geosciences

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

Massimiliano Bordoni 1,*, Roberto Valentino 2, Claudia Meisina 1, Marco Bittelli 3 and Silvia Chersich 1

1 Department of Earth and Environmental Sciences, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy; [email protected] (C.M.); [email protected] (S.C.) 2 Department of Chemistry, Life Sciences and Environmental Sustainability, University of Parma, Parco Area delleScienze157/A, 43100 Parma, Italy; [email protected] 3 Department of Agricultural Sciences, University of Bologna, 40 126 Bologna, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-0382-98-5840



Received: 9 November 2018; Accepted: 10 December 2018; Published: 12 December 2018


Abstract: The identification of the triggering mechanism of rainfall-induced, shallow landslides requires a complete understanding of the hydro-mechanical response of soil, which can be represented through the trends of the degree of soil saturation. In this paper, multiple annual cycles of soil saturation obtained through field monitoring were used to validate an empirical model based on climate data. Both field measurements and model outputs were used to conduct simplified slope stability analysis to evaluate the model chain capability in predicting the temporal occurrence of shallow failures. Field data were collected on a testsite slope located in Oltrepò Pavese (Northern Italy), where a shallow landslide occurred during the monitoring period. The experimental trends of the degree of saturation at various depths in the soil profile were compared with the calculated values and showed good agreement. Landslide triggering is reached when the soil is completely saturated. Both measured and modeled trends of soil saturation correctly identified the triggering time of the shallow landslide and the depth of the sliding surface, 1.0 m below the ground surface, in the test slope. The obtained results indicated the possibility of extending this approach for theassessment of the initiation time and the depth of shallow landslides, particularly for preliminary susceptibility evaluations, based on widely available climate data.

Keywords: shallow landslides; degree of saturation; slope stability analysis

1. Introduction Rainfall-induced shallow landslides are hazardous phenomena triggered by intense and concentrated rainfalls. These landslides develop in soil deposits that measure a few meters below the ground surface. When occurring close to cultivated or urbanized areas, they can cause significant economic damage to agricultural cultivation, buildings, and roads, in addition to human losses. In recent years, as a consequence of intense rainfalls, a huge number of shallow landslides have been recorded in many hilly and mountainous regions worldwide. Less-developed countries, in particular, have beenhitheavily by economic and human losses caused by shallow landslides [1]. To address the problem of shallow landslide risk management from a scientific perspective, it is fundamental to understand the hydro-mechanical response of soils to various rainfall events. Such knowledge can beused to identify the shallow landslide triggering mechanism and to recognize the

Geosciences 2018, 8, 472; doi:10.3390/geosciences8120472 www.mdpi.com/journal/geosciences Geosciences 2018, 8, 472 2 of 18 areas of potential slope instability. To conduct a reliable assessment of potentially unstable slopes overwide areas, it is necessary to consider the spatiallydistributed hydrological data. Pore water pressure is the hydrological variable most often used in simplified and physically based models for the identification of triggering conditions and slopes prone to shallow landslides [2,3]. Instead of pore water pressure, the soil volumetric water content or, alternatively, the degree of saturation above the groundwater level, can be used as an input hydrological variable for rainfall-induced shallow landslide analysis and the identification of potential instability [4–8]. It is worth remembering that the degree of saturation (Sr) of a soil is defined as follows:

Vw Sr = (1) Vv where Vw is the volume of water and Vv 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 [9–12]. The second advantage is the availability of measurements of soil moisture over large areas obtained through satellite sensors such as Advanced Scatterometer (ASCAT) [4,8,11,13–15]. Onthe site-specific scale, the continuous monitoring of the soil water content allows for identifying the potential instant of the occurrence of the shallow landslide, owing to the direct correlation between the antecedent rainfall and the triggering rainfall event conditions [3,16–19]. The implementation of the degree of saturation modeled at various depths through empirically or physically based approaches allows for the extension of distributed slope stability models to shallow landslides at the basin (regional) scale at tens (hundreds) of square kilometers. Some of these models use meteorological parameters such as rainfall amount, air temperature, and evapo-transpiration and disregard the geotechnical, physical, and hydrological features of the soil [10]. Because most of these models are based on waterbalance equations, they also require thephysical and hydrological properties of the soil, such as the soil water retention curve (SWRC) and the hydraulic conductivity function (HCF) parameters for solving the balance equations that simulate the three-dimensional distribution of the degree of the soil saturation [8,9,11,20]. Models of water balance need a high number of input parameters that are often not available, particularly with respect tolarge areas. To resolve this problem, [21] proposed a simplified empirical method for evaluating the degree of thesoil saturation at various depths on the basis of air temperature and rainfall amount as the driving variables. In this model, only four easily evaluated parameters strictly linked to the mean physical properties of the soil are considered [21]. The main objectives of the research described in this paper can be summarized in as follows: 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).

The first part of thispresent paper briefly describes the results of long-term field monitoring conducted on a test slope located in northeastern Oltrepò Pavese (Northern Italy), where several shallow landslides have occurred recently. Field measurements and observations were used as the benchmarks for the validation of the adopted models. In the second part of this paper, the degree of the soil saturation, measured at various depths of the test slope, was compared with the degree of saturation, estimated through an empirical model [21]. Both the monitored and estimated degree of the soil saturation at the various depths werethen used in Geosciences 2018, 8, 472 3 of 18

a slope stability model [5] to assess the slope safety factor (Fs). 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 The testsite slope is located in the northeastern part of Oltrepò Pavese (Northern Italy), a hilly region corresponding to the northern termination of the Apennines (Figure1). In this area, medium-lowpermeability arenaceous–conglomeratic bedrock, including the Monte Arzolo Sandstones and the Rocca Ticozzi Conglomerates, overlies impermeable silty–sandy, marly bedrock (Sant’AgataFossili Marls).The bedrock strata are sub-horizontal and dip east–northeast. The medium-low hydraulic conductivity of the arenaceous–conglomeratic bedrock is linked to its low primary porosity and to the limited number of fractures, which prevent the development of high secondary hydraulic conductivity. Deep-water circulation is thus confined in levels of less cementation or more fracturing at various depths in the bedrock. In the area surrounding the monitored slope, these levels correspond to horizons of poorly cemented gravels, sands, or conglomerates, with limited lateral extension and thickness between 0.2 and 1.0 m. These bodies are more widespread where the bedrock corresponds to the Rocca Ticozzi Conglomerates or the Monte Arzolo Sandstones and are rarer in the Sant’AgataFossili Marls. These bodies do not appear to constitute a continuous, more permeable level that can form a deep aquifer. The presence of water can be identified only in correspondence with the more permeable levels as isolated bodies. Above the bedrock levels, soils derived by bedrock weathering are present. These soils have dominant silty–clay or sandy–silt textures, and their thicknesses, determined through trench pits and micro boreholes, increase from a few centimeters up to 2.0 m from the top to the bottom of the slopes, owing to the presence of landslide accumulation areas. During the wet seasons, which include winter and spring, thin perched water tables of 0.1–0.2 m can form in the soils at the contact between the bedrock and the superficial deposits. These formations occur in shallower soil horizons during more intense rainfalls. This area has a continental climatic regime. In the last 10 years (2005–2014), the mean yearly temperature was 13 ◦C, and the mean yearly rainfall amount was 719.8 mm, based on measurements acquired at Canevino rain-gauge station by the Regional Agency for Environmental Protection (ARPA Lombardia). The morphological features of the studied slope can be considered typical of the surrounding area (Figure2). This slope is characterized by a medium-high topographic gradient with values around 30 ◦ in correspondence tothe monitoring station (Figure3). The slope elevation ranges from 210 to 170 m above sea level (a.s.l.), and the monitoring station is located at 185 m a.s.l. The vegetation types are mainly composed of grass and shrubs, in addition to a woodland of black locust (Robiniapseudoacacia) trees at the bottom of the slope. The roots of the living vegetation are present from the ground surface to depths of about 0.3–0.4 m. The testsite slope is representative of a wider area characterized by a high density of shallow landslides (Figures1 and2). The first and more significant event in terms of the number of triggered landslides occurred on 27–28April 2009. An extreme rainfall of 160 mm in 62 h was measured at the Cigognola rain gauge by the private Cooperative of Oltrepò Pavese Viticulturists—COPROVI (Figure1)[ 22]. This extreme rainfall triggered more than 1600 shallow landslides throughout the entire Oltrepò Pavese area [12,22]. The highest density, 51 landslides per km2, was registered in the area surrounding the testsite slope. Shallow landslides events also occurred during the following periods: March–April 2013 [23], when closely occurring rainfall events occurred with a high cumulative rainfall of 273.9 mm, Geosciences 2018, 8, 472x FOR PEER REVIEW 4 of 19 18 Geosciences 2018, 8, x FOR PEER REVIEW 4 of 19 measured by the rain gauge of the monitoring station installed in the testsite slope between 1 March 2013andasmeasured measured 30 by April by the the rain2013; rain gauge and gauge 28 of February ofthe the monitoring monitoring 2014–2 statMarch stationion installed201 installed4, owing in in the theto antestsite testsite intense slope slope rainfall between between event 1 1 ofMarch 68.9 mm2013and in 42 30 h, Aprilas registered 2013; and by 28 the February rain gauge 2014–2 of the March monitoring 2014,2014, owing station, to anfollowing intense 30 rainfall rainy event days of with 68.9 a cumulativemm in 42 h, asrainfall registered of 105.5 by the mm. rain Although gauge of theno monitoringphenomena station, were followingobserved 30in rainythe study days withslope a resultingcumulative from rainfallrainfall the 2013 of of 105.5 105.5rainfall mm. mm. Althoughevents, Although a shallow no phenomenano phenomenalandslide were was observedwere triggered observed in theduring studyin thethe slope 28study February resulting slope 2014–2fromresulting the March 2013from rainfall 2014the 2013event,15 events, rainfall am shallow fromevents, the landslide a monitoring shallow was landslide triggeredstation was(Figures during triggered 3 the and 28 during February4). This the location 2014–2 28 February Marchwasin very20142014–2 event,15close March proximity m 2014 from event,15 to the a monitoringsmall m scarp from station thatthe formedmonitoring (Figures during3 andstation 4the). This April(Figures location 2009 3 event.and wasin 4). veryThis close location proximity wasin tovery a small close scarpproximity that formedto a small during scarp the that April formed 2009 during event. the April 2009 event.

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

Figure 2. Detailed view of the testsite slope where thethe monitoring station was installed, showing evidenceFigure 2. ofDetailedof the the shallow shallow view landslides of landslidesthe testsite triggered triggereslope during whered during the th 27–28e monitoring the April 27–28April 2009 station event. 2009 was The installed,event. aerial photographThe showing aerial photographofevidence the area of was of the the captured shallowarea was by landslidescaptured Ditta Rossi by s.r.l.triggere Ditt (Brescia,a Rossid during s.r.l. Italy) (Brescia, the on 1827–28April May Italy) 2009. on 182009 May event. 2009. The aerial photograph of the area was captured by Ditta Rossi s.r.l. (Brescia, Italy) on 18 May 2009.

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

Figure 4. Field photograph of the shallow landslid landslidee triggered during the 28 February 2014–2 March Figure 4. Field photograph of the shallow landslide triggered during the 28 February 2014–2 March 2014 event. 2014 event. Onthe testsite slope, shallow landslides mainly affected the superficial superficial deposit above the Onthe testsite slope, shallow landslides mainly affected the superficial deposit above the bedrock and and the the slip slip surfaces surfaces located located at at depths depths ranging ranging from from 0.5 0.5 to to1m 1m from from the the ground ground surface, surface, in bedrock and the slip surfaces located at depths ranging from 0.5 to 1m from the ground surface, in correspondencein correspondence with with the the contact contact between between the the soil soil and and the the bedrock bedrock or or at at the the interfacesofthe interfacesofthe soil soil layers layers correspondence with the contact between the soil and the bedrock or at the interfacesofthe soil layers with differences in their hydrological and physical properties. Shallow landslide source areas were with differences in their hydrological and physical properties. Shallow landslide source areas◦ were◦ developed onon slopesslopes slightlyslightly steeper steeper than than that that at at the the monitoring monitoring station, station, ranging ranging between between 30 30°and and 35 . developed on slopes slightly steeper than that at the monitoring station, ranging between 30° and 35°.In particular, In particular, the source the source area ofarea the of shallow the shallo landslidew landslide occurring occurring on 2 Marchon 2 March 2014 had2014 the had same the slopesame 35°. In particular, the source area of the shallo◦ w landslide occurring on 2 March 2014 had the same slopeangle asangle that as of that the monitoringof the monitoring station (30station), and (30° the), and slip surfacethe slip was1.0surface m was1.0 belowthe m belowthe ground level ground [24]. slope angle as that of the monitoring station (30°), and the slip surface was1.0 m belowthe ground level [24]. level2.2. Soil[24]. Characterization at the TestSite Slope 2.2. SoilFrom Characterization apedological at point the TestSite of view, Slope the soil profile in the test site is composed of seven main soil 2.2. Soil Characterization at the TestSite Slope horizonsFrom (Table apedological1). The pedological point of view, features the soil of theprofile soils in were the describedtest site is accordingcomposed to of [ seven25]. An main organic soil From apedological point of view, the soil profile in the test site is composed of seven main soil horizonslayer (OL) (Table of 0–0.01 1). The m, dominatedpedological by features organic of soil the materials, soils were labeled described as A, according is the shallowest to [25]. level.An organic Below horizons (Table 1). The pedological features of the soils were described according to [25]. An organic layerthis horizon, (OL) of two0–0.01 weak m, aggregateddominated levelsby organic are present soil materials, until0.2 mlabeled below as theground A, is the shallowest level. A mineral level. layer (OL) of 0–0.01 m, dominated by organic soil materials, labeled as A, is the shallowest level. BelowA1 horizon this horizon, (labeled two as B) weak from aggregated 0.01 to 0.1 mlevels exhibits are thepresent obliteration until0.2 ofm allbelow or much theground of any level. original A Below this horizon, two weak aggregated levels are present until0.2 m below theground level. A mineralrock structure A1 horizon and shows (labeled an accumulationas B) from 0.01 of humifiedto 0.1 m exhibits organic the matter obliteration closely mixed of all withor much the mineral of any mineral A1 horizon (labeled as B) from 0.01 to 0.1 m exhibits the obliteration of all or much of any originalfraction. rock An Ak2structure horizon and from shows 0.1to an 0.2 accumulation m, labeled as of C, humified can be distinguished organic matter from closely the Bmixed layer with for a original rock structure and shows an accumulation of humified organic matter closely mixed with thehigh mineral diffusion fraction. of carbonate An Ak2coatings. horizon from The soil0.1to horizon 0.2 m, labeled below theas C, C can layer be isdistinguished characterized from by athe low, B the mineral fraction. An Ak2 horizon from 0.1to 0.2 m, labeled as C, can be distinguished from the B layerstrong for aggregation. a high diffusion An Apgk3 of carbonate horizon, coatings. from 0.2 Th toe 0.4soil m,horizon labeled below as D, the presents C layer similar is characterized structural layer for a high diffusion of carbonate coatings. The soil horizon below the C layer is characterized by a low, strong aggregation. An Apgk3 horizon, from 0.2 to 0.4 m, labeled as D, presents similar by a low, strong aggregation. An Apgk3 horizon, from 0.2 to 0.4 m, labeled as D, presents similar

Geosciences 2018, 8, 472 6 of 18 and pedological features with respect to the overlying layers, but it has a stronger aggregation, an accumulation of visible pedogenic calcium carbonate, and periods of stagnant water, whichhas preserved iron in a reduced state. Moreover, 0.4 m below theground level, the soil horizons are characterized by a lower amount oforganic matter, which shows better the mineral components of the grains of the horizons with respect to the ones close to the surface. A Bgk horizon (labeled as E), located from 0.4to 0.7 m, is a mineral horizon with strong gleying features, which is accompanied by evidence of pedogenic change, while a BCgk horizon (labeled as F) from 0.7to 1.1 m is a transitional horizon that records a subtle lithologic discontinuity, and it is dominated by the properties of the B master horizon. Between 1.1and 1.3 m, a Cgk horizon, labeled as G, is a mineral horizon or a series of layers that arenotaffected greatly by pedogenic processes, and its material is similar tothat from which the solum formed, in that it is characterized by calcic features with an accumulation of carbonates and a significant increase in the carbonate content, reaching35.3%. Weathered bedrock (WB) was identified at a depth of 1.3 m. According to [25], the soil should beclassified as Calcic Gleysol, owing to the presence of a deep calcic horizon (G horizon), where the carbonate content increases to 35.3%. Level G can then be considered to bethe least permeable level of the entire soil profile, as previously shown in similar pedological profiles having a calcic horizon that is at least 0.2-m thick [26]. Regarding the geotechnical and physical properties of the soil, horizons A, B, and C are assumed to havethe same characteristics (Table1).

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

Representative Soil Gravel Sand Silt Clay w P USCSClass γ φ’ c’ Depth L I Horizon m % % % % % % kN/m3 ◦ kPa A 0.01 B 0.1 12.3 12.5 53.9 21.3 39.8 17.2 CL 17.0 31 0.0 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 0 Note: wL: liquid limit; PI: plasticity index; USCS: Unified Soil Classification System; γ: unit weight; φ : friction angle; c0: cohesion; CL: clay of low plasticity; SM: silty sand; and WB: weathered bedrock.

The soil horizons have a high silt content of 51.1–65.6%, which tends to increase slightly with depth, andthe clay content is higher than 21.3% (Table1). The contents of sand and gravel remain low in the soil levels, at 0.5% and 7.5% in the G horizon, respectively. In contrast, the weathered bedrock immediately below the topsoil, with a sand content of 75%, is considered to be a sand lens (Table1). According to the Unified Soil Classification System (USCS), the soil horizons are prevalently non-plastic or slightly plastic soils (CL), with a liquid limit (wL) of 38.5–41.8% and a plasticity index (PI) of 14.3–17.2%. The unit weight (γ) shows a significant increase in the F horizon from 16.7 kN/m3 to 18.6 kN/m3 and then remains rather steady with respect to the depth (Table1). For the E, F, and G horizons, the peak shear strength parameters were determined through triaxial tests (Table1). The E and F horizons have a friction angle (φ0) between 31◦ and 33◦ and nil cohesion (c0). The G horizon is characterized by a friction angle equal to 26◦ and an effective cohesion of 29 kPa. The hydrological properties of the various horizons were determined through laboratory reconstruction of SWRCs and HCFs (Figure5). These functions were reconstructed by using a combination of the Wind–Schindler method (WSM; [28]), including the Hyprop instrument (UMS GmbH; Munich, Germany), and the vapor pressure method (VPM; [29]), including the WP4T device (Decagon Devices; Pullman, DC, USA) on the undisturbed soil samples. The experimental data were fitted through the models of [27,30]. The parameters of these models, including the saturated water content θs, the residual water content θr, the fitting parameters α and µ, and the saturated Geosciences 2018, 8, x FOR PEER REVIEW 7 of 19

(Table1). According to the Unified Soil Classification System (USCS), the soil horizons are Geosciencesprevalently2018 ,non-plastic8, 472 or slightly plastic soils (CL), with a liquid limit (wL) of 38.5–41.8% and7 of 18 a plasticity index (PI) of 14.3–17.2%. The unit weight (γ) shows a significant increase in the F horizon from 16.7 kN/m3 to 18.6 kN/m3 hydraulicand then remains conductivity rather K ssteadywere thenwith estimatedrespect to bythe using depth the (Table Marquardt 1). For algorithmthe E, F, and [31 ].G Althoughhorizons, thethe drying–wettingpeak shear strength hysteresis parameters phenomenon were ofdetermined these soils through has been triaxial deeply investigatedtests (Table elsewhere1). The E [24and,32 ],F forhorizons the purposes have a of friction the present angle work, (φʹ) itbetween has been 31° neglected and 33° and and the nil mean cohesion values (c ofʹ). the The Van G Genuchtenhorizon is andcharacterized Mualem parametersby a friction have angle been equal assumed. to 26° and All an ofeffective the soil cohesion levels had of 29 similar kPa. mean values of α −1 3 −3 µ (0.007–0.013The hydrological kPa ) and propertiesθr (0.01–0.03 of m them various; Table 2ho). Therizons andwereθ s determinedparameters werethrough slightly laboratory higher −6 −6 −1 untilreconstruction the depth ofof 0.6 SWRCs m. Moreover, and HCFsKs was (Figure quite 5). steady These around functions 1 ×·10 wereand reconstructed 2.5 ×·10 ms by ,using except a forcombination that at the of soil the level Wind–Schindler at 1.2 m below method the ground (WSM; (G [28]), level), including which wasthe theHyprop lowest instrument permeable (UMS soil −7 −1 horizonGmbH; (5Munich,·× 10 Germany),ms ; Table and2). the The vapor weathered pressure bedrock method (WB)level (VPM; [29]), at 1.4 including m below the the WP4T ground device had −7 −1 lower(Decagon values Devices; of both Pullman,Ks (3·× 10Washington)ms ; Table on 2the) and undisturbedµ (1.15; Table soil2 samples.) with respect The experimental to the soil layers data −1 above,were fitted although through it wascharacterized the models of[27] by similar and values[30]. The of θ parameterss and θr and aof higher these valuemodels, of α including(0.050 kPa the) than those in the soil horizons (Table2). saturated water content θs, the residual water content θr, the fitting parameters α and µ, and the saturated hydraulic conductivity Ks were then estimated by using the Marquardt algorithm [31]. Table 2. Main hydrological properties of the soil at various levels. Although the drying–wetting hysteresis phenomenon of these soils has been deeply investigated elsewhere [24,32], forRepresentative the purposes Depthof the presentα work, it µ has been θ sneglectedθ andr the meanKs values of Soil Horizon the Van Genuchten and Mualemm parameterskPa have−1 been- assumed.m3m −All3 ofm the3m −soil3 levelsms hadsimilar−1 −1 3 −3 − mean valuesC of α (0.007–0.013 0.2 kPa ) and θ 0.013r (0.01–0.03 1.43 m m ; Table 0.43 2). The 0.03 µ and2.5 θs ×parameters10 6 −6 wereslightlyD higher until the depth 0.4 of 0.6 m. Moreover, 0.013 1.43 Kswasquite 0.43 steady around 0.03 1 ×·102.5 ×−6 and10 −6 2.5 ×·10−6 msE−1, except for that 0.6 at the soil level 0.010 at 1.2 m 1.40 belowthe 0.42 ground 0.01(G level),1.5 which× 10 wasthe F 1.0 0.009 1.38 0.39 0.02 1.0 × 10−6 lowest permeable soil horizon (5·× 10−7 ms−1; Table 2). The weathered bedrock (WB)level at 1.4 m G 1.2 0.007 1.34 0.40 0.01 5.0 × 10−7 −7 −1 belowtheWB ground had lower values 1.4 of both Ks 0.050 (3·× 10 ms 1.15; Table 0.402) and µ (1.15; 0.01 Table3.0 2) with× 10− respect7 to the soil layers above, although it wascharacterized by similar values of θs and θr and a higher Note: α-µ: fitting parameters of Van Genuchten’s [27] model; θs: saturated water content; θr: residual water content; −1 valueand of K αs: (0.050 saturated kPa hydraulic) than conductivity. those in the soil horizons (Table 2).

FigureFigure 5.5.Soil water retention curves(SWRCs) of thethe soilsoil horizonshorizons atat thethe testsite.testsite. 2.3. Monitoring Equipment 2.3. Monitoring Equipment The integrated field monitoring station, installed atthe testsite slope on 27 March 2012, consists The integrated field monitoring station, installed atthe testsite slope on 27 March 2012, consists of a rain gauge (Model 52203, Young Comp., Traverse City, MI, USA), a thermo-hygrometer (Model of a rain gauge (Model 52203, Young Comp., Traverse City, MI, USA), a thermo-hygrometer (Model HMP155A, Campbell Sci. Inc., Logan, UT), a barometer (Model CS100, Campbell Sci. Inc., Logan HMP155A, Campbell Sci. Inc., Logan, UT), a barometer (Model CS100, Campbell Sci. Inc., Logan UT, UT, USA), an anemometer (Model WINDSONIC, Campbell Sci. Inc., Logan, UT, USA), and a net USA), an anemometer (Model WINDSONIC, Campbell Sci. Inc., Logan, UT, USA), and a net radiometer (Model NR-LITE 2, Kipp&Zonen, Delft, the Netherlands; Figure6). The meteorological radiometer (Model NR-LITE 2, Kipp&Zonen, Delft, the Netherlands; Figure 6). The meteorological sensors were linked to six time domain reflectometer (TDR) probes (Model CS610, Campbell Sci. Inc., sensors were linked to six time domain reflectometer (TDR) probes (Model CS610, Campbell Sci. Logan, UT, USA), installed at 0.2, 0.4, 0.6, 1.0, 1.2, and 1.4 m belowthe ground surface, to measure the Inc., Logan, UT, USA), installed at 0.2, 0.4, 0.6, 1.0, 1.2, and 1.4 m belowthe ground surface, to water content of the soil at various soil levels and that in the weathered bedrock (Figure6). Moreover, measure the water content of the soil at various soil levels and that in the weathered bedrock (Figure a combination of three tensiometers (Model Jet-Fill 2725, Soilmosture Equipment Corp., Santa Barbara, 6). Moreover, a combination of three tensiometers (Model Jet-Fill 2725, Soilmosture Equipment CA, USA) and three heat dissipation (HD) sensors (Model HD229, Campbell Sci., Logan, UT, USA) Corp., Santa Barbara, CA, USA) and three heat dissipation (HD) sensors (Model HD229, Campbell were installed at 0.2, 0.6, and 1.2 m belowthe ground level in various soil horizons to measure the pore water pressure [24].

Geosciences 2018, 8, x FOR PEER REVIEW 8 of 19

GeosciencesSci., Logan,2018 ,UT,8, 472 USA) were installed at 0.2, 0.6, and 1.2 m belowthe ground level in various8 ofsoil 18 horizons to measure the pore water pressure [24]. The field data were collected by a CR1000X datalogger (Campbell Sci. Inc., Logan, UT, USA) poweredThe fieldby a data photovoltaic were collected panel. by A a detailed CR1000X anal dataloggerysis of the (Campbell quality Sci.of the Inc., field Logan, data UT,has USA)been poweredreported byby a[24]. photovoltaic panel. A detailed analysis of the quality of the field data has been reported by [24]. 2.4. Modeling the Degree of the Soil Saturation 2.4. Modeling the Degree of the Soil Saturation To perform the slope stability analysis, the degree of thesoil saturation (Sr) at various depths in To perform the slope stability analysis, the degree of thesoil saturation (S ) at various depths the soil profile is required (Equation(2)). Table 3 summarizes the input parametersr used for the in the soil profile is required (Equation (2)). Table3 summarizes the input parameters used for the determination of Srfrom the field measurements of the water content (θ). Daily average values of determination of Sr from the field measurements of the water content (θ). Daily average values of Sr Srwere calculated through Equation(2)down to 1m (i.e., the depth of the sliding surface of the were calculated through Equation (2) down to 1m (i.e., the depth of the sliding surface of the shallow shallow landslide observed on 28 February 2014–2 March2014). The main objective was modeling landslide observed on 28 February 2014–2 March2014). The main objective was modeling the dynamics the dynamics of the degree of the soil saturation within the depth at which shallow landslides of the degree of the soil saturation within the depth at which shallow landslides usually develop in the usually develop in the sample slope. Thus, Sr trends were obtained 0.2, 0.4, 0.6, and 1.0 m belowthe sample slope. Thus, S trends were obtained 0.2, 0.4, 0.6, and 1.0 m belowthe ground surface, based on ground surface, basedr on TDR measurements obtained at the same depths by using the following TDR measurements obtained at the same depths by using the following equation: equation:

θ −θ = = r . Sr = Se = .(2) (2) θs − θr In Equation(2), the degree of saturation is assumed to be equal to the effective saturation, In Equation (2), the degree of saturation is assumed to be equal to the effective saturation, becausethe residual water content is negligible (Table 2). Although the sensitivity analyses of the becausethe residual water content is negligible (Table2). Although the sensitivity analyses of the possible deviations of both the θs and θr values and of the subsequent effects on the chain of models possible deviations of both the θs and θr values and of the subsequent effects on the chain of models is is desirable, such tasks are beyond the scope of this paper. desirable, such tasks are beyond the scope of this paper. Moreover, Equation(2)implies the assumption that the soil does not significantly change Moreover, Equation (2) implies the assumption that the soil does not significantly change volume volume as the degree of the soil saturation decreases (and soil suction increases). This assumption as the degree of the soil saturation decreases (and soil suction increases). This assumption has been has been considered reasonable for the sample slope soils, which have low compressibility and are considered reasonable for the sample slope soils, which have low compressibility and are free of free of expansive clays. expansive clays.

Figure 6. Schematic representation of the monitoring station and soil profile. Figure 6. Schematic representation of the monitoring station and soil profile.

The measured values of Sr were compared with the values calculated for the same depths by The measured values of Srwere 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 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. presented elsewhere [21]; only the main statements required for completeness are provided here. This simplified model considers that shallow soil undergoes drying and wetting phases that are This simplified model considers that shallow soil undergoes drying and wetting phases that are determined by complex climate processes; thus, it allows for the computation of the degree of the soil determined by complex climate processes; thus, it allows for the computation of the degree of the saturation by using readily available climate data, such as air temperature and daily rainfall. Although soil saturation by using readily available climate data, such as air temperature and daily rainfall. these two contributions are not independent of each other, they are considered separately in the model. Although these two contributions are not independent of each other, they are considered separately In particular, the dependence of Sr from the temperature is expressed through an exponential law, in the model. In particular, the dependence of Sr from the temperature is expressed through an in which the exponent is represented by the time-varying air temperature Tm. Such a law allows for the

Geosciences 2018, 8, 472 9 of 18 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. Regarding the dependence of Sr 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 [33–35]. In the simplified approach proposed herein, it is considered that the total rainfall amount does not completely infiltrate the soil due to the runoff. For this reason, the portion of the infiltrated rainfall hi* has been defined as follows: ( ∗ h h < (1 − Sr)nH hi = (3) (1 − Sr)nH h ≥ (1 − Sr)nH where h is the daily rainfall depth, n is the soil porosity, and H is the soil layer thickness. Moreover, the model assumes that only a portion of the infiltrated rainfall contributes toraising the degree of thesoil saturation, which is expressed through a constant calibration coefficient β* that includes both runoff and leakage. The reduction of the influence of the rainfall on the soil moisture after a certain lapse of time is expressed by a decreasing exponential relation. At each time step, the degree of the soil saturation is computed through the following equation: ∗ β v S = S e−ψTm + h∗e−ξ(t−ti). (4) r r(in) nH ∑i=1 i

Sr 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 Tm ◦ (in C); the second one, which considers infiltration, is a function of the daily rainfall depth hi, changing in time as well. For computation, Tm 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 Sr(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. It is expected that ψ should be correlated with the type of soil and its thermal conductivity properties, because the soil moisture response to temperature fluctuation is more rapid for sand than for clay. Moreover, it is expected that ψ is a function of the climate and should express a decrease in the effect given by the air temperature with an increase in the soil depth. Furthermore, it is expected that parameter ξ should be different for each type of soil in relation to the soil permeability, because greater hydraulic conductivity relates to a more rapid decrease of the accumulated water. As reported in Table3, a constant value of parameter ξ is selected for the various layers, because they are characterized by the same type of soil. Indeed, the modeled daily value of Sr 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 Sr of the C soil horizon, H was assumed to be equal to 0.2 m; to compute Sr 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. Geosciences 2018, 8, 472 10 of 18

Table3 summarizes the values of the parameters assumed for the model’s application. Parameters ψ, ξ, β*, and Sr(in) were calibrated through an adjustment procedure to get the best fit according to the measured values of Sr over the analyzed time span.

Table 3. Input data for the calculation of the degree of the soil saturation (Sr).

Field-Measured Sr Input Parameters for Sr Model Soil ψ ψ Depth m θ θ S β* ξ Horizon s r r(in) (Wet Season) (Dry Season) m3m−3 m3m−3 -- day−1 ◦C−1 ◦C−1 C 0.2 0.43 0.03 0.75 0.20 0.08 0.015 0.04 GeosciencesD 2018, 8, x FOR 0.4 PEER REVIEW 0.43 0.03 0.85 0.20 0.08 0.015 0.0410 of 19 GeosciencesE 2018, 8, x FOR 0.6 PEER REVIEW 0.42 0.01 0.92 0.35 0.08 0.009 0.0410 of 19 GeosciencesTableF 2018 3, 8summarizes, x FOR 1.0 PEER REVIEW the 0.39 values 0.02 of the0.94 parameters 0.40 assumed 0.08 for the 0.015 model’s application. 0.0610 of 19 Geosciences 2018, 8, x Note:FOR PEERθ : saturated REVIEW water content; θ : residual water content β*, ξ, and ψ are coefficients. 10 of 19 ParametersTable 3ψ ,summarizes ξ, β*, ands S r(in)thewere values calibrated of ther throughparameters an adjustmentassumed forprocedure the model’s to get application.the best fit GeosciencesTable 2018 3, 8summarizes, x FOR PEER REVIEW the values of the parameters assumed for the model’s application.10 of 19 Parametersaccording to ψ the, ξ ,measured β*, and S valuesr(in)were of calibrated Sr over the through analyzed an time adjustment span. procedure to get the best fit GeosciencesTableThe 2018 field3, 8summarizes, xmeasurements FOR PEER REVIEW the clearlyvalues showedof the thatparameters compared assumed with the for deeper the model’s soil horizons, application. different10 of 19 accordingParameters to ψ the, ξ ,measured β*, and S valuesr(in)were of calibrated Sr over the through analyzed an time adjustment span. procedure to get the best fit Table 3 summarizes the values of the parameters assumed for the model’s application. accordingParametershydrological to ψ the, ξ and ,measured β*, thermal and S valuesr(in) behaviorswere of calibrated Sr characterizedover the through analyzed the an soiltime adjustment horizons span. atprocedure shallow depths,to get the where best grass fit Table 3 summarizesTable 3. Input the data values for the calculationof the parameters of the degree assumed of the soil for saturation the model’s (Sr). application. Parametersand plant rootsψ, ξ, areβ*, and usually Sr(in) presentwere calibrated [r3,20,24]. through These differences an adjustment wereparticularly procedure to evident get the during best fit the according to theTable measured 3. Input values data for of theS overcalculation the analyzed of the degree time ofspan. the soil saturation (Sr). Parameters ψ, ξ, β*, and Sr(in)were calibratedr through an adjustment procedure to get the best fit accordingdry periods, to the withTable measured a 3. low InputField-measured number values data for of of StheSrrainfall over calculation the events, analyzed of the and degree Inputtime the wet ofParametersspan. the periods, soil saturationforS withrModel events (Sr). that weremore according to the measured values of Sr over the analyzed time span. frequentSoil in time.DepthTable To 3. consider Field-measuredInput data the for different Sther calculation soil behaviors, of the degree Input we assumedParametersof the soil different saturationforψ SrModel values (Sr). ofψ parameter ψ Field-measuredθs θr Sr Sr(in) β* Inputξ Parameters forSrModel forHorizonSoil the dry periodsDepthTablem 3. and Input wet data periods, for the indicatedcalculationin of Tablethe degree3 as theof the “wet (Wetsoil season”saturation Season)ψ and (Sr). the (Dry “dry Season)ψ season”, θs θr Sr(in) β* ξ Soil DepthTable 3. InputField-measured data for Sther calculation of the degree Input ofParameters the soil saturationforψ SrModel (Sr). ψ respectively,Horizon inm agreementm3m−3with m the3m− results3 - reported - by [36day] for−1 similar(Wet sites °CSeason)−1 in the Mediterranean(Dry °CSeason)−1 area. Field-measuredθs θr Sr Sr(in) β* Inputξ Parameters forSrModel HorizonSoil Depthm 3 −3 3 −3 −1 (Wet Season)ψ− 1 (Dry Season)ψ− 1 mθms mθmr Sr(in)- β -* dayξ °C °C TableSoilC4 showsDepth the0.2 timeField-measured intervals0.43 that0.03S haver been0.75 arbitrarily0.20 Input assumed0.08 Parameters to bedry 0.015 forψ S rModel seasons. It is0.04 worthψ noting Horizon m m3m−3 m3m−3 - - day−1 (Wet°C Season)−1 (Dry°C Season)−1 thatC for the C,0.2 D, and E0.43θ layerss a0.03 dryθr periodS0.75r(in) correlating 0.20β* strongly0.08ξ to the 0.015 “real summer time 0.04 span” was HorizonSoilD Depth0.4m 0.433 − 3 0.033 − 3 0.85 0.20 0.08−1 (Wet 0.015 Season)ψ− 1 (Dry 0.04Season)ψ− 1 mθms mθmr Sr(in)- β -* dayξ °C °C DC 0.40.2 0.43 0.03 0.850.75 0.20 0.08 0.015 0.04 assumed.HorizonE On0.6 them contrary,m0.423m− 3for them0.013 Fm− layer, 3 even0.92- if the0.35 - starting day0.08− day1 of(Wet the 0.009°C drySeason)−1 season wasthe(Dry°C 0.04Season) same,−1 it was DC 0.40.2 0.43 0.03 0.850.75 0.20 0.08 0.015 0.04 necessaryEF to extend0.61.0 them0.420.393m assumed− 3 m0.010.023 valuem− 3 of0.920.94 the- ψ parameter0.350.40 - day0.08 to−1 a wider lapse 0.0090.015°C−1 of timedue to 0.04°C0.06 the−1 delay of CD 0.20.4 0.43 0.03 0.750.85 0.20 0.08 0.015 0.04 the responseEF of1.00.6 deep soil0.390.42 levels to0.020.01 either the0.940.92 drying0.400.35 or wetting0.08 periods. 0.0150.009 0.060.04 DC Note:0.40.2 θs : saturated0.43 water content;0.03 θ0.850.75r: residual 0.20 water content0.08 β*, ξ, and 0.015 ψ are coefficients. 0.04 FE 1.00.6 0.390.42 0.020.01 0.940.92 0.400.35 0.08 0.0150.009 0.060.04 D Note:0.4 θs : saturated0.43 water content;0.03 θr0.85: residual 0.20 water content0.08 β*, ξ, and 0.015 ψ are coefficients. 0.04 EF 0.61.0 0.420.39 0.010.02 0.920.94 0.350.40 0.08 0.0090.015 0.040.06 Note: θs: TablesaturatedTable 4. 4.Time waterTime spans spanscontent; ofof dryseasons θ dryseasonsr: residual for water for the the various content various investigated β investigated*, ξ, and ψ arelayers. layers. coefficients. EF 1.00.6 0.390.42 0.020.01 0.940.92 0.400.35 0.08 0.0150.009 0.060.04 Note: θs: Tablesaturated 4. Time water spans content; of dryseasons θr: residual for water the various content investigated β*, ξ, and ψ layers.are coefficients. F 1.0 0.39 0.02 0.94 0.40 Dry0.08 Season 0.015 0.06 Note: θs: Tablesaturated 4. Time water spans content; of dryseasons θr: residual for water theDry various content Season investigated β *, ξ, and ψ arelayers. coefficients. SoilSoil horizon Horizon Note: θs: Tablesaturated 4. Time water spans content; of dryseasons θr: residualFromFrom for water theDry various content Season investigated β*, ξ,To and To ψ arelayers. coefficients. Soil horizon Table 4. Time spans of dryseasonsFrom for theDry various Season investigated To layers. Soil horizon 3030 June June 2012 2012 31 October31 October 2012 2012 Table 4. Time spans of dryseasonsFrom for theDry various Season investigated To layers. SoilC, horizon D, D, E E 301515 June June 20122013 2013 311 October October1 October 2013 2012 2013 From Dry Season To SoilC, horizon D, E 153015 June May 20132012 2014 131 October October31 October 2013 2012 2014 15 May 2014From Dry Season31 October To 2014 SoilC, horizon D, E 153030 MayJune June 201320142012 2012 311 October October30 January 2013 20142012 2013 30 June 2012From 30 JanuaryTo 2013 C, D,F E 301515 JuneMay June 201220142013 2013 311 October October30 January 2013 20122014 2014 30 June 2012 3031 JanuaryOctober 20132012 C, D,F E 1515 JuneMay May 20132014 2014 13130 October OctoberJanuary5 December 2013 2014 2014 30 June 2012 30 January 2013 C, D,F E 15 MayJune 20132014 313015 OctoberDecember OctoberJanuary 2013 2014 2014 30 June 2012 30 January 2013 F 15 MayJune 20132014 53130 December OctoberJanuary 2014 2014 TheThe field selected measurements values of theFclearly model showed parameters3015 JuneMay that 201220142013 comp wereinared good with305 December January agreement the deeper 20132014 2014 with soil those horizons, used different by [21] for 30 June 2012 30 January 2013 hydrologicalsimilarThe field types and measurements of soilthermal at other behaviors Fclearly sample showedcharacterized sites.15 TheJuneMay that 2013 input2014 comp the daily soilared valuehorizons with305 December January ofthe the at deeper 2014 shallowair2014 temperature soil depths, horizons, waswhere different calculated grass The field measurements Fclearly showed15 June that 2013 comp ared with30 January the deeper 2014 soil horizons, different hydrologicalandas aplant mean roots of and the are thermal daily usually temperatures behaviors present [3,20,24]. characterized over15 the May previousThes 2014 ethe differences 30soil days horizons5 toDecember wereparticularly consider at shallow2014 the delay depths, evident of the where soilduring response grass the hydrologicalThe field and measurements thermal behaviors clearly characterizedshowed15 May that 2014 comp the soilared horizons with5 December the at deeper shallow2014 soil depths, horizons, where different grass anddryto periods, theplant temperature roots with are a usuallylow fluctuations. number present of rainfall[3,20,24]. events Thes,e anddifferences the wet wereparticularlyperiods, with events evident that duringweremore the andhydrological plantThe field roots and measurements are thermal usually behaviors present clearly [3,20,24]. showedcharacterized thatThes compe the differences soilared horizons with wereparticularly the at deeper shallow soil depths, evidenthorizons, where during different grass the dryfrequent periods,The infield time. with measurements To a lowconsider number clearlythe ofdifferent rainfall showed soil events that behaviors, comp, and aredthe we wet with assumed periods, the deeper differe with soil ntevents values horizons, that of parameterweremore different hydrologicaldryand2.5. periods,plant Modeling roots withand the are thermala Slope usuallylow Stabilitynumber behaviors present of rainfall[3,20,24]. characterized events Thes, e theand differences soil the horizonswet wereparticularlyperiods, at shallow with events depths, evident that where duringweremore grass the frequenthydrologicalψ for the indry time. periodsand Tothermal consider and wet behaviors theperiods, different characterized indicated soil be inhaviors, Tablethe soil 3 we ashorizons theassumed “wet at season” differeshallownt and depths,values the “dryof where parameter season”, grass andfrequentdry periods,plant in roots time. with are To a usually lowconsider number present the ofdifferent rainfall[3,20,24]. soil events Thes behaviors,,e anddifferences the we wet assumed wereparticularlyperiods, differe withnt events values evident that of duringparameterweremore the ψandrespectively, for plant theGiven dry roots periods thein areagreement characteristics usually and wet withpresent periods, ofthe the [3,20,24]. results indicated sample reported Thes slope in eTable differences (Figure by 3[36] as3 )thefor and wereparticularly “wetsimilar the season” relatively sites andin lowevidentthe the Mediterranean thickness “dry during season”, of the the dryψfrequent for periods, the dryin time. withperiods To a lowconsider and number wet theperiods, ofdifferent rainfall indicated soil events be inhaviors,, Tableand the 3 we as wet theassumed periods, “wet season” differe with nt eventsand values the that “dry of parameterweremore season”, respectively,dryarea.landslide periods, Table with4 with inshows agreement respect a low the tonumber time its with extent, intervals theof rainfall theresults hypothesisthat events reportedhave , be ofand en theby the arbitrarily[36] infinite wet for periods, slopesimilar assumed was withsites appropriate to eventsin bedry the Mediterraneanthat seasons. for weremore the stability It is frequentrespectively,ψ for the indry time. periodsin agreement To consider and wet with theperiods, thedifferent results indicated soil reported be inhaviors, Table by 3 [36]we as theassumedfor “wetsimilar season”differe sitesnt inand values the the Mediterranean “dryof parameter season”, area.frequentworthanalysis. Table noting in Bothtime.4 showsthat field-measured To for considerthe the time C, D,the intervals andand different modeledE layers that soil Shavea r bedrtrendshaviors,y be perioden were arbitrarily we correlating used assumed as assumed the stronglydiffere input datatont tovaluesbedry inthe the “real seasons.of slope parameter summer stability It is ψarea.respectively, for theTable dry 4 periods inshows agreement andthe timewet with periods, intervals the results indicated that reportedhave in Tablebe enby arbitrarily 3[36] as thefor “wetsimilar assumed season” sites to andin bedry the the Mediterranean “dryseasons. season”, It is worthψtime modelfor span”the noting proposeddry was periods that assumed. for by and the [5]. wet C,On A D, detailedperiods,the and contrary, E indicated derivationlayers for a thedr iny of FTable period thelayer, model3 ascorrelatingeven the was if“wet the presented season”startingstrongly andday byto the [theof5], the “real and“dry drya season”,summer previousseason respectively,wortharea. Table noting 4 inthatshows agreement for the the timeC, with D, intervals and the Eresults layers that reported havea dry beperiod enby arbitrarily[36] correlating for similar assumed strongly sites to in tobedry the the Mediterranean “real seasons. summer It is timerespectively,wastheapplication span” same, was in toit theagreementassumed.was test necessary site On with based the to the contrary, onlyextend results on the field for reported assumed the measurements F la byyer, value [36] even offor was ifthe similar the reported ψ parameterstarting sites by dayin [24 tothe ].of a Mediterraneanthewider dry lapse season of area.timeworth span”Table noting was4 showsthat assumed. for the the time C,On D, theintervals and contrary, E layers that for havea thedry Fbe period laenyer, arbitrarily evencorrelating if the assumed startingstrongly to day tobedry theof the “realseasons. dry summer season It is wasthearea.timedue TableAccording same, to the4 showsit delay was to this necessaryofthe the model,time response intervals to which extend of is deepthat based the soilhaveassumed on levels thebeen limit valueto arbitrarily either equilibrium of the assumeddryingψparameter method, or to wetting bedrytheto a slope wider periods.seasons. safety lapse It factor ofis worthwasthetime span” noting same, was thatit assumed.was for necessary the C,On D, the toand contrary,extend E layers the for aassumed thedry F period layer, value correlatingeven of ifthe the ψ parameterstartingstrongly day to to the ofa widerthe“real dry summerlapse season of timedueworthFs isThe calculatednoting toselected the that delay asvalues for follows: of the the of C, theresponse D, model and Eof parameters layers deep soila dr levelswerey periodin to good either correlating agreement the drying strongly with or wetting those to the used “realperiods. by summer [21] for timetimeduewasthe span” same, to thewas it delay assumed.was ofnecessary the On response the to contrary,extend of deep the for soil assumed the levels F layer, tovalue either even of theifthe the dryingψ parameterstarting or wettingday to of a thewider periods. dry lapse season of timesimilar Thespan” types selected was of soilassumed. values at other of On the sample the model contrary, sites. parameters The for in theput were F daily lainyer, goodvalue even agreement of if thethe air starting temperature with daythose of used thewas dry bycalculated [21]season for wasthetimedueThe same, toselected the it delay was values necessaryof the of theresponse model to extend of parameters deep the soilassumed levelswerein valueto good either of agreement the dryingψparameter with or wetting those to a used wider periods. by lapse [21] for of similarwastheas a mean typessame, of of itthe soilwas daily at necessary other temperatures sample to extend sites. over Thethe the inassumed putprevious daily value value 30 daysof of the the to ψ airconsiderparameter temperature the to delaya waswider ofcalculated lapsethe soil of timeduesimilarThe types toselected the of delay soil values at of other the of theresponse sample model sites. of parameters deep The soil input levelswere dailyin to goodvalue either agreement of the the drying air temperature with or wetting those used was periods. calculatedby [21] for astimedueresponse a mean to to theof the the delay temperature daily of thetemperatures response fluctuations. of over deep the soil previous levels to either30 days the to drying consider or wetting the delay periods. of the soil assimilar a Themean types selected of of the soil valuesdaily at other temperaturesof the sample model sites. parameters over The the in putprevious were dailyin good value30 days agreement of the to airconsider temperature with thosethe delay used was ofbycalculated the[21] soil for responseThe selectedto the temperature values of the fluctuations. model parameters werein good agreement with those used by [21] for similaras a mean types of of the soil daily at other temperatures sample sites. over The the in putprevious daily value 30 days of the to airconsider temperature the delay was ofcalculated the soil response2.5. Modeling to the the temperature Slope Stability fluctuations. assimilar a mean types of of the soil daily at other temperatures sample sites. over The the in putprevious daily value30 days of the to airconsider temperature the delay was ofcalculated the soil 2.5.response Modeling to the the temperature Slope Stability fluctuations. as a mean of the daily temperatures over the previous 30 days to consider the delay of the soil response2.5. ModelingGiven to thethe the characteristicstemperature Slope Stability fluctuations. of the sample slope (Figure 3) and the relatively low thickness of the response2.5.landslide ModelingGiven towith thethe the characteristicstemperaturerespect Slope Stability to its fluctuations. extent,of the sample the hypothes slope (Figureis of the 3) infiniteand the sloperelatively was lowappropriate thickness for of the Given the characteristics of the sample slope (Figure 3) and the relatively low thickness of the 2.5.landslidestability Modeling analysis. with the respect Slope Both Stability tofield-measured its extent, the and hypothes modeledis ofSr thetrends infinite were slope used wasas the appropriate input data for in the Given the characteristics of the sample slope (Figure 3) and the relatively low thickness of the stability2.5.landslide Modeling analysis. with the respect Slope Both Stability tofield-measured its extent, the and hypothes modeledis ofSr thetrends infinite were slope used wasas the appropriate input data for in the slopeGiven stability the model characteristics proposed of by the [5]. sample A detailed slope de (Figurerivation 3) of and the themodel relatively was presented low thickness by [5], ofand the a stabilitylandslide analysis. with respect Both field-measuredto its extent, the and hypothes modeledis ofSr thetrends infinite were slope used wasas the appropriate input data for in the slopepreviousGiven stability application the model characteristics proposedto the test of bysite the [5]. based sample A detailed only slope on de field(Figurerivation measurements 3) of and the themodel relatively was was reported presented low thicknessby [24].by [5], ofand the a landslideslopestability stability analysis. with model respect Both proposed tofield-measured its extent, by [5]. theA anddetailed hypothes modeled deisrivation ofSr thetrends of infinite the were model slope used was wasas presented the appropriate input by data [5], for inand the a previousAccording application to this to model, the test which site based is based only on on the field limit measurements equilibrium method, was reported the slope by [24]. safety factor stabilitylandslide analysis. with respect Both tofield-measured its extent, the and hypothes modeledis ofSr thetrends infinite were slope used wasas the appropriate input data for in the previousslopeAccording stability application model to this toproposed model, the test which bysite [5]. based is A based detailed only on on the de field rivationlimit measurements equilibrium of the model method, was was reported presented the slope by [24]. safetyby [5], factorand a stabilityFs is calculated analysis. as follows:Both field-measured and modeled Sr trends were used as the input data in the slopeprevious stability application model proposedto the test bysite [5]. based A detailed only on de fieldrivation measurements of the model was was reported presented by [24].by [5], and a Fs is calculatedAccording as to follows: this model, which is based on the limit equilibrium method, the slope safety factor previousslope stability application model toproposed the test bysite [5]. based A detailed only on de fieldrivation measurements of the model was was reported presented by [24]. by [5], and a Fs is calculatedAccording as to follows: this model, which is based on the limit equilibrium method, the slope safety factor previous application to the test site based only on field measurements was reported by [24]. F s is calculatedAccording as to follows: this model, which is based on the limit equilibrium method, the slope safety factor F s is calculatedAccording as to follows: this model, which is based on the limit equilibrium method, the slope safety factor F s is calculated as follows:

Geosciences 2018, 8, 472 11 of 18

c0 + γz cos2 δ − σs
tan φ0 F = (5) s γz sin δ cos δ where c0 is the effective cohesion, γ is the unit weight of the soil, z is the depth below the ground surface where a potential sliding surface could develop, σs is the suction stress, δ is the slope angle, 0 s and φ is the soil shear strength angle. In Equation (5), σ allows for the calculation of Fs also in unsaturated conditions (Sr < 1.0; [5,37]). This parameter can be determined by considering Sr according to Equation (6) [37]: 1 S   µ σs = − r S µ/1−µ − 1 (6) α r where α and µ are the fitting parameters of the Van Genuchten equation, determined through the laboratory assessment of the SWRCs of the investigated soil levels (Table2 and Figure5). This relationship allows for calculating Fs based on thedegree of the soil saturation. Table5 summarizes the input data for the Lu and Godt model. The slope safety factor Fs was calculated considering a slope angle δ equal to 30.2◦ (Table5), at depths of 0.4, 0.6, and 1.0 m belowthe ground level, where Sr was measured. Fs was then determined by considering both the measured and modeled Sr values (Table5) and by considering the geotechnical properties of the soil measured at the investigated depths (Tables1 and5).

Table 5. Input data for the Fs model.

0 0 Soil Depth δ Sr γ φ c Horizon m ◦ - kN/m3 ◦ kPa Field measured— C 0.2 17.0 31.0 0.0 Modeled through the model of Valentino et al. [21] Field measured— D 0.4 16.7 31.0 0.0 Modeled through the model ofValentino et al. [21] 30.2 Field measured— E 0.6 16.7 31.0 0.0 Modeled through the model ofValentino et al. [21] Field measured— F 1.0 18.6 33.0 0.0 Modeled through the model ofValentino et al. [21]

3. Results and Discussions

3.1. Comparison between the Measured and Modeled Values of the Degree of the Soil Saturation Figure7 shows the time trends of the degree of thesoil saturation calculated through the model of [21] compared with the experimental measurements from the test site, in correlation with the rainfall amount. The Sr 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 (Table4). 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. The modeled and measured values of the degree of saturation were compared at four different depths: 0.2 m (Figure7a), 0.4 m (Figure7b), 0.6 m (Figure7c), and 1.0 m (Figure7d). The model was not applied to the deepest investigated layers (1.2 and 1.4 m belowthe ground surface) for two main reasons: The first is because previous research has shown that the model is not suitable for reproducing the soil hydrological behavior at depths greater than 1 m [21]. The second is because the observed landslides on the sample slope and in the surrounding zones involved only shallow soils within a thickness of 1m. Figure7 also shows the indications of two short periods in which rainfall data weremissing: between 31 August 2012 and 4 September 2012 and between 9 and 15 January 2014. For these periods, the model could not attain the values of the degree of saturation at the investigated soil depths due to the lack of rainfall data. Geosciences 2018, 8, x FOR PEER REVIEW 13 of 19 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

Geosciencesvalues of2018 Sr ,during8, 472 the first phase of the drying period, particularly for points at depths of −0.612 ofand 18 −1.0 m.

FigureFigure 7. 7.Comparison Comparisonbetween betweenthe themeasured measuredand andmodeled modeledvalues values ofof thethe degreedegree of of the the soil soil saturation saturation duringduring the the monitoring monitoring time time span span at at various various depths depths belowthe belowthe ground ground level: level: (a) ( 0.2a) 0.2 m; m; (b) ( 0.4b) 0.4 m; (m;c) 0.6(c) m;0.6 andm; and (d) 1.0(d) m.The1.0 m.The grey grey rectangles rectangles represent represent dry periods.dry periods.

It is interesting to note that in correspondence withall the investigated soil levels, the model reproduced the main hydrological behaviors in response to single rainfall events, particularly during periods of frequent rainfall separated by short time intervals (Figure7). The horizons up to0.6 m belowthe ground surfaces showthequick response torainfall in terms of increases in the degree of the soil saturation in both dry (summer) and wet (winter) periods (Figure7a–c). In these shallow layers, the degree of thesoil saturation frequently reaches values up to almost 0.9. For the soil horizon at Geosciences 2018, 8, 472 13 of 18

−1.0 m, only longer rainy periods during the winter provoked an increase of the degree of saturation of up to 0.9 (Figure7d). The saturated conditions were measured and calculated at −1.0 m only for the event of 18 February 2014–2 March 2014 (Figure7d), which triggered the shallow landslide near the monitoring station. The instability mechanism on the sample slope appeared to be linked to an increase in the degree of the soil saturation in the deeper soil horizons. This generally occurredas a consequence of an intense rainfall event in the wet season, provoking complete soil saturation (Sr = 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 (Figure7). For each soil layer, the reliability of the calculated values of Sr with respect to the measured values was evaluated by using the rootmeansquare error (RMSE) statistical index (Table6). 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 Sr 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 (Table6). 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 (Table6). 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 (Table6).

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

Soil Depth RMSE Horizon m 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

The very different performance of the model in different seasons is generally due to thesignificantly different hydrological response of the shallow soil to the climatic variables, such as the air temperature during winter (wet and cold season) and summer (dry and hot season). It should be highlighted that the complex interaction between the soil and the atmosphere cannot be adequately described only by the trend of air temperature and then by a unique set of the model parameters. Two effects in particular weredisregarded by the model: a) the presence of snow, which indeed does not have an immediate influence on the water content of the soil measured during winter; and b) the presence of shrubs and grass during summer, which increases the drying rate because of the water uptake of the plants. For these reasons, particularly during the dry regime, the model wasless efficient. Thus, different sets of parameters were chosen for different seasons. The arbitrary assumption of varying the input model parameters in correspondence with the selected dates implied that the modeled Sr 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 (Figure7c,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 Sr during the first phase of the drying period, particularly for points at depths of −0.6 and −1.0 m. Geosciences 2018, 8, 472 14 of 18

This is strictly linked with the fact that, at these depths, the soil moisture does not depend only on the air temperature and rainfall. Other more complex processes disregarded by the model, such as the water uptake ofplants, affect the drying of both shallow and deep soil layers. Second, the drying effect of high air temperatures during summer is progressively delayed at increasing soil depths. With respect to both of these aspects, the model was less accuratein reproducing the actual trend of the degree of the soilsaturation at depths greater than 0.4m below the ground surface in this test site. These results confirm thoseobserved in previous works for other sample sites [21]. On the contrary, during the wet season, when the probability of landslide occurrence is higher, the model has higher accuracy.

Geosciences 2018, 8, x FOR PEER REVIEW 14 of 19 3.2. Slope Safety Factor Trends

TheThis measured is strictly linked and calculated with the Sfactr values that, at were these used depths, to obtain the soil the moistureFs trends does by using not depend the Lu only and Godton the slope air temperature stability model and for rainfall. the same Other monitoring more complex time (Figure processes8). F sdisregardedwas calculated by the for model, levels at such 0.4, 0.6,as the and water 1.0 m uptake below ofplants, theground affect level. the drying of both shallow and deep soil layers.

Figure 8. Comparison of the safety factor obtained from the measured and modeled values of the 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: degree of the soil saturation during the monitoring time span at various depths belowthe ground (a) 0.4 m; (b) 0.6 m; and (c) 1.0 m. level: (a) 0.4 m; (b) 0.6 m; and (c) 1.0 m.

Second, the drying effect of high air temperatures during summer is progressively delayed at increasing soil depths. With respect to both of these aspects, the model was less accuratein reproducing the actual trend of the degree of the soilsaturation at depths greater than 0.4m below the ground surface in this test site. These results confirm thoseobserved in previous works for other sample sites [21]. On the contrary, during the wet season, when the probability of landslide occurrence is higher, the model has higher accuracy.

Geosciences 2018, 8, 472 15 of 18

Geosciences 2018, 8, x FOR PEER REVIEW 15 of 19 In fact, in the testsite slope and in the surrounding slopes with similar geological and geomorphological features, shallow landslides sliding surfaces were located between 0.4 m and 3.2. Slope Safety Factor Trends 1.0m below the ground level. The reconstruction of the trends at different depths allowed us to investigateThe measured the potential and differencescalculated S inr values the stability were conditionsused to obtain at these the depths,Fs trends with by theusing awareness the Lu and that Godtthe sliding slope stability surface of model the landslide for the same that monitoring actually occurred time (Figure was 1 m8). below Fs was the calculated slope surface. for levels at 0.4, 0.6, andA rather 1.0 m goodbelow agreement theground between level. the Fs trends obtained from the measured Sr values and those obtainedIn fact, from in the the modeled testsite Ssloper were and noted in (Figurethe su8rrounding). Similar toslopes that previously with similar observed geological for the andSr geomorphologicalannual cycles, the Ffeatures,s trends shallow at 0.4m showedlandslides a better sliding agreement surfaces withwerelocated respect tobetween the levels 0.4 atm 0.6and m 1.0m and below1.0 m belowthetheground ground level. The level reconstruction (Figure8). Moreover, of the tren theds agreement at different wasmuch depths allowed more evident us to investigate in the wet theseason, potential when differences thedegree ofin thethestability soil saturation conditions was higher at these than depths, 0.8, and withthe the F sawarenesstrends abruptly that the decreased sliding surfacewith respect of the to landslide the dry seasonthat actually (Figures occurred8 and9). was 1 m below the slope surface.

FigureFigure 9. ComparisonComparison between between the the safety safety factor factor obtained obtained from from the the measured measured and and modeled modeled values values of of thethe degree degree of of the the soil soil saturation saturation for for the the period period between between 1 1 Februa Februaryry 2014 2014 and and 3 3 April April 2014 2014 at at various various depthsdepths belowthe below the ground ground level: level: (a (a) )0.4 0.4 m; m; (b (b) )0.6 0.6 m; m; and and (c (c) )1.0 1.0 m. m.

A rather good agreement between theFs trends obtained from the measured Srvalues and those obtained from the modeled Srwere noted (Figure 8). Similar to that previously observed for the

Geosciences 2018, 8, 472 16 of 18

It should be stressed that becauseroots are present at a depth of 0.3–0.4m, root reinforcement can play a role in the slope stability. This root effect has not been included in the analysisin order to obtain a conservative assessment of Fs. Regarding the shallow landslide occurring between 28 February 2014 and 2 March 2014, both the Fs trends correctly identified the triggering time 1m belowthe ground surface, where the sliding surface actually developed (Figures8 and9). In particular, unstable conditions were attained for three days, 1–3March2014, by the Fs trend from the measured Sr but only for one day, 2 March 2014, by the Fs trend from the modeled Sr (Figure9).

4. Conclusions Long-term field measurements of the water contents at various soil depths were taken on a sample slope located in the northeastern Oltrepò Pavese (Northern Italy), where several rainfall-induced shallow landslides recently occurred. The measured water contents were used as benchmark values for the calibration and validation of an empirical model able to evaluate the degree of saturation of the soilbased on the air temperature and rainfall data. The comparison between the measured and modeled vales of the degree of the soil saturation showed that the empirical model was only partially able to reproduce the hydrological conditions at soil depths greater than 0.5 m below the ground surface over the considered period. In particular, the model appeared to be less efficient during dry regimes, although different sets of parameters were chosen for different seasons. Nevertheless, a fair agreement between the modeled degree of thesoil saturation and the experimental measurements were observed at depths of 0.2 m and 0.4 m, particularly during the wet season. Moreover, for the purposes of a simplified approach, the drying–wetting hysteresis phenomenon of the different soil layers was neglected. Both the measured and modeled values of the degree of saturation were used to obtain the Fs trends of the slope. Fs was calculated by assuming the sliding surface at different soil depths through the slope stability model proposed by [5]. Deliberately, in this research, Fs 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 Fs trends obtained from both the measured and modeled Sr values was observed. This result appeared useful in the following terms: if Fs, 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 Fs 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 Fs 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. It can be concluded that, aside from some limits of the chain of the two models [5,21], the degree of the soil saturation estimated only on the basis of readily available data, such as air temperature and rainfall, can be used as input for the preliminary slope stability analysis. The latter was performed through a simplified limit equilibrium method that appeared to give fairly good results at the slope scale, despite the sharp simplifications introduced for estimating the soil moisture. The proposed approach appears rather promising for application to distributed analysis over large areas, at least for a precautionary assessment of slope stability. However, to provide stability assessment for specific sites, the proposed methodology requires extremely detailed data and appropriate calibration. Moreover, it is worth noting that to apply the same approach to other areas, previous site-specific validation of both models is strongly recommended. Geosciences 2018, 8, 472 17 of 18

Within the limits of only preliminary analyses on wide areas, the obtained results imply the possibility of assessing the initiation time and depth of shallow landslides oneither a local or regional scale, where only rainfall and air temperature data are available.

Author Contributions: Conceptualization, M.B. and R.V.; Data curation, M.B., R.V., C.M., M.B., and S.C.; Investigation, M.B., M.B., and S.C.; Methodology, M.B., R.V., and C.M.; Supervision, C.M.; Validation, M.B. and M.B.; and Original draft preparation, M.B. and R.V. Funding: This research received no external funding. Acknowledgments: We thank Marco Tumiati for hisassistance withthe executions of the laboratory tests on the studied soils. We also thank the anonymous reviewers for their suggestions and contributions to this work. Conflicts of Interest: The authors declare no conflicts of interest.

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