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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
e-mail: [email protected]
L. Cascini
e-mail: [email protected]
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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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