Keywords

1 Introduction

One of the most important concepts in a landslide hazard assessment is travel distance, and its evaluation constitutes a key element for determining areas exposed to these events. There are several methodologies for estimating the travel length of landslides; for example, numerical models or physical scale models. Most commonly, distances are estimated based on empirical correlations obtained from the analysis of previous events. Landslide travel distances are measured and correlated with variables such as the angle of slope, the volume, types of materials, geological and geomorphological characteristics, and the maximum landslide height, among others (e.g., Corominas 1996; Finlay et al. 1999; Guo et al. 2014; Rickenmann 1999). Unfortunately, correlations are only applicable to the regions where they are developed, so it is necessary to produce local equations where landslide reach studies are scarce, especially in heavily populated tropical environments.

This study uses information from 123 events in the Andean zone of Colombia. Simple and multiple regression statistical techniques are applied to obtain linear equations with the best goodness of fit for determining the extent of landslides from certain influencing factors. Subsequently, the equations obtained are validated and the prediction capacity is compared with other models available in the literature. Finally, an application of the empirical-statistical models in the hazard zonation processes is presented.

2 Materials and Methods

2.1 Study Area

The information that serves as the basis for this study corresponds to the Andean zone of Colombia. This landslide-prone zone extends from the border with Ecuador in the south, to the border with Venezuela in the northeast, as shown in Fig. 1. The region has an area of 305000 km2, and an average elevation of 2000 m above sea level, ranging from areas close to sea level to peaks over 5000 m above sea level. This is the most populated area in the country, encompassing several cities connected by numerous roads. Many of the reported landslides are associated with the intensive road network, urban expansion, and industrial development.

Fig. 1
figure 1

Distribution map of the 123 landslides in the Andean region of Colombia

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From a physical point of view, this area offers a high degree of complexity due to the tropical climate conditions with high levels of rainfall. Rainfall amounts vary from 1500 mm to more than 3000 mm per year, while mean temperatures range between 8 °C in high mountain areas, up to 28 °C in the valley floors. The complex geology, with the presence of active geological faults in a predominant SW-NE direction, and highly variable soil thicknesses between a few centimeters and several meters, results in the occurrence of frequent landslides of multiple dimensions, and broad range of travel distances. These conditions contribute to dense vegetation cover and limit land use in the region, and negatively affect the terrain, in such a way that 91% of the total area of the Andean region in Colombia is located in a medium to high landslide hazard category (De Leon 2018).

2.2 Landslide Data

The Colombian Geological Survey oversees the management of a national digital inventory of landslides called the Mass Movement Information System (SIMMA). This system records, stores, and displays information on the most important landslides in Colombia. Records extend from the beginning of the twentieth century to the present, although most data correspond to events occurring over the last 30 years. The inventory is the result of extensive fieldwork undertaken by specialized professionals following the guidelines of the “Andean Multinational Project: Geosciences for the Andean Communities”. The database adopts the Cruden and Varnes (1996) classification system and distinguishes five types of failure mechanisms: fall, flow, lateral spread, slide, and topple.

For the purposes of this study, 5994 events corresponding to the period 1900–2019 were initially collected from the SIMMA inventory. An exhaustive depuration of the data was then undertaken. Lateral spreads and topples were excluded because landslide mobility models generally do not include these types of slope failures. In many cases, the information available, even though very useful in identifying the occurrence and characteristics of the landslides, was incomplete with respect to travel distance, or presented some inconsistency for analyses. It was, therefore, necessary to discard many records and use only those with complete information. The number of useful data points was then reduced from 5994 to only 123. This ensured only the most reliable information was used in the regression analyses, and that data volumes were similar to those reported in other studies (e.g., Guo et al. 2014; Qiu et al. 2018).

To validate the statistical models under development, data were divided into two subsets. The first subset was the training dataset from which empirical equations were obtained. The second corresponded to the test dataset, used to evaluate the accuracy of resulting models. Approximately 81% of the data were used to build the training dataset, and 19% to build the test dataset. Through simple random sampling, 100 landslides were selected to build the statistical models, and the remaining 23 for validation.

The spatial distribution of the landslides used for the analyses is shown in Fig. 1. Yellow triangles correspond to training landslide data and red triangles to test landslides data.

2.3 Definition of Terms

Certain attributes described the anatomy of the movement of each registered landslide. These attributes were subsequently used in an analysis of mobility events. The descriptions were based on those published by the IAEG (1990). The travel distance (L) was the horizontal distance from the crown of the sliding source to the toe of the displaced mass. The maximum landslide height (H) was the difference in elevation between the crown and the toe of the landslide. The slope angle (θ) referred to the mean value of the slope gradient before failure. The landslide area (A) was the horizontal projection of the landslide polygon that comprises the total area of the movement. The scheme of a landslide showing each of these attributes is shown in Fig. 2. Another of the attributes analyzed, but not shown in Fig. 2, was the volume (V), which referred to the total volume of the displaced mass. Volume was obtained by multiplying the total area affected by the average thickness of the landslide.

Fig. 2
figure 2

Modified from IAEG (1990)

Conceptual diagram of the anatomy of a landslide.

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Additionally, six qualitative attributes were collected to describe each landslide in the database. The same attributes were used to develop the statistical models.

  1. (1)

    The Geomorphological Environment attribute was divided into five types: denudational, structural, fluvial, glacial, and volcanic.

  2. (2)

    The Triggering Factor attribute was divided into six categories: rainfall, erosion, poor drainage management, undermining, mixed, and other (includes ice melt and artificial vibration).

  3. (3)

    The Water Content attribute was divided into four categories: dry, slightly moist, moist, and very moist.

  4. (4)

    The Lithology attribute was divided into five types: igneous rock, sedimentary rock, metamorphic rock, deposit, and mixed lithology.

  5. (5)

    The Landslide Type attribute was divided into four categories: rotational landslide, translational landslide, flow, and fall.

  6. (6)

    The Obstruction attribute was divided into three types: obstructed travel path, partial obstruction, and no obstruction.

2.4 Methods

Travel distance is evaluated using diverse analysis methods, including empirical, analytical, and numerical methods. Empirical methods, unlike analytical and numerical approaches, consider simpler parameters. For this reason, empirical methods are frequently used as a preliminary evaluation of travel distance when rheological parameters or mechanical details of the movement are not available or required. In addition, simple empirical tools offer a practical method of prediction, especially in regions where information is limited (Guo et al. 2014; Whittall et al. 2017). A common practice is to relate the mobility of landslides to the most important geometric parameters, mobility being generally represented by the travel distance, or the reach angle. As defined by Heim (1932), this is the angle of the line connecting the highest point from the source of the landslide with the distal margin of the displaced mass (Chen et al. 2015). It is calculated as the arctangent of the ratio H/L, which is equivalent to the coefficient of friction (Shreve 1968). Early authors noted a clear relationship between mobility and volume of the displaced mass (Hsü 1975; Scheidegger 1973). The incidence of other factors on the reach of mass movements was later confirmed.

Other authors consider a two-dimensional approach, such as the one described by Iverson et al. (1998). These researchers obtained a power-law relationship between the planimetric area and volume of the displaced mass through a mass balance approach, with an exponent equal to 2/3. This value was subsequently validated in later studies (e.g., Berti and Simoni 2007; Crosta et al. 2003; Scheidl and Rickenmann 2010). Empirical methods lead to prediction equations through the application of a variety of statistical tools but require validation and adjustment for local conditions, such as those presented here.

In this work, simple and multiple regression techniques were used to obtain the best prediction models to apply to the travel distances from the training dataset of the study region. Initially, the one-to-one relationships between the travel distance and main morphometric parameters were evaluated: maximum landslide height, slope angle, and displaced volume. Later, an area-volume model was obtained to validate the model of Iverson et al. (1998).

To improve the relationships obtained with the simple regression technique, multiple linear regression models were designed. The independent variables used in this analysis were three geometric variables (V, H, θ) and six qualitative variables (Geomorphological Environment, Water Content, Triggering Factor, Lithology, Landslide Type, and Obstruction). Two multiple regression methods were used: the backward elimination method, and the forward selection method. The elimination or selection criteria used were the p-value, and the adjusted coefficient of determination (adjusted R2) criteria. After obtaining the best prediction models, it was necessary to verify that the assumptions of the linear model were met, namely: linearity, normality, homoscedasticity, independence, and non-collinearity. This was achieved using the gvlma (), shapiro.test (), ncvTest (), durbinWatsonTest () and vif () functions of the R software, respectively; corresponding to different statistical tests that evaluated each of the assumptions.

The travel distance regression models were first validated by self-verification using the training landslides. The models were then applied to the test set, and the average errors of the two datasets were calculated. For local landslides to have a point of comparison, average errors were calculated after applying other correlation equations developed by other authors outside the study area. Mean absolute percentage error (MAPE) and root mean square error (RMSE) were used for this task. There were defined by Eqs. (1) and (2).

$$ {\text{MAPE}} = \frac{1}{n} \left( {\mathop \sum \limits_{i = 1}^{n} \left| {\frac{{\hat{y}_{i} - y_{i} }}{{y_{i} }}} \right| \times 100\% } \right) $$
(1)
$$ {\text{RMSE}} = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {\hat{y}_{i} - y_{i} } \right)^{2} }}{n}} $$
(2)

Where \(\hat{y}_{i}\) and \(y_{i}\) were the predicted and observed values, respectively, and \(n\) the number of observations. Using these two error measures together provided extra context on the quality of the fit.

An advantage of empirical models was that the inherent dispersion of the data made it possible to express outputs in quantitative statistical terms (McDougall 2017). Following this logic, and making use of statistical inference tools, it was possible to transform the prediction intervals for a given model in terms of exceedance probabilities. This made it possible to construct a preliminary landslide mobility hazard map. In this study, the models developed for both travel distance and landslide area were used to generate a preliminary hazard map from a landslide record that was not included in the training and test datasets.

3 Results and Discussion

3.1 Distribution of Landslides in the Andean Region

Table 1 shows the descriptive statistics for the numerical variables of the training dataset, including: number of observations (N), mean, standard deviation (StDev), median, range, skewness, and kurtosis. The variables of Table 1 present a positive skewness, so it was necessary to transform each by means of a logarithmic transformation, thus allowing them to comply with statistical normality.

Table 1 Descriptive statistics of the numerical variables of the database
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On the other hand, the database records six categorical variables, whose distribution conditions the statistical models since each category influences the mobility of landslides in a certain way. The Geomorphological Environment variable is distributed as follows: 39 events come from denudational environments, 34 from structural environments, 19 correspond to volcanic environments, and finally, glacial and fluvial environments have 4 events. The Triggering Factor variable has 60 landslides in the erosion category, 27 in the rainfall category, 4 in the mixed category, and 3 events in the remaining categories. Regarding the Water Content variable, 40 landslides were identified within the moist category, 31 within the slightly moist category, 17 within the very moist category, and 12 within the dry category. Regarding the Lithology, 32 landslides come from a lithology derived from igneous rocks, 27 landslides from a lithology of sedimentary rocks, 15 landslides from a lithology of metamorphic rocks, 13 landslides come from deposits, and 13 from a mixed lithology. The Landslide Type variable presents the following distribution: 59 landslides correspond to translational landslides, 34 to rotational landslides, 4 to falls, and 3 to flows. Regarding the Obstruction variable, 67 landslides had an obstruction in their travel path, 25 did not, and 8 landslides were partly obstructed.

3.2 Relationship Between Mobility and Landslide Volume

It is observed that the H/L ratio tends to decrease with an increase in landslide volume, i.e., the greater the volume, the greater the travel distance of the landslide. The first to notice this behavior was Heim (1932). Later, Scheidegger (1973) used this concept to make predictions through a regression line, establishing that the equivalent friction coefficient decreases with volume for values greater than 105 m3 and that below this threshold, movements exhibit a constant reach angle. Hsü (1975) arrived at a similar conclusion, and Corominas (1996) recognized that the volume of small events also influences landslide mobility.

Controversial conclusions have been reached when studying the effect of volume on the reach of mass movements. Kilburn and Sørensen (1998) developed an analytical model in which they observed a clear dependence of H/L on volume. Legros (2002) found a positive relationship between travel distance and volume for both volcanic submarine landslides and non-volcanic submarine landslides, despite the marked differences between the environments in which they are triggered. Budetta and de Riso (2004) also found a good correlation between the two variables for debris flows in Italy. In contrast, Okura et al. (2003) and Hunter and Fell (2003) did not find a clear relationship between volume and the H/L parameter. Some authors, such as Skermer (1985), have established that there is no clear relationship between H/L and volume, and that mobility is determined by the height of fall. The higher the landslide initiation is the greater will be the travel distance (Corominas, 1996). Staron and Lajeunesse (2009) stated that the correlation between the volume and mobility of a landslide is purely geometric, and does not contain information about the dynamics of the movement.

Figure 3 illustrates the relationship between travel distance and volume in a log–log plot for the study region. The line of best fit is shown along with its equation, the 95% confidence and prediction intervals, and the value of the coefficient of determination (R2). Observe that there is an increase in mobility with the increase in the displaced volume. Although this is in agreement with most of the studies presented in the literature, the coefficient R2 (0.52) indicates the model has a poor goodness of fit, since volume is not the only factor controlling landslide mobility.

Fig. 3
figure 3

Relationship between travel distance and landslide volume

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3.3 Relationship Between Travel Distance and Maximum Landslide Height

The relationship between these two variables is often used to model average equivalent coefficients of friction. Some studies examine the effects of topography on landslide mobility (e.g., Finlay et al. 1999; Hunter and Fell 2003). Basharat and Rohn (2015) confirm the relationship between travel distance and fall height in a logarithmic plot applied to earthquake-induced rockfall events in northeastern Himalayas, Pakistan. This relationship is explained by taking into account that the height of fall governs the potential energy, which makes it responsible for the speed of the landslide, and its travel distance when it is transformed into kinetic energy. Therefore, a greater height of fall leads to a higher speed, and thus a longer travel distance (Corominas 1996; Guo et al. 2014). Other authors indicate that maximum landslide height does not influence the extent of the displaced mass, and is of secondary importance, simply adding dispersion to the analysis (Davies 1982; Hsü 1975; Legros 2002). However, making height an independent variable improves multiple regression models (Finlay et al. 1999; Qiu et al. 2017). Figure 4 shows a trend of increasing travel distance with increasing maximum height. Nevertheless, the model does not present a strong goodness of fit (R2 = 0.45).

Fig. 4
figure 4

Relationship between travel distance and maximum landslide height

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3.4 Relationship Between Travel Distance and Slope Angle

In the literature, slope angle has an established negative relationship with travel distance. For example, numerical simulations by Okura et al. (2000) find a positive relationship between H/L and the slope angle: that is, the greater the angle, the shorter the travel distance. Hattanji and Moriwaki (2009), after analyzing a set of relict landslides in Japan, confirm that the equivalent friction coefficient increases with increasing slope steepness (Qiu et al. 2017). Hühnerbach and Masson (2004) conclude that the positive relationship between volume and travel distance supports the relationship with the angle of inclination, since it is common to associate large events with low slopes.

Figure 5 confirms the negative relationship between the travel distance and slope angle; however, the fit is very weak (R2 = 0.18). The data present a large dispersion around the line of best fit, which supports the hypothesis that a single factor, as the slope angle, is not capable of explaining the mobility of landslides.

Fig. 5
figure 5

Relationship between travel distance and slope angle

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3.5 Area-Volume Model

Sometimes mass movements not only propagate forward, but also laterally if orthogonal forces occurring during the movement exceed the basal friction of the soil (Strom et al. 2019). This condition creates the need to analyze the landslide area as a mobility index. The study by Iverson et al. (1998) is noteworthy in the literature. These authors establish that the planimetric area is proportional to the volume displaced with an exponent equal to 2/3. This value is in accordance with the assumption of geometric proportionality (Crosta et al. 2003).

Figure 6 illustrates the relationship between the landslide planimetric area and displaced volume for the study area training dataset (logarithmic relationship, base 10), whose equation is given by (3).

Fig. 6
figure 6

Line of best fit for the area-volume model

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$$ {\text{LogA}} = 1.012 + 0.624 {\text{LogV}} $$
(3)

Figure 6 shows a good fit between the variables, with a high coefficient of determination (0.84). The slope of the line is very close to that reported by Iverson et al. (1998). Through a hypothesis test, these authors derive a statistical significance of equaling the best-fit slope with a value equal to 2/3. Using relevant statistical inference tools, and the help of the t-statistic and p-value, our test results produce a t-statistic equal to −1.550, and a p-value of 0.124. Thus, it not possible to reject the null hypothesis that the data can be fitted to a linear model with a slope equal to 2/3 on a log–log plot.

Figure 7 shows the line resulting from the previous procedure, whose equation is given by (4).

$$ LogA = 0.827 + 2/3 LogV $$
(4)
Fig. 7
figure 7

Power-law relationship between planimetric area and landslide volume for different datasets in the form of Eq. (5)

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Additionally, Fig. 7 overlaps the regression lines for different international studies that validate Iverson et al. (1998). Equation (4) can be written as a power-law following the properties of the logarithm, according to Eq. (5).

$$ A = 6.71 V^{2/3} $$
(5)

The form of Eq. (5) is useful as it allows conclusions to be drawn about differences in mobility when different types of landslides and materials are analyzed under particular geological conditions. For example, Fig. 7 shows that landslides in the Andean region of Colombia exhibit much lower propagation values than reported in studies from other parts of the world. Most Andean events correspond to rotational and translational landslides. This contrasts with other studies focusing on phenomena with greater mobility, such as debris flows or lahars. The equation derived from the coarse debris flow research of Crosta et al. (2003) has a coefficient similar to that of this study. In Fig. 7, the line with the highest coefficient that accompanies the volume corresponds to the work of Iverson et al. (1998). That paper reports a value equal to 200 and is mostly applied to lahars. The implication of this value is that those phenomena can flood areas 30 times larger than other landslides in the database of this study. The analysis of this coefficient and the comparison for different regions is important since this contains information about the properties of the flow during the depositional phase (Scheidl and Rickenmann 2010).

3.6 Travel Distance Multiple Regression Model

Simple regression models show that the landslide travel distance cannot be explained with a single factor. For this reason, a multiple regression model is developed to improve the fit equations obtained with simple regression. Three geometric variables are used: V, H, and tan (θ) in logarithmic form, and the six qualitative variables from the study database. The regression model incorporates the four statistical variable selection methods described.

These results reveal that the volume of the displaced mass, the maximum height of the landslide, the slope angle, and the geomorphological environment were the most influential variables regarding travel distance. These variables were found to be statistically significant (p-value less than 0.05). The resulting equation for predicting the travel distance of landslides in the study region is expressed by Eq. (6).

$$ {\text{LogL}} = 0.263 + 0.156 {\text{LogV}} + 0.617 {\text{LogH}} - 0.521 {\text{Log}}\,{\text{tan}}\left( {\uptheta } \right) + {\text{GE}} $$
(6)

In Eq. (6) the value of the term “GE” (Geomorphological Environment) depends on the category that needs to be evaluated. The reference level is the denudation environment (GE = 0). For a structural environment, GE =  − 0.155; for a fluvial environment, GE =  − 0.149; for a volcanic environment, GE = 0.052; and for a glacial environment, GE = 0.053. Eq. (6) has a coefficient of multiple determination of 0.85, which represents a strong goodness of fit and means the model can explain 85% of the variability of the dependent variable. The statistical model satisfies the assumptions of linearity, normality, homoscedasticity, independence, and noncollinearity (all tests yield p-values greater than the 0.05 significance level used). The model was also tested for statistical significance with the help of the F statistic; obtaining a p-value below the significance level (0.05), i.e., this condition is met.

Equation (6) reflects the same trends observed in the one-to-one relationships. For example, coefficients that correspond to the volume and the maximum height are positive. That is; an increase in these variables leads to an increase in the response variable, which in this case is the travel distance. On the other hand, the coefficient value for slope angle is negative, reflecting an inverse relationship with the dependent variable, similar to what is shown in Fig. 5.

The statistical model reveals the importance of geomorphology as a factor influencing travel distance. The results show that landslides in volcanic and glacial settings are more mobile than in other environments. This is in agreement with international literature indicating volcanic events achieve greater travel distances due to their ability to involve larger volumes of water when compared with other landslide types (Hayashi and Self 1992; Korup et al. 2013; Siebert 1984; Ui 1983; Voight et al. 1983).

The model of Eq. (6) requires that practicing professionals have knowledge about the geomorphology of the study area: a requirement that can be limited in many situations. For this reason, an alternative statistical model with only numerical variables was developed using the backward elimination method, whose equation is given by:

$$ {\text{LogL}} = 0.286 + 0.159 {\text{LogV}} + 0.563 {\text{LogH}} - 0.618 {\text{Log}}\,{\text{tan}}\left( \theta \right) $$
(7)

Although this statistical model complies with all the assumptions evaluated for the previous one, the goodness of fit is lower, with a multiple R2 equal to 0.82.

3.7 Model Validation

To evaluate their predictive capacity, Eqs. (6) and (7) are applied to the two datasets (training and test). The models of Qiu et al. (2018) and Rickenmann (1999) are also applied to the same sets. Table 2 shows the results of calculating the errors in the predictions, applying the four models using Eqs. (1) and (2). Considering that the predicted values refer to the travel distance, an inverse transformation of Eqs. (6) and (7) is performed to obtain the response variable in correct units.

Table 2 Comparison of the prediction capacity for the proposed and international models for the estimation of the landslides travel distance. The units of the variables in the international models are the same as those used in Table 1
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In general, the MAPE for the models developed in this study are lower than for the international models. The Rickenmann (1999) model reports very large MAPE values that exceeds 200% because of the focus on debris flow research. Although the model of Qiu et al. (2018) reports low error values, it does not outperform the predictive capacity of the models developed here.

Regarding the RMSE, Eq. (6) has the lowest value among the evaluated models (93.67 m). Although this value may seem high, in long-runout landslides it represents only a small percentage of the total travel length, making it a good approximation. The best fit model for the study region has a MAPE equal to 31.25%, outperforming the alternative model (MAPE = 35.13%). This value is similar to the average error reported by other authors (Guo et al. 2014; Tang et al. 2012).

The previous results show that the models developed (full and alternative model) have a good prediction capacity for the Colombian Andes. Nevertheless, the models are limited, since they are specific to the study region, or in areas with similar geological and geomorphological settings. The errors in the predictions can be reduced if other variables that were not analyzed are considered. For example, the 3D effect of the travel path, the drag of material, the effect of pore pressure, and mechanical properties of the soil.

3.8 Application of Empirical-Statistical Models

The model of Eq. (6) is defined as an intermediate level model according to the guidelines of Fell et al. (2008), which allows its use in the elaboration of preliminary hazard maps. According to McDougall (2017), the prediction intervals of a statistical model can be translated as estimates of the probability of exceedance of the response variable (travel length or landslide area). For example, the line of best fit can be associated with a 50% exceedance probability (i.e., a 50% probability that future landslides of the same type and size will travel farther). Similarly, for a 95% prediction interval, the lower bound value is associated with an exceedance probability of 97.5%, and the upper bound with an exceedance probability of 2.5% (distribution of two tails). With different prediction intervals, more exceedance probability limits are obtained.

It is possible to obtain a preliminary landslide-mobility hazard map with these tools. As an example, a landslide in the study region not considered in the test and training datasets is used. This event corresponds to a landslide on October 26, 2007 in the municipality of Ricaurte, located in the department of Nariño, southern Colombia. The movement is classified as a rotational landslide developed in colluvium comprising strongly weathered rock blocks with a clayey matrix rich in iron oxides. The event is identified as wet and was triggered by pluvial erosion in a denudational environment. From the morphometric point of view, the maximum height is 80 m and it moved a total of 8000 m3 of material at an angle of 25°; the direction of motion with respect to north is 130°.

From the crown of the landslide, different probabilities of exceedance are calculated to define the hazard zones according to the models of Eqs. (3) and (6). The 50 and 95% prediction intervals are used, resulting in five hazard categories (Table 3). In summary, a travel distance and planimetric area values are obtained for each hazard category.

Table 3 Travel distance and landslide area limit values that define the hazard categories
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A 12.5 m resolution DEM of the event area and the ESRI software ArcGIS is used to create the preliminary hazard map. From the crown of the landslide, and with the help of the ArcMap Buffer 3D function, concentric circles are drawn as a guide to delimit each hazard level, and whose radii are determined by the travel distance indicated in Table 3. Additionally, concentric sectors are drawn on the circles with an area equal to that indicated in Table 3. The areal extent of each sector depends on the considered hazard level and takes into account the direction of movement (130° with respect to true north). The results of this procedure are shown in Fig. 8. This geometric approximation does not exactly represent reality since landslide forms will vary according to the conditions of each site. However, for practical purposes, and in preliminary phases of mapping, it is important to know the potential travel distance along with the planimetric area that may be reached by a landslide.

Fig. 8
figure 8

Preliminary hazard map showing the reach zones of the landslide in the municipality of Ricaurte in 2007

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Figure 8 represents an example of a preliminary hazard map built from two empirical-statistical models. Although at first glance it seems “very simple”, the map is highly effective in identifying the exposed elements around the zone of influence of the landslide; in this case, a road and a house are located within a moderate hazard level sector. This map serves as a guide for decision makers and land planners involved in landslide risk management.

4 Conclusions

In this study, a database of 123 well-documented landslides distributed was obtained across the Andean zone of Colombia. Most were rotational and translational landslides, and, to a much lesser extent, debris flows that exhibited a limited travel distance.

Various detailed statistical analyses were performed on a training subset of this dataset. The results of simple regressions reveal that travel distance is positively related to displaced volume and maximum slide height, and negatively related to slope angle. A strong correlation is observed between the planimetric landslide area and volume. Additionally, landslides from the study region follow the area-volume relationship proposed by Iverson et al. (1998). Differences in the proposed regression line, when compared with those presented by other authors, are accounted for by considering variations in failure mechanism of the different landslides included in the datasets.

Simple landslide travel-distance models are improved by incorporating a multiple regression model using stepwise statistical methods. Results show that volume, maximum crown height, slope angle, and geomorphological environment are the variables with a predominant effect on landslide travel distance in the Colombian Andean zone. The multiple regression analyses found there to be no significant contribution from variables such as triggering factor, water content, lithology, landslide type, and obstruction. An alternative model with only numerical variables was also constructed. The equations developed are appropriate for use in tropical areas such as the Colombian Andes and other tropical cordilleran regions (e.g., SE Asia).

The accuracy of the two models is evaluated using training and test sets from database. Satisfactory error values are obtained when compared with the values derived from other models applied to the study area.

Empirical-statistical modeling and resulting preliminary hazard map incorporate travel distance and the planimetric areas. The most important function of this map is to identify possible zones affected by landslide processes.