Analytic network process model for landslide hazard zonation

Engineering Geology 85 (2006) 281 – 294 www.elsevier.com/locate/enggeo

Analytic network process model for landslide hazard zonation K.M. Neaupane ⁎, M. Piantanakulchai Civil Engineering Program, Sirindhorn Int. Ins. of Technology, Thammasat University, Thailand Received 2 June 2005; received in revised form 22 February 2006; accepted 23 February 2006 Available online 2 May 2006

Abstract Various controlling factors such as lithology, slope angle, slope aspect, landuse, channel proximity etc. are generally considered for the landslide hazard assessment. Although outer dependence of these parameters to a landslide is inevitably taken into account, inter-dependence among the factors is seldom addressed. Analytic Network Process (ANP) is the multi-criteria decision making (MCDM) tool which takes into account such a complex relationship among parameters. In this research, an ANP model for landslide susceptibility is proposed, priority weights for each parameter controlling the landslide were determined, and a hazard map was prepared of an area in a fragile mountainous terrain in the eastern part of Nepal. The data used in the example were derived from published sources, aerial photographs and a topographic map. However, the procedures developed can readily incorporate additional information from more detailed investigations. © 2006 Elsevier B.V. All rights reserved. Keywords: Slope failure; Landslide; ANP; Hazard zonation

1. Introduction Landslide Hazard (LH) defines the physical attributes of a potentially damaging landslides in terms of mechanism, volume and frequency. A map portraying the geographical variations in the susceptibility of slopes to failure is referred to as a Landslide Hazard Map. A classical approach to LH mapping is based on the premise that the relative potential for slope failure can be assessed by reference to the existing distribution of failures. Researchers generally make the following fundamental assumptions as a basis for a LH map (Varnes, 1984; Hutchinson, 1995)

⁎ Corresponding author. Tel.: +66 2 9869009; fax: +66 2 9869112. E-mail address: [email protected] (K.M. Neaupane). 0013-7952/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2006.02.003

• Landslides will always occur in the same geological, geomorphological, hydrogeological, and climatic conditions as in the past, • Physical factors controlling a landslide can be identified, and a degree of hazard can be evaluated for classification. Much literature available on landslide hazard assessment methodologies broadly falls into three main approach groups: qualitative, quantitative and Artificial Intelligence (AI) approaches. In general, a qualitative approach is based on the subjective judgment of an expert or a group of experts whereas the quantitative approach is based on mathematically rigorous objective methodologies. Artificial Intelligence (AI) techniques can make use of heuristic knowledge or pattern matching technique as opposed to solving a set of mathematical equations. The AI broadly covers Artificial Neural

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Networks (ANN), Expert system, and other heuristic knowledge-based or rules-based techniques. 2. Literature review A comprehensive review of literature related to landslide hazard assessment has been presented and reviewed by Aleotti and Chowdhary (1999). The majority of these literature are excluded in this review; literature pertaining to the advancement of the assessment methods in recent years (1999–2005) are the focus of this review. 2.1. Quantitative approach Over the past two decades landslide hazard assessment portraying the spatial distribution based on quantitative analysis has gained widespread recognition. The enormous potential of Geographic Information System (GIS) in storing, processing and manipulating digital data has revolutionized the technology of hazard mapping. The direct comparison based on statistical relationship between contributory factors with landslide distribution is the strength of the statistical method. With the GIS, this process is easy since it comes with statistically powerful tools (both bivariate and multivariate) for analysis. Some of the literatures using GIS based statistical bivariate method have taken numerous parameters into consideration: lithology, slope angle, aspect, height, landuse, channel proximity etc. Aleotti and Chowdhary (1999) reviewed a large number of literature on the landslide hazard assessment; much of these literatures are devoted to statistical analysis. Recently, Suzen and Doyuran (2004) provided a GIS based comparison between bivariate and multivariate analysis in terms of speed and accuracy. Safety factor based susceptibility analysis is commonly done in soil engineering practice. These methods may not be suitable for regional scale but they provide sound engineering appraisal of an existing slope. In its simplest form, this approach involves calculation of stability index (safety factor) for each slope. GIS facilities can be used to simulate multiple scenarios based on variable factor hypothesis. If safety factors are assumed to be a random variable, a probability distribution function can be defined and failure uncertainties are derived based on some reliability index. Wu and Abdel-Latif (2004) used safety factor and failure probability based on the principal components of infiltration and groundwater response and predicted landslide hazards in the Cascade Mountains, Washington State (USA).

2.2. Artificial Intelligence approach Artificial Intelligence (AI) is regarded as an attempt to understand the processes of perception and reasoning that underlie successful problem-solving, and an attempt to incorporate the results in effective computer programs. Many of these developments in AI are, in principle, generally applicable to the realm of GIS. Hazard Assessment techniques make use of a set of reasonably well defined rules and therefore ideally suited for implementation as knowledge-based systems. In the last ten years there has been a significant increase in the application of Artificial Intelligence (AI) to many practical problems. Wislocki and Bentley (1991) described the development of a KBS for the determination of planning applications with respect to landslide hazard in South Wales. The system attempted to assess the landslide hazard that may affect proposed development sites and it produced output in the form of planning response options. Wang et al. (1994) used a KBS (expert system) for investigating potential landslides of a shearing zone. Artificial Neural Networks (ANN) are networks of highly interconnected neural computing elements that have the ability to respond to input stimuli and to learn to adapt to the environment. ANN establishes rules during learning phase and uses the rule to predict the output during recall. Neaupane and Achet (2004) successfully used Backpropagation Neural Networks (BPNN) to predict the low-speed landslide displacement in the higher Himalayas. From hazard mapping perspective, Lee et al. (2003a) created spatial database from GIS, extracted landslide related factors and fed to the ANN to analyze the susceptibility. Although ANNs are good at establishing rules between input and output, they do not explain how the decisions are reached. Fuzzy logic systems, on the other hand, can reason with the imprecise information by pulling away from logic that is crisp or Boolean (binary; 0 or 1). This method has an advantage over Boolean logic in that it mimics complex human reasoning in order to arrive at realistic conclusions about the imprecise and fuzzy nature of reality. In view of the fact that most routine geotechnical analysis are performed with deterministic models, and considering that the soil parameters are uncertain, fuzzy numbers can be assigned as input to get the fuzzy output. Juang et al. (1992) published pioneering work in the field of uncertainty modeling with fuzzy sets using Monte Carlo technique to sample values for input parameters, and used it for slope failure potential mapping. In their work, an evaluation tree consisting of two levels of factors affecting natural slopes

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was established and failure potential was rated in linguistic terms as very high, high, medium, low and very low. A slope failure potential index (SFPI), ranging from 0 to 1, was defined based on the final fuzzy set. Lee and Juang (1992) conducted a survey of expert opinions on slope failure in Southwestern Taiwan mudstone area, and assessed the failure potential of the mudstone slopes. Juang and Huang (1992) described how experts' judgment could be aggregated and assessed using fuzzy entropy principle. Likewise, Uromeihy and Mahdavifar (2005) calculated the so-called hazard potential index (HPI) using fuzzy sets and used the index to prepare the landslide hazard zonation map. Ercanoglu and Gokceoglu (2002) demonstrated the use of fuzzy logic and GIS for the assessment of landslide susceptibility in north of Yenice, NW Turkey. Binaghi et al. (1998) evaluated slope instability maps using fuzzy logic with Dempster– Shafer theory and compared the result with the probabilistic approach. Fuzzy logics are often combined with ANNs to form an intelligent hybrid system (Fuzzy neural network) to solve pattern recognition and mapping problems (Kumar et al., 2000). An example of such a hybrid system can be found in Ni et al. (1995) who identified and evaluated the slope failure potential using a fuzzy neural network model. Lu and Rosenbaum (2003) argued that the power of the ANN and Grey Systems approaches lies in employing the behavior of the system rather than knowledge of explicit relations. Using published data, the application of these techniques was illustrated to predicting the state of slope stability. 2.3. Qualitative approach Qualitative approaches of hazard assessment make use of expert(s) evaluation. In its simplest form, hazard zonation is carried out directly in the filed by engineering geologist and/or geomorphologists. This method was widely recognized during 1970s and 1980s (Aleotti and Chowdhary, 1999). Landslide susceptibility based on geological and geomorphological attributes continues to be popular especially for regional scale (Pachauri et al., 1998). Use of engineering geomorphology for desk study and its successful application to the road design in some of the geologically challenging environment has been reported by Hearn (2002). In another method of qualitative analysis, expert(s) select factors controlling landslides that are proportionate to the relative contributions. Such a system can make use of GIS for overlaying the weighted maps (Soeters and vanWesten, 1999). In the same line of research, analytical logical methods tentatively propose a relationship which

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links the weighted factors and predicts displacements (Bughi et al., 1996). Analytic Network Process (ANP) is the successor of the popular Analytic Hierarchy Process (AHP) model developed by Saaty (1980). The AHP is a Multi-Criteria Decision Making (MCDM) tool at the core of which lies a method for converting subjective assessments of relative importance to a set of overall scores or weights. The AHP is a top-down decision model and, therefore, the criteria and alternatives are assumed independent. However, bias could occur when the criteria and subcriteria are correlated with each other. Twenty five years after the publication of pioneering work in the field of AHP, Saaty (1980, 1996) developed the ANP model, which could handle this situation of inner dependence among elements in a network. Comprehensive collection of literatures involving AHP could be found in http://www.expertchoice.com. Some of the recent publications involving ANP are found in strategic policy planning (Ulutas, 2005; Erdogmus et al., 2006), industrial management (Karsak et al., 2002; Partovi, 2006) economics and finances (Niemura and Saaty, 2004), forest management (Wolfslehner et al., 2004). Some civil engineering applications of ANP are found in construction planning (Chen et al., 1998) and highway planning (Piantanakulchai, 2005). Much work and literature available on the application of AHP in geo-engineering are devoted to the development of relative weights of influential factors and incorporation of the weights into GIS system. As for example, Dai et al. (2001b) derived relative weights of influential factors affecting urban (Lanzhou city, China) geoenvironment using AHP, and the suitability potentials of urban landuse were evaluated and assessed using GIS. Similarly, Ayalew et al. (2004) used pairwise comparisons to arrive at the relative weights of landslide controlling factors, and used GIS to prepare landslide hazard assessment map for Tsugawa area of Agano River, Niigata Prefecture, Japan. Recently, Komac (2006) employed multivariate statistical analysis and concluded that the use of the AHP method gives a means to define the factor weights in the linear landslide susceptibility model. Researchers have taken numerous parameters (landslide controlling factors) into consideration for landslide hazard assessment namely lithology, slope angle, aspect, height, landuse, channel proximity etc. Although the outer dependence of these parameters to the landslide is inevitably taken into consideration, inner dependence among these factors is seldom addressed. Relationships between lithology and drainage network, slope and vegetation, aspect and rainfall etc. are easily identified and

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can be integrated in the ANP model. The ANP model, is therefore, ideally suited for landslide hazard assessment. 3. Theoretical background of ANP model Details on the Analytic Network Process (ANP) model can be found in Saaty (1999); the fundamentals are summarized here for completeness. The ANP model consists of the control hierarchies, clusters, elements, interrelationship between elements, and interrelationship between clusters. The modeling process can be divided into four steps for the ease of understanding which are described as follows: 3.1. Step I: pairwise comparison and relative weight estimation The ANP Control hierarchy provides overriding criteria for comparing each type of interaction in the network. Saaty (1999) proposed four basic control hierarchies, Benefits, Opportunities, Costs, and Risks (BOCR). It is, however, not necessary to include all control hierarchies in a model; it all depends on the relevance of criteria. The determination of relative weights in ANP is based on the pairwise comparison as in the standard AHP. Pairwise comparisons of the elements in each level are conducted with respect to their relative importance towards their control criterion based on the principle of AHP. Saaty (1980)suggested a scale of 1–9 when comparing two components (see Table 1). The score of aij in the pairwise comparison matrix represents the relative importance of the component on row (i) over the component on column (j), i.e., aij = wi / wj. The score of 1 represents equal importance of two components and 9 represents extreme importance of the component i over the component j.

The reciprocal value of the expression (1 / aij) is used when the component j is more important than the component i. If there are n components to be compared, the matrix A, is defined as 2 3 w1 =w1 w1 =w2 N w1 =wn 6 w2 =w1 w2 =w2 N w2 =wn 7 7 A¼6 4 v v v 5 2 wn =w1 wn =w2 N wn3=wn 1 a12 N a1n 6 1=a12 7 1 N a 2n 7 ¼6 ð1Þ 4 v v O v 5 1=a1n 1=a2n N 1 The core of AHP is that instead of assigning the weight wi and wj to the components i and j, the relative weight wi / wj is evaluated for every pair of components. After all pairwise comparison is completed the priority weight vector (w) is computed as the unique solution of Aw ¼ kmax w

ð2Þ

where λmax is the largest eigenvalue of matrix A. The n priority vector w is often normalized by α = Σi=1 wi. This ensures the uniqueness of w and provides that α becomes unity (Saaty, 1980). The consistency index (CI) of the derived weights could then be calculated by CI ¼

kmax −n n−1

ð3Þ

In general, if CI is less than 0.10, satisfaction of judgments may be derived (Saaty, 1980). With respect to any criteria, pairwise comparisons are performed in two levels, the element level comparison and the cluster level comparison.

Table 1 Scale of relative importance (Saaty, 1980) Intensity of importance

Definition

Explanation

1 3

Equal importance Moderate importance

5

Strong importance

7

Very strong or demonstrated importance

9

Extreme importance

2, 4, 6, 8 Reciprocals of above

Intermediate values between adjacent scale values If activity i has one of the above nonzero numbers assigned to it when compared with activity j, the j has the reciprocal value when compared with i

Two activities contribute equally to the objective Experience and judgment slightly favor one activity over another Experience and judgment strongly favor one activity over another An activity is favoured very strongly over another; its dominance demonstrated in practice The evidence favoring one activity over another is of the highest possible order of affirmation When compromise is needed

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3.2. Step II: formation of initial supermatrix Elements in ANP are the entities in the system that interacts with each other. They could be a unit of decision makers, criteria or sub-criteria (if exists), possible outcomes, and alternatives etc. The determination of relative weights mentioned above is based on pairwise comparison as in standard AHP. The weights are then put into the supermatrix that represents the interrelationships of elements in the system. The general form of the supermatrix is described in Fig. 1 where CN denotes the Nth cluster, eNn denotes the nth element in the Nth cluster, and Wij is a block matrix consisting of priority weight vectors (w) of the influence of the elements in the ith cluster with respect to the jth cluster. If the ith cluster has no influence to the ith cluster itself (a case of inner dependence), Wij becomes zero. The supermatrix obtained in this step is called the initial supermatrix. 3.3. Step III: formation of weighted supermatrix The initial supermatrix consists of several eigenvectors each of which sums to one. The initial supermatrix must be transformed to a matrix in which each of its columns sums to unity. To reduce the column sum to unity each of the elements in the block of the supermatrix is factored by its priority weight to the control criterion. The eigenvector obtained from cluster level comparison with respect to the control criterion is applied as the cluster weights. This results in a matrix of its columns each of which sums to unity. If any block in the supermatrix contains a column with all zero elements, it must be normalized by the cluster's weights to ensure the

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column sums to unity. The concept is similar to Markov Chain in that the sum of probabilities of all states equals to one. This matrix is called the stochastic matrix or weighted supermatrix. 3.4. Step IV: calculation of global priority vectors and weights In the final step, the weighted supermatrix is raised to limiting power to get the global priority vectors as in Eq. (4) lim W k

kYl

ð4Þ

If the supermatrix has the effect of cyclicity, there may be two or more N limiting supermatrices. In this case, the Cesaro sum is calculated as in Eq. (5) to get the average priority weights as follows:  X 1 Wik lim ð5Þ kYl N 4. Application of ANP model for landslide hazard zonation 4.1. Study area The geological construction of mountain system is inextricably linked to plate tectonics. Nepal typifies the geological zones and variety of rocks that makes up an orogenic mountain chain. The Himalayas are among the youngest major mountain systems in the world. The product of the monsoonal climate and the rapid and jerky uplift of the Himalayas with its massive erosion dictate the geo-dynamics of the region. On the southern margin of the Himalayas, Siwalik hills rise abruptly. The hills are formed from debris derived from the erosion of the rising Himalayas to the north. High levels of slope instability and erosion in the Siwalik are attributed to its geomorphology and intense rainfall and high rates of chemical weathering under humid sub-tropical climate. The study area lies in the eastern part of Nepal in low Himalayas (the Siwalik hills). The Dharan–Dhankuta road connects two eastern towns of Nepal, Dharan and Dhankuta. The terrain through which this road passes is considered to be among the most unstable in Nepal. The study area is chosen to demonstrate the application of ANP model for hazard zonation. 4.2. Data preparation

Fig. 1. General structure of the supermatrix.

Basic data were generated from aerial photographs of the area (1 : 25,000 scale), topographical maps (1 :

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50,000 scale) and geological map (1 : 200,000 scale). The element of air photo interpretation was considered for land use identification. The digital elevation model was created from the topographic map from which the slope and aspect maps were derived. The entire area was divided into grids; each cell of the grid having a dimension of 230 × 230 m. Priority weights obtained from the ANP model would be integrated with the cell information to evaluate the stability assessment of individual cell. 4.3. Landslide-controlling variables 4.3.1. Slope steepness and aspect The relation between landslides and slope gradient is affected by the interaction of geology with geographic process shaping the terrain. While steeper slopes provide greater potential energy to induce failure, they are also indicative of higher strength of materials. This trade-off between increased driving force and increased soil strength appears to reduce the importance of slope steepness (Roth, 1983). For zoning purpose slope inclinations are often grouped into ranges. Varnes (1978) noted that steepness of a slope in relation to the strength of slope forming material was very complex that the steep slope in competent rocks were more stable than the gentle slope in weaker formation. Fig. 2 shows distribution of slope angle grouped into three ranges as gentle, steep and very steep. The aspect of the slope or the slope direction has the potential to influence its physical properties and its susceptibility to failure. The process that may be

Fig. 2. Slope angle distribution.

Fig. 3. Slope aspect distribution.

operating include exposure to sunlight, drying winds and rainfall (Dai et al., 2001a). The weather and climate of Nepal are controlled by the seasonal alternation of the monsoon winds. The towering Himalayas play a critical role, blocking the northwesterly advances of moist, tropical air from the Bay of Bengal, and ultimately leading to its conversion to rain in the summer. On average 81% of the annual rainfall occurs during monsoon months between May and September, inclusive. It is therefore reasonable to assume that the slopes facing south and east are more susceptible to rain induced landslides whereas slopes facing north and west remain under rain shadow. The slope aspects of the study area is shown in Fig. 3. 4.3.2. Underlying geology Lithology (rock type) exerts a fundamental control on geomorphological characteristics of a landscape. The nature and rate of geomorphological process depend, to some extent, on the lithology and weathering characteristics of underlying materials. The landslide process, therefore, has direct correlation to lithology (Dai et al., 2001b). It is also noted that geological structure decides the type, distribution, state and movement rule of groundwater, which affects or triggers a landslide event. The geology of the study area is broadly divided into four units: Quaternary alluvium, sedimentaries, quartzite and

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Fig. 4. Geology and stream network distribution.

phyllite (Fig. 4). Phyllite is a low grade metamorphic rock derived from fine grained sediments and contains a large amount of aligned mica, which imparts a coarse splitting plane. Sedimentary rocks found in the area are weak and weatherable. Besides the geological formation, geological contact between formations also possesses the line of weakness. 4.3.3. Channel proximity Networks of drainage channels and associated drainage basins form complex functional entities not only for hydrological processes but also for geomorphological processes at large. The steady state tectonic mass flux resulting from orogenic uplift may be balanced by erosion till a montane system of ridges and valleys is established. Gorge incision, landsliding, ground-water seepage, fluvial depositions are thus the dominant geomorphological processes in orogen (Hovious et al., 1998). Lee et al. (2003b) reported that heterogeneity of channel morphology increases in proximity to low-order confluences prone to debris flows. Further, gully erosion is intense in hill slope and undercutting of the slope toes is a commonplace. Proximity of drainage lines thus can be taken as a factor that influences the landslides (Dai et al., 2001b). For zoning purpose, proximity to stream and/ or confluence is taken as one of the factors affecting the landslide occurrences. It is assumed that the presence of a confluence in an area will have combined effect and thus higher chances of triggering landslides.

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4.3.4. Landuse and vegetation cover There are much conflicting evidences in the literature concerning the effects of vegetation on slope stability. Based on the examination of natural terrain in Lantau Island, Franks (1999) reported that sparsely vegetated slopes are most susceptible to failure. However, Dai et al. (2001a) found that the density of landslide on bare land is relatively low as compared with that on grassland. Nilaweera and Nutalaya (2004) put forward the most convincing explanation on the effects of vegetation on landslide susceptibility and stated four factors to be accounted for. The hydrological factors (soil moisture depletion as a result of transpiration) and mechanical factors (root reinforcement) increase the stability of a slope. Surcharge from weight of trees may or may not do so depending upon the steepness of slope and potential failure mode. The wind-breaking is likely to decrease the factor of safety of a slope. The landuse system in the study area is divided into forest (higher trees), scrubland (bushy vegetation), agriculture land and bare land (Fig. 5). The effect of vegetation on landslide has been studied in view of the slope inclination. As for example, a moderately steep slope (30–60°) with forest cover is assumed to have benefited from vegetation coverage but the same cannot be said for a very steep slope (N60°). In the similar manner, the agriculture system (terraces) in the hilly areas is assumed to have relatively beneficial impacts on hill slope stability.

Fig. 5. Landuse distribution.

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4.3.5. Groundwater hydrology The effect of rainfall on the stability of slope should be studied in light of its ability to build up positive porepressure behind the slope face. A positive correlation between rainfall duration, intensity, pattern and the sequence of rainfall and landslide occurrence is reported by Nilsen et al. (1976) and Roth (1983) to which the soil permeability should be added (Tsaparas et al., 2002). VanWesten et al. (1997) summarized that the hydrological failure could be triggered by saturation of top soil during intense rainfall, formation of a perched water table in impermeable materials and reduction of shear strength and buildup of pore pressure behind slope face due to groundwater level rise. The study area covers approximately 5 × 5 km square of ridge, valley, crisscrossed with network of streams. The monsoon rainfall variation for such an area may be assumed minimal in regional scale. However, extreme geographical variations of rainfall may occur which could not be reliably quantified and therefore the effect of groundwater hydrology is not included in this study. 4.4. ANP model for landslide hazard assessment The ANP model is represented by a network structure indicating all dependences among clusters and determining the direction of influences. Fig. 6 illustrates a typical

ANP model for landslide hazard assessment. As shown in the figure, connections can be set among elements within a cluster (i.e., inner dependence) and between clusters (i.e., outer dependence). In a cumulative view, a cluster is connected to another when at least one of its elements is connected to at least one element of the other cluster. For the initial supermatrix calculation, pairwise comparisons were done between all elements influenced by other elements within the same cluster (nodal comparison). Relative weight vectors were calculated using Eq. (2). The matrix of relative weight vectors is called the initial supermatrix, which was multiplied by cluster weights, element by element, to arrive at the weighted supermatrix. Table 2 shows a sample of questionnaire used for cluster comparison, and a sample calculation for relative weight and consistency index. A similar procedure was followed for nodal comparisons. 4.5. Results and discussion Table 3 presents the initial supermatrix and the matrix of cluster weights. Table 4 illustrates weighted super matrix derived from the element by element multiplication of the initial supermatrix and the limiting supermatrix with global priority weights. The weighted supermatrix was raised to the power until its convergence using MATLAB.

Fig. 6. A typical ANP network for landslide hazard assessment.

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Table 2 Sample of cluster comparison questionnaire and relative weight calculation

The priority weights obtained from the ANP model were multiplied with the cell attributes to get the total risk score for a cell. Raw risk score (Xraw) alone could not reflect the relative meaning of risk, and therefore, the normalized risk score was used to construct the measurement scale (0 to 1). The raw score was normalized in such a way that the theoretical worst case scenario has a normalized score of 1, and the

theoretical best case scenario has a normalized score of 0. The risk score for the theoretical best condition (Xmin) was calculated using the lowest global risk score for the group of landslide controlling variables, i.e., a parcel of land with gentle slope angle, rain-shadow slope aspect, away from channel/drainage proximity, scrub land vegetation cover with strong lithology. On the contrary, the theoretical worst risk score (Xmax) was calculated

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Table 3 Initial supermatrix and cluster weight (a) Unweighted supermatrix Landslide controlling variables

Slope angle

Slope aspect

Land use and vegetation

Lithology

Gentle (G) Steep (S) Very steep (VS) Rain-side (R) Rain shadow (RS) Single stream (ST) Confluence (CON) No prox. (NP) Forest land (FL) Farm land (AL) Bare land (BL) Scrub land (SL) Weak (W) Strong (S) Geo-contact (GC)

Slope aspect

Proximity to channel

G

S

VS

R

RS

ST

CON

NP

Land use and vegetation FL

AL

BL

SL

Lithology W

S

GC

0.00 0.00 0.00 0.75 0.25 0.28 0.58 0.14 0.17 0.17 0.50 0.16 0.43 0.14 0.43

0.00 0.00 0.00 0.75 0.25 0.20 0.70 0.10 0.10 0.21 0.49 0.20 0.45 0.09 0.46

0.00 0.00 0.00 0.83 0.17 0.20 0.70 0.10 0.49 0.12 0.28 0.11 0.45 0.09 0.46

0.07 0.60 0.33 0.00 0.00 0.22 0.69 0.09 0.06 0.22 0.51 0.21 0.45 0.09 0.46

0.06 0.30 0.64 0.00 0.00 0.19 0.69 0.12 0.05 0.21 0.53 0.21 0.62 0.09 0.29

0.09 0.30 0.61 0.83 0.17 0.00 0.00 0.00 0.08 0.20 0.52 0.20 0.48 0.11 0.41

0.09 0.30 0.61 0.83 0.17 0.00 0.00 0.00 0.10 0.21 0.49 0.20 0.45 0.09 0.46

0.09 0.62 0.29 0.75 0.25 0.00 0.00 0.00 0.10 0.29 0.39 0.22 0.30 0.09 0.61

0.09 0.45 0.46 0.50 0.50 0.26 0.64 0.10 0.00 0.00 0.00 0.00 0.43 0.14 0.43

0.09 0.30 0.61 0.75 0.25 0.20 0.70 0.10 0.00 0.00 0.00 0.00 0.45 0.10 0.45

0.07 0.28 0.65 0.88 0.12 0.20 0.70 0.10 0.00 0.00 0.00 0.00 0.49 0.08 0.43

0.07 0.28 0.65 0.83 0.17 0.20 0.70 0.10 0.00 0.00 0.00 0.00 0.45 0.09 0.46

0.07 0.28 0.65 0.83 0.17 0.20 0.70 0.10 0.10 0.21 0.49 0.20 0.00 0.00 0.00

0.14 0.28 0.58 0.75 0.25 0.20 0.70 0.10 0.25 0.25 0.25 0.25 0.00 0.00 0.00

0.05 0.31 0.64 0.83 0.17 0.26 0.64 0.10 0.25 0.25 0.25 0.25 0.00 0.00 0.00

(b) Cluster weight Landslide controlling variables

Slope angle

Slope aspect Proximitiy to channel

Land use and vegetation

Lithology

Slope angle

Gentle (G) Steep (S) Very steep (VS) Rain-side (R) Rain shadow (RS) Single stream (ST) Confluence (CON) No prox. (NP) Forest land (FL) Farm land (AL) Bare land (BL) Scrub land (SL) Weak (W) Strong (S) Geo-contact (GC)

Slope aspect

Proximity to channel

G

S

VS

R

RS

ST

CON

NP

Land use and vegetation FL

AL

BL

SL

Lithology W

S

GC

0.00 0.00 0.00 0.38 0.38 0.22 0.22 0.22 0.08 0.08 0.08 0.08 0.32 0.32 0.32

0.00 0.00 0.00 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.49 0.49 0.49

0.00 0.00 0.00 0.16 0.16 0.16 0.16 0.16 0.14 0.14 0.14 0.14 0.54 0.54 0.54

0.29 0.29 0.29 0.00 0.00 0.10 0.10 0.10 0.22 0.22 0.22 0.22 0.39 0.39 0.39

0.39 0.39 0.39 0.00 0.00 0.07 0.07 0.07 0.15 0.15 0.15 0.15 0.39 0.39 0.39

0.39 0.39 0.39 0.22 0.22 0.00 0.00 0.00 0.10 0.10 0.10 0.10 0.29 0.29 0.29

0.50 0.50 0.50 0.29 0.29 0.00 0.00 0.00 0.06 0.06 0.06 0.06 0.15 0.15 0.15

0.56 0.56 0.56 0.16 0.16 0.00 0.00 0.00 0.07 0.07 0.07 0.07 0.21 0.21 0.21

0.58 0.58 0.58 0.13 0.13 0.15 0.15 0.15 0.00 0.00 0.00 0.00 0.14 0.14 0.14

0.41 0.41 0.41 0.18 0.18 0.18 0.18 0.18 0.00 0.00 0.00 0.00 0.23 0.23 0.23

0.58 0.58 0.58 0.13 0.13 0.13 0.13 0.13 0.00 0.00 0.00 0.00 0.16 0.16 0.16

0.52 0.52 0.52 0.08 0.13 0.20 0.20 0.20 0.00 0.00 0.00 0.00 0.20 0.20 0.20

0.65 0.65 0.65 0.12 0.12 0.11 0.11 0.11 0.12 0.12 0.12 0.12 0.00 0.00 0.00

0.43 0.43 0.43 0.12 0.13 0.15 0.15 0.15 0.30 0.30 0.30 0.30 0.00 0.00 0.00

0.61 0.61 0.61 0.13 0.13 0.12 0.12 0.12 0.14 0.14 0.14 0.14 0.00 0.00 0.00

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Proximity to channel

Slope angle

Table 4 Weighted supermatrix and limiting supermatrix with global weights (a) Weighted supermatrix Landslide controlling variables

Slope angle

Slope aspect

Land use and vegetation

Lithology

Slope aspect

Proximity to channel

G

S

VS

R

RS

ST

CON

NP

Land use and vegetation FL

AL

BL

SL

Lithology W

S

GC

0.00 0.00 0.00 0.29 0.10 0.06 0.13 0.03 0.01 0.01 0.04 0.01 0.14 0.04 0.14

0.00 0.00 0.00 0.13 0.04 0.03 0.12 0.02 0.02 0.04 0.08 0.03 0.22 0.04 0.23

0.00 0.00 0.00 0.13 0.03 0.03 0.11 0.02 0.07 0.02 0.04 0.02 0.24 0.05 0.25

0.02 0.17 0.10 0.00 0.00 0.02 0.07 0.01 0.01 0.05 0.11 0.05 0.18 0.04 0.18

0.02 0.12 0.25 0.00 0.00 0.01 0.05 0.01 0.01 0.03 0.08 0.03 0.24 0.04 0.11

0.04 0.12 0.24 0.18 0.04 0.00 0.00 0.00 0.01 0.02 0.05 0.02 0.14 0.03 0.12

0.05 0.15 0.31 0.24 0.05 0.00 0.00 0.00 0.01 0.01 0.03 0.01 0.07 0.01 0.07

0.05 0.35 0.16 0.12 0.04 0.00 0.00 0.00 0.01 0.02 0.03 0.02 0.06 0.02 0.13

0.05 0.26 0.27 0.07 0.07 0.04 0.10 0.02 0.00 0.00 0.00 0.00 0.06 0.02 0.06

0.04 0.12 0.25 0.14 0.05 0.04 0.13 0.02 0.00 0.00 0.00 0.00 0.10 0.02 0.10

0.03 0.11 0.27 0.16 0.02 0.04 0.13 0.02 0.00 0.00 0.00 0.00 0.11 0.02 0.10

0.04 0.15 0.34 0.07 0.01 0.04 0.14 0.02 0.00 0.00 0.00 0.00 0.09 0.02 0.00

0.05 0.18 0.42 0.10 0.02 0.02 0.08 0.01 0.01 0.03 0.06 0.02 0.00 0.00 0.00

0.06 0.12 0.25 0.09 0.03 0.03 0.11 0.02 0.08 0.08 0.08 0.08 0.00 0.00 0.00

0.03 0.19 0.39 0.11 0.02 0.03 0.08 0.01 0.04 0.04 0.04 0.04 0.00 0.00 0.00

(b) Limiting supermatrix Landslide controlling variables

Slope angle

Slope aspect Proximitiy to channel

Land use and vegetation

Lithology

Gentle (G) Steep (S) Very steep (VS) Rain-side (R) Rain shadow (RS) Single stream (ST) Confluence (CON) No prox. (NP) Forest land (FL) Farm land (AL) Bare land (BL) Scrub land (SL) Weak (W) Strong (S) Geo-contact (GC)

Slope angle

Slope aspect

Proximity to channel

G

S

VS

R

RS

ST

CON

NP

Land use and vegetation FL

AL

BL

SL

Lithology W

S

GC

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

0.025 0.111 0.194 0.116 0.028 0.025 0.085 0.014 0.027 0.027 0.051 0.025 0.124 0.025 0.123

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Proximity to channel

Gentle (G) Steep (S) Very steep (VS) Rain-side (R) Rain shadow (RS) Single stream (ST) Confluence (CON) No prox. (NP) Forest land (FL) Farm land (AL) Bare land (BL) Scrub land (SL) Weak (W) Strong (S) Geo-contact(GC)

Slope angle

291

292

K.M. Neaupane, M. Piantanakulchai / Engineering Geology 85 (2006) 281–294

using the highest global risk score for the group of landslide controlling variables, i.e., a parcel of land with very steep angle, rain-side slope aspect, confluence, bare land, and weak lithology. The cell score (raw-score) was normalized using the following equation: Xnormalized ¼

Xraw −Xmin Xmax −Xmin

ð6Þ

For a susceptibility map, the continuous set of data needs to be changed into two or more categories. The problem of clustering risk scores into groups depends on the subjective opinion of researchers. A number of classifiers are available namely natural breaks, quantile, equal intervals, K-means etc. Each classifier may lead to different results as they make very different statements about how values should be divided. The natural breaks, for example, identifies break points or jumps in data pattern whereas quantile classification system groups features by equal numbers. Similarly, equal interval scheme divides the range of values into equal sized subdivisions whereas K-means clustering partitions large amounts of data into K mutually exclusive clusters. In order to observe the spatial pattern in the landslide hazard map, normalized scores were grouped into different classes. The qualitative classification was based on the observation of frequency distribution of the normalized risk scores, and the pattern (peaks) in the histogram (Fig. 7). In fact, the distribution of risk score in the study area is not uniform. By setting appropriate interval of risk score, several groups of risk (peaks) in the histogram were observed. Therefore, K-means clustering was considered suitable for the partitioning of the data. The K-means clustering is one of the simplest unsupervised learning algorithms that solves the clustering problem. In this method, the centroid of each class is set to minimize the distance function through an iterative process. K-means clustering ensures a partition

in which objects within each cluster are as close to each other as possible, and as far from objects in other clusters as possible. In this study, the function “kmeans” in MATLAB was utilized to perform K-means clustering operation. The procedure involved is described as follows: • Step I: Based on the histogram result, number of classes (m) is decided, and the positions of centroids (cj) are initialized. • Step II: Each normalized score or data point (i) is assigned a class based on its proximity to the centroid. • Step III: When all risk scores have been assigned, the positions of centroids are recalculated. Steps I–II are repeated until the centroids no longer move. The centroid for each class of risk is the point to which the sum of distances from all risk scores in that class is minimized according to the distance measure specified, for example, squared Euclidian distance. Minimize z ¼

m X n X j¼1

ðjÞ

ðxi −cj Þ2

ð7Þ

i¼1

where xi(j) represents normalized score i that belongs to class j, cj is the centroid of the class j and n is the number of data points in that class. Using the K-means clustering, three relative classes of risk, with the centroids (0.13, 0.34, and 0.56), were identified for which the range of normalized raw scores are (0.0–0.24), (0.24–0.45) and (0.45–1.0), respectively. Accordingly, three relative classes of risks namely Low risk, Moderate risk and High risks were considered and a hazard map was produced (Fig. 8). Mostly, flat terrain with relatively gentle gradient falls in a low risk

Fig. 7. The histogram of normalized indices.

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successful application. Although ANP has been established as reliable tool for MCDM in finances and management filed, much remains to be explored on its application to geo-engineering cases. Because ANP could capture the complex relationship among landslide controlling factors supported by the opinion of geotechnical experts, it is ideally suitable for landslide hazard assessment. ANP uses the relative weights (as in AHP) that are clearly explained, therefore, error from the subjective judgment could be minimized to some extent. On the other hand, expert's evaluation provides rationale for better forecast of the event when no historical data exists as opposed to statistical models. References

Fig. 8. Landslide hazard assessment map.

group indicating that slope gradient played an important role in the classification system. The south-western part of the terrain is mostly high risk because of the synergetic effect of slope inclination, channel proximity, and weak lithology. The north and north-eastern parts of the area are composed of strong rocks with less tributaries incisions and, therefore, falls into low risk area. For the verification of the hazard map, a landslide map of the area produced by Transport Research Laboratory (TRL, 1997) was superimposed over the risk map. It is observed from the superimposed map (Fig. 8) that majority of the landslides are found scattered over high and moderate risk areas, but no landslides are recorded in the low risk area. Further, the Dharan–Dhankuta road, designed and constructed between 1974–1982, passes right through the study area as shown in Fig. 8. Hearn (2002) reported that despite a succession of rainstorm and floods in 1984, 1987 and 1988, and an earthquake of magnitude 6.6 Richter scale in 1988, this road has remained relatively intact. As observed from the hazard map, the majority of the alignment passes through relatively low and moderate risk areas. This validates the landslide hazard map produced by the methodology (ANP) presented in this paper. 5. Conclusion An ANP model for landslide hazard assessment was described, and priority weights obtained from the model was used to prepare a hazard map of a potentially unstable part in lesser Himalayas to demonstrate its

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