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O R I G I N A L P A P E R

Susceptibility analysis of shallow landslides source areas

using physically based models

Giuseppe Sorbino Carlo Sica Leonardo Cascini

Received: 15 May 2008 / Accepted: 15 July 2009 / Published online: 2 September 2009 Springer Science+Business Media B.V. 2009

Abstract Rainfall-induced shallow landslides of the flow-type involve different soils,

and they often cause huge social and economical disasters, posing threat to life and

livelihood all over the world. Due to the frequent large extension of the rainfall events,

these landslides can be triggered over large areas (up to tens of square kilometres), and

their source areas can be analysed with the aid of distributed, physically based models.

Despite the high potential, such models show some limitations related to the adopted

simplifying assumptions, the quantity and quality of required data, as well as the use of aquantitative interpretation of the results. A relevant example is provided in this paper

referring to catastrophic phenomena involving volcaniclastic soils that frequently occur in

southern Italy. Particularly, three physically based models (SHALSTAB, TRIGRS and

TRIGRS-unsaturated ) are used for the analysis of the source areas of huge rainfall-induced

shallow landslides occurred in May 1998 inside an area of about 60 km2. The application is

based on an extensive data set of topographical, geomorphological and hydrogeological

features of the affected area, as well as on both stratigraphical settings and mechanical

properties of the involved soils. The results obtained from the three models are compared

by introducing two indexes aimed at quantifying the ‘‘success’’ and the ‘‘error’’ provided

by each model in simulating observed source areas. Advantages and limitations of the

adopted models are then discussed for their use in forecasting the rainfall-induced source

areas of shallow landslides over large areas.

Keywords Shallow landslides Source area Triggering mechanism

Landslide susceptibility mapping Volcaniclastic soils

G. Sorbino

C. Sica (&)

L. CasciniDepartment of Civil Engineering, University of Salerno, Salerno, Italy

e-mail: [email protected]

G. Sorbino


L. Cascini


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DOI 10.1007/s11069-009-9431-y

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1 Introduction

Shallow landslides of the flow-type in granular soils represent one of the most insidious

landslide phenomena (Hungr et al. 2001) because of their high potential of causing damage

and human losses. This is due to the scarcity of warning signs in the pre-failure stage whenmonitoring systems are not available; the collapse and the high velocities in the post-failure

phase and the increase in the mobilised volumes during the downhill path, due to the

erosion of further soil and/or rock masses.

These landslides can involve different soils whose mechanical characteristics vary

significantly with differences in water content, sediment size and sorting. They can be

triggered by different factors, either natural or related to human activities; among

natural factors, rainfall is certainly one of the most frequent causes of landslides

occurrence. Significant examples are provided by multiple shallow phenomena peri-

odically occurring in New Zealand (Crozier 2005), in the Seattle area—Washington

(Baum et al. 2005), in California (Coe and Godt 2001; Coe et al. 2004), as well as in

Campania—southern Italy (Fiorillo and Wilson 2004; Guadagno and Revellino 2005;

Pareschi et al. 2000).

The relevance of consequence makes the assessment of the landslides susceptibility a

fundamental issue towards the forecasting of these phenomena. To this aim, different

conceptual assumptions, operational tools and techniques can be used at different map

scales, in relation to the available data set and the pursued aims (Fell et al. 2008a).

At intermediate-large scale (Fell et al. 2008a, 2008b), a promising approach for the

susceptibility analysis of the shallow landslides source areas relies on the use of the so-

called physically based models for their capability in reproducing the physical processesgoverning the landslides occurrence. Moreover, their general grid-based structure and the

wide availability of Geographic Information Systems provide a convenient framework that

allows the analysis over broad areas.

Physically based models generally couple a hydrologic model, for the analysis of pore-

water pressure regime, with an infinite slope stability model for the computation of the

Factor of Safety. Different types of distributed models have been proposed in the scientific

literature (e.g. Baum et al. 2002; Crosta and Frattini 2003; Montgomery and Dietrich 1994;

Pack et al. 1998; Savage et al. 2004; Terlien et al. 1995; van Asch et al. 1999; Ward et al.

1982; Wu and Sidle 1995) and, among them, those that use analytical solutions for the pore

pressure response to rainfall have the potential for the analysis of shallow landslide sourceareas.

These models rely on several simplifying assumptions that limit their applicability.

Particularly, steady or quasi-steady models (e.g. Montgomery and Dietrich 1994; Wu and

Sidle 1995) are limited to few unrealistic situations related to both rainfall characteristics

and in situ conditions (Iverson 2000). Transient models, used either in saturated or

unsaturated conditions of soils, are able to improve the effectiveness of susceptibility

analysis, accounting for the transient effects of varying rainfall on slope stability conditions

(e.g. Baum et al. 2002, 2008; Crosta and Frattini 2003; Iverson 2000; Savage et al. 2004),

but they generally need abundant and accurate spatial information. Moreover, they aresensitive to some of the required input data such as hydraulic properties of soils, initial

steady-state groundwater conditions and soil depths, whose correct evaluation is often

possible only using empirical models or inverse deterministic analyses (Godt et al. 2008;

Salciarini et al. 2006; Sorbino et al. 2007).

In order to achieve significant results, the application of physically based models

requires a deep understanding of the conceptual assumptions, the accurate definition over

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broad regions of the in situ conditions of soils, of the pore pressure regime characteristics,

as well as of the different triggering mechanisms. Moreover, a critical interpretation of

results needs a methodology based on the use of quantitative indexes (Crosta and Frattini

2003; Godt et al. 2008; Salciarini et al. 2006; Sorbino et al. 2007).

Accordingly, in this paper a relevant example is presented with reference to an area inCampania Region (southern Italy) of about 60 km2, systematically affected during the

centuries and in recent times by rainfall-induced shallow landslides of flow-type involving

volcaniclastic covers.

The study area and the occurred phenomena are accurately described together with the

available data set concerning the geological, geomorphological, hydrogeological and

geotechnical features. Then, the source areas of the most recent and catastrophic shallow

landslides of flow-type event occurred on May 1998 are simulated through the application

of three physically based models developed in a GIS framework: SHALSTAB (Mont-

gomery and Dietrich 1994), TRIGRS (Baum et al. 2002) and TRIGRS-unsaturated (Savage

et al. 2004).

Finally, the results obtained from the three models are compared by applying a set of

quantitative indexes, and a discussion is provided in order to highlight potential and

limitations of these models for the forecasting of the potential source areas.

2 The study area and the available data set

The Campania Region has systematically been affected in the last centuries by shallow

landslides of the flow-type occurring in volcaniclastic covers (Cascini et al. 2008a). Thesecovers derive from air-fall deposition of pyroclastic material originating from Late Qua-

ternary-Holocene explosive activity of Somma-Vesuvius and, subordinately, from Campi

Flegrei and Roccamonfina volcanic apparata. The volcaniclastic soils cover three main

distinct geoenvironmental contexts (Calcaterra et al. 2004; Cascini et al. 2005b) over an

area of about 3,000 km2 (Fig. 1a).

Fig. 1 a Air-fall pyroclastic deposits in the Campania region (modified after Cascini et al. 2008a):

1 carbonate bedrock; 2 tuff and lava deposits; 3 flysch and terrigenous bedrock; 4 alluvial and continental

deposits; 5 volcanic complexes; 6 isopachs of the pyroclastic products from the main eruptions. b Victims in

the Campania region caused by flow-type landslides in the period 1570–1998 (modified after Cascini et al.

2005b)

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As testified by about 700 events occurred during the last centuries (Cascini et al. 2008b),

shallow landslides of the flow-type frequently involve all the three contexts, in which

different features and consequences are assumed (Fig. 1). Among these, the most

destructive ones mainly occurred in the southern part of the region, where volcaniclastic

soils cover limestone bedrock (Brancaccio et al. 1999; Calcaterra et al. 2004; Cascini et al.2008b; Celico and Guadagno 1998; Di Crescenzo and Santo 2005; Guadagno et al. 2005;

Olivares and Picarelli 2001).

In this area, the most recent and catastrophic event occurred on 5–6 May 1998 and

caused 159 casualties and huge damages to four little towns (Bracigliano, Quindici, Sarno

and Siano) located at the toe of the so-called Pizzo d’Alvano massif (Fig. 2). According to

Cascini (2004), shallow landslides were triggered by a heavy rainfall storm from April 27

to May 5 characterised by a cumulated rainfall value of 300 mm, of which the 80% felt

during the last two days. These landslides rapidly propagated downslope and increased

their initial volume through the mobilisation and/or erosion of in-place soils and the

outermost portion of fractured bedrock, producing a total mobilised volume estimated of

about 2.0 9 106 m3. According to the classification proposed by Hungr et al. (2001), the

May 1998 landslides along the Pizzo d’Alvano slopes can be defined as complex landslides

as they showed characteristics that embrace, at least, three rapid flow type movements:

flowslides, debris flows and debris avalanches. As the present study mainly focuses on the

analysis of the source areas, May 1998 landslides will be referred to shallow landslides of

the flow-type from now on in this paper.

2.1 Geological, geomorphological and hydrogeological settings

The Pizzo d’Alvano massif has summit plains, and relatively steep slopes characterised by

deeply carved and rectilinear valleys and ravines (Fig. 3). These slopes are linked to the

lowland by gently piedmont alluvial fans of various ages and shapes. The relief is con-

stituted by a carbonate ridge built-up on a limestone, dolomitic-limestone and, subordi-

nately, marly-limestone lithological sequence, several hundred meters thick and Lower to

Upper Cretaceous aged (D’Argenio et al. 1973).

Fig. 2 a Overview of the Pizzo d’Alvano massif with the main May 1998 shallow landslides of flow-type

events; b daily rainfall recorded from 1 January to 1 June 1998 (the arrow indicates the landslides

occurrence); c an example of the occurred phenomena and (d) of the produced damage

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Both the high plains and the slopes of the massif are widely covered by volcaniclastic

soils, both as primary air-fall deposits and re-worked deposits (Rolandi 1979). The primary

deposits are located along the slopes, and they have thickness generally less than 5 m.

Their stratigraphical settings show a highly spatial variability characterised by uneven

sequences of pumiceous and ashy soil layers, sometimes with the presence of paleosoil

horizons. The deposits, re-worked by sheet-wash and mass-wasting processes, mainly

consist of debris and colluvium with depths up to 20 m. They can be found in the mor-

phological concavities, in the karstic depressions and at the toe of the valleys where the

presence of remoulded primary pyroclastic soils testifies the systematic occurrence of

landslides of the flow-type during the last centuries. Cascini and Sorbino (2004) reported in

detail about the typical stratigraphic columns of volcaniclastic soils for the different sectors

of the massif.

As for the morphological setting, the main features of the massif are shown in Fig. 3.

These morphological features can be included in the three hill slopes models, which arecharacterised by four main slope segments from the top downwards: the summit, the

shoulder slope, the backslope and the main channel. Referring to Cascini et al. (2008b) for

a detailed description of these models, it is worth noting that in all the models the summit

is not affected by natural geomorphic processes; the shoulder slope is influenced by erosive

processes; and the backslope is characterised by the presence of particular morphological

Fig. 3 Geomorphological map: 1 summit with ridges (r ) and endoreic plain (e); 2 inner gorge; 3 head of

valley; 4 open slope; 5 zero order basin; 6 channel (transient and main); 7 flank of channel; 8 bedrock scarp;9 nose; 10 triangular facet slope; 11 talus-debris slope and 12 alluvial fan (after Cascini et al. 2008a)

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concavities formed by paleo-drainage networks of the limestone bedrock the so-called

Zero Order Basins (zobs) (Cascini et al. 2008b; Dietrich et al. 1986; Guida 2003).

As it concerns the hydrogeological features, the massif structure is highly fractured and

karsified with a suspended groundwater flow system mainly located in the upper part of the

slopes. Along the hill slopes, perennial, seasonal and temporary springs are observed, andthey can generally be associated to the preferential flow paths allowed by sets of con-

vergent fractures forming (hierarchic and nested) wedge-like hydrostructures (Cascini et al.

2005b, 2008b).

2.2 Triggering mechanisms

On the basis of the geological, geomorphological and hydrogeological features, as well as

the anthropogenic factors, Cascini et al. (2005a, 2008b) recognised six different triggering

mechanisms characterising the source areas of the May 1998 landslides, respectively,

named M1, M2, M3, M4, M5 and M6 (Fig. 4). The M1 mechanism essentially occurred

inside colluvial hollows associated to zobs (Dietrich et al. 1986; Guida 2003) affected by

convergent subsuperficial groundwater circulation and temporary springs coming from the

bedrock towards the volcaniclastic covers. The mechanism M2 originated inside triangular-

shaped source areas, mainly in the upper portions of open slopes associated to outcropping

or buried bedrock scarps. The mechanism M3 produced complex-shaped landslides related

to laterally enlarging local instabilities, strictly influenced by anthropogenic elements such

as tracks. The mechanism M4 mainly occurred at the head of main channel originating

multiple landslides arranged as a grape. These mechanisms are strictly related to heavy

superficial water and contribute to the evolution of the head of valleys through the pro-gressive retrogression of the transient channel. The mechanism M5 triggered the soils

located along open slopes with a convex longitudinal profile resulting in sources areas with

shapes elongated in the maximum slope directions. Finally, the mechanism M6 developed

at the base of convex–concave hill slopes, in correspondence of natural or man-induced

breaks of the slope angle, involving limited volume of the soil covers.

2.3 Geotechnical data set

In order to analyse the identified triggering mechanisms by means of geotechnical models,

in situ and laboratory investigations were carried out (Cascini et al. 2005b) on: thestratigraphical conditions of the source areas; the mechanical properties of volcaniclastic

soils in both saturated and unsaturated conditions and the soil suction regime during dry

and wet seasons.

With reference to the stratigraphical conditions, the in situ investigations comprised

seismic refraction prospects and hand-dug shafts. The collected data revealed highly

variable stratigraphic conditions at the individual slope scale and allowed the identification

of quite homogeneous stratigraphic conditions within the four sectors of the massif,

respectively, facing the towns of Bracigliano, Quindici, Sarno and Siano (Fig. 2); (Cascini

and Sorbino 2004; Cascini et al. 2005a; Sorbino 2005).Physical and mechanical properties of the soils were obtained through an extensive

laboratory-testing programme on undisturbed and remoulded samples. Referring to Sor-

bino and Foresta (2002) and Bilotta et al. (2005) for a detailed description of both the

methodologies and experimental procedures, the main findings concerning the hydraulic

and shear strength properties of pyroclastic soils are briefly summarised in this article

(Fig. 5).

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The hydraulic properties of the ashy soils in saturated conditions were investigated by

means of conventional permeameter tests. In the unsaturated conditions, three different

laboratory equipments were utilised: Suction Controlled Oedometer, Volumetric Pressure

Plate Extractor and Richards Pressure Plate (Sorbino and Foresta 2002). In saturated

conditions, the estimated values of hydraulic conductivity were found to range from a

minimum of 5.0 9 10-6 m/s to a maximum of 4.8 9 10-5 m/s. For the pumice layers,

the data available in literature (Bilotta et al. 2005) for soils of analogous origin providesaturated hydraulic conductivity ranging between 1.0 9 10-5 m/s and 1.0 9 10-2 m/s.

As far as the hydraulic properties under unsaturated conditions are concerned, the

experimental values of volumetric water content and hydraulic conductivity are both

plotted against suction in Fig. 5b–c. As for the unsaturated hydraulic characteristics of

the pumice soils, they were determined numerically, using empirical relationships based

Fig. 4 Schematic of the typical triggering mechanisms for the May 1998 shallow landslides of flow-type:

1 bedrock, 2 volcaniclastic deposit, 3 track and 4 spring from bedrock (modified after Cascini et al. 2008a)

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on their grain size distribution (Fig. 5a). The saturated shear strength envelopes for ashy

soils provided effective friction angles ranging from 32 to 41 and effective cohesion

ranging from 0 to 5 kPa (Fig. 5d). The unsaturated shear strength was investigated onundisturbed ashy specimens by means of direct shear tests, as well as triaxial tests,

respectively, at different water contents and at variable applied suctions, in order to

reproduce the different in situ conditions during the year. The obtained results clearly

show a non-linear envelope of the shear strength with respect to suction, with the angle

of shearing resistance ranging between 20 and 30 (Bilotta et al. 2005).

Finally, soil suction regime characteristics were identified by means of in situ suction

data collected, from November 1999 to April 2002, at sites mainly located in the upper part

of the slopes (Cascini and Sorbino 2004). Suction data were taken at depths from the

ground surface ranging from 0.2 m to 4.0 m, using ‘‘Quick-Draw’’ portable tensiometers

and ‘‘Jetfill’’ in-place tensiometers. Collected data reveal that suction vary in a quitenarrow range, with minimum values of 1–2 kPa and maximum values of 65 kPa,

regardless of the measurement site, the depth and the rainfall regime. Analyses performed

on the whole suction data set (Cascini and Sorbino 2004) have also revealed that monthly

average suction values have time trend independent of the measurements site and related

only to the depth below the ground surface.

3 The analysis of May 1998 shallow landslides of flow-type

3.1 Physically based models

In order to simulate the source areas of May 1998 shallow landslide phenomena, three

physically based models SHALSTAB, TRIGRS and TRIGRS-unsaturated were used.

Referring to the related papers (Montgomery and Dietrich 1994; Baum et al. 2002; Savage

Fig. 5 Physical and mechanical properties of volcaniclastic soils: a grain size distribution; b, c soil water

characteristic curves and d shear strength of the main ashy soil classes (modified after Sorbino and Foresta

2002; Bilotta et al. 2005)

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et al. 2004) for the detailed description of the models, in the following a brief illustration of

their main features is provided.

For each cell, the selected models assume the soil as homogeneous and characterised by

a constant thickness, constant values of soil hydraulic conductivity and soil shear strength;

the local factor of safety is computed by means of the infinite slope stability model. Thesemodels differ in the conceptual assumptions adopted in the calculation of pore-water

pressures regime and, consequently, in the input data requirements.

SHALSTAB assumes that rainfall infiltration is in equilibrium with the steady-state,

saturated water flow parallel to the slope surface, above an impervious boundary. For each

cell, it considers the steady-state discharge equation as the product of the infiltration rate

and a ‘‘geometric contributing area’’, representing the upslope area that determines the

subsurface flux through the considered cell. The steady-state discharge is combined with a

general form for slope-parallel groundwater flow to estimate the relative water table depth

and, as a consequence, the relative pore-water pressure. For each grid cell, SHALSTAB

assumes constant thickness, hydraulic, physical and mechanical characteristics of the soil.

The TRIGRS model performs transient seepage analysis using the linearised solution of

Richards’ equation proposed by Iverson (2000) and extended by Baum et al. (2002) to the

case of impermeable bedrock located at a finite depth. The ground-water flow field is

modelled by superposition of a steady component and a transient component. The TRIGRS-

unsaturated model is able to predict pore-water pressure regime in unsaturated/saturated

conditions, coupling the simple analytic solution for transient unsaturated infiltration

proposed by Srivastava and Yeh (1991) to the original TRIGRS ’ equation (Baum et al.

2008; Savage et al. 2004). The soil water characteristic curves that the model adopts for the

unsaturated zone are those proposed by Gardner (1958). For each cell, both TRIGRS models furnish the safety factors at different depths and time intervals, and they use also a

simple method for routing of surface run-off from cells that have excess surface water (i.e.

where the rainfall intensity and upslope run-off exceed the saturated hydraulic conductivity

of the soil to adjacent down-slope cells where it can either infiltrate or flow farther

downslope. This partitioning and routing of excess rainfall is done instantaneously and

does not take into account the time-lag associated with open-channel flow dynamics.

Application of TRIGRS models requires the user to specify the initial steady ground-

water flow field and, from an operational point of view, they can take into account the

spatial heterogeneity of the in situ stratigraphical conditions and soil properties, allowing

the user to consider different values of soil characteristics in the cell.

3.2 Input data and analyses

For the back-analysis of May 1998 shallow landslides, the study area was divided into four

sectors (respectively, named Bracigliano, Quindici, Sarno and Siano) characterised by

quite homogeneous in situ conditions and soil properties (Table 1). With reference to these

sectors, the input data were derived directly from the available data set or through indirect

analyses. Particularly, a detailed Digital Terrain Model (3 m 9 3 m cells) was adopted to

describe the landscape topography of the study area prior to the landslide events. The DTMwas derived from interpolation of contour lines and elevation points of topographical map

at 1:5,000 scale produced in the early 1980s by the governmental agency ‘‘Cassa per il

Mezzogiorno’’ (Cascini et al. 2005b).

For the SHALSTAB model, the cover depths were assumed constant inside each sector

while, for both TRIGRS models, different cover depths were considered, in agreement with

the field data.

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Particularly, variable values of soil thickness values were derived from interpolation of the field data collected after the May 1998 events (Cascini et al. 2005b) and geomor-

phological analyses.

As for the mean values of the hydraulic conductivity and diffusivity, their selection was

based on the following indirect procedure. Three different infinite slope schemes (Sorbino

2005), representative of the stratigraphic conditions inside the above sectors, were con-

sidered (Fig. 6). Referring to these schemes, the transient rainfall-induced pore pressures

regime during the period 1 March 1998–5 May 1998 was analysed by using the finite

element code SEEP/W (Geo-Slope 2005), which solves the Richards’ equation. Referring

to Sorbino (2005) for a detailed description of the analyses, the geometric features of the

schemes are illustrated in the upper part of Fig. 6. The hydraulic properties were derived

Table 1 Parameters used for the modelling (constant values of soil unit weight, effective cohesion, and

friction angle were assumed respectively equal to 15 kN/m3, 5 kPa , and 38)

Sector Hydraulic

conductivity

k (m/s)

Soil depth

hSHALSTAB (m)

Diffusivity

DTRIGRS (m2 /s)

Parameters of Gardner’s curvesTRIGRS-unsaturated

a

(m-1)

Residual Water

Content hr

Saturated Water

Content hs

Sarno 1.0 9 10-5 2.65 5.9 9 10-5 6.3 0.20 0.66

Siano 8.0 9 10-6 2.80 5.6 9 10-5 7 0.20 0.60

Bracigliano 6.0 9 10-6 2.00 4.5 9 10-5 8 0.25 0.53

Quindici 6.0 9 10-6 2.25 4.5 9 10-5 8 0.25 0.53

Fig. 6 Pore-water pressure profiles obtained with the SEEP/W , TRIGRS and TRIGR-unsaturated codes:

(from the top to the bottom) the analysed schemes, F.E.M . versus TRIGRS , and F.E.M. versus TRIGRS-

unsaturated

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from the results of the laboratory tests (Fig. 5b, c) while rainfall intensities recorded during

the analysed period were assumed as boundary conditions at the slope surface. The same

schemes were analysed using TRIGRS and TRIGRS-unsaturated with different values of

the hydraulic properties varying in the range adopted for the finite element analyses.

Finally, the selected values of these properties were those providing the best fit of the porepressure distributions obtained through the two TRIGRS and SEEP/W codes (Fig. 6).

In details, for both models, the middle graphs of Fig. 6 show the adopted initial con-

ditions and the vertical distributions of the pore pressures obtained, respectively, by means

of TRIGRS and TRIGRS-unsaturated . Particularly, all the graphs highlight that the selected

parameters allow the TRIGRS model to define pore pressure values similar to those

computed by SEEP/W exclusively in the lower part of the schemes, characterised by the

complete saturation of the soil, while TRIGRS-unsaturated is able to describe the pore

pressure regime along the entire profile with good agreement.

As far as the analyses over large areas are concerned, TRIGRS and TRIGRS-unsaturated

boundary conditions were represented by hourly rainfall intensities recorded on the 4–5

May 1998 and characterised by a cumulative value of about 240 mm while, for the

SHALSTAB model, a critical rainfall intensity was adopted equal to 5 mm/day, corre-

sponding to the mean rainfall intensity during the 10 months before the landslide event.

This period was determined according to Iverson (2000) who evidenced that the conceptual

assumptions of a steady-state flow model are realistic only if the duration of the rainfall

event is much longer than a reference time, defined as the ratio between a representative

value of the contributing area and the saturated hydraulic diffusivity. For the Pizzo

d’Alvano massif, the hydraulic diffusivity was assumed equal to the mean value of the

characteristic saturated diffusivities in Table 1. The representative-contributing area wasassumed equal to the arithmetic mean of the contributing areas. These latter were com-

puted as the geometric mean between the contributing areas at both the scar and the toe of

each source area (Fig. 7).

As regards TRIGRS initial conditions, each sector was characterised by different initial

water table depths, providing mean suction values in the range of 0–10 kPa at the bedrock,

in agreement with the suction measurements (Cascini and Sorbino 2004). Particularly, the

water table configuration obtained by SHALSTAB for the critical steady-state intensity

characterising the period antecedent the events was modified to provide mean suction

values in the range of available suction measurements. The steady-state suction distribu-

tions used to compute mean initial suction values for TRIGRS and TRIGRS-unsaturated

Fig. 7 Procedure used to

compute the reference

contributing area ( A)

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were assumed, respectively, linear and exponential, according to the assumptions of both

the models. In the adopted procedure, the use of SHALSTAB allowed to take the conver-gence of subsurface flows during the period antecedent the events into account for the

initial conditions of both TRIGRS models.

In order to quantify the results of the two models and evaluate their relative efficacy in

the back-analysis of the May 1998 source areas, two indexes, respectively, named ‘‘success

index’’ (SI ) and ‘‘error index’’ (EI ), were defined (Sorbino et al. 2007). For each source

area (Fig. 8), the SI is the portion (in percentage) of the observed source area computed as

unstable by the models. The EI represents, for each mountain basin, the percentage ratio

between the areas computed as unstable located outside the observed source areas ( Aout ),

and the area of the basin not affected by triggering phenomena ( Astab). In order to evaluate

the efficacy of models for the whole area of Fig. 2, mean quantities of the earlier-men-tioned indexes (SI m and EI m) were also defined. SI m represents the mean value of SI

referred to the number of the source areas, while EI m is the mean value of EI referred to the

number of the mountain basins.

3.3 Results

The most significant scenarios resulting from SHALSTAB and TRIGRS applications are

illustrated in Figs. 9–11 together with the landslide shapes of the May 1998 event. Par-

ticularly, Fig. 9 depicts the unstable cells computed by SHALSTAB, corresponding to

critical rainfall intensity of 5 mm/day while, for the TRIGRS models, Figs. 10 and 11 show

the computed unstable areas at the estimated time of occurrence of the 1998 landslides,

corresponding to the initial mean suction value of 5 kPa. The figures clearly show the

different source areas provided by the three used models.

Particularly, also assuming the steady-state rainfall intensity equivalent to the May 1998

rainfall event, the SHALSTAB model furnishes more unrealistic scenarios than TRIGRS .

In order to quantify such differences, Fig. 12 shows the results provided by the models

for the whole study area, in terms of the quantitative indexes of Fig. 8. In details,

SHALSTAB provides the highest value of SI m (77%) that, however, is associated to a very

high value of EI m (38%) corresponding to a computed unstable area all over the Pizzod’Alvano massif about 10 times larger than the observed value of the source areas. From

the same figure, it can also be noted that, for values of EI m lower than 38%, TRIGRS gives

more satisfactory results, as it systematically provides higher values of SI m than those

obtained by SHALSTAB. The same figure shows the values of ‘‘Success’’ and ‘‘Error’’

indexes computed for TRIGRS-unsaturated model, evidencing an increase in the values of

Fig. 8 Definition of quantitative indexes

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‘‘Success’’ and a decrease in ‘‘Error’’ with respect to the above models, for every assumed

initial condition.

However, among the scenarios outlined with the two TRIGRS codes (Figs. 12 and 13),

the best results in terms of Success–Error indexes are certainly represented by those

obtained for initial conditions providing mean suction values in the range of 5–10 kPa. It

should be noted that these suction values are the same that were used by Cascini et al.

(2005a) for the best back-analysis of a shallow landslide occurred inside the sample area.

For these initial conditions, the EI m values correspond to a computed unstable area all over

the Pizzo d’Alvano massif of about twice the extension of the observed source areas. As for

the number of source areas, TRIGRS codes provide an estimation of about 20–30% greaterthan the observed ones.

In order to check the efficacy of both TRIGRS models in simulating the different

triggering mechanisms of Fig. 4, the EI m values computed for different initial conditions,

as well as the SI m values for each of the considered mechanisms are compared in Fig. 13. It

is worth noting that the highest values of SI m are systematically provided for the mecha-

nism M4.

With reference to the comparison of the results obtained by the two models, Fig. 13

highlights that, for all the mechanisms except M2, TRIGRS-unsaturated furnishes a slight

increase (about 5%) in the value of Success and a subsequent decrease in Error with respect

to the values of indexes computed by TRIGRS . For the M2 mechanism, the value of Success index obtained by TRIGRS-unsaturated is about 10% less than the one computed

by TRIGRS .

Despite such small differences, it is worth noting that the ratio between the number of

source areas related to each mechanism (totally or partially) simulated as unstable by both

TRIGRS models, and the number of 1998 shallow landslides’ source areas is quite high.

Fig. 9 Instability scenarios obtained with SHALSTAB

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With reference to the M4 mechanism, the earlier-mentioned ratio ranges between 80% and

90%.

3.4 Discussion

Examination of the modelling results provides a basis for some general comments on theuse of distributed, physically based models, partially confirming the theoretical assump-

tions and deepening some aspects deriving from their application.

First, according to conceptual assumptions of all the models, TRIGRS-unsaturated

represents the most adequate model for the analysis of shallow landslides source areas

occurred within the study area, providing the highest ratio between the ‘‘Success’’ and

‘‘Error’’ indexes. This model is able to take into account both the transient pore-water

pressures regime induced by short and intense rainstorms and the unsaturated conditions

(Savage et al. 2004; Baum et al. 2008) characterising the volcaniclastic covers (Cascini and

Sorbino 2004).

The TRIGRS model furnishes results that are very close to those provided by TRIGRS-

unsaturated . However, this finding is strictly related to the use of weighted values of

hydraulic properties available for the involved soils. Particularly, such parameters have

been selected by means of inverse analyses in order to take the unsaturated conditions of

volcaniclastic soils indirectly into account (Sorbino et al. 2007). Although TRIGRS shows

potential for the evaluation of transient pore-water pressures and stability conditions of

Fig. 10 Instability scenarios obtained with TRIGRS

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potential landslide source areas during rainfall (Godt et al. 2008; Salciarini et al. 2006), its

use is quite costly when the unsaturated conditions play a fundamental role for the pore-

water pressures regime.

Fig. 11 Instability scenarios obtained with TRIGRS-unsaturated

Fig. 12 ‘‘Success’’ and ‘‘Error’’ indexes obtained with the SHALSTAB, TRIGRS and TRIGRS-unsaturated

codes for the entire area of Pizzo d’Alvano massif

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On the other hand, the SHALSTAB theory of steady-state groundwater hydrology is not

consistent with the physical process leading to widespread shallow landsliding, and it

furnishes an overestimation of the extent and number of source areas. Moreover, results

from the application of quasi-steady-coupled models proposed in the literature to part of

the study area, yield similar overprediction errors (Chirico et al. 2002; Frattini et al. 2004).

Despite these limitations, the use of SHALSTAB may furnish useful guidance for assessing

initial conditions for the transient models.

As for the different triggering mechanisms, the M4 mechanism is modelled by all three

models as it conforms to the fundamental hypotheses of vertical infiltration and water table

accretion adopted by all the models.As for the remaining mechanisms, lower SI m values are mainly associated to local

boundary conditions not considered by the models. However, the values of success indexes

generally greater than zero indicate a partial modelling of source areas. Particularly, for the

M1 mechanism, the failure conditions are influenced by local hydraulic conditions that add

their effects to the convergent subsurface flow induced by zob morphology. According to

the analyses performed by Cascini et al. (2005a), this mechanism is characterised by a

retrogressive failure involving the toe of the slope, due to the pore-water pressures increase

caused by rainfall infiltration, and the mobilisation of the upper part of slope, due to the

local pressure increase induced by the temporary springs from underlying bedrock. The

presence of temporary springs is not captured by the TRIGRS models, and the effects of

local groundwater gradients should be taken into account to properly simulate springs-

induced triggering mechanisms (Cascini et al. 2008a). However, in many circumstances

the results partially capture these instabilities and confirm the potential of physically based

models to evaluate the failure conditions induced by convergent flows.

Similarly, the partial simulation of M6 mechanism may be addressed to an increase in

pore-water pressures related to concentration of subsurface flows, especially due to con-

cavity of slopes.

As for the M3 mechanism, TRIGRS and TRIGRS-unsaturated are theoretically able to

simulate the development of overland flows along the preferential patterns caused bytrackways and roads. Unfortunately, the cell width (3 m 9 3 m) of the used DTM is close

to width of typical trackways located in the study area and, moreover, the tortuous

trackways paths usually do not match the regular grid discretisation of the landscape. For

these reasons, M3 mechanisms are not well simulated by the TRIGRS models. Results for

Fig. 13 Results obtained with the TRIGRS codes for the different triggering mechanisms and initial mean

suction conditions

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the instabilities generated by this mechanism only identify unstable areas related to high

slope angles along road cuts and/or to the direct effects of rainfall infiltration.

In general, the assumptions of the TRIGRS models do not conform to the M2 and M5

mechanisms. Particularly, the effect of springs and impact loading phenomena that orig-

inate M2 mechanism are incompatible with theoretical basis of the models and, moreover,the location of source areas close to discontinuities poses some difficulties mainly related

to the inconsistency with infinite slope conditions.

4 Concluding remarks

Rainfall-induced shallow landslides of flow-type represent a worldwide natural hazard, and

the forecasting of the potential source areas is certainly a fundamental issue. In this regard,

the scientific literature proposes several approaches. Among them, a promising one is

based on distributed physically based models that are able to analyse stability conditions

using information about in situ conditions and mechanical properties of the involved soils.

In this paper, with reference to shallow landslides of flow-type, three physically based

models (SHALSTAB, TRIGRS and TRIGRS-unsaturated ) were used for the back-analyses

of a recent catastrophic event occurred in Campania (southern Italy), in order to evaluate

their potentialities and limitations in the simulation of the observed source areas.

To this aim, the input parameters of the models were chosen through the available

dataset and indirect analyses. In particular, for the transient models TRIGRS and TRIGRS-

unsaturated , the comparison of the pore pressure distributions obtained by the two models,

and the integration of the Richards’ equation for some representative stratigraphic schemesfurnished the hydraulic parameters used in the back-analyses.

The evaluation of the results provided by the three models was carried out through the

definition of two percentage indexes able to quantify the ‘‘Success’’ and the ‘‘Error’’ of

each model in interpreting the observed source areas. The obtained results highlight that

the transient models provide, for the same Success Index values, Error Index values lower

than those obtained by the steady-state SHALSTAB model. This latter provides a systematic

overestimation of the observed source areas, probably due to the transient characteristic of

the pore pressure regime at the shallow landslide triggering, which can be better interpreted

by the transient flow TRIGRS models. However, SHALSTAB surely represents a useful

tool for transient models application, providing the assessment of initial steady-stategroundwater conditions. Moreover, the TRIGRS-unsaturated is more suitable than TRIGRS

due to its capability to model transient infiltration process in unsaturated conditions

characterising the analysed shallow landslides events.

As for the simulation of the six recognised triggering mechanisms for the May 1998

events, both TRIGRS models provide the best results for the M4 mechanism because they

properly take into account the main characteristics of the triggering mechanism. Similar

good results are not obtained for the other mechanisms, as these last are related to local

boundary conditions that are not considered in the selected models—e.g. water inflows in

M1, bedrock scarps in M2, influence of anthropogenic elements in M3, and convex/ concave longitudinal slope profiles in M5 and M6.

Acknowledgments The Authors wish to express their deep gratitude to W. Z. Savage, R. L. Baum and,

above all, J. W. Godt of the US Geological Survey (Golden, CO) for making the TRIGRS-unsaturated code

available and for the fundamental support in its use.

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References

Baum RL, Savage WZ, Godt JW (2002) TRIGRS-A FORTRAN program for transient rainfall infiltration

and grid-based regional slope-stability analysis. US Geological Survey Open-File Report 02-0424.

Available via: http://pubs.usgs.gov/of/2002/ofr-02-424/

Baum RL, Coe JA, Godt JW, Harp EL, Reid ME, Savage WZ, Schulz WH, Brien DL, Chleborad AF,

Mckenna JP, Michael JA (2005) Regional landslide-hazard assessment for Seattle, Washington, USA.

Landslides 2(4):266–279

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 via: http://pubs.usgs.gov/of/2008/1159/

Bilotta E, Cascini L, Foresta V, Sorbino G (2005) Geotechnical characterization of pyroclastic soils

involved in huge flowslides. Geotech Geol Eng 23:365–402

Brancaccio L, Cinque A, Russo F, Sgambati D (1999) Osservazioni geomorfologiche sulle frane del

5-6Maggio 1998 del Pizzo d’Alvano (Monti di Sarno, Campania). In: Orombelli (ed) Studi geografici egeologici in onore di Severino Belloni, pp 81–123 (in Italian)

Calcaterra D, de Riso R, Evangelista A, Nicotera MV, Santo A, Scotto di Santolo A (2004) Slope insta-

bilities in the pyroclastic deposits of the carbonate Apennine and the Phlegrean district (Campania,

Italy). In: Picarelli L (ed) Proceedings of International Workshop ‘‘Flows 2003—Occurrence and

Mechanisms of Flows in Natural Slopes and Earthfill’’, Sorrento. Patron, Bologna, pp 61–75

Cascini L (2004) The flowslides of May 1998 in the Campania region, Italy: the scientific emergency

management. Rivista Italiana di Geotecnica 2:11–44

Cascini L, Sorbino G (2004) The contribution of soil suction measurements to the analysis of flowslide

triggering. In: Picarelli L (ed) Proceedings of International Workshop ‘‘Flows 2003—Occurrence and

Mechanisms of Flows in Natural Slopes and Earthfills’’, Sorrento. Patron, Bologna, pp 77–86

Cascini L, Cuomo S, Sorbino G (2005a) Flow-like mass movements in pyroclastic soils: remarks on the

modelling of triggering mechanisms. Rivista Italiana di Geotecnica 4:11–31Cascini L, Guida D, Sorbino G (2005b) Il Presidio Territoriale: una esperienza sul campo. Rubbettino

Editore, Catanzaro

Cascini L, Cuomo S, Guida D (2008a) Typical source areas of May 1998 flow-like mass movements in the

Campania region, southern Italy. Eng Geol 96:107–125

Cascini L, Ferlisi S, Vitolo E (2008b) Individual and societal risk owing to landslides in the Campania

region (southern Italy). Georisk 2(3):125–140

Celico P, Guadagno FM (1998) L’instabilita delle coltri piroclastiche delle dorsali carbonatiche in Camp-

ania: attuali conoscenze. Quaderni di Geologia Applicata 5(1):129–188 (in Italian)

Chirico GB, Longobardi A, Villani P (2002) Analisi idrologica del rischio di colate su vaste aree mediante

indici topografici, statici e dinamici. In: Proceedings of Conference ‘‘XXVIII Convegno di Idraulica e

Costruzioni Idrauliche’’, Potenza, 16–19 Sep 2002, vol 1, pp 401–410 (in Italian)

Coe JA, Godt JW (2001) Debris Flows Triggered by the El Nino Rainstorm of Feb 2–3, 1998, Walpert Ridgeand Vicinity, Alameda County, California. US Geological Survey Miscellaneous Field Studies Map

MF-2384. Available via: http://pubs.usgs.gov/mf/2002/mf-2384/

Coe JA, Godt JW, Tachker P (2004) Map showing recent (1997–98 El Nin o) and historical landslides, Crow

Creek and vicinity, Alameda and Contra Costa Counties, California. US Geological Survey Scientific

Investigations Map 2859. Available via: http://pubs.usgs.gov/sim/2004/2859/

Crosta GB, Frattini R (2003) Distributed modelling of shallow landslides triggered by intense rainfall. Nat

Hazards Earth Syst Sci 3:81–93

Crozier MJ (2005) Multiple-occurrence regional landslide events in New Zealand: hazard management

issues. Landslides 2(4):247–256

D’Argenio B, Pescatore T, Scandone P (1973) Schema geologico dell’Appennino meridionale (Campania-

Lucania). In: Proceedings of Conference ‘‘Moderne vedute sulla geologia dell’Appennino’’. Acc.

Nazionale dei Lincei, quad 183 (in Italian)Di Crescenzo G, Santo A (2005) Debris slides-rapid earth flows in the carbonate massifs of the Campania

region (southern Italy): morphological and morphometric data for evaluating triggering susceptibility.

Geomorphology 66:255–276

Dietrich WE, Wilson CJ, Reneau SL (1986) Hollows, colluvium, and landslides in soil-mantled landscapes.

In: Abrahams AD (ed) Hillslope processes. Allen and Unwin, Boston, pp 361–388

330 Nat Hazards (2010) 53:313–332

1 3

http://pubs.usgs.gov/of/2002/ofr-02-424/

http://pubs.usgs.gov/of/2008/1159/

http://pubs.usgs.gov/mf/2002/mf-2384/

http://pubs.usgs.gov/sim/2004/2859/

http://pubs.usgs.gov/sim/2004/2859/

http://pubs.usgs.gov/mf/2002/mf-2384/

http://pubs.usgs.gov/of/2008/1159/

http://pubs.usgs.gov/of/2002/ofr-02-424/

8/20/2019 17445647%2E2015%2E1028237


Fell R, Corominas J, Bonnard C, Cascini L, Leroi E, Savage WZ, On behalf of the JTC-1 Joint Technical

Committee on Landslides, Engineered Slopes (2008a) Guidelines for landslide susceptibility, hazard

and risk zoning for land use planning. Eng Geol 102(3–4):85–98

Fell R, Corominas J, Bonnard C, Cascini L, Leroi E, Savage WZ, On behalf of the JTC-1 Joint Technical

Committee on Landslides, Engineered Slopes (2008b) Guidelines’ commentary for landslide suscep-

tibility, hazard and risk zoning for land use planning. Eng Geol 102(3–4):99–111Fiorillo F, Wilson RC (2004) Rainfall induced debris flows in pyroclastic deposits, Campania (southern

Italy). Eng Geol 75:263–289

Frattini P, Crosta GB, Fusi N, Dal Negro P (2004) Shallow landslides in pyroclastic soils: a distributed

modelling approach for hazard assessment. Eng Geol 73:277–295

Gardner WR (1958) Some steady-state solutions of the unsaturated moisture flow equation with application

to evaporation from a water table. Soil Sci 85:228–232

Geo-Slope (2005) User’s guide. GeoStudio 2004, Version 6.13. Geo-Slope Int Ltd Calgary, Alberta, Canada

Godt JW, Baum RL, Savage WZ, Salciarini D, Schulz WH, Harp EL (2008) Transient deterministic shallow

landslide modeling: requirements for susceptibility and hazard assessments in a GIS framework. Eng

Geol 102:214–226

Guadagno FM, Revellino P (2005) Debris avalanches and debris flows of the Campania Region (southern

Italy). In: Jakob Hungr M, Hungr O (eds) Debris-flow hazard and related phenomena. Springer, Berlin,pp 489–518

Guadagno FM, Forte R, Revellino P, Fiorillo F, Focareta M (2005) Some aspects of the initiation of debris

avalanches in the Campania region: the role of morphological slope discontinuities and the develop-

ment of failure. Geomorphology 66:237–254

Guida D (2003) The role of the zero-order basin in flowslide-debris flow occurrence and recurrence in

Campania (Italy). In: Proceedings of International Conference on ‘‘Fast Slope Movements - Prediction

and Prevention for Risk Mitigation’’, Napoli, vol 1. Patron, Bologna, pp 255–262

Hungr O, Evans SG, Bovis MJ, Hutchinson JN (2001) A review of the classification of landslides of the flow

type. Environ Eng Geosci 7(3):221–238

Iverson RM (2000) Landslide triggering by rain infiltration. Water Resour Res 36(7):1897–1910

Montgomery DR, Dietrich WE (1994) A physically based model for the topographic control on shallow

landsliding. Water Resour Res 30:1153–1171Olivares L, Picarelli L (2001) Susceptibility of loose pyroclastic soils to static liquefaction: some pre-

liminary data. In: Proceedings of International Conference on Landslides—Causes, Impact and

Countermeasures, Davos, pp 75–84

Pack RT, Tarboton DG, Goodwin CN (1998) The SINMAP approach to terrain stability mapping. In:

Proceedings of 8th International Congress of the International Association of Engineering Geology and

the Environment, Vancouver, vol 2. Balkema, Rotterdam, pp 1157–1165

Pareschi MT, Favalli M, Giannini F, Sulpizio R, Zanchetta G, Santacroce R (2000) May 5, 1998, debris flow

in circum-Vesuvian areas (southern Italy): insights for hazard assessment. Geol 28(7):639–642

Rolandi G (1979) The eruptive history of somma-vesuvius. In: Cortini H, De Vivo B (eds) Volcanism and

Archaeology in Mediterranean Areas, pp 77–88

Salciarini D, Godt JW, Savage WZ, Conversini P, Baum RL, Michael JA (2006) Modeling regional initi-

ation of rainfall-induced shallow landslides in the eastern Umbria region of central Italy. Landslides3:181–194

Savage WZ, Godt JW, Baum RL (2004) Modeling time-dependent areal slope stability. In: Lacerda WA,

Erlich M, Fontoura SAB, Sayao ASF (eds) Landslides-evaluation and stabilization, Proceedings of 9th

International symposium on Landslides, vol 1. Balkema, Rotterdam, pp 23–36

Sorbino G (2005) Numerical modelling of soil suction measurements in pyroclastic soils. In: Tarantino A,

Romero E, Cui YJ (eds) Advanced experimental unsaturated soil mechanics, Proceedings of Inter-

national symposium, Trento. Taylor and Francis Group, London, pp 541–547

Sorbino G, Foresta V (2002) Unsaturated hydraulic characteristics of pyroclastic soils. In: Proceedings of

3rd International Conference on Unsaturated Soils, Recife, vol 1. Balkema, Rotterdam, pp 405–410

Sorbino G, Sica C, Cascini L, Cuomo S (2007) On the forecasting of flowslides triggering areas using

physically based models. In: Proceedings of 1st North American Landslides Conference, vol 1. AEG

Special Publication 23, pp 305–315Srivastava R, Yeh T-CJ (1991) Analytical solutions for one-dimensional, transient infiltration toward the

water table in homogeneous and layered soils. Water Resour Res 27:753–762

Terlien MTJ, van Westen CJ, van Asch TWJ (1995) Deterministic modelling in GIS-based landslide hazard

assessment. In: Carrara A, Guzzetti F (eds) Geographical information systems in assessing natural

hazards. Kluwer Academic Publisher, Dordrecht, pp 57–77

Nat Hazards (2010) 53:313–332 331

1 3

8/20/2019 17445647%2E2015%2E1028237


van Asch TWJ, Buma J, van Beek LPH (1999) A view on some hydrological triggering systems in

landslides. Geomorphology 30(1–2):25–32

Ward TJ, Li RM, Simons DB (1982) Mapping landslides in forested watersheds. ASCE J Geotech Eng Div

8:319–324

Wu W, Sidle RC (1995) A distributed slope stability model for steep forested basins. Water Resour Res

31:2097–2110

332 Nat Hazards (2010) 53:313–332

17445647%2e2015%2e1028237

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