ORI GIN AL PA PER

Critical rainfall to trigger landslides in Cunha Riverbasin, southern Brazil

Gean Paulo Michel • Roberto Fabris Goerl • Masato Kobiyama

Received: 22 May 2014 / Accepted: 10 September 2014 / Published online: 24 September 2014� Springer Science+Business Media Dordrecht 2014

Abstract In 2008, Rio dos Cedros city in Santa Catarina State, Brazil, suffered from

numerous landslides. The objective of the present study was, therefore, to apply the slope

stability model SHALSTAB to the Cunha River basin, which is located in this city, and to

estimate the rainfall necessary to trigger the landslides, which is defined as critical rainfall.

Some geotechnical parameters were determined through field survey and laboratory test. The

slope stability map elaborated with SHALSTAB was compared to the landslide inventory

map, which confirmed the good performance of this model for the study area. In the model

calibration, the values of the hydrologic ratio (q/T), which is the steady-state recharge (q) per

transmissivity (T), were determined in order to rearrange the classification of the slope

stability–instability conditions. After determining these values, the q value which is equiv-

alent to the critical rainfall was estimated. Based on the rainfall time series data from 1941 to

2011, the critical rainfall was determined 1,042.55 mm in 68 days, equivalent to a steady-

state recharge of 15.33 mm/day. This result implies that landslides in Rio dos Cedros city in

2008 were triggered by an association between intense rainfall and a long rainy period.

Keywords Landslides � SHALSTAB � Steady-state recharge � Critical rainfall

1 Introduction

There is a worldwide increase in life loss and material damages associated with natural

disasters. According to McDonald (2003), this increase is due to the rise in the number of

G. P. Michel (&) � M. KobiyamaInstituto de Pesquisas Hidraulicas, Universidade Federal do Rio Grande do Sul, Av. Bento Goncalves,9500, Caixa Postal 15029, Porto Alegre, RS 91501-970, Brazile-mail: geanpmichel@gmail.com

R. F. GoerlDepartamento de Geociencias, Universidade Federal de Santa Catarina, Campus Universitario,Trindade, Florianopolis, SC 88040-900, Brazil

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Nat Hazards (2015) 75:2369–2384DOI 10.1007/s11069-014-1435-6

people occupying susceptible areas as well as their low economic conditions that permit to

construct only very poor and unsafe houses. By using the available data of the Emergency

Disaster Data Base—EM-DAT of the Centre for Research on the Epidemiology of Disas-

ters—CRED, the temporal distribution of the world natural disasters during the period from

1900 to 2013 can be seen in Fig. 1. Though all kinds of disasters increase in frequency, the

hydrological disasters such as floods and landslides show the largest increase. It is noted that

about 50 % of people affected by the natural disasters suffered from the hydrological ones.

In Brazil, the recent occurrences of natural disasters have been more serious and det-

rimental, e.g., the landslides and floods in Santa Catarina State in 2008 (Frank and Se-

vegnani 2009), landslides in Angra dos Reis and Morro do Bumba regions in Rio de

Janeiro State in 2010 and landslides and floods in Teresopolis, Nova Friburgo and Pet-

ropolis cities in Rio de Janeiro State in 2011 (Avelar et al. 2011; Coelho Netto et al. 2011).

These disasters demonstrated that the Brazilian society is still unprepared to deal with such

hydrologically extreme events. Hence, it becomes more important to comprehend the

mechanisms that trigger the hydrological disasters and to establish adequate counter-

measures focusing on damage reduction.

Demonstrating how the disaster evolution performs during a city implementation from

floods to landslides, Kobiyama et al. (2010a) emphasized that the more attention might be

paid for landslides in Brazil. One of the most efficient countermeasures for reducing

landslide-related disasters is the mapping of susceptible areas.

To identify the locality of potential shallow landslide occurrence, there are several slope

stability models, e.g., SHALSTAB (Dietrich and Montgomery 1998; Montgomery and

Dietrich 1994), SINMAP (Pack et al. 1998) and TRIGRS (Baum et al. 2008). These models

have been worldwide accepted and utilized in the slope stability analysis (Cervi et al. 2010;

Chacon et al. 2006; D’Amato Avanzi et al. 2009; Huang and Kao 2006; Sorbino et al.

2009; Tarolli and Tarboton 2006; Terhorst and Kreja 2009; Yilmaz and Keskin 2009).

Applied for some Brazilian basins, SHALSTAB showed better performance than other

stability models (Vieira et al. 2009), specially on Cunha River basin (Michel et al. 2014);

thus, SHALSTAB was adopted in the present study.

SHALSTAB, in relation to the hydrological condition, adopts the assumption of O’loughlin

(1986), which considers a steady-state recharge that occurs when there is equilibrium between

inflows and outflows in the soil layer situated at a slope. This recharge allows predicting the

saturation level of the slopes. The above-mentioned condition never occurs naturally. However,

this assumption permits to simulate the effect of transient storms in increasing the water table,

generally responsible for triggering of landslides (Dietrich and Montgomery 1998; Hammond

et al. 1992). Though the effect of a transient storm could be simulated by the steady-state

recharge, there is no consensus about the numeric relation between them. According to Pack

et al. (2005), in the landslide modeling, the steady-state recharge is not related to a long-term

(e.g., annual) average of recharge, but related to a critical period of rainfall that can trigger

landslides. In the tropics where the soil is generally thicker, transient storms cannot trigger

landslides frequently because of the difficulty to significantly elevate the water table. Fur-

thermore, long rainy periods that resemble real steady-state recharge could lead the hillslope to

an unstable condition, allowing that a less intense storm triggers the landslide.

Dhakal and Sidle (2004) listed many studies about the characteristics of rainfall and

recharge associated with landslides. Some of them investigated the relationships between

the landslide occurrences and threshold values of rainfall for landslide hazard assessment,

prediction and warning systems. These studies generally consider the topographic and

geotechnical characteristics of the basin. Others studies are empirical and show the relation

between intensity and duration of the rainfall to trigger landslides (Caine 1980; Guzzetti

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et al. 2008; Saito et al. 2010). However, the relationship between the rainfall characteristics

(duration and amount) and the landslide triggering is still not very clear in cases where the

physical characteristics of the basin are considered.

In this context, the objectives of the present study were (1) to analyze the rainfall

associated with an extreme event occurred in Cunha River basin, Rio dos Cedros city,

Santa Catarina State, Brazil, in November 2008, by using some hydrological, geotechnical

and geomorphic analysis in association with SHALSTAB and (2) to determine the critical

rainfall necessary to trigger landslides.

2 Theory of SHALSTAB with soil cohesion

The Shallow Landsliding Stability Model (SHALSTAB) developed by Dietrich and

Montgomery (1998) is a mathematical computational model based on the combination

between a slope stability model and a hydrological model and freely available in the

internet. For stability analysis, this model uses the infinity slope theory and assumes the

hydrological steady state, the flow parallel to the surface and the Darcy’s law to estimate

the spatial distribution of the pore pressure. The simulations are performed in the ArcView

version 3.2, and the digital elevation model (DEM) provides data to calculate the upslope

drainage area and slope. Therefore, each pixel that composes the terrain contains a single

value to each morphometric parameter, enabling a discrete analysis.

The infinite slope analysis considers a uniform layer of soil over an infinite inclined

surface and ignores the effects caused by the boundaries. This analysis can be done in each

local where the slope length is much larger than the soil width, and only tangential stress

and normal stress at the base of the soil are considered.

The stability slope model is based on the Mohr–Coulomb law, in which, during the

rupture, the tangential stress is equal to the sum of the stabilizers efforts, i.e.,

s ¼ cþ ðr� uÞ � tan / ð1Þ

where s is the shear stress; c is the soil cohesion; r is the normal stress; u is the pore

pressure; and / is the soil internal friction angle. Considering the root strength and the

height of water table, Selby (1993) rewrote Eq. (1) and applied it to infinite slopes:

Fig. 1 Natural disaster occurrences and percentage of people affected by them from 1900 to 2013

Nat Hazards (2015) 75:2369–2384 2371

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qs � g � z � sin h � cos h ¼ cr þ cs þ ðqs � g � z � cos2 h� qw � g � h � cos2 hÞ � tan / ð2Þ

where cr is the root cohesion; cs is the soil cohesion; h is the slope; qs is the soil density; qw

is the water density; g is the gravitational acceleration; z is the soil depth; and h is the water

table level above the failure plane.

Dietrich et al. (1995) solved Eq. (2) for h/z that represents the proportion of the satu-

rated soil column at instability condition. Though in their formulations the cohesion term

was ignored, the present study considers soil cohesion term because it can play an

important role in stability of tropical soils. Then, it is obtained:

h

z¼ qs

qw

� 1� tan htan /

� �þ c

cos2 h � tan / � qw � g � zð3Þ

When the soil layer is completely dry, the term h/z in Eq. (3) is set to zero, and a

minimum slope angle for unconditional instability is obtained. When the slope is steeper, it

is classified as unconditionally unstable:

tan h� tan /þ c

cos2 h � qs � g � zð4Þ

When the soil layer is saturated, the term h/z in Eq. (3) is set to one, and a maximum

angle for unconditional stability can be obtained:

tan h� tan / � 1� qw

qs

� �þ c

cos2 h � qs � g � zð5Þ

If the situation does not correspond to Eqs. (4) or (5), the hydrological model is

incorporated to predict the wetness necessary to cause the instability. The hydrological

model used in SHALSTAB follows the principles of Beven and Kirkby (1979) and

O’loughlin (1986), where the soil saturation (w) is related to the upslope drainage area (a),

the unit contour length (b), the slope steepness (h), the soil transmissivity (T) and the

steady-state recharge (q) of a certain point, i.e.,

w ¼ q � ab � T sin h

¼ h

zð6Þ

Replacing w for h/z, Eqs. (3) and (6) can be equated. Then, combining the infinite slope

stability model and the hydrological model, a hydrologic ratio (q/T) can be obtained:

q

T¼ b

a� sin h � qs

qw

� 1� tan htan /

� �þ c

cos2 h � tan / � qw � g � z

� �ð7Þ

This is the main equation applied in SHALSTAB, which considers the soil cohesion.

Hence, it is very clear that only rainfall data are not sufficient to predict the stability

level of a slope. The slope stability depends on many hydrological, geotechnical and

topographic variables. Based on geotechnical and topographic input data, SHALSTAB

calculates a minimal hydrologic ratio (q/T) where the conditions for instability are satis-

fied. The higher the ratio q/T, the lower the probability of a slope destabilization.

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3 Materials and methods

3.1 Study area

Many cities in Santa Catarina were affected by landslides and floods in November 2008,

mainly those located in Itajaı Valley (Frank and Sevegnani 2009). The Rio dos Cedros city

was severely damaged, having 8,561 people directly affected by the event and 96 people

homeless. The disaster damaged 191 low-class and 96 middle-class houses, and the eco-

nomic losses reached around US$ 1,754,272, of which US$ 1,138,187 in agriculture, US$

250,553 in cattle raising, US$ 33,191 in industry and US$ 332,340 in basic services (Goerl

et al. 2009). The present study area is the Cunha River basin, a rural basin in Rio dos

Cedros city, where seven large rapid shallow translational landslides occurred (Fig. 2).

Due to the great accumulation of water in the soil, the material released from the slopes

turned into debris flows that delivered a lot of sediment to the main channels. Kobiyama

et al. (2010b) measured the geometry and estimated the initial volume of four landslides/

debris flows that occurred in this basin. Among these, the volume of the biggest was

estimated in 50,000 m3 with a width of approximately 60 m and a thickness of 10 m, while

the smallest volume was estimated in 6,000 m3, 40 m wide and 10 m thick. All the

landslides occurred in the basin are rainfall-induced without anthropic contribution.

The Cunha River basin has 16.35 km2, and its altimetry varies from 90 m to 860 m. The

Cunha River has a mean slope of 8 % and altimetric amplitude of 640 m. The basin is

composed of gneiss (94 %) and shale (6 %). The inceptisols, classified as cambisoils by the

Brazilian System of Soil Classification (EMBRAPA 2009), are predominant and occupy

about 75 % of the basin area (IBGE 2003). These soils are mainly associated with steep

slopes and are composed by clayey material in this basin. The other 25 % of the basin area

is occupied by ultisols (classified as argisols in Brazilian classification).

3.2 Input data

3.2.1 Topographic data

The digital terrain model (DTM) was elaborated based on 5-m contour lines, obtained

through field survey with a Leica ADS-40 airborne digital sensor. The contour lines were

interpolated by the ArcGis version 9.3 Topo to Raster extension resulting in a raster map

consisting in cells of 5 m of resolution.

The landslide scars were determined by visual analysis of the basin orthophotos in

1:5,000 scale and from more than 3,000 georeferenced points collected by field survey with

a D-GPS and a total station. All the points collected showed a subcentimetric precision in

plan-altimetry. After identifying three parts of landslides (initiation, transport and depo-

sition) in the field, the present study plotted only the initiation areas on the landslide

inventory map which was used for calibrating the SHALSTAB model.

3.2.2 Rainfall data

Even though SHALSTAB can be applied without rainfall data, the contextualization of the

results depends on the rainfall analysis. Therefore, the hourly rainfall data were extracted

from three rain gauge stations located in Rio dos Cedros city (Fig. 2). Although the rain

gauges were not situated in Cunha River basin and were distant about 6–12 km from the

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basin and among them, the rainfall series was analyzed and the measured values were very

similar among them. During the field survey in the basin, ravines, grooves or overland flow

were not observed, which permits to conclude that there is no surface flow with rainfalls of

low–medium intensity in the major part of Cunha River basin. That is why the present

study assumes that all the rainfall infiltrates into the soil layer.

3.2.3 Geotechnical data

The present study assumed that the landslide faces represent the failure triggering condi-

tions. Ten undisturbed soil samples were collected in the landslide scars, all of which are

situated in the same type of soil (cambisoil) that covers approximately 75 % of the basin

area. These soil samples were conducted to laboratory where tests were carried out to

obtain the geotechnical information. The shear strength parameters of soil (internal friction

angle and cohesion) were determined by direct shear test with undisturbed saturated soil

samples in drained conditions.

Fig. 2 Location and altimetry of Cunha River basin

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By the relation between mass and volume of the saturated soil, the saturated soil bulk

density was determined. The particle size distributions of soil samples were determined

and used to estimate the saturated hydraulic conductivity (Ks) by the HYDRUS-1D soft-

ware that contains the Rosetta Lite Version 1.1 model proposed by Schaap et al. (2001).

This model generates the soil hydraulic properties from soil textural data. Though Ks

generally decreases with soil depth, the present study considered its value constant along

the soil depth.

The estimation of soil depth of the basin was done by field observations on the land-

slides scars. All the landslides in the basin occurred at a similar depth (*10 m).The mean

depth where the slope failures occurred was considered the soil layer depth for the entire

basin (Fig. 3).

3.3 Critical rainfall determination procedure

SHALSTAB uses Eq. (7) to designate the stability degree of the slope. This equation is

solved for two hydrological variables: q and T. Hence, it is a parameter-free model where

the stability classification is determined by the q/T ratio. According to Dietrich et al.

(1995), the amount of rainfall necessary to destabilize the slope, which is called the critical

rainfall in the present study, is directly proportional to Ks of the soil at the ground surface

and inversely proportional to the decline rate of Ks by the increment of soil depth. Con-

sidering the variability of Ks, T can be obtained by the integration of this parameter along

the soil depth. This study considered that there is no variation of Ks, and then, T was

calculated by the product between Ks and the soil thickness. The transmissivity is a

parameter that estimates the facility how the water in the soil is drained by the slope.

Slopes where soils have high T can rapidly lower the water table level during or after a

heavy rainfall, which contributes positively to the slope stability. Therefore, the effective

application of the model requires the estimation of T.

Dietrich and Montgomery (1998) originally proposed seven stability classes in

SHALSTAB. The two extreme classes refer to Eqs. (4) and (5) which represent uncon-

ditionally unstable and unconditionally stable areas, respectively. The other five classes are

established according to the q/T ratio. The standard values of q/T used by SHALSTAB as

thresholds of the stability classification were set by statistical analysis of landslides which

occurred in predicted unstable areas and total unstable areas in the basin (Dietrich et al.,

1995). The q/T values were determined so that the results included the largest number of

landslides and the smallest total unstable areas in the basin. These values were set as

stability thresholds. The higher value of q/T implies the lower probability of instability.

For a better understanding of the mechanism involved in critical rainfall, the present

study reduced the five classes of stability established by q/T values to two. Thus, the terrain

is here classified in four classes: unconditionally unstable, unstable, stable and uncondi-

tionally stable. This classification requires only one value of q/T as stability threshold.

Table 1 shows a comparison between the original and proposed classification.

In SHALSTAB application, the present study compared the landslide inventory map

with the unstable areas identified by the model. The q/T values that represented the stability

threshold were determined when unstable pixels coincide with the landslides occurrences

of the inventory map. By changing the q/T values, a reclassification of the SHALSTAB

results was performed. Hence, four values of q/T were established for the stability

threshold, resulting in four different stability maps.

The variation in q/T values also causes to vary the number of unstable pixels within

landslide scars, as well as the total unstable area within the basin. The present study

Nat Hazards (2015) 75:2369–2384 2375

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assumed that only one unstable pixel within the landslide scar is sufficient for the model

success in prediction. The destabilization of a small area represented by few pixels can

destabilize a much larger volume of soil due to the relaxing of the slope strengths. When

there were different stability classes inside the same scar, the less stable class inside it

finally defined its classification.

In landslide modeling, the steady-state recharge (q) refers to a value to mimics the

behavior of ground saturation during a large storm (Dietrich and Montgomery 1998).

However, O’loughlin (1986) explained that a quasi-steady state occurs in basins where

drainage flux, hillslope outflow and the boundaries of saturation zones slightly vary. Then,

the present study considered that the conditions of the Cunha River basin during the

analyzed period resembled a quasi-steady state; thus, the real values of the rainfall series

were used in the modeling.

The determination of an actual q value requires the recognition of a rainfall period. The

ratio between the amount of rainfall and total time of this period may represents q (mm/

day). Though this period is associated with successive rainfall events which are capable to

trigger landslides, it is quite difficult to estimate its amplitude. To estimate the period able

to trigger landslides, a value of q was extracted from each q/T ratio which characterized the

four threshold conditions. The selection of q/T threshold values was executed by observing

the coincidence of predict unstable areas and registered landslides scars. After establishing

the q/T threshold values, the q values were calculated with the estimated value of T. These

values of q are related to an accumulated rainfall or critical rainfall.

Each value of q was sought within the rainfall series of the basin. A retrospective

accumulation of the rainfall from the triggering moment of landslides (9 a.m. of November

23, 2008) was calculated. Dividing the rainfall accumulated by the accumulated time,

several rainfall rate values that really occurred in the basin were obtained. When the value

Fig. 3 Head of a landslide in Cunha River basin

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of the rainfall rate becomes equal to the q value calculated from the ratio q/T, the period

and the critical rainfall related to the landslides triggering were determined.

4 Results and discussion

4.1 Geotechnical characteristics of soils

The mean of each input parameter was used in the modeling. According to Ohta et al.

(1983), the values of Ks on the hydrological modeling can be considered an order of

magnitude (about 10 times) higher than those obtained in laboratory measurement due to

the preferential pathways. The Ks values estimated by HIDRUS-1D are, on average, one

order of magnitude smaller than measured (Schaap and Leij 2000). Mota and Kobiyama

(2011) compared the values of Ks measured in laboratory with those estimated by HY-

DRUS-1D of some Brazilian soils whose sampling locations are very close to the present

study. They reported that the values of Ks estimated by HYDRUS-1D were, in general,

from 10 to 100 times smaller than the measured ones. Thus, the value of Ks obtained with

HYDRUS-1D was raised in one order of magnitude for the present study.

Since the values measured for soil strength were similar for all soil samples, their mean

values were applied for the entire basin. The values adopted in the present study are

showed in Table 2.

4.2 Analysis of the stability model

The results of SHALSTAB simulation, using the parameters of Table 2, are shown in

Fig. 4 where the classification is based on seven stability classes established originally by

Dietrich and Montgomery (1998). The model considered most of the flat areas as

unconditionally stable, even in saturation conditions. Steeper areas were classified as

unstable areas, even in low soil moisture conditions. The unconditionally unstable areas are

extremely steep areas. In the areas where topography is not very flat or very steep, the

hydrological parameters determined the classification. The upslope drainage area has a

large influence on the classification determination. Regions with high flow concentration

due to the relief convergent curvature are almost classified as unstable areas.

All the seven inventoried landslides coincided with the two more unstable classes.

Among them, only one was in the unconditionally unstable class and the others in the

second more unstable class. Although the unconditionally unstable class areas did not

Table 1 Comparison between original and proposed classification

Original classification Proposed classification

Unconditionally unstable (Eq. 4) Unconditionally unstable (Eq. 4)

log q/T \ -3.1 Unstable

-3.1 [ log q/T [ -2.8 qT� b

a� sin h � qs

qw� ð1� tan h

tan /Þ þ ccos2 h�tan /�qw �g�z

n o

-2.8 [ log q/T [ -2.5 or

-2.5 [ log q/T [ -2.2 Stable

log q/T [ -2.2 qT\ b

a� sin h � qs

qw� ð1� tan h

tan /Þ þ ccos2 h�tan /�qw �g�z

n o

Unconditionally stable (Eq. 5) Unconditionally unstable (Eq. 5)

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contain more incidences of landslides than the second unstable class, it can be said that

SHALSTAB performance was satisfactory for the Cunha River basin. The mathematical

condition that leads an area to be classified as unconditionally unstable is physically unreal.

The classification of an area as unconditionally unstable indicates an error in the estimation

of parameters, generally soil thickness or soil strength. In a lot of cases, the places where

the model indicated unconditionally instability are sites of bedrock exposure (Dietrich and

Montgomery 1998).

4.3 Critical rainfall

The rainfall condition in Rio dos Cedros city during the second semester of 2008 played a

relevant role for triggering landslides. The daily and accumulated rainfalls from August 1

to November 23, 2008 are demonstrated in Fig. 5. The accumulated rainfall during this

period reached 1,200 mm which is about 2/3 of the mean annual rainfall in the city.

The stability map generated by SHALSTAB was reclassified to obtain the correct

q/T value which could be thought to trigger landslides in this basin. This value of q/T was

varied for four different patterns of classification. The value of log q/T used in each

reclassification was as follows: -3.4, -3.3, -3.1 and -2.8. For selecting these values,

some criteria were used. The smallest value of log q/T (= -3.4) was established when at

least one unstable pixel remained inside each landslide scar. The largest value of log

q/T (= -2.8) was obtained when the unstable area in the basin became larger than stable

area and the simulation results became unreal. The other values were adopted based on

Dietrich and Montgomery (1998). The variation on the log q/T values caused the variation

of density of unstable pixels in the landslide scars (Fig. 6) as well as the total unstable area

in the basin (Table 3).

Using the q/T values adopted for the reclassifications, the value of T and rainfall data,

the values of q, the time period (total number of days) and critical rainfall were calculated

(Table 4). The rainfall series of the basin from 1941 to 2011 was analyzed. Analogous

rainfall periods with the same or higher accumulated rainfall were searched in order to

verify the singularity of the events related to the q values shown in Table 4. In the rainfall

series of the basin, any event similar to the one with the critical rainfall (1,042.55 mm) and

the period (68 days) related to the steady-state recharge of 15.33 mm/day was not found.

Furthermore, 14, 30 and 6 analogous events were identified for log q/T = -3.3, -3.1 and

-2.8, respectively.

Figure 7 shows the complete rainfall series of the basin with daily rainfall values

grouped for 3, 8, 28 and 68 days of accumulation. It is clearly noted that only the critical

rainfall related to 68 days of accumulation had never occurred till November 2008. The

dwellers of the region and the local media had not reported the occurrence of landslides

with similar magnitude in this basin. Therefore, those landslides in Cunha River basin in

Table 2 Model input values ofsoil parameters

Parameter Value

Internal friction angle of soil (/) 31�Cohesion (c) 11,900 N/m2

Saturated soil density (qs) 1,815 kg/m3

Soil depth (z) 10 m

Saturated hydraulic conductivity (Ks) 0.38 m/day

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November 23, 2008, were supposed to be triggered by the critical rainfall of 1,042.55 mm

in 68 days. It confirms quantitatively the conclusion of Kobiyama et al. (2010b) where, in

the case of landslides/debris flows in Cunha River basin, the triggering factor was not only

the rainfall intensity but also its accumulated value.

Fig. 4 Stability map of Cunha River basin, with seven original classes

Fig. 5 Daily and accumulates rainfall in Cunha River basin during the period from August 01, 2008, toNovember 23, 2008

Nat Hazards (2015) 75:2369–2384 2379

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For a complementary analysis, the accumulated rainfall and log q/T were calculated for

periods that vary from 1 to 100 days before the landslides occurrence. The rainfall data

series from 1941 to 2008 were verified in order to find the analogous rainfall periods for

each corresponding accumulated rainfall value. Figure 8 shows that in the range from 37 to

92 days of accumulation, there is no analogous period with the same accumulated rainfall,

except the period of 50 days that has one analogous. Although there are other periods

without analogous, the accumulation of 68 days (log q/T = -3.4) is the unique one that

can be supported by a log q/T threshold value adequate to the proposed method. Periods

shorter than 68 days are related to higher log q/T values. If these values are used as rainfall

threshold, excessive unstable area could be created in the basin. On the other hand, periods

Fig. 6 Reclassification of stability map with different values of log q/T: a -3.4; b -3.3; c -3.1; and d -2.8

Table 3 Areas in four stability classes in Cunha River basin with different values of log q/T

Class Percentage of area (%)

log q/T = -3.4 log q/T = -3.3 log q/T = -3.1 log q/T = -2.8

Unconditionally unstable 1.46 1.46 1.46 1.46

Unstable 5 6.61 11.51 22.2

Stable 34.51 40.97 28 17.31

Unconditionally stable 59.03 59.03 59.03 59.03

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longer than 68 days are related to smaller log q/T values. If used as rainfall threshold, it

could not detect the actual localities of landslides occurrence in this basin.

There are several empirical studies that proposed relations between rainfall thresholds

and triggering landslides (Caine 1980; Innes 1983; Larsen and Simon 1993; Aleotti 2004;

Cannon et al. 2008; Guzzetti et al. 2008; Dahal and Hasegawa 2008; Saito et al. 2010).

Although none of them could be applied for 68 days (1,632 h) of duration rainfall, all of

them were tested. The results obtained vary from -87 to ?30 % of the value estimated by

the physically based methodology adopted by this work (*0.64 mm/h). The most similar

value is from the equation proposed by Aleotti (2004), with a difference of approximately

26 %.

Other values of intensity tested and discarded by the present study (related to the

accumulated rainfall of 3, 8 and 28 days) were compared to the values obtained by the

empirical equations. The difference showed variability similar to the early comparison

between empirical equation and the selected intensity calculated by the present study.

Thus, for this case, it is difficult to define the specific rainfall intensity responsible for

triggering the landslides only with the empirical equation. This way, the physically based

methodology proposed in the present study can help to define it.

The q value responsible for triggering the landslides is under the condition of log q/

T = -3.4. This value is the smallest among the four conditions (Table 4) and is related to

Table 4 Values of q, period andaccumulated rainfall correspond-ing to four different values of logq/T

log q/T q (mm/day) Number of days Critical rainfall (mm)

-3.4 15.33 68 1042.55

-3.3 19.06 28 533.66

-3.1 27.09 8 216.76

-2.8 55.59 3 166.76

Fig. 7 Rainfall amount series: a 3 days; b 8 days; c 28 days; and d 68 days

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the longer period. Then, it is said that a long rainy period can be as significant as shorter

periods of heavy rainfall for triggering landslides in tropical thicker soils. Heavy rainfalls

that occurred during a short period have higher q values that did not match to the calculated

recharges responsible for triggering landslides. In case of these larger recharges remain for

longer periods; the number of landslides in the studied basin would be much larger. The

landslides which occurred in Cunha River basin were triggered by a smaller recharge that

remains sufficient time to lead some slopes to a less stable condition. In tropical soils,

generally much thicker, the triggering of landslides requires a significant elevation of the

water table which often is not likely to be caused by isolated transient storms.

5 Conclusion

Heavy rainfalls and/or long rainy periods are the main triggering factors for landslides in

Brazil. Then, the present study focused on the Cunha River basin, Rio dos Cedros city

(Brazil), in which a lot of landslides occurred with these factors in 2008. After gaining

several geotechnical parameters through field survey and laboratory test, SHALSTAB with

soil cohesion was applied to identify the areas susceptible to landslides. The simulation

results were compared to the landslides inventory map, which confirmed that this model

had a good performance for this basin.

Rearranging the stability classes from seven to four and comparing the stability map

with the landslide inventory, the log q/T value responsible for triggering the landslides was

determined. After that, assuming that the conditions in the basin resemble a quasi-steady-

state subsurface flow, the q value which is equivalent to the critical rainfall was estimated,

i.e., 15.33 mm/day. By a retrospective accumulation of the rainfall series from the moment

of the landslides occurrence, this q value corresponds to 68 days of accumulation and a

total rainfall of 1,042.55 mm. Analyzing the rainfall series in the study basin from 1941 to

2008, any period with similar characteristics was not found. The calculated q value refers

to a long period of accumulation. It indicates the importance of the water accumulation in

the soil layer since larger recharges for shorter periods which occurred many times since

Fig. 8 Values of log q/T and number of analogous rainfall periods for different ranges of rainfallaccumulation period

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1941 did not trigger large landslides. This result permits to emphasize that the accumulated

rainfall plays a very important role in the landslide triggering mechanism.

Although the steady-state recharge never really occurs in a basin, its value is used by

SHALSTAB to predict unstable areas. According to Dietrich and Montgomery (1998), this

recharge value is not real, but must represents the effect of large transient storms in the

wetness. However, the relation between steady state of recharge and transient storms still

remains unclear, and more work should be done for the question.

Notwithstanding the good performance of SHALSTAB in the present study, there are

still some uncertainties in the analysis. Due to the difficulty to estimate the variability of

several hydrological and geotechnical input parameters in the basin, they were all con-

sidered homogenous in the present study. It could lead to underestimation or overesti-

mation of parameters, which could consequently cause some incoherence to the modeling

results.

The stability map generated by the SHALSTAB classifies the area by a hydrologic ratio

(q/T), which is not very easy to interpret and requires that its results are contextualized for

each basin with different hydrological characteristics. Therefore, in addition to geotech-

nical and topographic parameters, the hydrological data should be measured for a more

precise landslide prediction. In case there is a large error in estimating q/T values, the final

error would spread to the calculation of steady-state recharge, critical rainfall and related

period.

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