Introduction

Landslides constitute the most frequent and damaging natural hazards threatening the human lives and properties in northern part of Algeria. The landslide incidences in a region have been of serious concern to the society due to the loss of life, natural resources, infrastructural facilities, and also posing problem for future urban development. The city of Constantine in northeast, which is the third largest city of Algeria, suffered from extensive and severe landslides causing serious damages to property and infrastructure (Machane et al. 2008; Guemache et al. 2011; Bourenane et al. 2014). The most recent landslides that occurred in 2002, 2003, 2004, 2006, and 2012 have caused substantial damage to several buildings and major infrastructures (such as the Sid Rached bridge, Ciloc buildings, Rhumel bridge, Mentouri university, Boussouf district, Benchargui district, Boudraa Salah district, the national road number 27, etc.). These landslides have alerted the authorities towards the seriousness of landslide management and prevention. However, there has been too little consideration of potential problems in land use planning and slope management. Recently, the Algerian authorities have been stressing the need for local planning authorities to take landslides into account at all stages of the landslide hazard mapping process. So far, few efforts have been made to predict or prevent these events which caused serious damages. Nowadays, the landslide disaster situation is further compounded by increased vulnerabilities related to rapidly growing population, unplanned urbanization, rapid development in high-risk areas, environmental degradation, and climatic change with the heavy rainfall. Landslide disasters also become the major obstacle in development process because their economic losses are relatively high.

Through scientific analysis, the landslide hazard map is of crucial importance in the economic planning of urban areas and engineering structures (Ercanoglu and Gokceoglu 2002). Therefore, the preparation of landslide hazard mapping is a basic tool for disaster management and planning development activities in urban and rural areas. The result of landslide research may provide valuable information that helps to forecast such events as well as to find measures to mitigate subsequent losses to future landslides.

Landslide hazard (LH) is defined as the probability of occurrence of landslides in a given area within a reference period of time (Varnes 1984). Landslide hazard mapping is associated to the division of area in homogenous zones and their ranking according to degrees of landslide hazard. LH is deduced from two aspects: (i) landslide susceptibility expressing the spatial probability of occurrence of a landslide for given predisposing terrain factors (lithology, slope, land use, etc.) in a given area (Brabb 1984; Crozier and Glade 2005) and (ii) the temporal dimension of landslides related to the occurrence of triggering events (rainfalls, earthquakes, etc.). However, LH is, often, restricted to landslide susceptibility and did not refer to the time occurrence of landslides because of the absence of historical landslide records. Consequently, most of the published hazard maps have only presented the spatial information of landslide hazard and did not refer to the time dimension of landslides.

The aim of this research is to present and compare detailed landslide hazard maps (LHMs) for the Constantine city (northeast of Algeria), using frequency ratio (FR), weighting factor (Wf), logistic regression (LR), weights of evidence (WOE), and analytical hierarchy process (AHP) methods in the framework of GIS. These models are tested, and the obtained results have been discussed. The results provide useful information about landslide risk mitigation and may serve as guidelines for land use planning in Constantine city.

The present paper is organized into four parts. The first part describes the landslide phenomena in the Constantine city and includes a related literature review of achieved works prior to this research; the second part presents the prepared landslide database; the third part describes the application of two statistical approaches, namely, the bivariate and multivariate with an expert knowledge-based model (AHP) for landslide hazard mapping in the studied area and, finally, the fourth part provides the validation and comparisons of the obtained LHMs.

Scientific literature review

A wide variety of methods and techniques for landslide hazard mapping have been developed and applied in literature, including qualitative and quantitative methods (Soeters and Van Westen 1996; Leroi 1996; Guzzetti et al. 1999; Aleotti and Chowdhury 1999; Van Westen et al. 2003; Dai et al. 2001). Recently, several attempts have been made to apply different methods of LHM and to compare results searching for the best suited model.

Qualitative methods are subjective, based on expert knowledge, and portray hazard zoning in descriptive terms. These methods can be classified into two groups. The first group is base on the geomorphologic analysis where the landslide hazard is determined directly using experiences and knowledge of experts; a direct relationship between existing landslides and causative terrain parameters is determined and used to construct landslide hazard. The second group is a qualitative map combination where a landslide hazard map is obtained by combining a number of landslide influence factor maps. The weights are assigned to subclasses of thematic maps based on the field knowledge of experts; therefore, a landslide inventory map is not needed. Moreover, there are qualitative methodologies which use weighting and rating procedures known as semi-quantitative methods. These methods are the analytic hierarchy process (AHP) (Saaty 1980; Barredo et al. 2000; Yalcin 2008) and the weighted linear combination (WLC) (Ayalew and Yamagishi 2005). The AHP method involves the creation of hierarchy of decision elements (factors) and the comparison between different pairs of elements in order to assign a weight and a consistency ratio for each element. While WLC approach is a concept which combines maps of landslide-controlling parameters, by applying a standardized score (primary-level weight) to each class of a certain parameter and a factor weight (secondary-level weight) to the parameters themselves. Although, results of these approaches are partly subjective, depending on the expert knowledge (Van Westen et al. 1997; Leroi 1996). The qualitative or semi-quantitative methods have proved their utility in the case of regional studies (Soeters and Van Westen 1996; Guzzetti et al. 1999).

Quantitative methods are based on numerical expressions of the relationship between causal factors and the landslides. The main concept of the indirect approaches is that the controlling factors of future landslides are the same as those observed in the past (Carrara et al. 1995). Two types of quantitative methods can be distinguished: deterministic and statistical (Aleotti and Chowdhury 1999). Deterministic methods are focuses on the analysis of the mechanical equilibrium of a potential slide block and calculate the slope safety factor (Zhou et al. 2003). Due to the need of exhaustive data from individual slopes, these methods are often effective to map only small areas. Statistical methods are based on the analysis of the functional relationships between landslide-controlling factors and the distribution of landslides. The statistical methods include the bivariate statistical models, the multivariate, the logistic regression, the fuzzy logic, the artificial neural network analysis, etc. These methods are formally very rigorous because they consider the interrelationships among the different causal factors.

Statistical methods are considered by the scientific community as more objective and more suitable for susceptibility and hazard mapping at medium and large scale (1:50.000, 1:25,000, and 1:10.000) because of their potential to minimize the expert subjectivity (Soeters and Van Westen 1996; Van Westen et al. 1997; Van den Eeckhaut et al. 2006; Thiery et al. 2007).

The statistical methods require the collection of a large amount of data in order to produce reliable results. Moreover, the geographic information system (GIS) is a valuable tool used to collect, to store, to process, manipulate, and to correlate the large amounts of data in order to build landslide hazard maps. Thus, GIS constitute a basic tool for landslide hazard mapping due to its efficiency in spatial data management, manipulation, and spatial analysis which allow the update of the hazard assessment procedures.

Geographical, geomorphological, and geological setting of the study area

The Constantine city is located in northeast of Algeria, at about 430 km east of the capital city of Algiers (Fig. 1). The study area concerns the master plan city perimeter that covers about 60 km2. The city of Constantine is highly affected by landslide hazards, due to its geomorphological, geological, climatic, and seismotectonic conditions, as well as the anthropogenic factors.

Fig. 1
figure 1

Geographical location and Digital Elevation Model (DEM) of the study area

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Geomorphologically, the Constantine area belongs to the northeast mountainous area of the Tellean Atlas, which is characterized by contrasting relief that combines mountains, plates, hills, and river plains. The altitude ranges from 300 to 1000 m and decreases from Northeast to Southwest. The hydrographic network is represented by two main rivers (Rhumel and Boumerzoug) with a permanent flow that are associated with the Mellah, Megharouel, and Chaabet El Klab rivers having temporary flow (Fig. 1).

Geologically, the Constantine region belongs to the external domain of the Tellean Atlas chain, a part of the North African Alps (Maghrebides), built during the main paroxysmal compressional phases of Eocene, Miocene, and Quaternary periods (Vila 1980; Letouzey and Tremolieres 1980). Lithologically, the studied area presents four main sedimentary units: (i) the Cretaceous marls and limestone bed rock that belongs to the Constantine neritic formation; (ii) the Cretaceous-Eocene marls and calcareous marls of the Tellian thrust sheet unit; (iii) the Mio-Pliocene sandy clays, marls and conglomerates; and (iv) the Quaternary alluvial terraces and lacustrine calcareous formations (Guiraud 1973; Vila 1980; Aris et al. 1998; Benaissa and Bellouche 1999; Bougdal et al. 2006). The Neogene clays and the conglomerates formations, covering a large surface of the Constantine urban plan, are very sensitive to the presence of the water with average-to-high plasticity, and then, constitute prone zones to landsliding.

The climate of the Constantine region is semi-arid, with a typical hot and relatively dry season between June and August and a wet season during December to April. The rainy period corresponds to December, January, and February with the rainfall amount ranges between 350 and 500 mm. However, the rainfalls are concentrated in a short period as rainstorms and super rainstorms representing a major landslide hazard factor in the area.

The Constantine city is characterized by an important economic, scientific, and cultural infrastructures as well as high population density (2.374 inhabitants/km2) (RGPH 2008). The city experienced significant urban changes during the different periods of its history; each period offers a particular developed urban area. Before and during the Ottoman period (prior to 1837), Constantine was built and limited to the stable bed rock. During the French period (1837–1962), the city expanded towards less stable zone. Since the Algerian independence (since 1962 up to now), the expansion of city has accelerated and unstable zones have been occurred. Since then, new settlements combined with inappropriate land use constitute the main factors of the increase of the frequency of landslides.

Spatial database construction using GIS

The first step for the production of LSM is data collection and construction of a spatial database from which the relevant landslide-conditioning factors have been extracted. A spatial database that considers the landslide-related factors is constructed for the study area. The reliability of LHMs depends, mostly, on the amount and the quality of the available data, the working scale, and the selection of the appropriate methodology of analysis and modeling.

Firstly, the landslide inventory map is prepared for the study area, based on the analysis of aerial photographs and satellite images, completed by field investigation. Secondly, eight possible causative factors such as lithology, slope, exposure, land use, rainfall, distance to stream, distance to road, and distance to fault have been identified, analyzed, and thematic layers have been derived and prepared from (Table 1): (i) the available national databases, (ii) aerial photographs and satellite images analyses, and (iv) field surveys. The thematic layers generated in GIS software have been re-sampled in a 10 m × 10 m grid size in order to facilitate the easy raster-based computation. All maps were geo-referenced in the local projection system of Algeria (UTM zone 32 WGS 84—Geodetic Reference System). The statistical treatment of the data has been performed by using Excel 2007 and Xl Stat 2014 trial version software.

Table 1 Spatial database of the study area
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Landslide characteristics and inventory map

The landslide inventory map is considered as the basis and the most fundamental step in landslide hazard mapping. Landslide inventory maps provide the spatial distribution of existing landslides and their properties. These maps can be prepared using different techniques depending on the scope of the work, the extent of the study area, the scales of base maps, the quality and detail of the accessible information, and the available resources to carry out the work. The landslide inventory map of the study area (Fig. 3a) has been prepared at 1:10,000 scale, from the analysis and interpretation of aerial photographs, recent high resolution satellite images, field surveys, and available literature. Aerial photographs (Fig. 3d) were taken in 1980, at a scale of 1:10,000 by the National Institute of Cartography (INCT). Alsat 2A panchromatic satellite image (Fig. 3b) with spatial resolution of 2.5 m was taken in 2011 at a scale of 1:10,000. A satellite image of Google Earth (Fig. 3c) taken between 2003 and 2013 has been also used for visual detection of landslide occurrences in the study area.

In some cases, recent landslide locations have been identified from Alsat 2A satellite images and from Google Earth data. Field investigation has been conducted between 2008 and 2013 (Fig. 2) to verify and complete the photo interpretation, check the sizes and shapes of landslides, identify the types of movements, the materials involved, and the activity of failed slopes. In addition, all the available literature including historical landslide reports, scientific publications, thesis, dissertations, and archives from local authorities have been gathered and examined in order to complete the landslide inventory map (Arcadis 2003; Bougdal 2007; Machane et al. 2008; Guemache et al. 2011). The landslide database is obtained by integrating the collected data and then imported into GIS to create the landslide inventory map at 1:10,000 scale. After that, the landslide vector map is transformed into a grid database at 10 × 10 m cell size. The geometrical (perimeter, area, and maximal length) and geomorphological characteristics (typology and state of activity) of landslides have been determined clearly and stored in a GIS database using Arc GIS 9.1 software.

Fig. 2
figure 2

Field photographs showing the characteristics and types of recently occurred landslides in the study area: a rotational slides over the road of Massinissa, b rotational slides in Boussouf, c rotational slides along road in Benchergui, d fall slides in Benchergui, e rotational slides in Chabet El Merdja, and f rotational slides of the Rhumel bridge in Massinissa

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The obtained landslides perimeter covers an area of 7.124 km2 that represents 12 % of the total urban area. The most landslide-prone zones are located in the left bank of the Rhumel river and in the most urbanized zone of the Constantine city, as shown in Fig. 3a. An example of recent landslides identified in the study area and their morphological characteristics is shown in Fig. 2.

Fig. 3
figure 3

a Landslide inventory map of the study area and examples of different types of optical remote sensing images used for determination of landslides in the Constantine city. b Section of an aerial photo at 1:10,000 scale taken in 2002. c Section of a satellite image of Google Earth. d Section of a satellite image (Alsat 2A) at a scale of 1:10,000 taken in 2012 (the white dashed line marks the scarp)

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According to the landslide classification proposed by Varnes (1978), active landslides can be grouped into three main types: translational, rotational, and fall. The most failures (72 %) correspond to rotational debris slides, 26 % correspond to translational slides, and the remaining (2 %) are rockfalls. The rotational slides are located along streams but in more gentle slopes compared to the translational slides and occur mainly in Miocene marly clay deposits. The translational slides of variable sizes are located on steep slopes and affect the Miocene conglomerates and the Cretaceous marly-limestone of the Tellean thrust sheet. Mostly, the determined landslides had occurred as a result of heavy rainfalls. Landslide activity reaches its maximum during and just after rainy events. During the heavy rainfall of 2002–2003, 2003–2004, and 2005–2006 winters, the accumulated precipitation reached 460–800 mm and many landslides have been occurred and reactivated in the studied area (Chemin forestier, Chabet El Merdja - Sotraco-Boudraa Salah, Bardo, Poudriere, Boussouf, and Massinissa). Besides, runoffs related to snow melting and rain as well as infiltrations in the schistose marl, favored by the high permeability of these fissured rocks, increase the interstitial pressure and make them less resistant to shear stresses and making them prone zones to gravitational movements.

In the analysis, landslide boundaries have limited only to detachment zones of active landslides (Atkinson and Massari 1998; Van den Eeckhaut et al. 2006). But, in some places where there are signs of further movement such as cracks and tilted trees, the upper portions of accumulation zones were also included.

In this study, the landslide inventory is randomly divided into two independent groups, one for model training (70 %) and the other for validation (30 %) (Chung and Fabbri 2003, 2008). The landslide inventory map is helpful to understand the different triggering factors that controlling the different types of slope movement (Fig. 3).

Landslide-conditioning factors

Lithology

Lithology is one of the most important factors that influence the occurrence of landslides. Lithology with its structural and property variations may lead to variation in strength and permeability of rocks and soils. The lithological map of the study area (Fig. 4a) defined ten (10) main lithological classes. The “Miocene marly–clay” class dominates in the study area (28 %) and has the highest landslide density (61.5 %) as shown in Table 2. While the neritic limestone class without landslide density (0).

Fig. 4
figure 4figure 4

Landslide-conditioning factors of the study area: a Lithological map. Legend: (1) Quaternary Colluviums, conglomerate and Thick fill; (2) Quaternary recent alluvial terraces; (3) Quaternary ancient alluvial terraces; (4) Quaternary lacustrine limestones; 5) Pliocene lacustrine limestones; (6) Miocene conglomerates; (7) Miocene marly clay; (8) Flysh Massylian (Upper cretaceous); 9) Tellian Calcareous marls (Cretaceous-Eocene); (10) Neritic limestone (Cenomanian-Turonian). b Slope angle map. c Exposure map. d Land use type. e Rainfall map. f Distance to rivers map. g Distance to roads map. h Distance to faults

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Table 2 Frequency ratio values of the landslide-conditioning factors
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Slope

Slope is the main causative factor because the shear forces are directly influenced by the slope gradient (Dai et al. 2001). As the slope gradient increases, it is correlated with the increased likelihood of failure. The slope gradient map of the study area was divided into five slope angle classes (Fig. 4b). The slope varies from 0 to 5° in the plain area to near vertical cliffs >45° in the steep areas. Land surfaces falling within the classes (5–15°) are strongly predominant (62 % of the total area). Landslide density is the highest in the 5–15° class, followed by the 0–5° class (Table 2). Only few landslides fall in the 15–30° class, and no landslides are observed in the 30–45° and >45° classes.

Exposure

In landslide hazard studies, exposure is considered to be an important factor influencing slope stability, since exposure related parameters, such as exposure to sunlight, drying winds, and rainfall (degree of saturation), control the concentration of the soil moisture, which in turn determinant parameter for the occurrence of landslides (Magliulo et al. 2008). The study area was classified into eight directions (Fig. 4c). Both South to West facing slopes and West to North facing slopes slightly predominate (55 % of the study are) over North to South facing slopes (26 %). The North to East facing slopes area is relatively less frequent (18 %), while only 0.2 % of the land surface is perfectly flat zone (Table 2). Therefore, in the east exposure, the landslide density is relatively low (12.5 %) and increases with the orientation angle reaching its maximum in the west exposure (43 %).

Land use

Land use is also related to the triggering and causal factors of the landslides. The woody vegetation with large and strong root systems provides both hydrological and mechanical effects that generally stabilize slopes (Gray and Leiser 1982). On the contrary, landslides occur in unvegetated or irrigated cultivated areas due to the lack of the previously mentioned effects. Five land use classes have been identified and considered in the region (Fig. 4d). Most of the study area is covered by the urban area with 37 % of the study area. The low surface is represented by forests (8 %). The correlations with landslide density showed that the high landslide density is concentrated on the two layers (Table 2): the agriculture land (39 %) and barren land (22 %). This high landslide density can be explained by a very high activity (or high cultivated areas) of clear-cut logging as well as the increase in inappropriate new highland settlements under population growth.

Rainfall

Rainfall is widely considered as the main triggering factor of landslides hazard. Rainfall causes a change in the moisture content of the soil. Changes in moisture content increase the interstitial pore water pressure, seepage pressure, and soil weight and reduce cohesion. Precipitation database from 04 meteorological stations (Constantine, Ain El Bey, Hamma Bouziane and Fourchi) located in the vicinity of the study area has been used to create a mean annual precipitation map (Fig. 4e) by using Kriging interpolation (Isaaks and Srivastava 1989). The average seasonal precipitation from the period 1980 to 2012 ranges from 350 to 500 mm. The landslide density percentage in each rainfall class is shown in Table 2. It appears that the highest density of landslides occurs in the 400–500 mm rainfall area (45 %). This indicates clearly that landslides are directly related to precipitation.

Distance to streams

The proximity to the drainage lines is also an important controlling factor of the occurrence of landslides. Streams may negatively affect the stability by eroding the slopes or by saturating the material. Five equal buffer zones have been created within the study area in order to determine the distance to streams area affected by landslide (Fig. 4f). The correlation of the respective distance class with the landslides occurrences indicates clearly that locations close to rivers show increased landslide activity (Table 2). The analysis shows that about 30 % of landslides occur within 50 m distance to streams especially on the left bank of the Rhumel river. It is also observed that as the distance from drainage line increases, the landslide frequency decreases.

Distance to roads

Distance to roads has been considered as one of the most important anthropogenic factors influencing landslides because road-cuts are usually the source of instability (Ayalew and Yamagishi 2005). Extensive excavations, application of external loads, and vegetation removal are among the most common actions observed along the road network slopes, during their construction. These actions are also responsible for landslide triggering, that is why, the road network and buffer zones should be evaluated during the analysis. The study area has been divided into five different buffers categorized to designate the influence of the road on the slope stability (Fig. 4g). It seems that 29 % of landslides occur within 0–150 m class, after which the frequency decreases rapidly (Table 2).

Distance to faults

Faults are zones of weakness, characterized by heavily fractured rocks which are prone to instability. Proximity (buffers) to these structures increases the probability of occurrence of landslides (Pradhan and Lee 2009). The study area has been divided into five equal area classes (Fig. 4h). The figure shows that the landslides density is higher within a distance of 200 m far from the faults (Table 2) and then the density decreases rapidly.

Landslide hazard mapping

As mentioned previously, the main purpose of the present study is to investigate and compare the landslide hazard mapping in Constantine city using five (5) models such as FR, AHP, Wf, WOE, and LR in the Constantine city, northeast of Algeria. For verification, the accuracy of results has been confirmed using the landslide inventory map.

Frequency ratio (FR) method

The FR model is one of the common methods in landslide hazard assessment. The key advantage of the FR method is the fact that it is easy to apply and the obtained results are readily intelligible. The FR method allows on to derive spatial relationship between the distribution of landslides and their conditioning factors. The FR is the ratio between the percentage of landslides in a given class and the percentage of the area in the same class. The Landslide Hazard Index (LHI) is calculated by a summation of each factor ratio value (Lee and Min 2001), as expressed in Eq. (1):

$$ \mathrm{L}\mathrm{H}\mathrm{I} = {\mathrm{F}\mathrm{r}}_1 + {\mathrm{F}\mathrm{r}}_2 + {\mathrm{F}\mathrm{r}}_3+\dots \dots + {\mathrm{F}}_{\mathrm{rn}} $$
(1)

Where LHI is the Landslide Hazard Index and Fr is the rating of each factor’s type or range. In relationship analysis, the ratio is that of the area where landslides occurred to the total area, so that a value of 1 is an average value. If the value is >1, it means a high correlation and a value lower than 1 means a lower correlation. Therefore, the frequency ratios of each factor’s type are calculated from the relationship with the landslide events as shown in Table 2.

Finally, the FR of each layer classes has been determined and a landslide hazard map (Fig. 5) has been produced prepared using the LHI map, as given in Eq. (1).

Fig. 5
figure 5

Landslide hazard map obtained using the frequency ratio method

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In the FR model, according to Table 2, lithological characteristics of the study area constitute an important factor in landslide occurrence. The Quaternary lacustrine calcareous and Miocene marly clay units are found to be more susceptible and exhibited higher frequency ratio values, respectively, of 4.71 and 2.15. The slope angle is among causes of sliding because it is strongly linked to the involved forces. The (15–30°) class has the highest value of FR (1.69), while, the slope class between 0 and 15° contains the lower value of FR (0.56) indicating clearly that the FR increases proportionally with the slope angle. Slope exposure analyses shows that most of the landslides occurred at the north (1.63), west (1.54), and flat (1.5) directions. The variation in the vegetation in a given area is a parameter that affects seriously the slope failures, and the landslide hazard decreases with the presence of vegetation. This is confirmed in this study, where the land use analysis showed that the landslide commonly occurred in the uncultivated agriculture (3.20) and barren areas (1.98). For the closer distances to the rivers, FR values greater than one (1) have been obtained indicating a high probability of landslide occurrence. The distances between 100 and 150 and 150–200 m have higher values of FR, respectively, 1.36 and 1.23, indicating a high probability of landslide occurrence. The distance to road is usually taken into account in landslide hazard assessments. The proximity to roads gives, respectively, values 0.95 and 1.02 for distances between 0 to 50 and 50 to 100 m. Also, the obtained results show that as the distance from faults increases, the landslide frequency increases (Table 2). The intervals 150–200 and >200 m show a FR values of, respectively, 0.62 and 1.24. FR analysis shows that higher FR values were distributed in higher precipitation zones (Table 2) with 1.33 observed in (450–500 mm) class and 1.35 (400–450 mm) class. This means that the landslide probability increases with the amount of precipitation.

Weighting factor (Wf) method

The weighting factor (Wf) method (Cevik and Topal 2003) known also as the InfoVal method used in this study is a modification of the statistical index (Wi) method, namely, the bivariate statistical method (Van Westen 1997). It is outlined and considered in many works as a simple and quantitatively suitable method in landslide hazard mapping.

The statistical index (Wi) method is based on a statistical correlation of the predisposing factors and the distribution of landslide areas. For each predisposing factor, the density of the landslide of the training set in each class is evaluated. The weight value for each class is defined as the natural logarithm of the landslide density in the categorical unit divided by the landslide density in the entire map:

$$ Wi= In\;\frac{\mathrm{Densclass}}{\mathrm{Densmap}}= In\left(\frac{Npix(Si)/ Npix(Ni)}{SNpix(Si)/ SNpix(Ni)}\right) $$
(2)

Where Wi is the weight given to the class of a particular thematic layer, Densclass is the landslide density within the thematic class, Densmap is the landslide density within the entire thematic layer, Npix (Si) is the number of landslide pixels in a certain thematic class, Npix (Ni) is the total number of pixels in a certain thematic class, and n is the number of classes in the thematic map. SNpix (Ni) is the number of pixels of all landslide, and SNpix (Ni) is the total number of all pixels. The natural logarithm is used to accommodate the large variation in the weights.

However, the statistical index method considers that each parameter/thematic map has an equal effect on landslides, which may not be the case in reality (Oztekin and Topal 2005). Therefore, a weighting factor (Wf) for each parameter map has been evaluated. For this purpose, first, the Wi value of each pixel has been determined by the statistical index method, then, all pixel values belonging to each layer are summed. By using the maximum and minimum of all layers, the results are stretched (Cevik and Topal 2003). Finally, the weighting factor ranging from 1 to 100 for each layer is determined by the following equation:

$$ {W}_f=\frac{\left({\mathrm{TWi}}_{\mathrm{value}}\right)-\left({\mathrm{MinTWi}}_{\mathrm{value}}\right)}{\left({\mathrm{MaxTWi}}_{\mathrm{value}}\right)-\left({\mathrm{MinTWi}}_{\mathrm{value}}\right)}*100 $$
(3)

Where Wf is the weighting factor calculated for each layer, TWivalue is the total weighting index value of cells within the landslide bodies for each layer, MinTWivalue is the minimum total weighting index value within the selected layers, and Max TWivalue is the maximum total weighting index value within the selected layers.

By using the Eq. (3), the weighting factor (Wf) values of each layer have been determined and reported in Table 3. For the analyses, the Wf value for each layer has been multiplied by the Wi value of each attribute, and finally, all causal factor maps have been summed in order to generate the final landslide hazard map (Fig. 6) from the Infoval or weighting factor. The resulted map has been reclassified by dividing the total number of elements (Wf value), mainly, into five distinct classes using the standard deviation method: low (−23 to −0.89), moderate (−0.89 to 1.03), high (1.03 to 2.40), and very high hazard (2.40 to 5.85). To control the accuracy of the landslide hazard maps produced by Wf method, the landslide inventory map and hazard map have been statistically compared.

Table 3 Weighting values (Wi) calculated, for each class of the selected landslide causal factors
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Fig. 6
figure 6

Landslide hazard map obtained using the weighting factor method

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Logistic regression (LR) method

The logistic regression (LR) is one of the most common statistical approach used in geosciences especially in landslide assessment. Logistic multiple regression allows one to evaluate a multivariate regression relationship between a dependent (landslides) and independent variables (such as slope angle, exposure, and lithology). As stated by Lee and Sambath (2006), logistic regression is useful for predicting the presence or absence of a characteristic or outcome based on value of a set of predictor variables. The important advantages of LR is that, through addition of an appropriate link function to the usual linear regression model, the variables may be either continuous or discrete, or any combination of both types, and they do not necessarily have normal distributions (Lee and Sambath 2006; Lee and Pradhan 2007). In the present study, the dependent variable is a binary variable representing the presence (1) or the absence (0) of a landslide, while the independent variables can be continuous, discrete, dichotomous, or a mix of any of these.

The algorithm of logistic regression applies maximum likelihood estimation after transforming the dependent variable into a logic variable representing the natural logarithm of the odds of the dependent occurring or not (Atkinson and Massari 1998; Bai et al. 2010). The mentioned model can be expressed according to following equation (Lee and Pradhan 2007):

$$ P=\left(\frac{1}{1+{e}^{-z}}\right) $$
(4)

Where P is the estimated probability of landslide occurrence, varying from 0 to 1 on an S-shaped curve, and Z is the a linear combination defined as by the following Equation (Eq. 5) and its value varies from −∞ to +∞:

$$ Z = \mathrm{intercept} + {b}_1{x}_1+{b}_2{x}_2+{b}_3{x}_3+\dots +{b}_{nXn} $$
(5)

Where here, b 1, b 2, b 3, and b n are the slope coefficients of the logistic regression model and x 1, x 2, x 3, and x n are the independent variables.

Using the logistic regression model, the spatial relationship between landslide occurrence and landslide affecting factors is assessed. For this purpose, the spatial databases of all the conditioning factors and landslides have been converted into grid format and, then, into Excel data format files to be used in the statistical package XLSTAT 2014 trial version. Then, the correlation between landslide event and landslide affecting factors has been estimated, and the logistic regression model has been run to obtain the coefficients of the landslide-conditioning factors. The Hosmer and Lemeshow test showed that the goodness of fit of the equation can be accepted because the significance of chi-square is larger than 0.05 (0.09). A higher R-square value of Cox and Snell R 2 (0.892) and Nagelkerke R 2 (1.365) indicates a better model. The relative operating characteristic (ROC) value of 0.9502 indicates a good correlation between the independent and dependent variables.

The weighting of the factor classes is based on the percentage area of landslides in the homogenous units. The percentage area of landslides which depend on each factor has been identified by calculating the ratio of the observed landslide area to the area of homogeneous units. The weight factor for each class of a specific factor has been calculated by summing the ratios for each class in different units. Weight factors have been transferred to the quantitative values from 0 to 10. The class with the maximum of the summation percentage area has been given a weight of 10, and the in other classes, the given weight is <10 based on their proportions.

The weight factor and the logistic regression coefficient for each thematic layer are shown in Table 4. Finally, the binary logistic regression model developed for the study area is given in Eq. 6:

Table 4 Logistic regression coefficients for each class of the selected landslide causal factors
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$$ \begin{array}{l}Z=-1,099+1.99*\mathrm{lithology}(1)+2.184*\mathrm{lithology}(2)+1.256*\mathrm{lithology}(3)+2.048*\\ {}\mathrm{lithology}(4)+2.105*\mathrm{lithology}(5)-0.008*\mathrm{lithology}(5)+2.112*\mathrm{lithology}(6)-0,005*\\ {}\mathrm{lithology}(8)-0,028*\mathrm{lithology}(9)-0.007* Slope(1)+1.552* Slope(2)+1.926* Slope(3)+\\ {}1.890* Slope(4)+1.255*\mathrm{Slope}(5)-0.220* Exposure(1)+1.256* Exposure(2)+2.016*\\ {} Exposure(3)+1.255*\mathrm{landuse}(1)+2.001*\mathrm{landuse}(2)+1.803*\mathrm{landuse}(3)+1.952*\mathrm{landuse}\\ {}(4)+1.675*\mathrm{landuse}(5)+2.100*\mathrm{landuse}(6)-0.012* Precipitation(1)+1.699* Precipitation\\ {}(2)+1.540* Precipitation(3)+1.255* Precipitation(4)+1.255* River(1)+1.417* River(2)+\\ {}1.709* River(3)+2.197* River(4)+1.6707* River(5)+2.197* Road(1)+1.5195* Road(2)\\ {}+1.761* Road(3)+1.120* Road(4)+2.064*\mathrm{Fault}(1)+2.097*\mathrm{Fault}(2)-0.082*\mathrm{Fault}(3)+\\ {}2.010*\mathrm{Fault}(4)\end{array} $$
(6)

According to Table 4 and Eq. 6, land use, precipitation, distance to streams, and distance to roads are positively related to the occurrence of landslides because of their positive coefficients. On the other hand, slope degree has a positive role in landslides occurrence except for the (0–5°) class which has a negative effect with a values of −0.007. In the case of the slope exposure, south (0), north (1.25), east (2.01), and west (0) facings have positive coefficients. Unlikely, flat facing has a value of −0.22. For the precipitation factor, results showed that only rainfall classes ranging from 350 to 400 did not have any role in landslides occurrence with a coefficient value of 0.875, while the remaining classes are positively related to the probability of landslides formation. Based on the results of the logistic regression for the lithology factor, it appears that the lithological formations of groups 7, 9, and 10 (Table 4) have an inverse effect on landslide hazard with a negative values of −0.008, −0.005, and −0.028, respectively, while the remaining classes have a positive relation with the landslide occurrence showing positive value has been observed.

The probability of landslide occurrence has been calculated by using the above logistic regression coefficients. The probability ranges from 0.94 to 1. The obtained landslide hazard map has been obtained based on the logistic regression model (Fig. 7). The probability map has been divided into four hazard classes: very low (0.9444–0.9991), low (0.9991–0.9996), moderate (0.9996–0.9998), and high (0.9998–1).

Fig. 7
figure 7

Landslide hazard map obtained using the logistic regression method

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Analytical hierarchy process

The analytical hierarchy process (AHP) is a theory of measurement dealing with quantifiable and intangible criteria applied to numerous cases, such as decision theory and conflict resolution (Vargas 1990). This technique has been already used for landslide hazard mapping and widely applied, and the results showed encouraging (Ayalew et al. 2005; Yalcin et al. 2011). The popularity of the AHP is due to its simplicity, flexibility, ease of use, and interpretation. The AHP is a multi-objective, multi-criteria decision-making approach, enables to organize, analyze, and solve complex decision problems (Saaty 1980). It is based on three major main steps: decomposition, comparative judgment, and synthesis of priorities. The decomposition principle is applied to structure complex problems into component factors and hierarchies them. The comparative judgment principle of AHP requires pair-wise comparison of the decomposed elements within a given level of hierarchal structure with respect to the next higher level. The synthesis principle of AHP takes each of the derived ratio local scale priorities in the various levels of the hierarchy and constructs a composite set of priorities for the elements at the bottom of the hierarchy. The AHP provides a numerical fundamental scale, ranging from 1 to 9 to calibrate the quantitative and qualitative performances of the priorities (Table 5) (Saaty 2008). This matrix ultimately enters in expert choice (EC) software and calculates the final weight for each conditioning factor with a consistency ratio (CR) expressed as:

$$ \mathrm{C}\mathrm{R} = \left(\mathrm{C}\mathrm{I}/\mathrm{R}\mathrm{I}\right) $$
(7)
Table 5 Fundamental scale for pair-wise comparisons (Saaty 2000)
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Where RI is the average of the resulting consistency index depending on the order of the matrix given by Saaty (1980) and CI is the consistency index expressed as:

$$ \mathrm{C}\mathrm{I} = \left({\lambda}_{\max }-n\right)/\left(n-1\right) $$
(8)

Where λ max is the largest or principal eigenvalue of the matrix and can be easily calculated from the matrix, and n is the order of the matrix. If CR is less than 10 %, then the matrix can be considered as having an acceptable consistency (Saaty 1977). A CR greater than 10 % requires revision of the judgment in the matrix due to an inconsistent treatment of particular rating factor. Finally, the landslide hazard map using AHP model has been constructed by using the following equation:

$$ {\mathrm{LHI}}_{\mathrm{AHP}}=\mathrm{Lithology} \times {\mathrm{W}}_{\mathrm{AHP}} + \mathrm{land}\ \mathrm{use} \times {\mathrm{W}}_{\mathrm{AHP}} + \mathrm{Slope}\;\mathrm{degree} \times {\mathrm{W}}_{\mathrm{AHP}}+\mathrm{slope}\;{\mathrm{ExposurexW}}_{\mathrm{AHP}}+\mathrm{distance}\ \mathrm{from}\ \mathrm{rivers} \times {\mathrm{W}}_{\mathrm{AHP}}+\mathrm{distance}\ \mathrm{from}\ \mathrm{roads} \times {\mathrm{W}}_{\mathrm{AHP}}+\mathrm{Distance}\ \mathrm{t}\mathrm{o}\ \mathrm{faults} \times {\mathrm{W}}_{\mathrm{AHP}}+\mathrm{Altitude} \times {\mathrm{W}}_{\mathrm{AHP}}+\mathrm{Precipitation} \times {\mathrm{W}}_{\mathrm{AHP}} $$
(9)

Where, WAHP is the weightage for each landslide-conditioning factor.

Using AHP method, the levels and weight values of the conditioning factors have been defined and calculated (Table 6). According to the degree of importance, land use, lithology, and slope appear as the most important factors that influence landslide occurrence with, respectively, values of 0.231, 0.228, and 0.166, whereas distance to fault is the less influencing landslide occurrence with a value of 0.03 (Table 6). The following values: λmax = 08.08, CI = 0.011 (1.14 %) and CR = 0.008, means that the pair-wise matrix is consistent (threshold CR < 0.10) and can be used for assigning the weight criteria. Using the above factors evaluation and its weights, the equation for landslide hazard is given as below:

Table 6 Preferences and weights of conditioning factors by analytical hierarchy
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$$ {\mathrm{LHI}}_{\mathrm{AHP}}=0.228\times \mathrm{Lithology}+0.231\times \mathrm{Precipitation}+0.166\times \mathrm{Slope}+0.09\times \mathrm{Land}\kern.4em \mathrm{use}+0.102\times \mathrm{Distance}\kern.4em \mathrm{t}\mathrm{o}\kern.4em \mathrm{streams}+0.088\times Exposure+0.061\times \mathrm{Distance}\kern.4em \mathrm{from}\kern.4em \mathrm{roads}+0.030\times \mathrm{Distance}\kern.4em \mathrm{t}\mathrm{o}\kern.4em \mathrm{faults}. $$
(10)

The weight values of the different factor classes have been determined based on the percentages of the area of each class covered by the landslide area (Table 7). In the presence of lithology, the higher percentage of the area of Miocene marly clay factor class covered by the landslide, thus it was given highest factor class weight value, i.e., 100, which when multiplied with the factor weight gave the actual weight value of 22.8 as shown in Table 7. The lowest percentage of area of Neritic limestone factor class covered by the landslide was given the lowest factor class weight value of 0, when multiplied with the factor weight yield gave the value of 0. Similarly, the weight values of different factor classes have been determined and seen in Table 7.

Table 7 Weight values of factor classes by analytical hierarchy process
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As a result of the AHP analyses, a landslide hazard map has been established for the urban area of Constantine city (Fig. 8) by summation of all weighted layers as given in Eq. (10). The resulting landslide hazard map presents four hazard classes following the LHI value: 33.5 % (2.921 < LHI > 6.831) of the area falls in very low hazard class, 27.3 % (6.831 < LHI > 8.407) in low hazard class, 20 % (8.407 < LHI > 11.307) in medium hazard class, while very small portion 19.3 % (11.307 < LHI > 16.4) of the area falls in the high hazard class.

Fig. 8
figure 8

Landslide hazard map obtained using the analytical hierarchy process method

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Weights of evidence method

The weights of evidence (WOE) is a statistical method that uses the log linear form of the Bayesian probability model to estimate the relative importance of evidence by statistical means. This method was first applied to the identification of mineral potential (Bonham-Carter et al. 1989) and then to landslide susceptibility and hazard mapping (Van Westen 1993; Van Westen et al. 2003; Suzen and Doyuran 2004).

This method calculates the weight for each landslide predictive factor (B) based on the presence or absence of landslides (L) within the area as follows (Bonham-Carter 1994):

$$ {W}^{+}= In\frac{p\left(B/L\right)}{P\left(B/\overline{L}\right)} $$
(11)
$$ {W}^{-}= In\frac{p\left(\overline{B}/L\right)}{P\left(\overline{B}/\overline{L}\right)} $$
(12)

Where P is the probability of ratio and ln is the natural logarithm (logit), in order to estimate the conditional probability of landslide occurrence. B is the presence of the predictive factor, and L is the presence of landslide. The overbar sign “¯” represents the absence of the class and/or landslide. Positive W + and negative W − weights are indications of the positive and negative correlations between the landslides occurrence and the presence of the predictable variable, respectively.

The difference between the positive and negative weights, as computed for each class of each parameter analyzed, is known as the weight contrast WC:

$$ \mathrm{W}\mathrm{C} = {W}^{+}\hbox{--}\ {W}^{\hbox{--} } $$
(13)

The magnitude of the contrast reflects the overall spatial association between the predictable variable and landslides. The value of WC is typically between 0 and 2; when the value of C tends to zero, the presence of the considered parameter does not affect the distribution of landslides in the area; whereas, when C is approximately two or more, the correlation is significant (Barbieri and Cambuli 2009).

In this study, firstly, the various thematic maps showing the landslides affecting factors have been overlapped with the landslide map. On the basis of these intersections, for each of the landslide-related factors, the weights, contrasts, and weights of evidence probability values have been calculated using Eqs. 11, 12, and 13 (Table 8). Then, the conditional independence has been tested before the integration of the patterns predictor to map the landslide hazard. The chi-square values to test the conditional independence between all pairs of binary patterns for each factor have been calculated at the 95 % significance level and 1° of freedom. The calculated chi-square values are greater than values of the table (7.9) suggest that the pairs are not significantly different.

Table 8 Weighting values (WC) calculated, for each class of the selected landslide causal factors
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The resulting contrast, as shown in Table 8, indicates directly the importance of each factor for the landslides occurrence. The contrast is positive for favorable factors to the occurrence and negative for unfavorable factors to the occurrence of landslides. Results of contrast value (Table 8) analysis showed that factors with highest landslide probabilities correspond to Miocene marly clay and Quaternary Colluviums formations, the agriculture land, the (450–500 mm) of precipitation, (5–15°) of slope, the flat of slope exposure, the (100–150 m) of distance to river classes. It can also be concluded from Table 8 that the contrasts of the factors indicate that there is no relation with the occurrence of landslides, as evidenced by the weights close to 0. For instance, distance from road classes show values near zero, indicates that the distance from roads is not a very sensitive predicting factor in the study area.

Weights are assigned respectively to the classes of each thematic layer, to produce weighted thematic maps, which have been overlaid and numerically added according to Eq. (14) in order to produce a Landslide Hazard Index (LHI) map:

$$ {\mathrm{LHI}}_{\mathrm{WC}} = \mathrm{W}\mathrm{C}\ \mathrm{Slope} + \mathrm{W}\mathrm{C}\ \mathrm{Exposure} + \mathrm{W}\mathrm{C}\ \mathrm{Fault} + \mathrm{W}\mathrm{C}\ \mathrm{River} + \mathrm{W}\mathrm{C}\ \mathrm{Precip} + \mathrm{W}\mathrm{C}\ \mathrm{Landuse} + \mathrm{W}\mathrm{C}\ \mathrm{Road} + \mathrm{W}\mathrm{C}\ \mathrm{Lithology} $$
(14)

where WC Slope, WC Exposure, WC Fault, WC River, WC Precip, WC Land use, WC Road, and WC Lithology are distribution-derived weights relative to slope, exposure, fault, distance to river, precipitation, land use, distance to road, and lithology maps, respectively.

Thus, the landslide hazard map (Fig. 9) of Constantine city is prepared from the respective LHI values. The range of landslide hazard is classified into four categories: very low (−8.58–−1.8), low (−1.8–0.7), moderate (0.7–3.15), and high (3.15–9.55).

Fig. 9
figure 9

Landslide hazard map obtained using the weights of evidence method

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In this study, the LHMs have been divided into four classes based on the standard deviations method, since the data obtained values in the LHMs by using the FR, Wf, LR, WOE, and AHP models show a normal distribution (Suzen and Doyuran 2004; Ayalew et al. 2005; Yalcin et al. 2011).

Validation and comparison of landslide hazard maps

The most important task, in landslide hazard modeling, is to perform the validation of the predicted results. Without validation, the predicted models and prepared maps are less useful and without scientific significance (Chung and Fabbri 2003). There are different ways to validate LHM using mathematical and statistical tools. The most useful methods to represent the quality and the performance of LHM used in the literature are the receiver operating characteristics (ROC) and the statistics rules for spatial effective LHMs. The validation process has been performed by comparing the known landslide location data with the LHMs. In this comparison, the landslide activity map is matched with the LHMs. Then, the distribution of current landslide area is determined according to the landslide hazard classes in order to test if the percentage of landslides is effectively increasing with the hazard degree.

The ROC curve is one of the statistical techniques that can be used to provide predictions of the performance and to compare the different models (sensitivity vs. specificity). The area under ROC prediction curve (AUC) characterizes the quality of a forecast system by describing the system’s ability to anticipate correctly the occurrence or nonoccurrence of a predefined “event” (Yesilnacar and Topal 2005; Chung and Fabbri 2003; Lee et al. 2003). The ROC curves can be summarized quantitatively based on the area under the ROC curve, which gives the accuracy of the developed model for predicting the landslide hazard. The quantitative–qualitative relationship between AUC and prediction accuracy can be given as follows: 0.9–1, excellent; 0.8–0.9, very good; 0.7–0.8, good; 0.6–0.7, average; and 0.5–0.6, poor (Yesilnacar and Topal 2005).

In this study, ROC curves have been obtained by comparing the landslide training pixels 30 % (2558 landslide pixels) with the six LHMs and the area under curves has been calculated. Figure 10 shows the ROC curves for the six landslide models. The validation results showed that the prediction accuracy of LHMs, produced by FR, WOE, AHP, Wf, Wi, and LR are, respectively, 86.59, 82.38, 77.86, 77.58, 76.77, and 70.45 %. The obtained results indicate that the use of FR for generating LSM provides more accurate prediction in comparison with WOE, AHP, Wf, Wi, and LR. Hence, it is concluded that all the employed models in this study show reasonably good accuracy in predicting the landslide hazard of the study area.

Fig. 10
figure 10

Receiver operating characteristics (ROC) curves representing quality of the five models used

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Also, the resulted LHMs have been verified using the two rules for spatial effective LHMs: First, the percentages of landslides increased concurrently with the degree of hazard and the observed landslide should belong to the high hazard class, and second, the high hazard class should cover only small areas (Bai et al. 2010; Can et al. 2005; Pradhan and Lee 2010a; Pourghasemi et al. 2012c). The percentages of existing landslides falling into the four hazard classes have determined and presented in Table 9. It is deduced that the smaller amount of landslides was distributed in the low and very low hazard classes, and the higher amount of landslides were scattered in the high hazard class of the LHMs. Table 9 shows that the high hazard classes, found by using all the methods, contain 51 to 53 % of the active landslide zones, while the moderate zones give 26 % of the active landslide zones and about 13 % of the active landslide zones coincide within the moderate hazard class. The very low hazard zones show less than 7.5 % of the active landslide zones in all used methods. The results of Table 9 show that the percentages of landslides increase effectively from low to very high hazard and the high hazard class covers only small areas.

Table 9 Active landslide zones falling into the various classes of the landslide hazard maps
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According to the obtained LHM from the FR model, 13 % of the total area falls in very low landslide hazard (Fig. 11). Low, moderate, and high hazard zones represent, respectively, 20, 17, and 13 % of the total area. In the established LHM with WOE model, 24 % of the total area belong to very low landslide hazard. Low and moderate hazard zones give, respectively, 26 and 25 % of the total area. While the high zones values give approximatively 24 %. The obtained LHM by using the AHP model shows 33.5 % of the total area in very low landslide hazard. Low, moderate, and high hazard zones give, respectively, 27, 20, and 19 % of the total area (Fig. 11). The produced LHM through the Wf method gives small percentages (13 %) for the high hazard areas, while the very low, low, and moderate hazard areas are 22, 36, and 27 %, respectively. The LR method results are very low (40 %), low (28 %), moderate (21 %), and high (11 %). The high hazard zones percentages in the FR, AHP, Wf, and LR methods show small values of 13 % (Fig. 11), while the low hazard zones percentages in the FR, AHP, Wf, WOE, and LR methods show high values more than 25 %.

Fig. 11
figure 11

Histograms showing the relative distribution of various hazard classes of different landslide hazard maps

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Discussion and conclusion

Landslides are among the most damaging natural hazards constituting a significant constraint for urban development in the Constantine city. Therefore, a landslide hazard map depicting the most vulnerable areas to landslides appears as a fundamental tool in risk management as an integral part of land use planning in the hazard prone areas. From scientific literature, various methods have been suggested for landslide hazard mapping, including heuristic, statistical, and deterministic based approaches. In recent years, several attempts have been made to apply different methods of LHM and to compare results in order to select the best suitable model.

In this research, we compare the obtained results of landslide hazard mapping by using five different methods: FR, Wf, LR, WOE, and AHP in the Constantine city, northeast of Algeria. The used methods are based on real, field-surveyed data, i.e., the spatial distribution of both landslides and/or the causal factors. Firstly, a landslide location has been identified by using aerial photographs and satellite images interpretation supported by available literature and field surveys. As a result, 70 % of identified landslides have been used as training data and the remaining (30 %) have been used to validate the models. Eight landslide-conditioning factors including lithology, slope gradient, slope exposure, land use, distance from roads, distance from streams, distance from faults, and precipitation have been considered for which to derive maps have been derived by using various GIS tools. The LHMs have been classified into five classes: very low, low, medium, and high using the standard deviation classifier. After that, the obtained LHM has been validated by comparison with known landslide locations.

According to the obtained area under the curve (AUC), the FR model showed higher prediction performance (86.59 %) than WOE (82.38 %), AHP (77.86 %), Wf (77.58 %), and LR (70.45 %) models. Hence, we concluded that all the employed models in this study give reasonably good accuracy in predicting landslide hazard for the Constantine city. Also, the accuracy results procedure by using statistics rules showed that the density of the landslides increases from low to very high hazard zone, and on the other hand, the high percentage of the landslides has been occurring in very high hazard area which covers the lower percentage the study area validating hence our results.

Such results have been observed in models such as FR, AHP, LR, and artificial neural network ANN (Yılmaz 2009; Pradhan and Lee 2010a; Park et al. 2012; Nourani et al. 2013); heuristic and bivariate statistical models, probabilistic, bivariate, and multivariate models (Pradhan and Youssef 2010; Tien Bui et al. 2011a; Kevin et al. 2011; Ozdemir and Altural 2012; Shahabi et al. 2012). Ayalew et al. (2005), Esmali Ouri, and Amirian (2009), through their works, stated that AHP model was better than the LR in Sado Island, Japan, and Iran, respectively. Yalcin (2008) reported that AHP method is a more realistic landslide susceptibility map than when using the bivariate statistical models (Wi and Wf). Also, Yalcin et al. (2011) found that the results of using the Wf method are better than the FR, AHP, Wi, and LR models in Trabzon, NE, Turkey. For landslide hazard analysis at Cameron area, Pradhan and Youssef (2010) showed that the FR model is provided better in predictions of landslides than bivariate and LR models. Yalcin (2008) evaluated the accuracy of the application of FR, LR, and ANN for landslide susceptibility mapping in the Ardesen (Turkey). The results showed that the AHP method provided realistic results of landslide susceptibility than the Wi and Wf methods. Pourghasemi et al. (2013) presented the results of application of LR, SI, and AHP models for landslide susceptibility mapping in the north of Tehran metropolitan, Iran. The validation results indicated that the LR model is better in predictions of landslide susceptibility than using the SI and AHP models.

The resulted LHMs in this study may constitute a helpful tool for planners, decision makers, and engineers in slope management and future development planning in the city of Constantine. They may serve as useful guides for planners and engineers in choosing suitable locations for the implementation of developments. As the results are given at large scale, the exact extent of the slope instability areas and the details of high hazard area classes are determined, this will be useful for need further detailed site-specific studies. The area falling in the predicted high hazard zone is required to be monitored, and remedial and preventive measures may be initiated to protect life and property from future landslides. Also, it is worthy to mention that the same method can be used elsewhere in the northern part of Algeria where similar geological, geomorphological, and climatic feature prevails.