J. Mt. Sci. (2

Abstract: affected by landslides inin differentexists. The is a relevanliterature merosion or farea analysconsisting opyroclastic repeatedly special seassimulated smaller thasimulated ecm are comanalysis taka spatially vresults of thliterature contributionover large shows howanalyses maslope instabfully achievbe confidensmaller spec

Largeby Rai

CUOM

DELLA

Depart

Citatiounsatur

© Scie

Received: 20Accepted: 1

2015) 12(4): 78

Unsaturated either super

n adjacent ort seasons wtriggering an

nt issue for tmostly provifor landslidessis for a caof unsaturate(air-fall) voaffected by

sons. For a source areas

an those obseroded areas mparable withkes into accouvariable soil che paper areand also

n about the area. The ad

w the combinay help with bility mechanved, can specntly performecific areas.

-area Ainfall: A

O Sabatino

A SALA Mari

tment of Civil En

on: Cuomo S, Drated shallow de

ence Press and I

0 August 2014 February 2015

83-796

shallow soil rficial soil err overlapping

when a differnalysis of boththe hazard anides specific s. The paper pase study of ed shallow d

olcanic soils erosion an

past catastrs of shallowserved in thewith thickne

h the in-situ unt high raincover use. Mo consistent wprovide a application

dded value isnation of diunderstandi

nisms. Only cific physicalled at detaile

AnalysisA Case o

http://orci

ia http://o

ngineering, Un

Della Sala M (20eposits. Journal

Institute of Mou

e-

deposits maosion or shasource areas

rent soil such these procenalysis while

approaches proposes a la

Southern Ideposits of lo

that have bnd landslidesophic event,

w landslides e field while ss greater thevidences, iffall intensity

ore in generalwith the prev

methodologof distinct ts that the paistinct large-ng the dominonce this go

ly-based analed scales and

s of Soil of Unsa

id.org/0000-0

orcid.org/000

iversity of Saler

015) Large-areal of Mountain S

untain Hazards

-mail: jms@im

ay be allow and

ction esses e the

for arge-taly, oose been s in

the are the

an 5 f the and

, the vious gical tools aper area nant al is lyses d for

KeySlop

Int

mayet ain agreoutconeithoccsearainSimKonRahChe

botIn anafor stepQRanawhe

Erosioaturated

0001-8024-03

0-0003-2772-

rno, Via Giovan

a analysis of soicience 12(4). DO

and Environme

mde.ac.cn

ywords: Soilpe instability

troduction

In unsaturay cause eith

al. 2011) or laadjacent or at amount o

tlet of mountnsequences. her superficicurs in a largesonal meteonfall patterns

milar events ng, Brasil ahardjo et al. en and Zhang

This paperth superficialfact, a deep

alysis of the any hazard

p towards a RA, (Fell et alalysis is neether distinc

n and Ld Shallo

319; e-mai

-5020; e-mail

nni Paolo II, 132

l erosion and laOI: 10.1007/s11

ent, CAS and Sp

DOI: 10

l Erosion; Lamechanism;

n

ated steep sher superficiaandslides (Caoverlapping of debris mtain basins wCascini et aial erosion e area of Sou

orological cos and pore whave also b

and Canada2004; Cuomg 2014).

r focuses on l soil erosion

p understandtriggering sanalysis. ThQuantitative. 2008). Part

ecessarily rect types of

Landslidow Depo

il: scuomo@un

: maria.dellas

2, 84084 Fiscian

andslides induce1629-014-3242-

pringer-Verlag B

http://jm0.1007/s11629

ndslide; Soil Modelling

hallow deposal soil erosioascini et al. 2areas. Cons

may be convewith importan

al. (2014) oor shallow

uthern Italy inditions, de

water pressurbeen recordea (Zhang etmo and Della

the triggerin and shallowding and a qstage is a relhis is, in ture Risk Analyticularly, a mequired to slope instab

des Indosits

nisa.it

ala@virgilio.it

no (SA), Italy

ed by rainfall: A7

Berlin Heidelber

ms.imde.ac.cn9-014-3242-7

783

Suction;

sits, rainfall on (Acharya 2010, 2013b)sequently, a eyed at the nt economic outline that

landsliding n particular pendent on

re in the soil.ed in Hong t al. 2000, a Sala 2013;

ing stage of w landslides. quantitative levant issue rn, the first ysis, namely

multi-hazard understand

bilities may

duced

t

A case of

rg 2015

)

.

J. Mt. Sci.(2015)12(4): 783-796

784

occur within the same area. The potential transformation of both processes (erosion and landsliding) in flow-like mass movements (Hutchinson 2004) is outside the scope of this paper, but it has been discussed in the recent literature (Cascini et al. 2013b).

For any type of slope instability, rainfall infiltration and runoff generation are important processes, which strongly depend on the slope angle, rainfall intensity and duration, soil initial conditions, hydraulic and mechanical properties of soils, as discussed by Cuomo and Della Sala (2013). Moreover, high rainfall intensity and slope angles cause high sediment concentrations as recorded in flume experimental tests in Hu et al. (2013). For unsaturated soils, which are widespread in Mediterranean Countries, the difference between the air pressure (ua) and the pore water pressure (uw) is commonly defined as matric suction (Fredlund et al. 1978), also simply named as soil suction; it will be referred as ua-uw later on. The suction affects the soil conductivity and volumetric water content as commonly described through the so-called Soil Water Characteristic Curves (SWCCs). The suction increases the effective stresses acting on the solid skeleton of the soil, thus reducing the chances for different types of slope instability and even preventing any instability. The suction also increases the soil shear strength by adding a suction-proportional term according to Fredlund et al. (1978). Experimental results and discussions about the important role of soil suction on the soil mechanical behaviour are reported in the literature, for instance, for the pyroclastic (air-fall) volcanic soils originated in Southern Italy by the Somma-Vesuvius volcano (Sorbino and Foresta2002; Bilotta el al. 2005; Cascini et al. 2010; Cascini et al. 2014).

The superficial soil erosion affects the first centimeters of soil below the ground surface and can be distinguished in rainsplash erosion or overland flow erosion. The rainsplash erosion, i.e. the mobilization of solid particles due to the raindrops impacts, depends on the impact forces - which are related to the rainfall intensity, soil mechanical properties, topography, vegetation and land use. The rainsplash erosion is generally diffuse in a mountain basin. In addition, the overland flow erosion, i.e. the mobilization of solid particles due to overland flow, relates to flow

velocity and to tangential and uplift forces applied to the ground surface by the water and solid particles driven by flow. The overland flow erosion may be diffused (sheet erosion) or localize either into rills, gullies (Tang et al. 2013) or channels (Merritt et al. 2003). Regardless of the triggering mechanism, estimates of the eroded soil thickness can be obtained either through physically-based models, which integrate mathematical equations describing the main processes for soil erosion, or empirical models - based on relationships derived from statistical analyses of data collected from field experiments. Physically-based models (e.g. LISEM model; Hessel and Jetten 2007; Cuomo et al. 2015) are usually applied to analyze the response of a single mountain basin (or a cluster of very few mountain basins), due to their large computational times. The empirical models are usually preferred over large areas as they can be easy implemented for limited datasets and they are particularly useful in first-step analyses aimed at identifying the source areas of soil erosion (Merritt et al. 2003). For this reason, an empirical quantitative model will be used in this paper to perform the superficial soil erosion analyses.

The shallow landslides typically involves a some-meters-thick soil mass due to distinct triggering mechanisms (Cascini et al. 2008), related to specific hydraulic and static boundary conditions applied at the ground surface and/or at the bedrock contact (Cascini et al. 2010 2013a). The shallow landslides can be categorized as translational slides with reference to landslide classifications proposed by Hutchinson (1988) and Cruden and Varnes (1996). The failure onset of rainfall-induced shallow landslides is strictly related to the increase of pore water pressure (and/or decrease of soil suction in unsaturated slopes), and to the subsequent reduction of the mean effective stresses and shear strength. The failure stage of shallow landslides can be analyzed through either qualitative or quantitative models. The qualitative approaches are mostly used for ranking the susceptible areas based on the worst combinations of the predisposing factors and referring to the expert-judgment as well. The quantitative approaches deserve special consideration because pore water pressure increase (or soil suction decrease in unsaturated soils) and soil shear mobilization can be computed, and

J. Mt. Sci.(2015)12(4): 783-796

785

amount of potential unstable mass evaluated. Most models compute the factor of safety for a DTM (Digital Terrain Model) cell-by-cell with acceptable computational times, even over large areas (Sorbino et al. 2007, 2010). In this paper, a quantitative physically-based model is used to analyze the potential onset of landslides.

It is worth noting that current literature poorly addresses the cases whether superficial soil erosion and shallow landslides occur inside a same area. The principal scope of this paper is to propose a large-area analysis for two different types of slope instability, superficial erosion and landslide. Two separate but quantitative spatial-distributed analyses will be performed. Thus, it will be possible integrating the results achieved at any cell of the DTM. In addition to this novelty, the role of soil suction which relates to the meteorological seasons will be explicitly taken into account. This will be another added value of the paper to the current literature.

1 Case Study

The study area is the eastern part of the “Amalfi Coast” (Southern Italy) which is located along the Gulf of Salerno (Figure 1a), and has an extent approximately equal to 80 km2. This site is a UNESCO World Heritage Site for the beauty of its landscapes and picturesque villages, attracting for thousands of tourists every year.

The Lattari Mountains are mainly composed of limestone, accumulated in the Mesozoic on a carbonate platform (data from Autorità di Bacino

DestraSele 2012). There is evidence of strong (compressional) deformation during the Miocene and Quaternary ages, and the effects of modern tectonic movements are visible as nearly vertical outcrops of bedrock bounded by fault planes. Geomorphology of the site testifies to the occurrence of erosion-deposition cycles and high steep reliefs exist on the east side of the Coast (Figure 1a), up to 1444 m a.s.l. (San Michele mount), sloping towards the sea. Three main physiographic systems can be distinguished: i) steep carbonate hillslopes with several bedrock outcrops; ii) steep rectilinear channels; iii) colluvial valleys heavily modified by anthropogenic activities. Many funnel-shaped mountain basins exist in the study area, with a high order of drainage networks, steep stream channels and a preferential orientation from north to south. The outlets of the basins generally correspond to the urban areas of the main municipalities. In Figure 1a, the principal mountain basins (also named catchments, hereafter) are indicated, and the largest catchment (Reginna Maior) is 33 km2, with a stream channel 10 km long, extending from Chiunzi mount (880 m a.s.l.) to the shoreline. It is also shown in Figure 1a with the slope angle map obtained by a 20m×20m DTM. The shape and location of the catchments with drainage area equal to or higher than 0.25 km2, herein named “sub-basins”, are reported in Figure 1b. They were obtained through an automatic procedure available in a GIS platform (Calvello et al. 2012). As discussed by Calvello et al. (2013), the sub-basins can be used as terrain zoning units (TZUs). In this paper, the computed erosion soil thickness will be represented cell-by-

Figure 1a) Principal mountain basins of the study area and slope angle map derived from a 20 m × 20 m DTM (Digital Terrain Model); b) hillshade of the study area and sub-basins derived from the same DTM (Data from Autorità di BacinoDestraSele 2012).

J. Mt. Sci.(2015)12(4): 783-796

786

cell or, alternatively, averaged over the 88 sub-basins of Figure 1b.

The prevailing soil types can be schematized as follows: i) on the ridges, pyroclastic deposits were derived from falling ashes, sands and pumices; ii) along the hillslopes, the deposits of pyroclastic soils and debris are prevalent and consist of ashes/pumices and carbonate clasts accumulated by colluvial processes; iii) in the valleys, loose fluvial deposits of angular gravels and pebbles are observed.

The unsaturated shallow deposits of pyroclastic (air-fall) volcanic soils originated from the explosive eruptions of the Somma-Vesuvius volcano in southern Italy (Bilotta et al. 2005; Cascini et al. 2008; Cascini et al. 2010). Particularly, large amounts of pyroclastic materials were ejected into the atmosphere during the volcanic eruptions, transported by the prevailing winds and deposited in a very large area (about 3000 km2), which also includes the “Amalfi Coast” (Cascini et al. 2014). Pyroclastic soils mainly consist of silty sands or sandy silts (ash soils) and coarse sands or sandy gravels (pumice soils). The details on the soil origin and later pedogenetic processes are provided by Guadagno et al. (2005), while an advanced soil mechanical characterization in saturated and unsaturated conditions is given by Bilotta et al. (2005). The pyroclastic deposits are susceptible to superficial soil erosion as discussed in recent contributions (Cascini et al. 2009; De

Falco et al. 2011; Della Sala 2014).Furthermore, distinct triggering mechanisms of shallow landslides can occur (Cascini et al. 2008), mostly related to specific hydraulic and static boundary conditions applied at the ground surface and/or at the bedrock contact (Cascini et al. 2010, 2013a).

The map of the soil thickness (Figure 2a) shows that: i) along the hillslopes, the soil deposits are generally less than 2 m thick; ii) at toe of hillslopes, the soil thickness may exceed 5 m. The land use of the study area (Figure 2b) consists of: i) forests, broad-leaved forest, mixed forests, natural grassland, Mediterranean scrub, transitional woodland scrub and sparsely vegetated areas, especially located in the upper part of hillslopes, ii) agricultural areas including olive groves and annual and permanents crops on gentle slopes.

Climate information and the temporal-spatial distribution of critical rainfall in the region can be found in Cascini et al. (2014). For the sake of clarity, it is useful to note that the annual precipitation is generally about 1000 mm, the mean monthly temperature ranges from 10 to 25 degrees; the dry season begins in June and finishes in September while the wet season lasts from October to May.

Several rainfall-induced slope instabilities have occurred in the past (October 1899, 1910, 1954, among others), with catastrophic consequences recorded in the villages located at the outlet of the basins. Most of the events occurred in

Figure 2 a) Thickness of pyroclastic soil deposits (data from Autorità di BacinoDestraSele 2012); b) Landuse cover map: 111: continuously urbanized area, 112: discontinuously urbanized area, 123: harbour areas, 223: olive groves, 241: temporary and permanent crops, 242: complex cultivation patterns, 243: agriculture and natural vegetation, 3111: forests with prevalence of oaks and other evergreen broadleaf, 3112: forests with prevalence of deciduous oaks, 3113: mixed forests with prevalence of other native broadleaf, 3114: forests with prevalence of chestnut, 31312: mixed forests of coniferous and broadleaf with prevalence of deciduous oaks, 3211: continuous grasslands, 3212: discontinuous grasslands, 3231: high mediterranean scrub, 3232: low Mediterranean scrub, 324: areas with forest and shrub vegetation in evolution, 333: sparsely vegetated areas (data from Corine Land Cover IV livello 2006).

J. Mt. Sci.(2015)12(4): 783-796

787

October and January while the majority of fatalities were recorded in October and November (Cascini et al. 2009). Based on a comprehensive data-set about the past slope instabilities and soil suction measurements in pyroclastic soil deposits of the Campania region, Cascini et al. (2014) classify the temporal-spatial occurrence and the typology of slope instabilities. Particularly, the past events are categorized as: i) local, e.g. September 2010, 114.2 mm of cumulative rainfall in 3 hours in 10 km2 or, ii) widespread, e.g. October 1954, 504 mm of cumulative rainfall in 8-16 hours in 80 km2. As far as the occurrence period and the slope instability type, a remarkable distinction is also proposed (Cascini et al. 2014). In September and October, (period 1 later on), the soil suction is 20-30 kPa and mostly erosion phenomena occur; in November and December, the soil suction is 10-20 kPa (period 2), and both erosion phenomena and shallow landslides may occur; from January to May, the soil suction is lower than 10 kPa (period 3), and shallow landslides are triggered. Finally, from June to August, the soil suction is higher than 30 kPa (period 4), and only local erosion phenomena and small-size shallow landslides may be triggered.

Among the most catastrophic past events, it is worth mentioning the slope instabilities occurred on 25-26 October 1954, which caused 325 fatalities and huge damages (Cascini et al. 2009) (Figure 3). While the effects of this event are well documented, major uncertainties concern: i) the rainfall features, as a 504 mm cumulative rainfall was registered in a uncertain time interval comprising between 8 and

16 hours (Tranfaglia and Braca 2004; Cascini et al. 2009; De Luca et al. 2010; Tessitore et al. 2011), ii) type of slope instabilities, as the distinction among eroded areas and landslides is unclear. As it concerns the latter issue, the available inventory map of slope instabilities (Figure 3) may also include areas where actually severe erosion processes occurred. Conversely, local erosion processes – which greatly contributed to the total discharge of sediments – may not be included in the map. Therefore, the type and genesis of slope instabilities that occurred on October 1954 are still controversial issues.

The paper will analyse the October 1954 event, providing an explanation of this event and also a quantitative validation of the observations reported by Cascini et al. (2014), as far as the type and seasonal period for different slope instabilities.

2 Superficial Erosion Analysis

2.1 Methods and input

The spatial distribution of superficial soil erosion and the amount of mobilized sediments are here analyzed through the Universal Soil Loss Equation (USLE) model (Wischmeier and Smith 1978). Originally based on regression analyses of soil loss rates in US experiments, theUSLE model is widely used to predict long-time average soil loss due to runoff-originated soil erosion (Li et al. 2013) and, in some cases, applied to the analysis of single-rainstorm-induced soil loss. The latter is expressed as the weight of the sediments eroded in a unitary area, and it is estimated using an empirical equation, which takes in account the main factors for erosion process: rainfall erosivity (R), soil erodibility (K), slope-length (L, dimensionless), slope-steepness (S, dimensionless), cover and management factor (C, dimensionless) and support practice (P, dimensionless). The rainfall erosivity (R) expresses the attitude of the rainfall to produce soil erosion. R depends on several variables such as the rainfall intensity, cumulated rainfall and kinetic energy (Foster 1982; Wischmeier 1959). The erodibility factor (K) represents the resistance of the soil to both soil detachment and transport and it is generally related to the soil texture, aggregate stability, shear

Figure 3 Inventory map of slope instabilities occurred on 25-26 October 1954 (data from Autorità di BacinoDestraSele 2012).

J. Mt. Sci.(2015)12(4): 783-796

788

strength and infiltration capacity (Toy et al. 2002). The erodibility (K) increases as the soil conductivity diminishes. The latter is, in turn, related to the seasonal soil suction. Thus, soil suction can be explicitly related to the soil erodibility (K).The product of slope-length factor (L) and slope-steepness factor (S), is commonly called as “topographic factor” (LS), and it is related to the upslope contributing area (Moore and Burch 1986). The cover factor (C) takes into account the preventative action of the vegetation on the erosion process and is dependent on cover type and management practices of the vegetal cover at the time of the rain. Finally, the P factor (P) is related to the protective effects of support practice such as terracing and contour tillage.In this paper, the seasonal dependence of some input factors is taken into account with special emphasis on soil suction and the input data are selected as follows.

A DTM of the study area was obtained from a topographical map at 1:25,000 scale and consists of 218,349 cells, each 20 m × 20 m large. This detail for the topography was assumed adequate to the size of study area and to the purposes of the present study, based on Calvello et al. (2013). The rainfall erosivity (R) was evaluated in relation to the rainfall intensity (I) referring to the procedures of Wischmeier and Smith (1978) and Foster (2004).The rainfall intensity (I) was assumed equal to 31.5 or 63 mm/h, based on the above mentioned field data collected during the critical rainstorm of

25-26 October1954. The erodibility factor (K) was estimated with reference to the initial soil conductivity, which depends on the seasonal soil suction. The latter was assumed equal to 20 or 30 kPa, which is a typical range of values for the autumn season in the Campania region (Cascini et al. 2014). To this end, the Soil Water Characteristic Curves (SWCCs) reported in Cuomo and Della Sala (2013) were referred. Thus, the suction was explicitly referred for the back-analysis of the 25-26 October 1954 event. However, the erosion analysis was also extended to distinct values of suction (10 or 40 kPa) in order to highlight the role which the soil suction plays towards the severity of the erosion scenarios. The topographic factor (LS) was derived from upslope contributing area, and computed from the DTM. The cover factor (C) was taken from De Falco (2011), who estimated the value of C in the Campania region, depending on the seasonal period. Finally, the protective effect of the support practices was disregarded in the paper (P assumed equal to 1) for the sake of simplicity. The input data and the analyzed cases are given in Table 1. It is worth noting that the suction was fixed lower or higher than 10 kPa, and different hypotheses were made for the rainfall intensity and duration, while keeping the cumulated rainfall as constant.

The output of the USLE model (i.e. soil loss) was post-processed for any analyzed case to discuss the potential onset of soil erosion in the study area

Table 1 Input data for large-area analysis of soil erosion

Case* 1 2 3 4 5 6 7 8

I (mm/h) 63 31.5 63 31.5 63 31.5 63 31.5

Duration (h) 8 16 8 16 8 16 8 16

Erosivity R(MJ mm ha-1 h-1) 9170.24 4353.61 9170.24 4353.61 9170.24 4353.61 9170.24 4353.61

Initial suction (kPa) ≥ 10** ≥ 10** 0 – 10*** 0 - 10*** 0 - 10*** 0 - 10***

Initial conductivity (mm/h) < 1 < 1 5-20 5-20

Erodibility K (t h MJ-1 mm-1) 0.0523 0.0523 0.0457 0.0457

LS factor SV SV SV SV

C factor 0.014 SV 0.014 SV

P factor 1 1 1 1

Notes: I, Rainfall intensity; LS factor, Topographic factor (slope-length and slope-steepness factor); C factor, Cover factor; P factor, Practice factor; SV, Spatially Variable; *, Cumulated rainfall is 504 mm for all the cases; **, From medium to very high suction according to Cascini et al. (2014); ***, Low suction according to Cascini et al. (2014).

J. Mt. Sci.(2015)12(4): 783-796

789

as a function of the seasonal suction. Particularly, an estimate of the average erosion thickness was derived from the computed soil loss. This was done assuming a soil unit weight equal to 15 kN/m3. In addition, a representative soil diameter (d90) was selected from the grain size distribution of the superficial ashy soil (namely, ashy soil B in Bilotta et al. 2005) and significant eroded thicknesses were fixed. As a novel proposal, the reference erosion thickness values were assumed equal to 5, 25 or 50 times the d90. It entails that three significant classes were individuated for the erosion thickness: i.e. 1, 5 and 10 cm. Doing so, the cells (N) with different severities of erosion – from 1 to more than 10 cm – were mapped for each computational case of Table 1.

2.2 Results

The erosion analysis of the area affected by the 1954 rainstorm highlighted some interesting insights. For the discussion of the results, Figure 4 shows the extent of the area where the computed erosion thickness was higher than 1, 5 or 10 cm (labelled as “Aeros”) normalized to the extent of the study area (Atot), which is 80 km2.

Firstly, a simulated erosion thickness equal or higher than 1 cm had a global extent larger than

that observed in the field, independent of the rainfall intensity and suction. In detail, the best simulation of the field evidences was obtained assuming: i) rainfall intensity (I) equal to 31.5 mm/h, ii) cover land use factor (C) as a spatially-distributed variable, and iii) soil suction (ua-uw) higher than 10 kPa (case 4 of Table 1). A similar result was also obtained lowering the suction to 0-10 kPa and assuming a constant value for C throughout the study area (case 8 of Table 1). In both cases, the simulated erosion scenario slightly overestimated the in-situ evidence (Figure 4).

In parallel, an erosion thickness higher than 5 cm was simulated inside an area similar to that observed in the field for the cases 1 and 5 of Table 1. These latter cases correspond to a rainfall intensity equal to 63 mm/h and the factor C is assumed to be homogeneous inside the whole study area (C=0.014). Indeed, the area where the computed erosion thickness was higher than 5 cm is an underestimation of the field evidence (Figure 4).

Finally, the portion of the study area where the simulated erosion thickness was higher than 10cm was much smaller than that observed (Figure 4).

Despite the simplicity of the used model, the results achieved – either the overestimation of cases 4 and 8 or the underestimation of cases 1 and 5 – allowed the investigation of some key features of the 1954 event. In fact, all over the study area, a good matching of the total affected area with the in-situ evidence was obtained while assuming: i) average suction as equal to about 10 kPa and ii) average rainfall intensity between 31.5 and 63 mm/h. It is worth noting that both these assumptions are consistent with the field data (Sect. 2.1). It entails that the average erosion thickness was comprised in the range from 1 to 5 cm, which was the output of cases 1, 4, 5 and 8. Indeed, all of these cases can be considered reasonable estimates of the erosion scenarios that occurred during the 1954 event.

As a validation of the computed scenarios, Figure 5 proposes the spatial distribution of the cells (each 20 m × 20 m) computed as eroded for the four cases mentioned before. It can be seen that the qualitative agreement between Figures 3 and 5 is acceptable, provided that the scope of the paper is to compare the susceptibility of the study area to superficial erosion and landsliding. Therefore, in the next section landslide analysis will beerformed

Figure 4 Comparison between the slope instabilities area (Atot) in the inventory map of Figure 3 and the area (Aeros) where simulated erosion thickness is higher than 1, 5 or 10 cm, for the cases listed in Table 1.

J. Mt. Sci.(2015)12(4): 783-796

790

and the scenarios of Figure 5 will be later referred to be further discussed.

3 Landslide Analysis

3.1 Methods and input

The Landslide triggering zones were analyzed through the TRIGRS-unsaturated model (Savage et al. 2004) which implements a transient seepage analysis using the linearised solution of Richards’ equation (1931) proposed by Iverson (2000) and extended by Baum et al. (2008) to the case of impermeable bedrock located at a finite depth. The unsaturated soil conditions and the soil water characteristic curves are dealt with using Gardner’s model (Baum et al. 2008). For each cell of the DTM (which is here the same as the one used for the erosion analysis), the TRIGRS model computes the soil strength and the mobilized shear stress at

different depths for unsaturated conditions with negative pore water pressures and saturated conditions with positive pore pressures. It is important to note that the depth of the initial water table determines both the positive and negative values of the initial pore water pressures. In particular, the initial soil suction at the ground surface depends on the initial water table. Then, an infinite slope stability analysis was carried out for each cell, independent of the surrounding ones, and the minimum factor of safety (FS) was computed as well as the corresponding depth of slip surface and pore water pressure.

To do so, the slope angle map of Figure 1a was used as input. A soil thickness map at 1:25,000 scale was used (Figure 2a, data from Autorità di Bacino DestraSele 2012) which distinguishes among five classes of soil thickness (from < 0.5m to > 20m). Thus, the spatial variation of soil thickness was taken into account while soil mechanical properties were assumed to be constant

Figure 5 Cell-by-cell spatial distribution of eroded thickness for different cases (1, 4, 5 and 8) of Table 1.

J. Mt. Sci.(2015)12(4): 783-796

791

throughout the soil cover. This last hypothesis is widely realistic for thickness < 5 m, as it is for the test area. It is worth mentioning that previous studies on similar sites (for slopes geomorphology, bedrock type and soil lithology) outlined the chance to successfully analyze over large area the onset of slope failures (Sorbino et al. 2007, 2010). This is possible, provided that the key mechanical properties such as the soil strength and the soil conductivity have been previously calibrated and validated for the test area (Sorbino et al. 2007, 2010). Based on the similarities between the study area and another site (Pizzo d’Alvano massif, 10 km far away from Amalfi Coast) and considering the number of studies about the triggering stage of past shallow landslides (Cascini et al. 2008, 2010, among others), for this case study the mechanical soil properties were selected referring to Sorbino et al. (2010) who successfully back-analyzed the extent and location of triggering areas of past shallow landslides for the Pizzo d’Alvano massif. It entails that in the present paper the soil unit weight ( totγ )was 15 kN/m3, the friction angle (ϕ’) was 38°, the effective cohesion (c’) was 5 kPa and the soil hydraulic conductivity ranged from 6×10-6 to 1×10-5 m/s and the saturated diffusivity was varied from 4.5×10-5 to 5.9×10-5 m2/s. The effects of vegetation on the stability conditions of the

shallow soil deposits – e.g. water interception and root reinforcement – were considered negligible, as in Sorbino et al. (2010). The boundary conditions were represented by the rainfall intensity and duration measured on 25-26 October 1954. Due to the uncertainties about the time pattern of the measured rainfall, the accumulated rainfall amount (504 mm) was kept constant while the duration was assumed equal to 8 hours (Cascini et al. 2009) or 16 hours (Tessitore et al. 2011; Frosini 1955; Esposito et al. 2003). A constant rainfall intensity was assumed in both the two cases (63 or 31.5 mm/h, respectively), which correspond to the same cases referred to in the erosion analysis.

As far as the back-analysis of the October 1954 event, two depths of the initial water table were considered, which correspond to a mean suction (along soil depth and over the whole study area) equal to 20 or 30 kPa, as indicated by Cascini et al. (2014) for September-October (period 1). The analyses were also extended to other cases to evaluate the effects of both a different soil suction which, in turn, affects the initial soil conductivity. Specifically, in a first set of cases, different depths of the initial water table were considered, corresponding to average suction equal to 10 or 40 kPa. In a second set of cases, distinct hydraulic properties of pyroclastic soil deposits were

Table 2 Input data for large-area analysis of landslides (Unit for duration: hour; Unit for suction: kPa; Unit for hydraulic conductivity: m/s; Unit for diffusivity: m2/s)

Case I Duration Suction^ Hydraulic Conductivity+ Diffusivity+

Parameters of Gardner’s curves RIGRS-unsaturated+ α (m-1) θr θs

1 63 8 14.59 * 1×10-5 5.9×10-5 6.3 0.20 0.66 2 31.5 16

3 63 8 16.43 * 1×10-5 5.9×10-5 6.3 0.20 0.66 4 31.5 16

5 63 8 20.13 ** 1×10-5 5.9×10-5 6.3 0.20 0.66 6 31.5 16

7 63 8 27.50 ** 1×10-5 5.9×10-5 6.3 0.20 0.66 8 31.5 16

9 63 8 38.58 *** 1×10-5 5.9×10-5 6.3 0.20 0.66 10 31.5 16

11 63 8 16.43 * 6×10-6 4.5×10-5 8 0.25 0.53 12 31.5 16

13 63 8 16.43 * 8×10-6 5.6×10-5 7 0.20 0.60 14 31.5 16

Notes: I, Rainfall intensity (mm/h); θr, Residual water content; θs, Saturated water content; ^, Initial suction at the ground surface; *, Medium suction; **, High suction; ***, Very high suction according to Cascini et al. (2014); +, Data from Sorbino et al. (2010).

J. Mt. Sci.(2015)12(4): 783-796

792

assumed, once again derived from Sorbino et al. (2010). The list of the most significant cases and input data are reported in Table 2. In all the cases, the rainfall intensity was lower than the saturated soil conductivity and the TRIGRS model assumed that the runoff was not generated at any cell of the DTM. This entails that each cell of DTM was computed as fully independent from the surrounding cells as either for the water supply from ground surface of the computation of the local factor of safety.

The calibration and validation of the TRIGRS model was twofold and concerned the capability of the model to reproduce: i) stable conditions for slopes before rainfall in the whole test area and ii) the location and the extent of slope instabilities that occurred in 1954 in the study area.

The results achieved for each case are herein discussed with reference to the number (N) of cells with a factor of safety (FS) ≤ 1.0. The ratio between the unstable simulated area (Aunst) and total extent of study area (Atot) was also evaluated. The global response of the study area to rainfall was compared to October 1954 field observations either for back-analysis of this event or to assess the severity of future scenarios.

3.2 Results

The calibration of the input parameters allowed the TRIGRS model to accurately simulate the stable conditions of the hillslopes before rainfall. In fact, only the 2% of the cells were evaluated as unstable before rainfall. This result could be explained in relation to local approximations of either the DTM or the soil cover map as well as to the local reinforcement due to vegetation not included into the model.

On the other hand, the results achieved for the simulation of the October 1954 event (cases 5 to 8; i.e. “high” suction equal to 20-30 kPa, as recorded in the field for the occurrence season) provided estimates of the extent of the unstable areas that were much smaller than the areas that failed during the event for both the selected rainfalls. A comparison is provided in Figure 6.

For suction in the "medium" range (cases 1 to 4), and "very high" range (cases 9 and 10), the results furnished an underestimation of the triggering areas of 1954 event, with the exception of

the cases with16 hours of rainfall. In these last cases, the unstable area was three times larger than the triggering areas of the 1954 event. The explanation is a combination of relative low suction and relative low rain intensity. A lower suction in the subsoil gives the soil a higher conductivity. The relative lower intensity means a lower loss of infiltrating water by run-off. These two factors are in favour of a rapid wetting of the soil profile and eventual rise of the groundwater. Thus, both factors contribute to slope instability.

These results outlined that the rainfall intensity and duration heavily affect the stability conditions of the slopes when the initial suction is low, but these rainfall characteristics have a smaller effect when the initial suction is higher than 20 kPa. In addition, the initial conditions of unsaturated soils play an important role in the slope stability conditions; in particular, for the same rainfall conditions: i) when the initial suction is "medium", the unstable areas are greater than in other cases; ii) when the initial suction is "high" or "very high", the global simulated area of instability is smaller (Figure 6). With reference to the soil hydraulic properties, the analyses showed a minor role of these parameters on the stability analyses (cases 11 to 14) within the analyzed range.

As far as the spatial distribution of the simulated unstable areas, Figure 7 shows the

Figure 6 Comparison between the slope instabilities area (Atot) reported in the inventory map of Figure 3 and the area (Aunst) where simulated factor of safety is lower than 1.0 and, for the cases listed in Table 2.

J. Mt. Sci.(2015)12(4): 783-796

793

simulation labeled as 1, 2, 5 and 6 in Figure 6 and Table 2. The limited agreement between the field evidence (Figure 3) and the simulated unstable areas (Figure 7) motivate the discussion of the results – obtained for different types of slope instability such as superficial soil erosion and landslides – which is developed in the following section.

4 Discussion

The erosion and landslide analyses were performed separately but they were both quantitative spatial-distributed analyses. Thus, in principle, the results achieved for any cell of the DTM can be integrated. In the paper, a simplified choice was made, i.e. to assume some threshold values for both types of analyses, then labeling any cell of the DTM as “eroded”, “failed” or “susceptible to both erosion and landslide”. A cell was considered “eroded” when the computed eroded soil thickness was higher than 5cm; a cell was computed as “failed” when the Factor of Safety (FS) was lower or equal to 1.0; when both the above

conditions are satisfied, the cell was labelled as “susceptible to both erosion and landslide”. This procedure implicitly assumed that the quality (or, equivalently, the uncertainty) of both the analyses was comparable.

The main results of the analyses showed that the study area may be affected by shallow landslides and soil erosion in different periods of the year depending on: i) rainfall characteristics, ii) soil suction and iii) soil cover. Figure 8 shows the results of a susceptibility analysis performed on the basis of the results of case 1 of Table 1 (for erosion) and cases 5 and 1 of Table 2 (for landslides). Particularly, a sub-basin was defined as “susceptible to erosion” where ≥ 13 cells are computed as eroded more than 5 cm, which corresponds to a mobilized volume of≥ 260 m3. In addition, a sub-basin was labeled “susceptible to landslide” where ≥ 13 cells are computed with a Factor of Safety (FS) ≤ 1.0, which correspond to 5200 m3 for a slip surface 1.0 m deep. Of course, depending on the simulation case, sub-basins were found as either susceptible either to erosion or to erosion and landslides. In the scenario of Figure 8a (corresponding to the limit between “medium” and “high” suction (20 kPa), only a few sub-basins were

Figure 7 Cell-by-cell spatial distribution of factor of safety for different cases (1, 2, 5 and 6) of Table 2.

J. Mt. Sci.(2015)12(4): 783-796

794

prone to landslides; while, lowering the suction to 15 kPa (Figure 8b), most of sub-basins were prone to both erosion and landslides.

Based on these results, it seems that the study area is more susceptible to soil erosion processes in the autumn season. The amount of the eroded material depends on the rainfall characteristics, soil erodibility and soil cover. When an extraordinary rainfall event occurs in Autumn, as happened on 25-26 October 1954, the eroded area and the mobilized material increase, causing a sudden increase of the sediment discharge at the outlet of the basins. The analyses also showed that the occurrence of shallow landslides depends on soil suction that assumes different values during the year. In particular, the study area is more susceptible to the triggering of shallow landslides when the soil suction is lower than 20 kPa (in Winter and in Spring).

In addition, for a past event, the simulated source areas of shallow landslides were fewer than those areas recorded during the event and the total soil volume mobilized during the event was found not to be exclusively related to the landslide occurrence. On the other hand, the zones with a simulated erosion thickness greater than 5 cm were comparable to the areas recorded in the field, where the rainfall intensity was assumed to be very high and soil cover characteristics assumed as spatially variable.

5 Conclusions

The paper dealt with a case study of unsaturated shallow deposits of loose pyroclastic (air-fall) volcanic soils of Southern Italy, repeatedly affected by erosion and landslides in special seasons. Two separate quantitative spatially distributed analyses – for erosion and landsliding – were performed, the results of which were later integrated at any cell of the DTM. In each analysis, the role of soil suction which relates to the meteorological seasons was explicitly taken into account.

The results of the paper were consistent with the literature. In particular, for a past catastrophic event in the study area, the simulated source areas of the shallow landslides were smaller than those observed in the field while the simulated eroded areas with thickness greater than 5 cm were comparable with the in-situ evidence, when the analysis took into account a high rainfall intensity and a spatially-variable soil cover use. More generally, a methodological contribution was provided about the analysis of different slope instability phenomena over a large area. The main added value to the literature was that the paper showed how the combination of large-area analysis may help understanding the dominant slope instability mechanisms.

Figure 8 Superposition of erosion and landslides analyses (a sub-basin is defined “susceptible to erosion” whether ≥ 13 cells are eroded ≥ 5 cm or “susceptible to landslide” whether ≥ 13 cells have FS≤1.0. a) superposition of case 1 of Table 1 and case 5 of Table 2 (suction about 20 kPa). b) superposition of case 1 of Table 1 and case 1 of Table 2 (suction about 15 kPa).

J. Mt. Sci.(2015)12(4): 783-796

795

Acknowledgement

The authors wish to thank the Basin Authority Campania Sud (ex DestraSele), which provided the

data necessary to develop this work and the PhD Programme in Civil and Environmental Engineering of the University of Salerno which provided the funding to develop the research.

References

Acharya G, Cochrane T, Davies T, Bowman E (2011) Quantifying and modeling postfailure sediment yields from laboratory-scale soil erosion and shallow landslide experiments with silty loess. Geomorphology 129: 49-58. DOI: 10.1016/j.geomorph. 2011.01.012.

Autorità di Bacino Destra Sele (2012) Available online at: http://www.autoritabacinodestrasele.it/(accessed on 2013-02-05)

Baum RL, Savage WZ, Godt JW (2008) TRIGRS-A Fortran program for transient rainfall infiltration and grid-based regional slope-stability analysis, version 2.0. US Geological Survey Open-File Report 2008–1159. Available online at: http://pubs.usgs.gov/of/2008/1159/(accessed on 2012-01-10)

Bilotta E, Cascini L, Foresta V, et al. (2005) Geotechnical characterization of pyroclastic soils involved in huge flowslides. Geotech Geol Eng 23: 365-402. DOI: 10.1007/ s10706-004-1607-3

Calvello M, Cascini L, Cuomo S, et al. (2012) Applicazione dei metodi di base ed intermedi all’areale delle piroclastiti (Application of basic and intermediate methods to the district of pyroclastic soils). In Criteri di zonazione della suscettibilità e della pericolosità da frane innescate da eventi estremi (piogge e sisma), Composervice S.r.l, Padova, Italy. pp 119-130 (In Italian)

Calvello M, Cascini L, Mastroianni S (2013) Landslide zoning over large areas from a sample inventory by means of scale-dependent terrain units. Geomorphology: 33-48. DOI: 10.1016/j.geomorph.2012.10.026

Cascini L, Cuomo S, Guida D (2008) Typical source areas of May 1998 flow-like mass movements in the Campania region, southern Italy. Engineering Geolology 96: 107-125. DOI: 10.1016/j.enggeo.2007.10.003

Cascini L, Cuomo S, Pastor M (2013a) Inception of debris avalanches: remarks on geomechanical modelling. Landslides 10(6): 701-711. DOI: 10.1007/s10346-012-0366-0

Cascini L, Cuomo S, Pastor M, Sacco C (2013b) Modelling the post-failure stage of rainfall-induced landslides of the flow-type. Canadian Geotechnical Journal 50(9): 924-934. DOI: 10.1139/cgj-2012-0375.

Cascini L, Cuomo S, Pastor M, et al. (2010) Modelling of rainfall-induced shallow landslides of the flow-type. ASCE’s Journal of Geotechnical and Geoenvironmental Engineering, 136(1): 85-98. DOI: 10.1061/(ASCE)GT.1943-5606.0000182

Cascini L, Sorbino G, Cuomo S, et al. (2014). Seasonal effects of rainfall on the shallow pyroclastic deposits of the Campania region (southern Italy). Landslides 11(5): 779-792. DOI: 10.1007/s10346-013-0395-3

Cascini L, Cuomo S, Ferlisi S, et al. (2009) Detection of mechanisms for destructive landslides in Campania region-southern Italy. In: Picarelli L, Tommasi P, Urciuoli G, et al. (Eds.), Rainfall-induced landslides: mechanisms, monitoring techniques and nowcasting models for early warning systems. Proceedings of the first Italian Workshop on Landslides, 8–10 June 2009 Naples, Italy. Studio Editoriale Doppia voce, Naples, Italy. vol 1, pp 43-51.

Chen, HX, Zhang, LM (2014) A physically-based distributed cell model for predicting regional rainfall-induced slope failures. Engineering Geology 176: 79-92. DOI: 10.1016/j.enggeo. 2014.04.011

Corine Land Cover IV livello (2006) Available online at: http://www.sinanet.isprambiente.it/it/sia-ispra/download-mais/corine-land-cover. (accessed on 2013-02-05)

Cruden DM, Varnes DJ (1996) Landslide Types and Processes. In: Landslides Investigation and Mitigation, Turner AK and Schuster RL (eds.), Transportation Research Board, Special report no. 247, National Research Council, National Academy Press, Washington DC, USA. pp 36-75.

Cuomo S, Della Sala M (2013) Rainfall-induced infiltration, runoff and failure in steep unsaturated shallow soil deposits. Engineering Geology 162: 118-127. DOI: 10.1016/j.enggeo. 2013.05.010.

Cuomo S, Della Sala M, Novità A (2015) Physically-based modeling of soil erosion induced by rainfall in small mountain basins. Geomorphology 243: 106-115, DOI: 10.1016/j.geomorph. 2015.04.019.

De Falco M (2011) Approcci innovativi per l'identificazione del degrado per erosione idrica in ambienti agro-forestali mediterranei (Innovative approaches for the identification of soil degradation due to erosion in Mediterranean sites). PhD dissertation. University Federico II of Naples, Italy. p 294. (In Italian)

De Luca C, Furcolo P, Rossi F, et al. (2010) Extreme rainfall in the Mediterranean. Proc. Intern. Workshop on “Advances in statistical hydrology”, STAHY 2010, Taormina, Italy, May 23-25, 2010. p 11. Available online at: http://www. risorseidriche.dica.unict.it/Sito_STAHY2010_web/proceedings.htm(accessed on 2013-03-10)

Della Sala M (2014) Genesis and mechanisms of rainfall-induced hyperconcentrated flows in granular soils. PhD dissertation at the University of Salerno, Fisciano Italy. p 258 .

Esposito E, Porfido S, Violante C, et al. (2003) Disaster induced by historical floods in a selected coastal area (Southern Italy). In: Thorndy VR, Benito G, Barr Iendos M, et al. (eds.), Proceedings of the PHEFRA (Palaeofloods, Historical Data and Climatic Variability), International Workshop, Barcelona. CSIC-Centro de CienciasMedioambientales Serrano, Madrid, Spain. pp 143-148.

Fell R, Corominas J, Bonnard C, et al. (2008) Guidelines for landslide susceptibility, hazard and risk zoning for land use planning. Engineering Geolology 102(3-4): 85-98. DOI: 10.1016/j.enggeo.2008.03.022.

Foster GR (1982) Modeling the erosion process. In: Haan CT, Johnson HP, Brakensiek DL (eds.), Hydrologic modeling of small watersheds. American Society of Agricultural Engineers Monograph, pp 297-380.

Fredlund DG, Morgenstern NR, Widger RA (1978) The shear strength of unsaturated soils. Canadian Geotechnical Journal 15(3): 313-321. DOI: 10.1139/t78-029

Frosini P (1955) Il nubifragio di Salerno del 25-26 Ottobre 1954 (The 25th – 26th October 1954 rainstorm in Salerno). Giornale Genio Civile (Journal of Civil Engineering) 3-4: 179-188. (In Italian)

Guadagno FM, Forte R, Revellino P, et al. (2005) Some aspects of the initiation of debris avalanches in the Campania Region: the role of morphological slope discontinuities and the development of failure. Geomorphology 66: 237-254. DOI: 10.1016/j.geomorph.2004.09.024

J. Mt. Sci.(2015)12(4): 783-796

796

Hessel R, Jetten VG (2007) Suitability of transport equations in modelling soil erosion for a small loess plateau catchment. Engineering Geology 91(1): 56-71. DOI: 10.1016/j.enggeo. 2006.12.013

Hu MJ, Pan HL, Wei HZ, et al. (2013) Landslides & debris flows formation from gravelly soil surface erosion and particle losses in Jiangjia Ravine. Journal of Mountain Science 10(6): 987-995. DOI: 10.1007/s11629-012-2526-z.

Hutchinson JN (1988) In: Bonnard C (ed.), Morphological and geotechnical parameters of landslides in relation to geology and hydrogeology. State of the art report, vol 1. Proceedings of the 5th International Symposium on Landslides, Lausanne, Switzerland. pp 3-35.

Hutchinson JN (2004) Review of flow-like mass movements in granular and fine-grained materials. Proc. of the Int. Workshop “Flows 2003 - Occurrence and Mechanisms of Flows in Natural Slopes and Earthfill”. pp 3-16.

Iverson RM (2000) Landslide triggering by rain infiltration. Water Resource Research 36(7): 1897-1910.

Jain M K, Kothyari U C (2000) Estimation of soil erosion and sediment yield using GIS. Hydrological Sciences Journal 45(5): 771-786. DOI: 10.1029/2000WR900090

Li XS, Wu BF, Zhang L (2013) Dynamic monitoring of soil erosion for upper stream of Miyun Reservoir in the last 30 years. Journal of Mountain Science 10(5): 801-811. DOI: 10.1007/s11629-013-2559-y.

Merritt WS, Latcher RA, Jakeman AJ (2003) A review of erosion and sediment transport models. Environmental Modelling and Software 18: 761-799. DOI: 10.1016/S1364-8152(03)00078-1

Moore ID, Burch GJ (1986) Modeling erosion and deposition: Topographics effects. Transaction ASAE 29: 1624-1640. DOI: 10.13031/2013.30363

Rahardjo H, Lee TT, Leong EC, et al. (2004) A flume for assessing flux boundary characteristics in rainfall-induced slope failure studies. Geotechnical Testing Journal 27 (2): 145-153.

Richards LA (1931) Capillary conductions of liquids through porous mediums. Journal of Applied Physics 1: 318-333.

Savage WZ, Godt JW, Baum RL (2004) Modeling time-dependent areal slope stability. In: Lacerda WA, 582 Erlich M, Fontoura SAB, Sayao ASF (eds.), Landslides-evaluation and stabilization. Proceedings of 9th International symposium on Landslides. Balkema Editor, Rotterdam, The Netherlands. Vol 1, pp 23-36.

Sorbino G, Foresta V (2002) Unsaturated hydraulic characteristics of pyroclastic soils. In: Jucà JFT, de Campos TMP, Marinho FAM (eds.), Unsaturated soils. Proceedings of

the 3rd international conference on unsaturated soils, UNSAT 2002, 10–13 March 2002, Recife (Brazil). Swets & Zeitlinger Publishers, Lisse, The Netherlands. Vol 1, pp 405-410.

Sorbino G, Sica C, Cascini L, Cuomo S (2007) On the forecasting of flowslides triggering areas using physically based models. In: Schaefer VR, Schuster RL, Turner AK (eds.), Proc. First North American Landslide Conference, 3-8 June 2007 Vail, Colorado (USA), AEG Special Publication 23, ISBN: 978-0- 975-4295-3-2. pp 305-315.

Sorbino G, Sica C, Cascini L (2010) Susceptibility analysis of shallow landslides source areas using physically based models. Natural hazards 53(2): 313-332. DOI: 10.1007/ s11069-009-9431-y

Tang WJ, Liu HH, Liu BY (2013) Effects of gully erosion and gully filling on soil degradation in the black soil region of Northeast China. Journal of Mountain Science 10(5): 913-922. DOI: 10.1007/s11629-013-2560-5.

Terranova O, Antronico L, Coscarelli R, et al. (2009) Soil erosion risk scenarios in the Mediterranean environment using RUSLE and GIS: an application model for Calabria (southern Italy). Geomorphology 112(3): 228-245. DOI: 10.1016/j.geomorph.2009.06.009

Tessitore S, Di Martire D, Martino R, Calcaterra D (2011) Comparison of 2D models for the simulation of the October 1954 debris flow and flood event at Maiori (Campania region, Italy). Italian Journal of Engineering Geology and Environment 1: 513-522. DOI: 10.4408/IJEGE.2011-03.B-057.

Toy TJ, Foster GR, Renard KG (2002) Soil Erosion: Process, Prediction, Measure and Control. John Wiley and Sons, Inc. New York, USA. p 338.

Tranfaglia G, Braca G (2004) Analisi idrologica e meteorologica dell’evento alluvionale del 25-26 Ottobre 1954: confronto con le serie storiche e valutazione del periodo di ritorno di eventi analoghi. (Hydrological analysis of the 25th–26th October 1954 rainstorm: comparison of the hystorical series and the return periods of similar events). Pubblicazione GNDCI n. 2870, ISBN 88-88885-03-X. pp 295-348. (In Italian)

Zhang J, Jiao JJ, Yang J (2000) In situ infiltration studies at a hillside in Hubei Province, China. Engineering Geology 57: 31-38. DOI: 10.1016/S0013-7952(99)00126-X

Wischmeier WH (1959) A rainfall erosion index for a universal soil loss equation. Soil Science Society of America Journal, 23(3): 246-249. DOI: 10.2136/sssaj1959.036159950023000 30027x

Wischmeier WH, Smith DD (1978) Predicting Soil Erosion Losses: A Guide to Conservation Planning. USDA Agricultural Handbook No. 537. p 58.