Geometrical characteristics of earthquake-induced landslides and correlations with control factors: a case study of the 2013 Minxian,Gansu, China, <Emphasis Type="Italic">Mw</Emphasis> 5.9 event

Geometric parameters are useful for characterizing earthquake-triggered landslides. This paper presents a detailed statistical analysis on this issue using the landslide inventory of the 2013, Minxian, China Mw 5.9 earthquake. Based on GIS software and a 5-m resolution DEM, geometric parameters of 635 coseismic landslides (with areas larger than 500 m²) were obtained, including height, length, width, reach angle (arc tangent of the height-length ratio), and aspect ratio (length-width ratio). The fitting relationship of height and length from these data is H = 0.6164L + 0.4589, with an average reach angle of 31.65°. The landslide aspect ratios concentrate in the range of 1.4～2.6, with an average of 2.11. According to the plane geometric shapes and aspect ratios, the landslides are classified into four categories: transverse landslide (LA1, L/W ≤ 0.8), isometric landslide (LA2, 0.8 < L/W ≤ 1.2), longitudinal landslide (LA3, 1.2 < L/W ≤ 3), and elongated landslide (LA4, L/W > 3). Statistics of these four types of landslides versus ten classified control factors (elevation, slope angle, slope aspect, curvature, slope position, distance to drainages, lithology, seismic intensity, peak ground acceleration, and distance to seismogenic fault) are used to examine their possible correlations and the landslide-prone areas, which would be helpful to the landslide disaster mitigation in the affected area.     

Developing an algorithm for automated geometric analysis and classification of landslides incorporating LiDAR-derived DEM

Amending landslides inventories is immensely important to policy and decision makers alike. Sliding creates geometric shapes on the Earth’s surface. This study presents the utilization of LiDAR high-resolution digital elevation model (DEM) in the Alborz Mountains, Iran to refurbish the existing landslide inventory dataset by implementing the proposed algorithm. The method consists of the automated derivation of landslide geometry (length, width, and area) followed by classification of landslide types considering length, width and flow direction. This study has used the trapezoidal rule for numerical integration to develop the proposed algorithm. The landslides were then classified into four types (very long, long, very wide, and wide) based on slope, length, and width. This geometric classification of landslides is based on the geographical coordinates, slope angle (θ), length (L), and width (W), and further failure flow direction. A total of 95 landslides were updated from the existing inventory database. The proposed method was verified and evaluated by field observations; and 14 samples were tested to determine the relative error. The results demonstrated that the mean percentage relative error is 0.496% in length and width and 0.008% in area, related to the GIS analysis. The accuracy performance of determining the landslide’s type is 92%. The purposefulness of this algorithm is to increase the accuracy performance of landslides geometry analysis and automated measurements associated with the usual GIS platforms such as ArcGIS.     

Landslide dam formation susceptibility analysis based on geomorphic features

Global climate change has increased the frequency of abnormally high rainfall; such high rainfall events in recent years have occurred in the mountainous areas of Taiwan. This study identifies historical earthquake- and typhoon-induced landslide dam formations in Taiwan along with the geomorphic characteristics of the landslides. Two separate groups of landslides are examined which are classified as those that were dammed by river water and those that were not. Our methodology applies spatial analysis using geographic information system (GIS) and models the geomorphic features with 20?×?20 m digital terrain mapping. The Spot 6 satellite images after Typhoon Morakot were used for an interpretation of the landslide areas. The multivariate statistical analysis is also used to find which major factors contribute to the formation of a landslide dam. The objective is to identify the possible locations of landslide dams by the geomorphic features of landslide-prone slopes. The selected nine geomorphic features include landslide area, slope, aspect, length, width, elevation change, runout distance, average landslide elevation, and river width. Our four geomorphic indexes include stream power, form factor, topographic wetness, and elevation–relief ratio. The features of the 28 river-damming landslides and of the 59 non-damming landslides are used for multivariate statistical analysis by Fisher discriminant analysis and logistic regression analysis. The principal component analysis screened out eleven major geomorphic features for landslide area, slope, aspect, elevation change, length, width, runout distance, average elevation, form factor, river width, stream power, and topography wetness. Results show that the correctness by Fisher discriminant analysis was 68.0 % and was 70.8 % by logistic regression analysis. This study suggests that using logistic regression analysis as the assessment model for identifying the potential location of a landslide dam is beneficial. Landslide threshold equations applying the geomorphic features of slope angle, angle of landslide elevation change, and river width (H _L/W _R) to identify the potential formation of natural dams are proposed for analysis. Disaster prevention and mitigation measures are enhanced when the locations of potential landslide dams are identified; further, in order to benefit such measures, dam volume estimates responsible for breaches are key.     

Fractal trees and Horton's laws

Fractal trees as a model for drainage systems are described in its generalized non-homogeneous form from the viewpoint of fractal geometry. Box covering techniques are used to show the numerical equivalence between the Hausdorff-Besicovitch dimension and the similarity dimension of the fractally-dominant dust formed by the sources. In this way, the similarity relationD=log (N)/log (1/r) is reinterpreted in terms of bifurcation and length ratio (r _B andr _L ) asD=log (r _B )/log (r _L ). We test this relation for non-homogeneous exact fractal trees and two natural drainage systems. The fact thatr _B andr _L are common parameters in quantitative geomorphology allows a trivial stimation of the fractal dimension of well-known drainage basins.     

三峡库区滑坡规模与发育特征研究

研究滑坡规模及发育特征对开展滑坡风险评价和解析地貌演化过程具有重要意义。以三峡库区为研究区,通过GIS技术和数理统计分析滑坡面积、体积、厚度、发育密度等特征参数及发育规律,以及采用变维分形理论研究滑坡规模与地质环境因素的分形特征。研究结果表明：土、岩质滑坡空间发育模式具有区域性和集群式特点,且不同类型滑坡在空间分布上具有集聚性和规模不均匀性。滑坡发育规模和时序变形速率均存在幂律规则,表明滑坡系统具有自组织临界性。发现滑坡规模具有变维分形特征,同时揭示出滑坡规模与地质环境因素之间的敏感性关系。研究结果对认识三峡库区滑坡发育规律及实现滑坡风险评价具有重要作用。     

Do Skeletal Networks Derived from Water Bodies Follow Horton's Laws?

The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D _m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D _f) of the whole MSN computed through box-counting method.     

Rock mass characterization by fractal dimension

Fractal theory is used in the present study to develop a more reliable method for rock mass characterization. Field studies have been carried out in opencast mines of dolomite, limestone, fluorite; sandstone and shale in coalmines. Fractal dimension of blasted fragments (D_frag) and in situ rock blocks (D_{in situ}) is calculated using size distribution curves according to Schumann's model. Based on the co-relation between Uniaxial Compressive Strength (UCS) and D_frag, it is observed that change in fractal dimension is nominal beyond the UCS value of 20. From the co-relation between Bieniawaski's Rock Mass Rating (RMR) and D_{in situ}, it is found that there is a sharp increase in fractal dimension for RMR greater than 40. Co-relation between RMR and D_frag/D_{in situ} shows that as RMR increases, D_frag/D_{in situ} ratio decreases. Rock mass classification based on fractal geometry is suggested.     

Fractal trees and Horton''s laws

Fractal trees as a model for drainage systems are described in its generalized non-homogeneous form from the viewpoint of fractal geometry. Box covering techniques are used to show the numerical equivalence between the Hausdorff-Besicovitch dimension and the similarity dimension of the fractally-dominant dust formed by the sources. In this way, the similarity relationD=log (N)/log (1/r) is reinterpreted in terms of bifurcation and length ratio (r _B andr _L ) asD=log (r _B )/log (r _L ). We test this relation for non-homogeneous exact fractal trees and two natural drainage systems. The fact thatr _B andr _L are common parameters in quantitative geomorphology allows a trivial stimation of the fractal dimension of well-known drainage basins.     

The perimeter-area fractal model and its application to geology

Perimeters and areas of similarly shaped fractal geometries in two-dimensional space are related to one another by power-law relationships. The exponents obtained from these power laws are associated with, but do not necessarily provide, unbiased estimates of the fractal dimensions of the perimeters and areas. The exponent (D_AL) obtained from perimeter-area analysis can be used only as a reliable estimate of the dimension of the perimeter (D_L) if the dimension of the measured area is D_A=2. If D_A<2, then the exponent D_AL=2D_L/D_A>D_L. Similar relations hold true for area and volumes of three-dimensional fractal geometries. The newly derived results are used for characterizing Au associated alteration zones in porphyry systems in the Mitchell-Sulphurets mineral district, northwestern British Columbia.     

基于ArcGIS的滑坡空间分布的变维分形研究——以江西省宁都县为例

滑坡空间分布的定量研究对了解滑坡的发育特征具有实际意义,能够为滑坡的防治提供重要依据.为了了解滑坡的空间分布特征,以江西省宁都县1：5万地质灾害调查数据为基础,基于ArcGIS空间分析叠加模块,对滑坡空间分布规律应用变维分形理论进行定量研究,揭示出滑坡空间分布与地形地貌、岩土体类型、高程、坡度均呈二价累计和分形分布,使得滑坡与各因素之间的关系从定性分析上升到定量研究,并计算出分维值,说明了分维值的意义.     

基于ArcGIS的滑坡空间分布的变维分形研究——以江西省宁都县为例

滑坡空间分布的定量研究对了解滑坡的发育特征具有实际意义，能够为滑坡的防治提供重要依据.为了了解滑坡的空间分布特征，以江西省宁都县1：5万地质灾害调查数据为基础，基于ArcGIS空间分析叠加模块，对滑坡空间分布规律应用变维分形理论进行定量研究，揭示出滑坡空间分布与地形地貌、岩土体类型、高程、坡度均呈二价累计和分形分布，使得滑坡与各因素之间的关系从定性分析上升到定量研究，并计算出分维值，说明了分维值的意义.     

长江三峡黄腊石和黄土坡滑坡分形分维分析

为了探索复杂滑坡轨迹结构演化及其稳定性定量分析计算的新途径, 利用分形分维理论, 分析三峡库首区黄腊石滑坡和黄土坡滑坡边界轨迹的几何分形结构, 并采用盒维数法分别求得黄腊石滑坡西部活动性滑坡群、东部小滑坡群和整个滑坡系统及黄土坡滑坡分形结构的特征性斜率曲线和分维值.计算结果表明: 每个滑坡群的轨迹结构具有其特征性的分维值, 轨迹结构越复杂, 结构层次越清楚, 分维值越高.其中, 黄腊石滑坡西部活动性滑坡群的分维值最高, D =1.483, 黄土坡滑坡的分维值最低, D =1.111.主要结论包括: (1) 滑坡边界轨迹存在统计上的自相似性, 具有分形结构特征; (2) 滑坡轨迹结构的宏观扩展变形过程是一个增维过程, 而不是降维过程; (3) 滑坡轨迹结构越复杂, 有序性越好, 分维值越高, 其稳定性越差; 因此, 分数维可作为衡量滑坡轨迹结构复杂性和稳定性的重要标志.      

Seismic hazards assessment of Kumaun Himalaya and adjacent region

The ongoing continent?Ccontinent collision between Indian and Eurasian plates houses a seismic gap in the geologically complex and tectonically active central Himalaya. The seismic gap is characterized by unevenly distributed seismicity. The highly complex geology with equally intricate structural elements of Himalaya offers an almost insurmountable challenge to estimating seismogenic hazard using conventional methods of Physics. Here, we apply integrated unconventional hazard mapping approach of the fractal analysis for the past earthquakes and the box counting fractal dimension of structural elements in order to understand the seismogenesis of the region properly. The study area extends from latitude 28°N?C33°N and longitude 76°E?C81°E has been divided into twenty-five blocks, and the capacity fractal dimension (D ₀) of each block has been calculated using the fractal box counting technique. The study of entire blocks reveal that four blocks are having very low value of D ₀ (0.536, 0.550, 0.619 and 0.678). Among these four blocks two are characterized by intense clustering of earthquakes indicated by low value of correlation fractal dimension (D _c ) (0.245, 0.836 and 0.946). Further, these two blocks are categorized as highly stressed zones and the remaining two are characterized by intense clustering of structural elements in the study area. Based on the above observations, integrated analysis of the D _c of earthquakes and D ₀ of structural elements has led to the identification of diagnostic seismic hazard pattern for the four blocks.     

Integrating intensity–duration-based rainfall threshold and antecedent rainfall-based probability estimate towards generating early warning for rainfall-induced landslides in parts of the Garhwal Himalaya,India

In order to generate early warning for landslides, it is necessary to address the spatial and temporal aspects of slope failure. The present study deals with the temporal dimension of slope failures taking into account the most widespread and frequent triggering factor, i.e. rainfall, along the National Highway-58 from Rishikesh to Mana in the Garhwal Himalaya, India. Using the post-processed three-hourly rainfall intensity and duration values from the Tropical Rainfall Measuring Mission-based Multi-satellite Precipitation Analysis and the time-tagged landslide records along this route, an intensity–duration (I–D)-based threshold has been derived as I?=?58.7D ^?1.12 for the rainfall-triggered landslides. The validation of the I–D threshold has shown 81.6 % accuracy for landslides which occurred in 2005 and 2006. From this result, it can be inferred that landslides in the study area can be initiated by continuous rainfall of over 12 h with about 4-mm/h intensity. Using the mean annual precipitation, a normalized intensity–duration relation of NI?=?0.0612D ^?1.17 has also been derived. In order to account for the influence of the antecedent rainfall in slope failure initiation, the daily, 3-day cumulative, and 15- and 30-day antecedent rainfall values associated with landslides had been subjected to binary logistic regression using landslide as the dichotomous dependent variable. The logistic regression retained the daily, 3-day cumulative and 30-day antecedent rainfall values as significant predictors influencing slope failure. This model has been validated through receiver operating characteristic curve analysis using a set of samples which had not been used in the model building; an accuracy of 95.1 % has been obtained. Cross-validation of I–D-based thresholding and antecedent rainfall-based probability estimation with slope failure initiation shows 81.9 % conformity between the two in correctly predicting slope stability. Using the I–D-based threshold and the antecedent rainfall-based regression model, early warning can be generated for moderate to high landslide-susceptible areas (which can be delineated using spatial integration of preconditioning factors). Temporal predictions where both the methods converge indicate higher chances of slope failures for areas predisposed to instability due to unfavourable geo-environmental and topographic parameters and qualify for enhanced slope failure warning. This method can be verified for further rainfall seasons and can also be refined progressively with finer resolutions (spatial and temporal) of rainfall intensity and multiple rain gauge stations covering a larger spatial extent.     

Controlling parameter analyses and hazard mapping for earthquake-triggered landslides: an example from a square region in Beichuan County, Sichuan Province, China

On May 12, 2008, at 1428 hours (Beijing time), a catastrophic earthquake, with a magnitude of Ms 8.0, struck the Sichuan Province, China. About 200,000 landslides, as a secondary geological hazard associated with the earthquake, were triggered over a broad area. These landslides were of almost all types such as shallow, disrupted landslides, rock falls, deep-seated landslides, and rock avalanches. Some of these landslides damaged and destroyed large part of some towns, blocked roads, dammed rivers, and caused other serious damages. The purpose of this study is to detect correlations between landslide occurrence and the surface rupture plane, ground shaking conditions (measured by peak ground acceleration, PGA), lithology, slope gradient, slope aspect, topographic position, and distance from drainages by using two indices, landslide area percentage (LAP) and the landslide number density (LND), based on geographic information system (GIS) technology and statistical analysis method in a square region (study area) of Beichuan County, Sichuan Province, China. There were 5,096 landslides related with the earthquake which were delineated by visual interpretation and selected field checking throughout the study area. The total area (horizontal projection) of the 5,096 landslides is about 41.103 km². The LAP, which is defined as the percentage of the plane area affected by landslides, was 10.276 %, and the LND, means the number of landslides per square kilometers, was 12.74 landslides/km². Statistical analysis results show that both LAP and LND have a positive correlation with slope gradient and a negative correlation with distance from the surface rupture. However, the correlation between the occurrence of landslides with PGA, topographic position, and distance from drainages are uncertain, or has just a little positive correlation. The correlation between landslide and slope aspect also shows the effect of the directivity of the seismic wave. The Zbq formation had the most concentrated landslide activity with the LND value of 21.78 landslides/km _, ² and the ∈₁ q Gr. geological units had the highest LAP value. Furthermore, weight index (W _i) model is performed with a GIS platform to derive landslide hazard index map. The success rate of the model was 71.615 % and, thus, it was valid. In addition, comparison of five landslide controlling parameters’ influence on landslide occurrences was also carried out.     

Volume-based soil particle fractal relation with soil erodibility in a small watershed of purple soil

The particle size distribution in small watershed changes under different land uses and affects soil erodibility. The aims of this study were (1) to investigate the volume fractal dimension of particle size distribution under different land uses in a typical small watershed of purple soil, (2) to estimate soil erodibilities of various land uses utilizing the Erosion-Productivity Impact Calculator (EPIC) model and the nomogram (NOMO) model, and (3) to relate volume fractal dimension with the soil erodibility used in the Universal Soil Loss Equation (USLE) in purple soil areas. Laser diffractions and double-logarithmic model were used to measure and calculate volume fractal dimension values. The results show that soil volume fractal dimensions were well linearly fitted to the double-logarithmic model with high correlation coefficients of 0.902–0.936 under six land uses in the small watershed. The averaged volume fractal dimension values under different land uses, from high to low were in the order of Zea mays L, Ipomoea batatas, Citrus reticulata Blanco, Setaria viridis, Robinia pseudoacacia L, Pinus massoniana Lamb. The volume fractal dimension was positively correlated to clay particle fraction (R = 0.933). The average soil erodibility values under different land uses from high to low were in the order of Setaria viridis, Citrus reticulata Blanco, Pinus massoniana Lamb, Zea mays L, Ipomoea batatas, Robinia pseudoacacia L while average soil erodibilities from high to low values were in the order of Setaria viridis, Citrus reticulata Blanco, Zea mays L, Ipomoea batatas, Pinus massoniana Lamb, Robinia pseudoacacia L. The soil erodibilities calculated by the two models were similar, and positively correlated (R = 0.630–0.877). The volume fractal dimension values of six land uses were negatively correlated to both soil erodibility estimated by EPIC and by NOMO models. Moreover, the correlations of the volume fractal dimension values of Zea mays L, Ipomoea batatas and Citrus reticulata Blanco estimated by EPIC or NOMO were lower than those of Pinus massoniana Lamb, Robinia pseudoacacia L and Setaria viridis. Further research is needed to determine the influence of volume fractal dimension on the soil erodibility under different land use and managements.     

Do Skeletal Networks Derived from Water Bodies Follow Horton's Laws?

The aim of this short note is to test whether the morphological skeletal network (MSN) of water bodies that resembles a river network follows Horton's laws. A fractal relationship of MSN of a water body is also shown. This investigation shows that the MSN of the Nizamsagar reservoir follows Horton's laws. Furthermore, this reservoir has a fractal dimension (D _m) of 1.92 which was computed by using two morphometric quantities and the fractal dimension of the main skeletal length (d). This value tallies exactly with the fractal dimension (D _f) of the whole MSN computed through box-counting method.     

Rainfall thresholds for prediction of shallow landslides around Chamoli-Joshimath region,Garhwal Himalayas,India

Majority of landslides in the Indian sub-continent are triggered by rainfall. Several attempts in the global scenario have been made to establish rainfall thresholds in terms of intensity-duration and antecedent rainfall models on global, regional and local scales for the occurrence of landslides. However, in the context of the Indian Himalayas, the rainfall thresholds for landslide occurrences are not yet understood fully. Neither on regional scale nor on local scale, establishing such rainfall thresholds for landslide occurrences in Indian Himalayas has yet been attempted. This paper presents an attempt towards deriving local rainfall thresholds for landslides based on daily rainfall data in and around Chamoli-Joshimath region of the Garhwal Himalayas, India. Around 128 landslides taken place in last 4 years from 2009 to 2012 have been studied to derive rainfall thresholds. Out of 128 landslides, however, rainfall events pertaining to 81 landslides were analysed to yield an empirical intensity–duration threshold for landslide occurrences. The rainfall threshold relationship fitted to the lower boundary of the landslide triggering rainfall events is I?=?1.82 D ^?0.23 (I?=?rainfall intensity in millimeters per hour and D?=?duration in hours). It is revealed that for rainfall events of shorter duration (≤24 h) with a rainfall intensity of 0.87 mm/h, the risk of landslide occurrence in this part of the terrain is expected to be high. Also, the role of antecedent rainfall in causing landslides was analysed by considering daily rainfall at failure and different period cumulative rainfall prior to failure considering all 128 landslides. It is observed that a minimum 10-day antecedent rainfall of 55 mm and a 20-day antecedent rainfall of 185 mm are required for the initiation of landslides in this area. These rainfall thresholds presented in this paper may be improved with the hourly rainfall data vis-à-vis landslide occurrences and also data of later years. However, these thresholds may be used in landslide warning systems for this particular region of the Garhwal Himalayas to guide the traffic and provide safety to the tourists travelling along this pilgrim route during monsoon seasons.     

滑坡分维特征及其预测意义

本文依据分形理论，采用盒维数法计算了西藏樟木地区滑坡及其水系的空间分维。分析了分维的变化特征。发现滑坡高潮期前存在不同幅度的降维现象，滑坡区滑坡活动程度不同，其水系分维在不同观察尺度下变化幅度有显着的差别。探讨了分维的预测意义。     

Natural fracture profiles,fractal dimension and joint roughness coefficients

Summary Thirteen natural rock profiles (Barton and Choubey, 1977) are analyzed for their fractal properties. Most of the profiles were found to approximate fractal curves but some also showed features of specific wavelengths and amplitudes superimposed on fractal characteristics. The profiles showed fractal dimensions from 1.1 to 1.5 covering a range of selfsimilar and self-affine curves. The analysis results suggest a negative correlation between fractal dimension,D, and amplitude,A. Joint roughness coefficients (JRC) show a positive correlation with amplitude,A, and a negative correlation with fractal dimension,D. A numerical model of fracture closure is used to investigate the effects of different profile characteristics (D, A and sample size) on the nature of dilation and contact area, using the natural profiles and synthetic fractional Brownian motion profiles. Smooth profiles (low JRC, highD, lowA) display many small contact regions whereas rough fractures (high JRC, lowD, highA) display few large contact areas. The agreement with published experimental data supports the suggested correlations between JRC and the fractal parameters,A andD. It is suggested that observed scale effects in JRC and joint dilation can be explained by small differential strain discontinuities across fractures, which originate at the time of fracture formation.