京都大学 / 新制・課程博士 / 博士(工学) / 甲第23151号 / 工博第4795号 / 新制||工||1750(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 澤田 純男, 教授 清野 純史, 准教授 後藤 浩之 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The purpose of this study is to develop probabilistic hazard maps for EskiSehir including &lsquo / Peak Ground Acceleration&rsquo / values for 10% probability of exceedance in 50-year and 100-year periods at different site classes. A seismotectonic map has been prepared in the Geographical Information Systems environment by compiling instrumental seismicity and neotectonic data for the study area. The seismic sources have been defined spatially in six areal zones, characterized by a commonly used recurrence law and a maximum magnitude value. Four attenuation relationships have been selected being one of them totaly developed from the strong-motion records of Turkey. After the implementation of a seismic hazard model by using SEISRISK software, the probabilistic seismic hazard curves and maps were developed based on the selected attenuation relationships, at &lsquo / rock&rsquo / and &lsquo / soil&rsquo / sites, with a probability of exceedance of 10% in 50-year and 100-year periods. At rock sites the highest levels of hazard were calculated based on the predictive relationship of Abrahamson and Silva (1996), whereas the lowest ones based on the one of Boore et al. (1996). On the other hand the highest hazard levels were determined at soil sites based on the attenuation relationship of Ambraseys et al. (1996), whereas the lowest ones based on the one of Boore et al. (1997). For EskiSehir, the peak ground acceleration values calculated based on attenuation relationship by Boore et al. (1997) were found to be applicable for 10% probability of exceedance in 50 and 100 years, taking into consideration the fact that a considerable portion of the city is founded over alluviums.

No description available.

Este trabalho contempla os estudos realizados para elaboração de uma carta de eventos perigosos (hazard) de uma área de aproximadamente 45 km², no município de Ouro Preto/MG, a partir de dados geológicos e geotécnicos, gerados em trabalhos de mapeamento geotécnico, com o uso dos recursos de redes neurais artificiais e da probabilidade condicional. Os dados prévios foram tratados e um conjunto de 15 mapas e cartas elaborado, a saber: topográfico, de substrato rochoso, material inconsolidado, de uso e ocupação, de inventário dos movimentos de massa gravitacionais (escorregamentos translacionais, escorregamentos translacionais tipo de material), de declividade, de rumo da inclinação das encostas, das unidades geológico-geotécnicas, das seções típicas das unidades geológico-geotécnicas, da resistência ao cisalhamento, do contraste de permeabilidade e da superfície potencial de ruptura, associado a uma tabela com as características das unidades geológico-geotécnicas. Os modelos de redes neurais artificiais e probabilidade condicional foram desenvolvidos para o uso em MATLAB utilizando um conjunto de 11 mapas e cartas dentre os citados anteriormente. A análise dos dados prévios frente aos modelos foi desenvolvida no sentido de avaliar a sua qualidade e a sua adequação ao modelo proposto. Concluiu-se sobre a necessidade de dados específicos que nem sempre são gerados em trabalhos rotineiros, como: levantamento da atividade, velocidade, volume e data de ocorrência, entre outros para caracterização das feições de movimentos de massa gravitacionais; estudo detalhado dos parâmetros de resistência dos materiais e das descontinuidades presentes no substrato rochoso; dados de estações pluviométricas para estudos da intensidade e distribuição da chuva na região, entre outras informações. / This work shows the studies developed for elaboration of the landslide hazard map of the area of 45 km², approximately, in the municipality of Ouro Preto, in the state of Minas Gerais, Brazil, from data generated in geotechnical mapping, with the use of artificial neural networks and conditional probability methods. The previous data were processed and was elaborated a set of 15 maps and charts: topographic, lithologies, unconsolidated material, land uses, inventory (landslides, translational slides, translational inventory - type of geological material, slope, slope inclination direction, geological - geotechnical units, typical topographic profile of the geological and geotechnical units, the shear strength categories, hydraulic conductivity contrasts, potential failure surfaces and a table with characteristic of the geological and geotechnical units. The procedures of the artificial neural networks and conditional probability were developed for use in MATLAB using a set of 11 maps among the 15 elaborated. A analysis of the previous data prepared and the data necessary for models was developed to evaluate its suitability. The main conclusion is that the routine mapping and inventories do not consider important attributes, such as activity, movement rate, volume, landslide date and others aspects of the features; detailed study about shear strength of geological materials and discontinuities and rainfall data.

Este trabalho contempla os estudos realizados para elaboração de uma carta de eventos perigosos (hazard) de uma área de aproximadamente 45 km², no município de Ouro Preto/MG, a partir de dados geológicos e geotécnicos, gerados em trabalhos de mapeamento geotécnico, com o uso dos recursos de redes neurais artificiais e da probabilidade condicional. Os dados prévios foram tratados e um conjunto de 15 mapas e cartas elaborado, a saber: topográfico, de substrato rochoso, material inconsolidado, de uso e ocupação, de inventário dos movimentos de massa gravitacionais (escorregamentos translacionais, escorregamentos translacionais tipo de material), de declividade, de rumo da inclinação das encostas, das unidades geológico-geotécnicas, das seções típicas das unidades geológico-geotécnicas, da resistência ao cisalhamento, do contraste de permeabilidade e da superfície potencial de ruptura, associado a uma tabela com as características das unidades geológico-geotécnicas. Os modelos de redes neurais artificiais e probabilidade condicional foram desenvolvidos para o uso em MATLAB utilizando um conjunto de 11 mapas e cartas dentre os citados anteriormente. A análise dos dados prévios frente aos modelos foi desenvolvida no sentido de avaliar a sua qualidade e a sua adequação ao modelo proposto. Concluiu-se sobre a necessidade de dados específicos que nem sempre são gerados em trabalhos rotineiros, como: levantamento da atividade, velocidade, volume e data de ocorrência, entre outros para caracterização das feições de movimentos de massa gravitacionais; estudo detalhado dos parâmetros de resistência dos materiais e das descontinuidades presentes no substrato rochoso; dados de estações pluviométricas para estudos da intensidade e distribuição da chuva na região, entre outras informações. / This work shows the studies developed for elaboration of the landslide hazard map of the area of 45 km², approximately, in the municipality of Ouro Preto, in the state of Minas Gerais, Brazil, from data generated in geotechnical mapping, with the use of artificial neural networks and conditional probability methods. The previous data were processed and was elaborated a set of 15 maps and charts: topographic, lithologies, unconsolidated material, land uses, inventory (landslides, translational slides, translational inventory - type of geological material, slope, slope inclination direction, geological - geotechnical units, typical topographic profile of the geological and geotechnical units, the shear strength categories, hydraulic conductivity contrasts, potential failure surfaces and a table with characteristic of the geological and geotechnical units. The procedures of the artificial neural networks and conditional probability were developed for use in MATLAB using a set of 11 maps among the 15 elaborated. A analysis of the previous data prepared and the data necessary for models was developed to evaluate its suitability. The main conclusion is that the routine mapping and inventories do not consider important attributes, such as activity, movement rate, volume, landslide date and others aspects of the features; detailed study about shear strength of geological materials and discontinuities and rainfall data.

Abstract A wildfire is an uncontrollable fire in an area of combustible fuel that occurs in the wild or countryside area. Wildfires are becoming a deadly and frequent event in Europe due to extreme weather conditions. In 2018, wildfires profoundly affected Sweden, Finland, and Norway, which were not big news before. In Norway, although there is well–organized fire detection, warning, and mitigation systems, mapping wildfire risk areas before the fire occurrence with georeferenced spatial information, are not yet well-practiced. At this moment, there are freely available remotely sensed spatial data and there is a good possibility that analysing wildfire hazard areas with geographical information systems together with multicriteria decision analysis (GIS–MCDA) and frequency ratio models in advance so that subsequent wildfire warning, mitigation, organizational and post resilience activities and preparations can be better planned.  This project covers eight counties of Norway: Oslo, Akershus, Østfold, Vestfold, Telemark, Buskerud, Oppland, and Hedmark. These are the counties with the highest wildfire frequency for the last ten years in Norway. In this study, GIS-MCDA integrated with analytic hierarchy process (AHP), and frequency ratio models (FR) were used with selected sixteen–factor criteria based on their relative importance to wildfire ignition, fuel load, and other related characteristics. The produced factor maps were grouped under four main clusters (K): land use (K1), climate (K2), socioeconomic (K3), and topography (K4) for further analysis. The final map was classified into no hazard, low, medium, and high hazard level rates. The comparison result showed that the frequency ratio model with MODIS satellite data had a prediction rate with 72% efficiency, followed by the same model with VIIRS data and 70% efficiency. The GIS-MCDA model result showed 67% efficiency with both MODIS and VIIRS data. Those results were interpreted in accordance with Yesilnacar’s classifications such as the frequency ratio model with MODIS data was considered a good predictor, whereas the GIS-MCDA model was an average predictor. When testing the model on the dependent data set, the frequency ratio model showed 72% with MODIS & VIIRS data, and the GIS-MCDA model showed 67% and 68% performance with MODIS and VIIRS data, respectively. In the hazard maps produced, the frequency ratio models for both MODIS and VIIRS showed that Hedmark and Akershus counties had the largest areas with the highest susceptibility to wildfires, while the GIS-MCDA method resulted to Østfold and Vestfold counties. Through this study, the best independent wildfire predictor criteria were selected from the highest to the lowest of importance; wildfire constraint and criteria maps were produced; wildfire hazard maps with high-resolution georeferenced data using three models were produced and compared; and the best, reliable, robust, and applicable model alternative was selected and recommended. Therefore, the aims and specific objectives of this study should be considered and fulfilled.

No description available.

Past earthquakes have demonstrated that Indian sub-continent is highly vulnerable to earthquake hazards. It has been estimated that about 59 percent of the land area of the Indian subcontinent has potential risk from moderate to severe earthquakes (NDMA, 2010). Major earthquakes in the last 20 years such as Khillari (30th September 1993), Jabalpur (22nd May 1997), Chamoli (29th March 1999) and Bhuj (26th January 2001) earthquakes have resulted in more than 23,000 deaths and extensive damage to infrastructure (NDMA, 2010). Although it is well known that the major earthquake hazard prone areas in India are the Himalayan region (inter-plate zone) and the north-east region, (subduction zone) the seismicity of Peninsular India cannot be underestimated. Many studies (Seeber et al., 1999; Rao, 2000; Gangrade & Arora, 2000) have proved that the seismicity of Peninsular India is significantly high and may lead to earthquakes of sizeable magnitude. This necessitates a seismic zonation for the country, as well as various regions in it. Seismic zonation is the first step towards an effective earthquake risk mitigation study. Seismic zonation is a process in which a large region is demarcated into small zones based on the levels of earthquake hazard. Seismic zonation is generally carried out at three different levels based on the aerial extent of the region, importance of site and the population. They are micro-level, meso-level and macro-level. The macro-level zonation is generally carried out for large landmass such as a state or a country. The earthquake hazard parameters used for macro-level zoning are generally evaluated with less reliability. The typical example of a macro-level zonation is the seismic zonation map of India prepared by BIS-1893 (2002), where the entire India is demarcated into four seismic zones based on past seismicity and tectonic conditions. Generally the macro-level seismic zonation is carried out based on peak horizontal acceleration (PHA) estimated at bedrock level without giving emphasis on the local soil conditions. Seismic zonation at the meso-level is carried out for cities and urban centers with a population greater than 5,00,000. The earthquake hazard parameters, for the meso-level zonation are evaluated with greater degree of reliability, compared to the macro-level zoning. The micro-level zonation is carried out for sites which host critical installations such as nuclear power plants (NPPs). As the NPPs are considered as very sensitive structures, the earthquake parameters, for the micro-level zonation of the NPP sites are estimated with a highest degree of reliability. The local soil conditions and site effects are properly counted for carrying out the micro as well as the meso-level zonation. Several researchers have carried out meso-level zonation considering effects of all major earthquake hazards such as PHA, site amplification, liquefaction (Mohanty et al., 2007; Nath et al., 2008; Sitharam & Anbazhagan, 2008 etc.) Even though the above definitions and descriptions are available for various levels of zonation, the key issue lies in the adoption of the suitable one for a given region. There are only a few guidelines available regarding the use of a particular level of zonation for a given study area. Based on the recommendation of the disaster management authority, the government of India has initiated the seismic zonation of all major cities in India. As it is evident that large resources are required in order to carry out seismic site characterization and site effect estimation, both the micro and meso-level zonations cannot be carried out for all these cities. Hence there is a need to propose appropriate guidelines to define the suitability of each level zonation for various re-gions in the country. Moreover there are many methodologies available for site characterization and estimation of site effects such as site amplification and liquefaction. The appropriateness of these methodologies for various levels of seismic zonations also needs to be assessed in order to optimize use of resources for seismic zonation. Hence in the present study, appropriate techniques for site characterization and earthquake hazard estimation for regions at different scale levels were determined. Using the appropriate techniques, the seismic zonation was carried out both at the micro and macro-level, incorporating all major earthquake hazards. The state of Karnataka and the Kalpakkam NPP site were chosen for the macro and micro−level seismic zonation in this study. Kalpakkam NPP site is situated in Tamil Nadu, India, 70 kilometres south of Chennai city. The NPP site covers an area of 3000 acres. The site is situated along the Eastern coastal belt of India known as Coromandel coast with Bay of Bengal on the east side. The NPP site host major facilities such as Indira Gandhi Centre for Atomic Research (IGCAR), Madras Atomic Power Station (MAPS), Fast Reactor Fuel Reprocessing (FRFC) Plant, Fast Breeder Test Reactor (FBTR), Prototype Fast Breeder Reactor (PFBR) etc. The state Karnataka lies in the southern part of India, covering an area of 1,91,791 km2, thus approximately constituting 5.83% of the total geographical area of India. Both the study areas lie in the Indian Peninsular which is identified as one of the most prominent and largest Precambrian shield region of the world. The first and foremost step towards the seismic zonation is to prepare a homogenised earthquake catalogue. All the earthquake events within 300 km radius from the boundary of two study areas were collected from various national and international agencies. The earthquake events thus obtained were found to be in different magnitude scales and hence all these events were converted to the moment magnitude scale. A declustering procedure was applied to the earthquake catalogue of the two study area in order to remove aftershocks, foreshocks and dependent events. The completeness analysis was carried out and the seismicity parameters for the two study areas were evaluated based on the complete part of earthquake catalogues. The next major step toward the estimation of earthquake hazard and seismic zonation is the identification and mapping of the earthquake sources. Three source models, mainly; 1) linear source model, 2) point source model and 3) areal source model were used in the present study for characterizing earthquake sources in the two study areas. All the linear sources (faults and lineaments) within 300 km radius from the boundary of two study areas were identified and mapped from SEISAT (2000). In addition to SEISAT (2000), some lineaments were also mapped from the works of Ganesha Raj & Nijagunappa (2004). These lineaments and faults were mapped and georeferenced in a GIS platform on which earthquake events were then super-imposed to give seismotectonic atlas. Seismotectonic atlas was prepared for both the study areas. The point source model (Costa et al. 1993; Panza et al. 1999) and areal source model (Frankel, 1995) were also adopted in this work. Deterministic and probabilistic seismic hazard analysis was found to be appropriated for micro, meso and macro-level zonations. Hence in the present study, the seismic hazard at bedrock level, both at the micro and macro-level were evaluated using the deterministic as well as the probabilistic methodologies. In order to address the epistemic uncertainties in source models and attenuation relations, a logic tree methodology was incorporated with the deterministic and probabilistic approaches. As the deterministic seismic hazard analysis (DSHA) considers only the critical scenario, knowing the maximum magnitude that can occur at a source and the shortest distance between that source and the site and the peak horizontal acceleration (PHA) at that site is estimated using the frequency dependent attenuation relation. Both for the micro as well as the macro-level, the DSHA was carried out, considering grid sizes of 0.001◦ × 0.001◦ and 0.05◦ × 0.05◦respectively. A MATLAB program was developed to evaluate PHA at the center of each of these grid points. The epistemic uncertainties in source models and attenuation relations have been addressed using a logic tree approach (Bommer et al., 2005). A typical logic tree consists of a series of nodes to which several models with different weightages are assigned. Allotment of these weightages to different branch depends upon the degree of uncertainties in the model, and its accuracy. However the sum of all weightages of different branches at a particular node must be unity. Two types of seismic sources are employed in DSHA and they are linear and smoothed point sources. Since both the types of sources were of equal importance, equal weightages were assigned to each of them. The focal depth in the present study was taken as 15 km. The attenuation properties of the region were modelled using three attenuation relations, Viz. Campbell & Bozorgnia (2003), Atkinson & Boore (2006) and Raghu Kanth & Iyengar (2007). The attenuation relation proposed by Raghu Kanth & Iyengar (2007) was given higher weightage of 0.4 since it was devel-oped for the Indian peninsular region. The attenuation relations by Atkinson & Boore (2006) and Campbell & Bozorgnia (2003) which were developed for Eastern North American shield region, shared equal weightages of 0.3. Maps showing spatial variation of PHA value at bedrock level, for both micro and macro-level are presented. Response spectra at the rock level for important location in the two study areas were evaluated for 8 different periods of oscillations, and the results are presented in this thesis. Probabilistic seismic hazard analysis (PSHA) incorporating logic tree approach was per-formed for both micro as well as macro-level considering similar grid sizes as in DSHA. Two types of seismic sources considered in the PSHA are linear sources and smoothed gridded areal sources (Frankel, 1995) with equal weightage distribution in the logic tree structure. Smoothed gridded areal sources can also account the scattered earthquake events. The hypocentral distance was calculated by considering a focal depth of 15 km, as in the case of DSHA method. A MAT-LAB program was developed for PSHA. The same attenuation relations employed in DSHA were used in PSHA as well with the same weightage allotment in logic tree structure. Considering all major uncertainties, a uniform hazard response spectrum (UHRS), showing the variation of PHA values with the mean annual rate of exceedance (MARE), was evaluated for each grid point. From the uniform hazard response spectrum, the PHA corresponding to any return period can be evaluated. Maps showing the spatial variation of PHA value at bedrock level, corresponding to 475 year and 2500 year return periods for both micro and macro-level are presented. Response spectra at the rock level for important location in two study areas were evaluated for eight different periods of oscillations, and the results are presented in this thesis. In order to assess various earthquake hazards like ground motion amplification and soil liquefaction, a thorough understanding of geotechnical properties of the top overburden soil mass is essential. As these earthquake hazards strongly depend on the geotechnical properties of the soil, site characterization based on these properties will provide a better picture of these hazards. In the present study, seismic site characterization was carried both at the micro and macro-level using average shear wave velocity for top 30 m overburden (Vs30). At the micro-level, the shear wave velocity profile at major locations was evaluated using multichannel analysis of surface waves (MASW) tests. MASW is an indirect geophysical method used in geotechnical investigations and near surface soil characterization based on the dispersion characteristics of surface waves (Park et al., 1999). The MASW test setup consists of 24-channel geophones of 4.5 Hz capacity. A 40 kg propelled energy generator (PEG) was used for generating surface wave. Based on the recordings of geophones, the dispersion characteristics of surface waves were evaluated in terms of a dispersion curve. The shear wave velocity (Vs) profile at a particular location was determined by performing inversion analysis (Xia et al., 1999). After the evaluation of V s profile at all major locations, the site characterization at the micro-level was carried out as per NEHRP (BSSC, 2003) and IBC (2009) recommendations. Maps showing the spatial distribution of various site classes at the micro-level are presented in this thesis. Standard penetration tests were also carried out in the site as part of subsurface investigation and in this study a new correlation between V s and corrected SPT-N values was also developed. Apart from carrying out site characterization, low strain soil stiffness profile was evaluated based on SPT and MASW data. In this work, seismic site characterization at the macro-level was also carried out. As it is not physically and economically viable to carry out geotechnical and geophysical testing for such a large area, like the Karnataka state, the seismic site characterization was carried out based on topographic slope maps. Wald & Allen (2007) has reported that the topographic slope is a perfect indicator of site conditions. Based on the correlation studies carried out for different regions, Wald & Allen (2007) has proposed slope ranges corresponding to each site class. In this study, the topographic map for the entire state of Karnataka was derived from ASTER Global Digital Elevation Model GDEM. This thesis also presents a comparison study between the Vs30map generated from topographic slope data and Vs30map developed using geophysical field tests, for Bangalore and Chennai. Based on this study, it is concluded that topographic slopes can be used for developing Vs30maps for meso and macro-level with reasonable accuracy. The topographic map for macro-level was generated at a grid size of 0.05◦ × 0.05◦. Based on the value of slope at a particular grid point, the Vs30for that grid point was assigned as per Wald & Allen (2007). A similar procedure was repeated for all the grid points. Spatial variation of various seismic site classes for the macro-level has been presented in this work. The site amplification hazard was estimated for both micro and the macro-level. The assessment of site amplification is very important for shallow founded structures and other geotechnical structures like retaining walls and dams, floating piles and underground structures as the possible earthquake damages are mostly due to extensive shaking. The site amplification hazard at the micro-level was estimated using 1D equivalent linear ground response analyses. The earthquake motion required for carrying out ground response analysis was simulated from a target response spectrum. 1D equivalent linear analyses were performed using SHAKE 2000 software. Spatial variations of surface level PHA values, site amplification, predominant frequency throughout the study area are presented in this work. As it is not physically viable to assess site amplification hazard at the macro-level using the 1D ground response analysis, the surface level PHA value for the entire state of Karnataka was estimated using a non-linear site amplification technique pro-posed by Raghu Kanth & Iyengar (2007). Based on the site class in which particular grid belongs and bedrock level PHA value, the amplification for that grid point was evaluated using regression equations developed by Raghu Kanth & Iyengar (2007). The liquefaction hazard both at the micro and macro-level was evaluated and included in this thesis. The micro-level liquefaction hazard was estimated in terms of liquefaction potential index (LPI) based on SPTN values (Iwasaki et al., 1982). As the LPI was evaluated by integrating the factor of safety against liquefaction (FSL) at all depths, it can effectively represent the liquefaction susceptibility of the soil column. LPI at the micro-level was evaluated by both deterministic as well as the probabilistic approaches. In the deterministic approach, the FSLat a particular depth was evaluated as the ratio of the cyclic resistance of the soil layer to the cyclic stress induced by earth-quake motion. The cyclic stress was estimated as per Seed & Idriss (1971), while the cyclic soil resistance was characterised from the corrected SPT-N values as proposed by Idriss & Boulanger (2006). However in the probabilistic method, the mean annual rate of exceedance (MARE) of factor of safety against liquefaction at different depth was estimated using SPT field test data by considering all uncertainties. From the MARE curve, the FS L for 475 year and 2500 year return period were evaluated. Once FS L at different depth were evaluated, the LPI for the borehole is calculated by integrating FS L for all depths. The liquefaction hazard at the macro-level was estimated in terms of SPT and CPT values required to prevent liquefaction at 3 m depth, using a probabilistic approach. The probabilistic approach accounts the contribution of several magnitudes acceleration scenarios on the liquefaction potential at a given site. Based on the methodology proposed by Kramer & Mayfield (2007), SPT and CPT values required to resist liquefaction corresponding to return periods of 475 years and 2500 years were evaluated at the macro-level. It has been observed that the spatial distribution of intensity of each these hazard in a region is distinct from the other due to the predominant influence of local geological conditions rather than the source characteristics of the earthquake. Hence it’ll be difficult to assess risk and vulnerability of a region when these hazards are treated separately. Thus, all major earthquake hazards are to be integrated to an index number, which effectively represents the combined effect of all hazards. In the present study, all major earthquake hazards were integrated to a hazard index value, both at the micro as well as macro-level using the Analytical Hierarchy Process (AHP) proposed by Saaty (1980). Both micro and macro-level seismic zonation was performed based on the spatial distribution of hazard index value. This thesis also presents the assessment of earthquake induced landslides at the macro-level in the appendix. Landslide hazards are a major natural disaster that affects most of the hilly regions around the world. This is a first attempt of it kind to evaluate seismically induced landslide hazard at the macro-level in a quantitative manner. Landslide hazard was assessed based on Newmark’s method (Newmark, 1965). The Newmark’s model considers the slope at the verge of failure and is modelled as a rigid block sliding along an incline plane under the influence of a threshold acceleration. The value of threshold acceleration depends upon the static factor of safety and slope angle. At the macro-level, the slope map for the entire state of Karnataka was derived from ASTER GDEM, considering a grid size of 50 m × 50 m. The earthquake motion which induces driving force on the slope to destabilize it was evaluated for each grid point with slope value 10 degree and above using DSHA. Knowing the slope value and peak horizontal acceleration (PHA) at a grid point, the seismic landslide hazard in terms of static factor of safety required to resist landslide was evaluated using Newmark’s method. This procedure is repeated for all grid points, having slope value 10 degree and above.