baum, Domenico Calcaterra, and Pantaleone De Vita.
2021. "Incorporating the Effects of Complex Soil Layering and Thickness Local Variability into Distributed Landslide Susceptibility Assessments" *Water* 13, no. 5: 713.
https://doi.org/10.3390/w13050713