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  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">NHESS</journal-id>
<journal-title-group>
<journal-title>Natural Hazards and Earth System Science</journal-title>
<abbrev-journal-title abbrev-type="publisher">NHESS</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Nat. Hazards Earth Syst. Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1684-9981</issn>
<publisher><publisher-name>Copernicus GmbH</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/nhess-15-2461-2015</article-id><title-group><article-title>Detailed and large-scale cost/benefit analyses of landslide prevention vs. post-event actions</article-title>
      </title-group><?xmltex \runningtitle{Cost/benefit analyses of landslide prevention vs. post-event actions}?><?xmltex \runningauthor{G.~Salbego~et~al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Salbego</surname><given-names>G.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Floris</surname><given-names>M.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Busnardo</surname><given-names>E.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Toaldo</surname><given-names>M.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Genevois</surname><given-names>R.</given-names></name>
          
        </contrib>
        <aff id="aff1"><institution>Dipartimento di Geoscienze, Università degli Studi di Padova, Via G.
Gradenigo 6, 35100, Padova, Italia</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1"> (mario.floris@unipd.it)</corresp></author-notes><pub-date><day>6</day><month>November</month><year>2015</year></pub-date>
      
      <volume>15</volume>
      <issue>11</issue>
      <fpage>2461</fpage><lpage>2472</lpage>
      <history>
        <date date-type="received"><day>19</day><month>January</month><year>2015</year></date>
           <date date-type="rev-request"><day>12</day><month>February</month><year>2015</year></date>
           <date date-type="rev-recd"><day>8</day><month>October</month><year>2015</year></date>
           <date date-type="accepted"><day>18</day><month>October</month><year>2015</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015.html">This article is available from https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015.html</self-uri>
<self-uri xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015.pdf">The full text article is available as a PDF file from https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015.pdf</self-uri>


      <abstract>
    <p>The main aim of this paper is to
test economic benefits of landslide prevention measures vs. post-event
emergency actions. To this end, detailed- and large-scale analyses were
performed in a training area located in the northeastern Italian pre-Alps
that was hit by an exceptional rainfall event occurred in November 2010. On
the detailed scale, a landslide reactivated after 2010 event was
investigated. Numerical modeling demonstrated that remedial works carried out
after the landslide – water-removal intervention such as a drainage trench
– could have improved slope stability if applied before its occurrence.
Then, a cost/benefit analysis was employed. It defined that prevention would
have been economically convenient compared to a non-preventive and passive
attitude, allowing a 30 % saving relative to total costs. On the large
scale, one of the most affected areas after 2010 event was considered. A
susceptibility analysis was performed using a simple probabilistic model,
which allowed to highlight the main landslide conditioning factors and the
most hazardous and vulnerable sectors. In particular, such low-cost analysis
demonstrated that almost 50 % of landslides occurred after 2010 event
could be foreseen and allowed to roughly quantify benefits from regional
landslide prevention. However, a large-scale approach is insufficient to carry
out a quantitative cost/benefit analysis, for which a detailed case-by-case
risk assessment is needed. The here proposed approaches could be  used as a
means of preventive soil protection in not only  the investigated case
study but also  all those hazardous areas where preventive measures are
needed.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

      <?xmltex \hack{\newpage}?>
<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>Landslides are one of the most dramatic natural hazards along with
earthquakes and floods. For this reason, hazard and risk assessment has been
the main aim of a large number of scientific papers (Corominas et al., 2014
and reference therein), focusing on geomorphological (Baek and Kim, 2015;
Cardinali et al., 2002; Devoto et al., 2014) and multi-disciplinary or
statistical approaches (Sterlacchini et al., 2007; Dai et al., 2002). The
level of risk is generally defined as the intersection of hazard with the
value of the elements at risk by way of their vulnerability (Crozier and
Glade, 2006; Alexander, 2002). This assumption is generally based on a great
number of variables; vulnerability of element at risk is closely related to
the type of landslide, and frequency-based hazard assessment often relies on
a few decades of knowledge of slope instabilities. Fortunately, previous years'
measurements have been thoroughly collected thanks to GIS databases, web
information sharing and a greater awareness of landslide risk. This
attitude allowed some authors to calculate the costs of damages due to slope
instabilities within many environments around the world: from 1972 to 2007,
landslides and rockfalls cost EUR 520 million and caused 32 fatalities in
Switzerland (Hilker et al., 2009), while in the United States a USD 1–2
billion expense in economic losses and about 25–50 deaths per year have been
estimated (Schuster and Fleming, 1986), e.g., USD 9 million expense in only
direct cost losses in Colorado during 2010 (Highland, 2013). Historical
research indicates that more than 50 593 people died, went missing or were
injured in 2580 landslides and floods in Italy, where 26.3 % of the 8102
municipalities have been hit by slope instabilities between 1279 and 2002
(Guzzetti et al., 2005b); economic loss related to the single destructive
landslide at Ancona (Marche region) in 1982 was estimated at USD 700 million
(Alexander, 1989). On the global scale, 2620 landslides were recorded during
the 7-year period of 2004–2010, causing a total of 32 322 fatalities (Petley,
2012). Besides these historical data, the need for landslide damage
prediction is very strong if we want to implement preventive measures against
slope instabilities, even at a large scale. Within a small test site of about
20 km<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> north of Lisbon (Portugal), cumulative risk
expressed in direct costs for buildings and roads was calculated to be about
EUR 5 million (Zêzere et al., 2008). In southern India, the triggering
of many landslides hanging over 20 km long roads could cost from
USD 90 840 to 779 500, with an average annual total loss estimated at
USD 35 000 (Jaiswal et al., 2010). These expenses highlight how much people
need protective measures against landslides and floods, which cause
USD billions every year in damages and economic losses. This need can be
summarized in the term “risk management”, referring to the full range
of procedures and tasks that ultimately lead to the implementation of
rational policies and appropriate measures for risk reduction (Crozier and
Glade, 2006). One important task in risk management is the evaluation of
benefits from preventive actions which can encourage authorities and
population to invest money for preventing damage due to slope failures. To
this end, the estimation of the most landslide-prone areas and of the
effectiveness of possible preventive measures is needed.</p>
      <p>Scientific literature offers a variety of different methods to assess risk
and economic losses due to landslide events; both of these features
represent the central topic when decision makers are called to act toward
prevention, and thus an in-depth analysis is needed in order to obtain the best
result with the least effort. The first problem to solve is the scale of
analysis; many authors prefer a regional-scale approach, which necessarily
leads to a qualitative or semi-quantitative analysis due to the impossibility
of obtaining or considering data from every landslide (Von Ruette et al., 2011). In
this kind of approach, the probability that a landslide could cause damage
is accounted for through hazard or susceptibility maps, which are the start
point of the analysis. These maps are next overlaid with information
concerning elements at risk and their economic value, defined by maps of
probability of direct monetary loss per year (Blahut et al., 2014) or by
quantification of economic losses at municipal level (Pellicani et al.,
2014). However, other authors focus on a slope-scale approach,
in which information on landslide events and local features need to be wisely
considered. Despite the fact that every event has to be evaluated one by
one, this analysis usually allows quantitative assessment of landslide costs
and losses; in this way, different alternatives can be thoughtfully weighted
(Crosta et al., 2005) and local toolboxes for vulnerability assessment can
be created (Papathoma-Köhle et al., 2015). The slope-scale approach can also
help in the realization of a cost/benefit analysis, a topic rarely
investigated in the scientific literature despite being of paramount importance, which
consists of an economical comparison between the cost of prevention and the
cost of the rebuilding what have been lost (Boonyanuphap, 2013; Crosta
et al., 2005; Frattini and Crosta, 2006). Thus, given a specified landslide
event which caused various damages, costs of rebuilding are well known,
while costs related to a potential prevention plan depend on what type of
preventive work is chosen and on what business company is selected. Every
one of these last features has to be generally evaluated on a case-by-case
basis.</p>
      <p>In this work, we have considered the effects of an exceptional rainfall event
that hit the Italian pre-Alps of the Vicenza province (NE Italy) in 2010
(Floris et al., 2012, 2013) to perform a cost/benefit analysis of landslide
prevention vs. post-event actions. To achieve this goal, slope-scale (detailed) and
large-scale (1 <inline-formula><mml:math display="inline"><mml:mo>:</mml:mo></mml:math></inline-formula> 10 000) analyses (Lee and Min, 2001) were carried out.
On the slope scale, numerical simulations and cost/benefit estimation were
performed on a landslide reactivated by the 2010 rainfall event to define
if preventive measures could avoid the reactivation of the instability and
if they could effectively carry an economic benefit, as a result of an
effective risk management methodology. On the large scale, a landslide
susceptibility analysis was carried out in one of the most affected sectors
(Marosticano Hills; Fig. 1) after the 2010 event to verify if instability
phenomena could be foreseen and to estimate possible benefits from regional-scale prevention measures before the rainfall event.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p>Lithological map of the study area with the location of landslides
considered in the detailed cost/benefit analysis (Carrè and Molvena) and
of landslide data sets used in the large-scale analysis.</p></caption>
        <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015-f01.jpg"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <title>Case study</title>
      <p>In recent years, Italy has been hit by several exceptional rainfall events,
causing damages to public and private buildings, infrastructures and
activities. One of these events hit the province of Vicenza (Veneto Region)
in 2010. This event lasted from 31 October to 2 November; the average of the
rainfall measured by the 11 rain gauges located in the affected area was
336 mm and the maximum cumulative rainfall registered by one of the rain
stations was 500 mm (Floris et al., 2012, 2013). In the
following days, a great flood hit plain territories and 500 warnings of
landslides, distributed over 20 municipalities, were received at the Soil
Protection Division. Many of these slope failures affected the Marosticano
area, a 110 km<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> territory located in the northeastern sector of the
province (Fig. 1). Here, landslides were classified as
rotational/translational slides and earth flows (following the classification
proposed by Varnes, 1978). These failures involved mostly silty-clay soils,
i.e., the weathering products of Late Paleocene–Early Miocene extrusive
magmatic rocks. Weathering of basic bedrock led to the typical geological and
geomorphological environment within Vicenza's pre-Alps hilly belt, where
basalt and tuffaceous rock outcrops are sporadic because a variable thickness
of eluvial and colluvial deposits is present. The November 2010 event
highlighted the partial lack of preventive and maintenance works, a soil
defense attitude which has still to be acquired by authorities and population
at the present time but is more needed today than in the past, because the
frequency of exceptional rainfall events in Italy has increased in the last
decades (Floris et al., 2013), with one damaging event about every 20 years
(Floris and Bozzano, 2008); thus, the November 2010 event represents only one
element of this developing trend. As a result, without any kind of soil
protection, Vicenza's administration had to face EUR 300 million of
remediation works and about EUR 1 billion of infrastructure and building
losses. In this paper, we tried to estimate possible benefits from preventive
actions before 2010 in the Marosticano area, where the costs for
post-landslide remediation works amounted to about EUR 20 million.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F2"><caption><p>View of Carrè landslide.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015-f02.pdf"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p>Carrè landslide cross section used in the numerical simulations.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015-f03.pdf"/>

      </fig>

      <p>On the slope scale, we chose to focus our attention on a roto-translational
slide occurred in the Carrè municipality (Fig. 2); this landslide is
located on an unstable slope which was affected by past and recent
instabilities – including during the 2010 event – forcing authorities to
demolish an old house and rebuild the main road, with a total direct cost of
EUR 60 000. The landslide body lies above a basaltic bedrock and involves a
few-meters-thick eluvium–colluvium layer. The landslide area covers about
5500 m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> (100 m length <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 65 m width), with a 1 m high main
scarp. Field data resulted in a supposed shear surface located within the first
shallower meters (inside layer B shown in Fig. 3), where a decrease of
strength occurred in silty-clay soils due to pore pressure rising. On the
large scale, the entire territory of Marosticano hills was investigated.</p>
</sec>
<sec id="Ch1.S3">
  <title>Methods</title>
<sec id="Ch1.S3.SS1">
  <title>Detailed-scale analysis</title>
      <p>Detailed-scale analysis aimed to define if a specific preventive work
employed before the 2010 event could have either avoided landslide or not.
A numerical model was implemented in order to study slope stability along with
remedial measure which was actually realized after the slide: a drainage
trench, whose planned task was to reduce the water table by 2 m from the surface
and get rid of the most important landslide triggering factor (Roggia, 2014).
The analysis was performed with Itasca's FLAC<sup>®</sup> 7,
a finite-difference software for numerical modeling of 2-D continua (ITASCA,
2011). It is a commonly used code in geosciences because of the numerous
constitutive models implemented which allow the study of deformation and yield
in every node of the grid; each one of these nodes follow a linear or
non-linear tension-deformation rule in response to forces or boundary
conditions. The analysis began with a well-defined conceptual model built on
the whole available geological and geotechnical knowledge. Slope was
represented by three different lithotypes: a basaltic bedrock at the bottom, a
clay-mineral rich eluvium interface “B” in the middle and a colluvium
horizon “A” at the top (Fig. 3). This geotechnical setting was deducted
from field observations and laboratory tests, along with other technical and
geophysical surveys performed by local authorities. Slope conditions were
then modeled using back analysis: we had at our disposal ranges of strength
parameters from professional reports (Massagrande, 2012; Naldi, 2014) and
FLAC user manuals (ITASCA, 2011), and we also knew approximately where slip
surface was localized; in this analysis we set the water table at the ground
surface because it was assumed as the conceivable limit condition for the
slope during the 2010 event. Back analysis allowed us to calibrate strength
parameters, which have been used to simulate the effects of the drainage
trench.</p>
      <p>After we proved that a drainage trench could have effectively avoided
landslide occurrence during the 2010 event, the next step was to understand
if this kind of preventive work could have been also economically convenient.
Thus, drainage trench costs were compared with the total cost of all remedial
measures (which included the reshaping of the slope and the drainage trench
itself) applied after the landslide occurrence. The so-called cost/benefit
analysis was used to compare landslide prevention costs with the total cost
of landslide remediation works. Such an approach is generally employed in
economics and  aims to compare the economic efficiency of various
alternatives used to reach a specific objective. This method verifies whether
benefits brought by one alternative are greater than the related costs
(Momigliano and Nuti, 2001). Cost/benefit methodology permits a multi-year
analysis, and for this reason every monetary resource has to be carried back
to the first time of policy implementation. In order to get all amounts fully
comparable throughout the years, it is necessary to apply a discount rate.
Equation (1) is employed to determine the value (present value, PV) of a <inline-formula><mml:math display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula>
monetary resource available at future time <inline-formula><mml:math display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>, assuming a <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> discount rate:
            <disp-formula id="Ch1.E1" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">PV</mml:mi><mml:mfenced open="(" close=")"><mml:mi>X</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mi>X</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Considering the flow of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> costs and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> benefits, the real
expense comparison is expressed by NPV (net present value), defined as the
difference between the benefits and costs throughout the years, as in
Eq. (2) (Frattini and Crosta, 2006):
            <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">NPV</mml:mi><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow><mml:mi mathvariant="normal">T</mml:mi></mml:munderover><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow><mml:mi mathvariant="normal">T</mml:mi></mml:munderover><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Thus, the cost/benefit analysis allowed us to compare the preventive costs
with the total remedial costs of the Carrè landslide. In a process like this,
the definition of all amounts has been a critical point: <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> costs
were set to preventive drainage trench expenses, obtained from remedial work
projects (Roggia, 2014) which include the costs of the analysis on the
stability of the slope; however, due to the impossibility to
calculate the indirect costs of losses, we set <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> benefits to the
total amount of remedial works. We have calculated NPV for 20 years because
it is the return period of exceptional rainfall events related to the
triggering of landslides (Floris et al., 2012, 2013). Furthermore, 20 years
is the limit for a cost/benefit analysis because of the possible changes in
the inflation rate and in the discount rate. Hence, a return period of
20 years could represent a good choice to have an overview of the benefits
from prevention measures in the study area. Cost/benefit analysis permitted
us to consider the annual maintenance cost, too: protective measures
management generally reveals to be as fundamental as prevention itself,
because the lack of surveillance can be considered as much as a preparatory
factor. This amount was set to EUR 400 per year, because many inspections
could be realized by sight or with basic instrumentations. Here, a discount
rate of 1.6 % was applied, obtained from the website of Italian Economy
and Finance Department and referred to 15 years Euro-BTP <inline-formula><mml:math display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> notes (15 years
represent the nearest interval to our 20 years preventive policy).</p>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Large-scale analysis</title>
      <p>In order to understand whether landslides that occurred in 2010 could have been foreseen and
to quantify possible benefits from pre-event measures before the rainfall
event, a spatial analysis over the Marosticano area was performed. This
represents a crucial step toward landslide prevention, because it would have
been impossible to decide where to intervene without a clear overview on
landslide susceptibility and on more hazardous areas. Statistical analysis
was employed assuming that landslide occurrence is generally determined by
landslide-related factors and that future landslides will occur under the
same conditions as past landslides (Chung et al., 1995; Lee and Pradhan,
2006). A very common bivariate analysis known as “frequency ratio” was
adopted: spatial landslide predictability was calculated from the analysis of
the relation between landslides and most important landslide conditioning
factors (Lee and Pradhan, 2007; Zhu and Huang, 2006). In order to achieve the
final map, the landslide inventory data set and environmental factor data layers
were collected from the Spatial Data Infrastructure of the Veneto Region
(<uri>http://idt.regione.veneto.it/</uri>). Morphometric (elevation, slope,
curvature, aspect) and non-morphometric (river distance, road distance,
lithology and land use) environmental factors were considered. As in the
majority of probabilistic spatial analyses, every single factor needed to be
reclassified and divided in sub-categories of values (see Table 3 of
Sect. 4.2); because this is a crucial initial step of the analysis, we tested
numerous classifications, taking into account natural breaks in the
distribution of continuous data, geomorphic and geological features of the
study area and the distribution and size of landslides (Floris et al., 2011).
Then, a table for each landslide-related factor was created and compiled with
the following values: <inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msubsup><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the number of pixels where
landslide occurred within class <inline-formula><mml:math display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> of factor <inline-formula><mml:math display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula>; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:msub><mml:msubsup><mml:mi>N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, the total pixels where landslide
occurred within the entire area; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the
number of pixels where landslide did not occur within class <inline-formula><mml:math display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> of factor <inline-formula><mml:math display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula>;
<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:msubsup><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the total
pixels where landslide did not occur within the entire area; and <inline-formula><mml:math display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>, the number of factors in the study area.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Soil properties which lead to slope failure under fully saturated conditions.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">Layer A</oasis:entry>  
         <oasis:entry colname="col3">Layer B</oasis:entry>  
         <oasis:entry colname="col4">Bedrock</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Model</oasis:entry>  
         <oasis:entry colname="col2">Mohr–Coulomb</oasis:entry>  
         <oasis:entry colname="col3">Mohr–Coulomb</oasis:entry>  
         <oasis:entry colname="col4">Mohr–Coulomb</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Density [kg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col2">1900</oasis:entry>  
         <oasis:entry colname="col3">1900</oasis:entry>  
         <oasis:entry colname="col4">2700</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Bulk modulus [Pa]</oasis:entry>  
         <oasis:entry colname="col2">5 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">1 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">3 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>10</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Shear modulus [Pa]</oasis:entry>  
         <oasis:entry colname="col2">2 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">5 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">1 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>10</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Cohesion [Pa]</oasis:entry>  
         <oasis:entry colname="col2">1 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">6 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">6 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Tension [Pa]</oasis:entry>  
         <oasis:entry colname="col2">1 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">6 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">1 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Friction angle [<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> ]</oasis:entry>  
         <oasis:entry colname="col2">23</oasis:entry>  
         <oasis:entry colname="col3">15</oasis:entry>  
         <oasis:entry colname="col4">31</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p>Cost/benefit analysis for the Carrè landslide: total remedial costs of
EUR 57 000 were considered a benefit which had to be reduced by the
prevention and maintenance costs. The final saving was obtained by summing all
years' savings.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry namest="col1" nameend="col6" align="center">Discounted amounts </oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Year</oasis:entry>  
         <oasis:entry colname="col2">Cost</oasis:entry>  
         <oasis:entry colname="col3">Benefit</oasis:entry>  
         <oasis:entry colname="col4">Cost</oasis:entry>  
         <oasis:entry colname="col5">Benefit</oasis:entry>  
         <oasis:entry colname="col6">Net present value</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">1</oasis:entry>  
         <oasis:entry colname="col2">EUR 17 652.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 17 363.76</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>17 363.76</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">2</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 387.04</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>387.04</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">3</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 380.72</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>380.72</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">4</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 374.51</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>374.51</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">5</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 368.39</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>368.39</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">6</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 362.38</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>362.38</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">7</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 356.46</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>356.46</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">8</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 350.64</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>350.64</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">9</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 344.91</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>344.91</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">10</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 339.28</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>339.28</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">11</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 333.74</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>333.74</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">12</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 328.29</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>328.29</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">13</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 322.93</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>322.93</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">14</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 317.66</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>317.66</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">15</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 312.47</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>312.47</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">16</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 307.37</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>307.37</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">17</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 302.35</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>302.35</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">18</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 297.41</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>297.41</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">19</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 292.56</oasis:entry>  
         <oasis:entry colname="col5">EUR 0.00</oasis:entry>  
         <oasis:entry colname="col6">EUR <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>292.56</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">20</oasis:entry>  
         <oasis:entry colname="col2">EUR 400.00</oasis:entry>  
         <oasis:entry colname="col3">EUR 57 000.00</oasis:entry>  
         <oasis:entry colname="col4">EUR 287.78</oasis:entry>  
         <oasis:entry colname="col5">EUR 41 008.39</oasis:entry>  
         <oasis:entry colname="col6">EUR 40,720.61</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry namest="col1" nameend="col2" align="center">Discount rate </oasis:entry>  
         <oasis:entry colname="col3">1.60 %</oasis:entry>  
         <oasis:entry namest="col4" nameend="col5" align="center"><inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math></inline-formula> net present value </oasis:entry>  
         <oasis:entry colname="col6">EUR 17 277.75</oasis:entry>  
         <oasis:entry colname="col7"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>Frequency ratio index (FRI) represents the ratio of the landslide occurrence
probabilities to the non-occurrence probabilities for a given class within a
factor. FRI is calculated using Eq. (3) (Jaafari et al., 2014; Lee and
Min, 2001; Lee and Pradhan, 2007):
            <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">FRI</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msubsup><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:msubsup><mml:msubsup><mml:mi>N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msubsup></mml:mrow></mml:mfrac><mml:mfrac><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:msubsup><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">pix</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The larger the ratio is, the stronger the relationship between landslide
occurrence and the given factor attribute (Jaafari et al., 2014). A value of
1 represents an average value, but a value &gt; 1 means that the
percentage of the landslide is higher than the area without landslide and
refers to a higher correlation with conditioning factors; a value &lt; 1 means lower correlation. In the case under investigation we set 1.6 as the
lower limit to infer a correlation between landslide and conditioning
factors. The landslide susceptibility index (LSI) is then obtained summing all
factor index contributions, as in Eq. (4) (Yalcin et al., 2011):
            <disp-formula id="Ch1.E4" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi mathvariant="normal">LSI</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">FRI</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">FRI</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">FRI</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="normal">…</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">FRI</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Thus, LSI allows creating a susceptibility map and defining which areas are
more prone to landslide, given a specific geological, geomorphological and
anthropic environment and landslide type.</p>
      <p>To test the good of fitness and the forecasting power of the adopted model,
success and predictive rate curves were calculated (Chung and Fabbri, 2003).
The success rate curve helped to quantify how the prediction image (i.e.,
susceptibility map) fits the landslides occurred in the study area,
comparing LSI values with the entire data set of instability phenomena before
2010. The predictive rate curve was calculated comparing LSI values and
landslides occurred after the 2010 rainfall event; this curve helped in the
classification of susceptibility levels and in the evaluation of the
percentage of 2010 landslides which could be foreseen.</p>
      <p>Finally, on the basis of results from detailed-scale analysis (i.e.,
percentage of benefits from prevention measures), we roughly evaluated
possible savings from large-scale pre-event actions by subtracting the
possible costs of prevention in the predictable unstable areas from the
total costs of post-event actions.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <title>Results</title>
<sec id="Ch1.S4.SS1">
  <title>Detailed-scale analysis</title>
      <p>In the back analysis, after numerous numerical simulations with different
soil properties, a fully saturated slope collapsed with parameters in Table 1. Slope was unstable only if the eluvium layer “B” was set with
low-strength parameters: this assumption was quite consistent with the
presence of a clay mineral-rich layer (Toaldo, 2014). Plasticity zones were
concentrated in this thin layer where soil did not have sufficient shear
strength, so movement was allowed (Fig. 4). This result was considered
acceptable, since we obtained a shear surface and a morphological setting
comparable to field surveys and observations. Instability was also confirmed
by the calculated factor of safety (FoS) &lt; 1. The FoS was calculated
with the shear strength reduction method (Dawson et al., 1999; Matsui
and San, 1992) implemented in FLAC, which is a method widely used for
analyzing stability of rock and soil slopes (Dawson and Roth, 1999; Soren et
al., 2014; Zettler et al., 1999). The same parameters were reutilized in the
second model, where the water table was reduced by 2 m for a 30 m distance,
simulating the planned drainage trench and its activation. This securing
measure stabilized the slope, with a FoS &gt; 1. Thus, if the Carrè
administration had created the drainage trench before the landslide event and
not after it, this preventive work could have avoided the landslide itself. A
part of those EUR 60 000 could have been saved, along with other tens of
thousands of Euros spent in incalculable indirect costs (emergency actions,
social cost due to inaccessibility of the road).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><caption><p>Distribution of plasticity zones during Carrè landslide in the case
of the water table at the ground surface. Insets show the direction
of displacement vectors in different parts of the landslide body.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015-f04.pdf"/>

        </fig>

      <p>Table 2 shows the results obtained from the cost/benefit analysis applied to
the
Carrè landslide: local administration spent EUR 57 000 in remediation
costs, while the preventive works amount would have cost EUR 17 652. Thus,
considering a 20-year policy and 400 Euros per year in maintenance expenses, a
total amount of EUR 17 277 would have been saved (30 % of the total
remediation costs). This amount must be kept under advisement especially by
local administrations, which could have allocated these funds to other
activities, soil protection plans or possibly other preventive works. We
supposed that geological, geomorphological and geotechnical considerations
could be even valid for other landslides, which happened within the same
background and environment conditions of Carrè (similar lithology, slope
angle, land use, road distance and rainfall intensity); thus, the
cost/benefit methodology was employed at three landslide sites in the Molvena
municipality, located a few kilometers from Carrè. Drainage intervention
was assumed, and the economic study proved that of the total EUR 130 000 spent
in remediation works, about 40 % would have been saved with a preventive
policy (Salbego, 2014).</p>
</sec>
<sec id="Ch1.S4.SS2">
  <title>Large-scale analysis</title>
      <p>FRI was calculated for each class belonging to eight landslide-related
factors. For morphometric factors, every class was carefully chosen after
repeated analysis, performed to isolate the best landslide pre-conditioning
range of values. In this particular case, a temporal validation was chosen
(Chung and Fabbri, 2003): the model was built with an input data set of
landslides which occurred before the November 2010 event, and then predictability
and validation assessments were made using a test data set of landslides
occurred during the same event. First, the input data set was obtained after a
search for landslide perimeter data and triggering areas (Trigila, 2014),
scanning every available source (field surveys, orthophotos and GIS shading
capabilities). The only available data for the test data set were point
features, so a buffer of 10 m around each element was applied (Adami et al.,
2012). Table 3 shows that earth flows are predisposed by altered massive
(basaltic) rocks, slope angle between 13 and 23<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and
elevation from 245 m to 420 m a.s.l. Higher and steeper slopes are more
susceptible to translational or rotational slides, which usually occur on
altered stratified (tuffaceous) bedrock. The success rate curve (Fig. 5) shows
what part of the assessed landslide susceptible area is actually an unstable
area. It represents the cumulative percentage (fraction; <inline-formula><mml:math display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis) of
landslides in the input data set with respect to susceptibility classes
(expressed as the portion of the study area with susceptibility above a given
value; from greater to lower; <inline-formula><mml:math display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis): a hypothetical curve coinciding with a
diagonal from 0 to 100 % would be equivalent to a totally random
assessment, so the further up away the success rate curve is from that
diagonal the better the model has been created (Remondo et al., 2003). Curves
for slides and earth flows are both far up from the diagonal, so the result
is quite convincing. Then, we used the November 2010 landslides to test the
forecasting power of this model by calculating predictive rate curves. Figure 6
shows that the validation data set did not perform as well as the first one,
but both curves are higher than the random diagonal, so results are
acceptable even in this case. The susceptibility map confirmed the results of
statistical analysis, as shown in Fig. 7: most susceptible areas for
translational/rotational slides are located at greater elevation and slope,
nearer to the roads than earth flows, which occur at lower elevation and slope.
Analysis confirmed what occurred during the November 2010 event: heavy
rainfall caused instabilities mainly along roads (90 % of the total
damage), so they need to be kept under control and be protected with
preventive works.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3"><caption><p>Frequency ratio index (FRI) for each category of input factors.
Values from medium to high susceptibility are shown in bold.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col3" align="center">Morphometric factors </oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Elevation (m a.s.l.)</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">80–145</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 145–245</oasis:entry>  
         <oasis:entry colname="col2">0.5</oasis:entry>  
         <oasis:entry colname="col3">1.5</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 245–314</oasis:entry>  
         <oasis:entry colname="col2"><bold>1.7</bold></oasis:entry>  
         <oasis:entry colname="col3"><bold>1.7</bold></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 314–420</oasis:entry>  
         <oasis:entry colname="col2"><bold>3.3</bold></oasis:entry>  
         <oasis:entry colname="col3"><bold>1.7</bold></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">&gt; 420–577</oasis:entry>  
         <oasis:entry colname="col2"><bold>12.2</bold></oasis:entry>  
         <oasis:entry colname="col3">1.0</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Slope (<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">0–13</oasis:entry>  
         <oasis:entry colname="col2">0.4</oasis:entry>  
         <oasis:entry colname="col3">0.6</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 13–23</oasis:entry>  
         <oasis:entry colname="col2"><bold>2.0</bold></oasis:entry>  
         <oasis:entry colname="col3"><bold>1.9</bold></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 23–33</oasis:entry>  
         <oasis:entry colname="col2"><bold>2.3</bold></oasis:entry>  
         <oasis:entry colname="col3"><bold>1.7</bold></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">&gt; 33–74</oasis:entry>  
         <oasis:entry colname="col2">1.5</oasis:entry>  
         <oasis:entry colname="col3">0.8</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Curvature</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Very concave</oasis:entry>  
         <oasis:entry colname="col2">1.5</oasis:entry>  
         <oasis:entry colname="col3">1.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Concave</oasis:entry>  
         <oasis:entry colname="col2"><bold>1.6</bold></oasis:entry>  
         <oasis:entry colname="col3">1.4</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Flat</oasis:entry>  
         <oasis:entry colname="col2">0.7</oasis:entry>  
         <oasis:entry colname="col3">0.7</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Convex</oasis:entry>  
         <oasis:entry colname="col2">1.3</oasis:entry>  
         <oasis:entry colname="col3">1.4</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Very convex</oasis:entry>  
         <oasis:entry colname="col2"><bold>1.7</bold></oasis:entry>  
         <oasis:entry colname="col3">0.6</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Aspect</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">North</oasis:entry>  
         <oasis:entry colname="col2">1.2</oasis:entry>  
         <oasis:entry colname="col3">0.7</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">East</oasis:entry>  
         <oasis:entry colname="col2">0.7</oasis:entry>  
         <oasis:entry colname="col3">0.9</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">South</oasis:entry>  
         <oasis:entry colname="col2">1.4</oasis:entry>  
         <oasis:entry colname="col3">1.1</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">West</oasis:entry>  
         <oasis:entry colname="col2">0.5</oasis:entry>  
         <oasis:entry colname="col3">0.9</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \hack{\addtocounter{table}{-1}}?><?xmltex \floatpos{t}?><table-wrap id="Ch1.T4"><caption><p>Continued.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col3" align="center">Non-morphometric factors </oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Road distance (m)</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">0–25</oasis:entry>  
         <oasis:entry colname="col2">1.3</oasis:entry>  
         <oasis:entry colname="col3">0.5</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 25–50</oasis:entry>  
         <oasis:entry colname="col2"><bold>1.6</bold></oasis:entry>  
         <oasis:entry colname="col3">0.6</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 50–75</oasis:entry>  
         <oasis:entry colname="col2">1.4</oasis:entry>  
         <oasis:entry colname="col3">1.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 75–100</oasis:entry>  
         <oasis:entry colname="col2">1.3</oasis:entry>  
         <oasis:entry colname="col3"><bold>1.6</bold></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 100–200</oasis:entry>  
         <oasis:entry colname="col2">0.6</oasis:entry>  
         <oasis:entry colname="col3">0.8</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">&gt; 200</oasis:entry>  
         <oasis:entry colname="col2">0.8</oasis:entry>  
         <oasis:entry colname="col3">1.2</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">River distance (m)</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 0–100</oasis:entry>  
         <oasis:entry colname="col2">0.5</oasis:entry>  
         <oasis:entry colname="col3">0.4</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 100–200</oasis:entry>  
         <oasis:entry colname="col2">1.5</oasis:entry>  
         <oasis:entry colname="col3">1.7</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 200–300</oasis:entry>  
         <oasis:entry colname="col2"><bold>2.0</bold></oasis:entry>  
         <oasis:entry colname="col3">1.5</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 300–400</oasis:entry>  
         <oasis:entry colname="col2">1.1</oasis:entry>  
         <oasis:entry colname="col3"><bold>1.8</bold></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">&gt; 500–1000</oasis:entry>  
         <oasis:entry colname="col2">0.2</oasis:entry>  
         <oasis:entry colname="col3">0.2</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">&gt; 1000</oasis:entry>  
         <oasis:entry colname="col2">0.2</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Lithology</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Weathered massive bedrock</oasis:entry>  
         <oasis:entry colname="col2">1.2</oasis:entry>  
         <oasis:entry colname="col3"><bold>2.5</bold></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Stratified rocks</oasis:entry>  
         <oasis:entry colname="col2">1.1</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Weathered stratified bedrock</oasis:entry>  
         <oasis:entry colname="col2"><bold>2.7</bold></oasis:entry>  
         <oasis:entry colname="col3"><bold>1.7</bold></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Layered rocks</oasis:entry>  
         <oasis:entry colname="col2">1.1</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Fluvial deposits</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Alluvial deposits</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Eluvial/colluvial</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Land use</oasis:entry>  
         <oasis:entry colname="col2">Slides</oasis:entry>  
         <oasis:entry colname="col3">Flows</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Classes</oasis:entry>  
         <oasis:entry colname="col2">FRI</oasis:entry>  
         <oasis:entry colname="col3">FRI</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Urban</oasis:entry>  
         <oasis:entry colname="col2">0.8</oasis:entry>  
         <oasis:entry colname="col3">0.6</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Industrial</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Extractive</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Green areas</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Arable</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Seasonal cultivation</oasis:entry>  
         <oasis:entry colname="col2">0.1</oasis:entry>  
         <oasis:entry colname="col3">1.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Permanent cultivation</oasis:entry>  
         <oasis:entry colname="col2">0.2</oasis:entry>  
         <oasis:entry colname="col3">0.3</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Woody</oasis:entry>  
         <oasis:entry colname="col2">0.3</oasis:entry>  
         <oasis:entry colname="col3">0.7</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Grassland</oasis:entry>  
         <oasis:entry colname="col2">1.6</oasis:entry>  
         <oasis:entry colname="col3">1.1</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Shrubby</oasis:entry>  
         <oasis:entry colname="col2">1.1</oasis:entry>  
         <oasis:entry colname="col3">1.6</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Sparse vegetation</oasis:entry>  
         <oasis:entry colname="col2"><bold>6.2</bold></oasis:entry>  
         <oasis:entry colname="col3"><bold>2.2</bold></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Water body</oasis:entry>  
         <oasis:entry colname="col2">0.0</oasis:entry>  
         <oasis:entry colname="col3">0.0</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T5"><caption><p>Levels of susceptibility assigned on the basis of the degree
of prediction of different landslide index ranges.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Slides</oasis:entry>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">FRI</oasis:entry>  
         <oasis:entry colname="col2">Area (%)</oasis:entry>  
         <oasis:entry colname="col3">Nov. 2010 Lds. (%)</oasis:entry>  
         <oasis:entry colname="col4">Level of susc.</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">12–30</oasis:entry>  
         <oasis:entry colname="col2">10</oasis:entry>  
         <oasis:entry colname="col3">20</oasis:entry>  
         <oasis:entry colname="col4">Very high</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">10–12</oasis:entry>  
         <oasis:entry colname="col2">20</oasis:entry>  
         <oasis:entry colname="col3">34</oasis:entry>  
         <oasis:entry colname="col4">High</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">9–10</oasis:entry>  
         <oasis:entry colname="col2">20</oasis:entry>  
         <oasis:entry colname="col3">30</oasis:entry>  
         <oasis:entry colname="col4">Medium</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">6–9</oasis:entry>  
         <oasis:entry colname="col2">30</oasis:entry>  
         <oasis:entry colname="col3">16</oasis:entry>  
         <oasis:entry colname="col4">Low</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">3–6</oasis:entry>  
         <oasis:entry colname="col2">20</oasis:entry>  
         <oasis:entry colname="col3">0</oasis:entry>  
         <oasis:entry colname="col4">Very low</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Flows</oasis:entry>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">FRI</oasis:entry>  
         <oasis:entry colname="col2">Area (%)</oasis:entry>  
         <oasis:entry colname="col3">Nov. 2010 Lds. ( %)</oasis:entry>  
         <oasis:entry colname="col4">Level of susc.</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">11–14</oasis:entry>  
         <oasis:entry colname="col2">10</oasis:entry>  
         <oasis:entry colname="col3">22</oasis:entry>  
         <oasis:entry colname="col4">Very high</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">10–11</oasis:entry>  
         <oasis:entry colname="col2">20</oasis:entry>  
         <oasis:entry colname="col3">36</oasis:entry>  
         <oasis:entry colname="col4">High</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">8–10</oasis:entry>  
         <oasis:entry colname="col2">20</oasis:entry>  
         <oasis:entry colname="col3">27</oasis:entry>  
         <oasis:entry colname="col4">Medium</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">5–8</oasis:entry>  
         <oasis:entry colname="col2">30</oasis:entry>  
         <oasis:entry colname="col3">13</oasis:entry>  
         <oasis:entry colname="col4">Low</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">3–5</oasis:entry>  
         <oasis:entry colname="col2">20</oasis:entry>  
         <oasis:entry colname="col3">2</oasis:entry>  
         <oasis:entry colname="col4">Very low</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><caption><p>Success rate curves showing how the adopted model fits the
instability conditions of the study area.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015-f05.pdf"/>

        </fig>

      <p>Table 4 shows FRI ranges of susceptibility levels used for classifying
prediction maps of Fig. 7. The area was classified as having high, medium,
low or very low susceptibility on the basis of the shape of predictive rate
curves (Chung and Fabbri, 2003; Floris et al., 2011). About 50 % of 2010
landslides fall in high and very high susceptibility levels, it means that
such instabilities could be foreseen before the 2010 rainfall event.
Consequently, a part of the EUR 20 million expended for post-event actions
in the Marosticano area could be saved: taking into account results from
detailed analysis, 30 % of about EUR 10 million.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><caption><p>Predictive rate curves showing how the adopted model fits
the instabilities triggered by the November 2010 rainfall event.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015-f06.pdf"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><caption><p>Translational/rotational slide and earth flow susceptibility maps.
The classification of susceptibility is based on the results
of the validation, interpreting predictive rate curves of Fig. 6.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://nhess.copernicus.org/articles/15/2461/2015/nhess-15-2461-2015-f07.pdf"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <title>Discussion and conclusions</title>
      <p>In this paper, we dealt with detailed and large-scale analyses aimed to
quantify possible benefits from landslide prevention: to this end we have
considered the 2010 exceptional rainfall event that hit the pre-Alps sectors
of the Vicenza province (NE Italy), triggering hundreds of instabilities.</p>
      <p>On a detailed scale, we have considered the reactivation of the Carrè
landslide after the 2010 event: it moved frequently in the past, destroying an
old house and the provincial road. Numerical modeling demonstrated that a
drainage trench, which was included in the project of post-event remediation
works, could have been a good preventive measure to improve slope stability
if applied before the landslide itself. Prevention costs were compared to
those relative to remedial works, usually applied after the landslide
occurrence. It was possible to define a saving of 30 % on the total amount
(about EUR 60 000), surely a great economic improvement for local
administrations (confirmed by cost/benefit analyses performed within the
environment of Molvena and not included in this paper). It is important to
note that in the analysis we did not include the tens of thousands of Euros
spent on incalculable indirect costs, such as emergency actions and social
costs due to inaccessibility of the road. Thus, if the municipalities of the
Vicenza province had acted before the 2010 event, an important amount of money
would have been saved and possibly reutilized for other purposes.</p>
      <p>On a large scale, we performed a susceptibility analysis in the Marosticano
hills, which were one of the most affected areas after the 2010 event; this
analysis considered landslides occurring before 2010 along with the natural
variability of geological, geomorphological and geotechnical features of
soils involved in slope failures. This method allowed us to understand which
factors are related to landslides occurrence and to point out the most
susceptible sectors of the study area. The key index of this approach, called
the “frequency ratio index”, provided classes of values within each factor
which are more inclined to cause landslide events. The definition of slide
and flow susceptibility maps, along with the obtained indexes, allowed us to
give a solid basis to the observations related to the 2010 rainfall event:
spatial analysis defined that areas near the roads and placed over basaltic
and tuffaceous weathered bedrock were generally the territories more
frequently hit by landslides, as effectively occurred during the November
2010 event. Comparing the results from susceptibility analysis with the
spatial distribution of landslides triggered by 2010 rainfall event, we found
that 50 % of the instabilities (including the Carrè and Molvena
landslides) fall in areas classified as highly and very highly susceptible; hence
such instabilities could be foreseen. Therefore, a part of the EUR 20 million
expended for post-event actions in the Marosticano hills could be
preserved by prevention measures. We could not get enough data on the cost of
post-event actions for the foreseeable landslides; because magnitude of
instabilities and damages were very similar all over the area (Floris et al.,
2012) we can reasonably suppose that such costs can reach the 50 % of the
total (about EUR 10 million). Taking into account results from slope-scale
analysis, where we estimated a saving potential of 30 % from pre-event
actions, up to EUR 3 million could be saved by regional landslide-hazard
assessment.</p>
      <p>Even if large-scale analysis helped us to roughly estimate possible benefits
from landslide prevention in the study area, such approach cannot define
where to act with preventive works; indeed, results of spatial analysis
showed that the majority of the study area would need to be defended –
regardless of money and time – in order to take care for all the most
susceptible environments. Therefore, preventive works must be planned on a
detailed scale with regards to those specific slopes which show
instabilities occurred in the past. This is an important factor because
landslides are frequently consequent upon partial or complete reactivation
of existing landslide bodies, often triggered by rainfall (Floris and
Bozzano, 2008, and references therein). Despite the limits of large-scale
analyses, they are very low-cost investigations which can be easily
performed by technicians of local and regional authorities and can be used
as preliminary study to identify the most hazardous areas where to perform
detailed surveys, supporting decision making and land use planning
(Akgun, 2012).</p>
      <p>In this work we performed quite simple analyses, which considered landslides
occurred in the past (before and during the 2010 rainfall event), to point
out possible benefits from landslide prevention on different scales. In
order to perform forecasting analyses, a complete risk assessment has to be
carried out to evaluate cost/benefit ratio of pre-event actions; more
refined models recently proposed by some authors (Bordoni et al., 2015;
Gioia et al., 2015) would be recommended to improve both spatial and
temporal prediction of landslides and induced damages on slope and large
scales. However, the adoption of more refined tools could affect the costs of
landslide prevention assessment; therefore, a cost/benefit analysis is
always a primary crucial step before choosing between the numerous
investigation methods proposed in the scientific literature (Dai et al.,
2002, and references therein; Guzzetti et al., 2005a), which often lead to
very similar results (Othman et al., 2015) depending mainly on site
characteristics and available data (Lagomarsino et al., 2015).</p>
      <p>The case study we dealt with in this paper can effectively contribute to
improve our awareness and knowledge on prevention benefits. It is real
evidence which proves that avoiding landslide occurrence represents a
sustainable policy to deal with the social side of risk mitigation. This
methodology can also provide an economic point of view for the global landslide
issue, giving authorities the appropriate tool to face this ever-growing
problem. To this end, new-generation early warning systems should be
developed for monitoring and preventing instabilities on local and regional
scales (Manconi et al., 2015; Segoni et al., 2015); thanks to the new
availability of free data from spaceborne sensors and of WebGIS low-cost
solutions, such systems represent reliable and cost-efficient tools to
reduce landslide risk (Stähli et al., 2015). Afterwards, prevention is
effectively possible from the economic point of view to the architectural
one and could represent an efficient way to defend every defenseless
territory.</p>
</sec>

      
      </body>
    <back><ack><title>Acknowledgements</title><p>This research was financially supported by the Italian Ministry of Education,
University and Research: national research project (PRIN 2010-11) (principal
investigator: Rinaldo Genevois, Department of Geosciences).
<?xmltex \hack{\newline\newline}?>
Edited by: F. Guzzetti<?xmltex \hack{\newline}?>
Reviewed by: D. Calcaterra and two anonymous referees</p></ack><ref-list>
    <title>References</title>

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