# A Simplified Approach to Assess the Soil Saturation Degree and Stability of a Representative Slope Affected by Shallow Landslides in Oltrepò Pavese (Italy)

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{r}) of a soil is defined as follows:

_{w}is the volume of water and V

_{v}is the volume of the voids in a soil representative elementary volume. The advantages of using the degree of saturation are twofold. The first advantage is the availability of empirical or physically based methods that allow for the modeling of thedegree of the soil saturation based on the physical properties of the soil and the meteorological parameters [9,10,11,12]. The second advantage is the availability of measurements of soil moisture over large areas obtained through satellite sensors such as Advanced Scatterometer (ASCAT) [4,8,11,13,14,15].

- a)
- To calibrate and validate, on a site-specific scale, a simplified empirical model able to assess the degree of the soil saturation on the basis of readily available data, such as air temperature and rainfall;
- b)
- To validate, on a site-specific scale, a slope stability model that assumes thedegree of the soil saturation as the input data in order to evaluate the capability of the model to extendovera wide area; and
- c)
- To investigate the possibility of assessing the safety factor of a slope, only on the basis of readily available data, by coupling the two models validated with respect to (a) and (b).

_{s}). Slope stability analysis was conducted on the test slope to verify the capability of the model to reproducea shallow landslide that occurred during the monitoring time span, between 28February2014 and 2March 2014. These analyses were performed to investigate the possible future implementation of the two models to obtain preliminary predictions of rainfall-induced shallow landslides on aregional scale.

## 2. Materials and Methods

#### 2.1. TestSite Slope Geological Setting and Landslide Distribution

^{2}, was registered in the area surrounding the testsite slope.

#### 2.2. Soil Characterization at the TestSite Slope

_{L}) of 38.5–41.8% and a plasticity index (P

_{I}) of 14.3–17.2%.

^{3}to 18.6 kN/m

^{3}and then remains rather steady with respect to the depth (Table 1). For the E, F, and G horizons, the peak shear strength parameters were determined through triaxial tests (Table 1). The E and F horizons have a friction angle (φʹ) between 31° and 33° and nil cohesion (cʹ). The G horizon is characterized by a friction angle equal to 26° and an effective cohesion of 29 kPa.

_{s}, the residual water content θ

_{r}, the fitting parameters α and µ, and the saturated hydraulic conductivity K

_{s}were then estimated by using the Marquardt algorithm [31]. Although the drying–wetting hysteresis phenomenon of these soils has been deeply investigated elsewhere [24,32], for the purposes of the present work, it has been neglected and the mean values of the Van Genuchten and Mualem parameters have been assumed. All of the soil levels had similar mean values of α (0.007–0.013 kPa

^{−1}) and θ

_{r}(0.01–0.03 m

^{3}m

^{−3}; Table 2). The µ and θ

_{s}parameters were slightly higher until the depth of 0.6 m. Moreover, K

_{s}was quite steady around 1 ×·10

^{−6}and 2.5 ×·10

^{−6}ms

^{−1}, except for that at the soil level at 1.2 m below the ground (G level), which was the lowest permeable soil horizon (5·× 10

^{−7}ms

^{−1}; Table 2). The weathered bedrock (WB)level at 1.4 m below the ground had lower values of both K

_{s}(3·× 10

^{−7}ms

^{−1}; Table 2) and µ (1.15; Table 2) with respect to the soil layers above, although it wascharacterized by similar values of θ

_{s}and θ

_{r}and a higher value of α (0.050 kPa

^{−1}) than those in the soil horizons (Table 2).

#### 2.3. Monitoring Equipment

#### 2.4. Modeling the Degree of the Soil Saturation

_{r}) at various depths in the soil profile is required (Equation (2)). Table 3 summarizes the input parameters used for the determination of S

_{r}from the field measurements of the water content (θ). Daily average values of S

_{r}were calculated through Equation (2) down to 1m (i.e., the depth of the sliding surface of the shallow landslide observed on 28 February 2014–2 March2014). The main objective was modeling the dynamics of the degree of the soil saturation within the depth at which shallow landslides usually develop in the sample slope. Thus, S

_{r}trends were obtained 0.2, 0.4, 0.6, and 1.0 m belowthe ground surface, based on TDR measurements obtained at the same depths by using the following equation:

_{s}and θ

_{r}values and of the subsequent effects on the chain of models is desirable, such tasks are beyond the scope of this paper.

_{r}were compared with the values calculated for the same depths by using the empirical model proposed by [21] (Equation (4)). A detailed derivation of the model is presented elsewhere [21]; only the main statements required for completeness are provided here.

_{r}from the temperature is expressed through an exponential law, in which the exponent is represented by the time-varying air temperature T

_{m}. Such a law allows for the reproduction of the seasonal trend of the degree of thesoil saturation following the mean temperature fluctuations. In fact, air temperature has an indirect effect on the soil moisture, because it is a key variable in the evapo-transpiration process. Therefore, air temperature can be considered to bea good proxy for the seasonal climate processes that affect the soil moisture.

_{r}from rainfall, it is well known that the balance between runoff and infiltration is quite complex for unsaturated soils, and many authors have described in detail this phenomenon related to shallow landslides [33,34,35].

_{i}* has been defined as follows:

_{r}is then expressed through the sum of the two main contributions, which could be considered independent from each other. The first one is a function of the time-changing air temperature T

_{m}(in °C); the second one, which considers infiltration, is a function of the daily rainfall depth h

_{i}, changing in time as well. For computation, T

_{m}is calculated as a mean of the average daily air temperature in a previous time period of 30 days, after a phase of calibration, which considered the drying speeds on aseasonal scale in the tested slope [21]. The coefficient ψ (in °C

^{−1}) assumes the meaning of a numerical damping, and S

_{r(in)}is a calibration parameter linked to the initial state of the soil in terms of saturation. β* expresses the contribution to the degree of saturation given by the amount of infiltrated rainfall, also considering the amount of water thatcould be lost asrunoff and leakage, according to the soil type. The numerical coefficient ξ assumes the meaning of a damping coefficient whose dimension is the inverse of time (i.e., day

^{−1}), and t is the day of computation. This coefficient is related to the decrease in the water discharge with an increase in the distance from the soil surface due to differences in soil permeability.

_{r}represents the average value of the degree of saturation over a soil column of height H, characterized by a given porosity n. In order to apply this model to the described sample site, the degree of saturation was computed at different depths by assuming in each case that the soil column depth (H) was equal to the depth of the measuring point. In other words, to compute S

_{r}of the C soil horizon, H was assumed to be equal to 0.2 m; to compute S

_{r}of the D soil horizon, H was assumed to be equal to 0.4 m; and H was equal to 0.6 m and 1m for soil horizons E and F, respectively. The model calibration was carried out separately for each soil horizon.

_{r(in)}were calibrated through an adjustment procedure to get the best fit according to the measured values of S

_{r}over the analyzed time span.

#### 2.5. Modeling the Slope Stability

_{r}trends were used as the input data in the slope stability model proposed by [5]. A detailed derivation of the model was presented by [5], and a previous application to the test site based only on field measurements was reported by [24].

_{s}is calculated as follows:

^{s}is the suction stress, δ is the slope angle, and φ′ is the soil shear strength angle. In Equation (5), σ

^{s}allows for the calculation of F

_{s}also in unsaturated conditions (S

_{r}< 1.0; [5,37]). This parameter can be determined by considering S

_{r}according to Equation (6) [37]:

_{s}based on thedegree of the soil saturation.

_{s}was calculated considering a slope angle δ equal to 30.2° (Table 5), at depths of 0.4, 0.6, and 1.0 m belowthe ground level, where S

_{r}was measured. F

_{s}was then determined by considering both the measured and modeled S

_{r}values (Table 5) and by considering the geotechnical properties of the soil measured at the investigated depths (Table 1 and Table 5).

## 3. Results and Discussions

#### 3.1. Comparison between the Measured and Modeled Values of the Degree of the Soil Saturation

_{r}values were reconstructed for the time between 30 June 2012 and 5 December 2014, covering about 29 months. The trend analyses began at the start of the first dry period (Table 4). In fact, the first months of the monitoring (between 27 March 2012 and 2 June 2 2012) were disregarded, becauseall the devices needed some time to reach equilibrium and stability.

_{r}= 1) when the antecedent degree of saturation is higher than 0.8. The permanent completely saturated conditions for 1, 2, and 3 March 2014appear to prove the development of a thin, perched water table starting from the G level at −1.2 m [24]. Prolonged dry periods during summer provoked a significant decrease in the degree of the soil saturation at each investigated layer. The drying phase in the shallow layers down to 0.6 m was faster than that in the deeper soil layers (Figure 7). For each soil layer, the reliability of the calculated values of S

_{r}with respect to the measured values was evaluated by using the rootmeansquare error (RMSE) statistical index (Table 6). The RMSE values were determined by considering three different conditions: all records, a simulation of the dry season, and a simulation of the wet season. It is worth noting that although many assumptions were involved in the evaluation of S

_{r}and all the records, a fair agreement occurred between the model and experimental measurements at −0.2m and −0.4m, as indicated by the RMSE indices equal to 0.07 and 0.08, respectively (Table 6). On the contrary, for the deeper soil layers, the agreement wasweaker, as indicated by an RMSE between 0.11 and 0.14. This wasparticularly true during the dry seasons, when the RMSE indices were0.15–0.16 at 0.6 and 1 m below theground, respectively (Table 6). Generally, for all of the investigated levels, the RMSE values of the wet season weresignificantly lower as compared with the values of the dry season, with differences ranging between 0.05 and 0.10 along the soil profile (Table 6).

_{r}values underwent a sudden decrease (increase) at the beginning of dry(wet) season with respect to the previous trend. Although this assumption wasnot consistent with the measured degree of saturation, particularly at −0.6 and −1.0 m belowthe ground level (Figure 7c,d), the roughness of the model made it necessary. Two main aspects can be highlighted. The first addresses the poor correspondence between the measured and calculated values of S

_{r}during the first phase of the drying period, particularly for points at depths of −0.6 and −1.0 m.

#### 3.2. Slope Safety Factor Trends

_{r}values were used to obtain the F

_{s}trends by using the Lu and Godt slope stability model for the same monitoring time (Figure 8). F

_{s}was calculated for levels at 0.4, 0.6, and 1.0 m below theground level.

_{s}trends obtained from the measured S

_{r}values and those obtained from the modeled S

_{r}were noted (Figure 8). Similar to that previously observed for the S

_{r}annual cycles, the F

_{s}trends at 0.4m showed a better agreement with respect to the levels at 0.6 m and 1.0 m belowthe ground level (Figure 8). Moreover, the agreement wasmuch more evident in the wet season, when thedegree of the soil saturation was higher than 0.8, and the F

_{s}trends abruptly decreased with respect to the dry season (Figure 8 and Figure 9).

_{s}.

_{s}trends correctly identified the triggering time 1m belowthe ground surface, where the sliding surface actually developed (Figure 8 and Figure 9). In particular, unstable conditions were attained for three days, 1–3March2014, by the F

_{s}trend from the measured S

_{r}but only for one day, 2 March 2014, by the F

_{s}trend from the modeled S

_{r}(Figure 9).

## 4. Conclusions

_{s}trends of the slope. F

_{s}was calculated by assuming the sliding surface at different soil depths through the slope stability model proposed by [5]. Deliberately, in this research, F

_{s}was calculated on the basis of the soil water content instead of the soil suction, while the two modes were investigated and compared elsewhere [24]. Fairly good correspondence between the F

_{s}trends obtained from both the measured and modeled Sr values was observed. This result appeared useful in the following terms: if F

_{s}, calculated on the basis of measured hydrologic variables, can be considered reliable, on the other hand, in situations where field measurements are lacking, a preliminary evaluation of the slope stability could be carried out based only on the rainfall and air temperature. In particular, the performance of both the F

_{s}trends can be considered rather good in identifying the triggering time and position of the sliding surface of a shallow landslide that actually occurred during the monitoring period in conditions of complete saturation. This result proved that apotential error in the evaluation of the degree of the soil saturation does not substantially affect the assessment of the safety factor. Nonetheless, the assessment of the F

_{s}values appeared to be rather conservative during wet periods (winter), when the occurrence of shallow landslides is more probable, and at higher depths within a soil thickness of 1m, where sliding surface development is prevalent.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of the monitored experimental slope and a geological and landslide distribution sketch map of the surrounding area.

**Figure 2.**Detailed view of the testsite slope where the monitoring station was installed, showing evidence of the shallow landslides triggered during the 27–28 April 2009 event. The aerial photograph of the area was captured by Ditta Rossi s.r.l. (Brescia, Italy) on 18 May 2009.

**Figure 3.**Stratigraphic section along the testsite slope [24].

**Figure 4.**Field photograph of the shallow landslide triggered during the 28 February 2014–2 March 2014 event.

**Figure 7.**Comparison between the measured and modeled values of the degree of the soil saturation during the monitoring time span at various depths belowthe ground level: (

**a**) 0.2 m; (

**b**) 0.4 m; (

**c**) 0.6 m; and (

**d**) 1.0 m.The grey rectangles represent dry periods.

**Figure 8.**Comparison of the safety factor obtained from the measured and modeled values of the degree of the soil saturation during the monitoring time span at various depths belowthe ground level: (

**a**) 0.4 m; (

**b**) 0.6 m; and (

**c**) 1.0 m.

**Figure 9.**Comparison between the safety factor obtained from the measured and modeled values of the degree of the soil saturation for the period between 1 February 2014 and 3 April 2014 at various depths below the ground level: (

**a**) 0.4 m; (

**b**) 0.6 m; and (

**c**) 1.0 m.

**Table 1.**Main geotechnical, physical, and hydrological properties of the soils at various levels [24].

Soil Horizon | Representative Depth | Gravel | Sand | Silt | Clay | w_{L} | P_{I} | USCSClass | γ | φ’ | c’ |
---|---|---|---|---|---|---|---|---|---|---|---|

m | % | % | % | % | % | % | kN/m^{3} | ° | kPa | ||

A | 0.01 | 12.3 | 12.5 | 53.9 | 21.3 | 39.8 | 17.2 | CL | 17.0 | 31 | 0.0 |

B | 0.1 | ||||||||||

C | 0.2 | ||||||||||

D | 0.4 | 1.6 | 11.0 | 59.5 | 27.9 | 38.5 | 14.3 | CL | 16.7 | 31 | 0.0 |

E | 0.6 | 8.5 | 13.2 | 51.1 | 27.2 | 40.3 | 15.7 | CL | 16.7 | 31 | 0.0 |

F | 1.0 | 2.4 | 12.2 | 56.4 | 29.0 | 39.2 | 15.9 | CL | 18.6 | 33 | 0.0 |

G | 1.2 | 0.5 | 7.5 | 65.6 | 26.4 | 41.8 | 16.5 | CL | 18.2 | 26 | 29.0 |

WB | 1.4 | 0.2 | 75.0 | 24.8 | 0.0 | - | - | SM | 18.1 |

_{L}: liquid limit; P

_{I}: plasticity index; USCS: Unified Soil Classification System; γ: unit weight; φʹ: friction angle; cʹ: cohesion; CL: clay of low plasticity; SM: silty sand; and WB: weathered bedrock.

Soil Horizon | Representative Depth | α | µ | θ_{s} | θ_{r} | K_{s} |
---|---|---|---|---|---|---|

m | kPa^{−1} | - | m^{3}m^{−3} | m^{3}m^{−3} | ms^{−1} | |

C | 0.2 | 0.013 | 1.43 | 0.43 | 0.03 | 2.5 × 10^{−6} |

D | 0.4 | 0.013 | 1.43 | 0.43 | 0.03 | 2.5 × 10^{−6} |

E | 0.6 | 0.010 | 1.40 | 0.42 | 0.01 | 1.5 × 10^{−6} |

F | 1.0 | 0.009 | 1.38 | 0.39 | 0.02 | 1.0 × 10^{−6} |

G | 1.2 | 0.007 | 1.34 | 0.40 | 0.01 | 5.0 × 10^{−7} |

WB | 1.4 | 0.050 | 1.15 | 0.40 | 0.01 | 3.0 × 10^{−7} |

_{s}: saturated water content; θ

_{r}: residual water content; and K

_{s}: saturated hydraulic conductivity.

Soil Horizon | Depth m | Field-Measured S_{r} | Input Parameters for S_{r} Model | |||||
---|---|---|---|---|---|---|---|---|

θ_{s} | θ_{r} | S_{r(in)} | β* | ξ | ψ (Wet Season) | ψ (Dry Season) | ||

m^{3}m^{−3} | m^{3}m^{−3} | - | - | day^{−1} | °C^{−1} | °C^{−1} | ||

C | 0.2 | 0.43 | 0.03 | 0.75 | 0.20 | 0.08 | 0.015 | 0.04 |

D | 0.4 | 0.43 | 0.03 | 0.85 | 0.20 | 0.08 | 0.015 | 0.04 |

E | 0.6 | 0.42 | 0.01 | 0.92 | 0.35 | 0.08 | 0.009 | 0.04 |

F | 1.0 | 0.39 | 0.02 | 0.94 | 0.40 | 0.08 | 0.015 | 0.06 |

_{s}: saturated water content; θ

_{r}: residual water content β*, ξ, and ψ are coefficients.

Soil Horizon | Dry Season | |
---|---|---|

From | To | |

C, D, E | 30 June 2012 15 June 2013 15 May 2014 | 31 October 2012 1 October 2013 31 October 2014 |

F | 30 June 2012 15 June 2013 15 May 2014 | 30 January 2013 30 January 2014 5 December 2014 |

Soil Horizon | Depth m | δ | S_{r} | γ | φ′ | c′ |
---|---|---|---|---|---|---|

° | - | kN/m^{3} | ° | kPa | ||

C | 0.2 | 30.2 | Field measured— Modeled through the model of Valentino et al. [21] | 17.0 | 31.0 | 0.0 |

D | 0.4 | Field measured— Modeled through the model ofValentino et al. [21] | 16.7 | 31.0 | 0.0 | |

E | 0.6 | Field measured— Modeled through the model ofValentino et al. [21] | 16.7 | 31.0 | 0.0 | |

F | 1.0 | Field measured— Modeled through the model ofValentino et al. [21] | 18.6 | 33.0 | 0.0 |

**Table 6.**Rootmeansquare error (RMSE) indices of the modeled trends of the degree of saturation for the investigated soil depths.

Soil Horizon | Depth m | RMSE | ||
---|---|---|---|---|

All Records | Dry Season | Wet Season | ||

C | 0.2 | 0.07 | 0.10 | 0.05 |

D | 0.4 | 0.08 | 0.11 | 0.06 |

E | 0.6 | 0.11 | 0.16 | 0.06 |

F | 1.0 | 0.14 | 0.15 | 0.09 |

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**MDPI and ACS Style**

Bordoni, M.; Valentino, R.; Meisina, C.; Bittelli, M.; Chersich, S.
A Simplified Approach to Assess the Soil Saturation Degree and Stability of a Representative Slope Affected by Shallow Landslides in Oltrepò Pavese (Italy). *Geosciences* **2018**, *8*, 472.
https://doi.org/10.3390/geosciences8120472

**AMA Style**

Bordoni M, Valentino R, Meisina C, Bittelli M, Chersich S.
A Simplified Approach to Assess the Soil Saturation Degree and Stability of a Representative Slope Affected by Shallow Landslides in Oltrepò Pavese (Italy). *Geosciences*. 2018; 8(12):472.
https://doi.org/10.3390/geosciences8120472

**Chicago/Turabian Style**

Bordoni, Massimiliano, Roberto Valentino, Claudia Meisina, Marco Bittelli, and Silvia Chersich.
2018. "A Simplified Approach to Assess the Soil Saturation Degree and Stability of a Representative Slope Affected by Shallow Landslides in Oltrepò Pavese (Italy)" *Geosciences* 8, no. 12: 472.
https://doi.org/10.3390/geosciences8120472