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Background: Three groups of factors related to topography, geology and hydrology have influence on the triggering of shallow landslides in soil material. In this paper a single representative factor (T-factor) for the topography is proposed, which can be used to define threshold values for the possibility of shallow soil slides. This study was carried out in the Dayi area, Guizhou Province, China. During a heavy rainfall event on June 6, 2011, 230 shallow soilslides were triggered. In some slopes, no shallow landslides were triggered even though some of the topographical factors point to unstable high probability. Results: We isolated and analyzed the influence of the topography on the triggering of shallow landslides in catchments with almost identical hydrological and geological conditions and propose a new T-factor as a topographical indicator which is a combination of the slope angle, the upslope contributing area, the cross-section, and the free-face of a (potential) shallow landslide. Higher T-factor values are related to higher probabilities of shallow landsliding. The probability assessment with the topographical factor T was successfully validated in other areas of the USA and Japan. Conclusions: Without information on the geological and rainfall conditions, a quick and primary prediction of shallow landsliding using the topographical factor T is proposed. Additionally a new R-factor is proposed as a rainfall indicator, which is a combination of the 1 hour rainfall and cumulative rainfall before the landslide event and the annual rainfall. Higher R-factor values are generally related to higher probabilities of shallow landsliding. The primary probability factor P, which is the combination of T and R, gives a final indication of the probability of shallow landsliding. Keywords: Topographical threshold factor, Rainfall threshold factor, Shallow landsliding, Dayi catchment Background conditions, vegetation and rainfall. Thus, prediction of Shallow landslides are common in mountainous areas after landslide susceptibility is difficult because an enormous intense rainfall or long term rainfall. They are natural amount of spatial data must be acquired from the region phenomena that pose a serious natural hazard in many and processed (Park et al. 2013). No one, however, takes full countries. Shallow landslides cause not only considerable advantage of the fact that shallow failures are, in general, financial losses but also major ecological and environmental strongly controlled by surface topography (especially lateral problems such as increased soil erosion rates and overload concavity) through shallow subsurface flow convergence of sediments in rivers downstream. Shallow translational and increased soil saturation by infiltration of water (Borga landsliding is the most commonly observed failure mode in et al. 2002). soil material (Meisina and Scarabelli 2007). The occurrence The shallow landslides are mainly influenced by topo- of these landslides is controlled by various spatial and cli- graphical factors: slope gradient (a very sensitive factor) matic factors, such as geology, topography, hydrogeological and lateral concavity in relation to the upstream contrib- uting area which induced convergence of subsurface water flow, increase in groundwater height and hence * Correspondence: firstname.lastname@example.org decrease in slope stability. As hydrological processes are State Key Laboratory of Geohazard Prevention and Geoenvironment considered to have a major influence on slope stability, Protection, Chengdu University of Technology, Chengdu 610059, China © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 2 of 17 the occurrence of landslides is thus controlled twofold Study area by slope gradient and lateral concavity (Hennrich and Many shallow landslides on slopes covered with soil Crozier 2004). were triggered in the Dayi catchment Guizhou Province, Although in these studies topography has been China by a rainstorm on June 6, 2011. They were most reported as an important factor for slope stability, only 0.5 - 1 m in depth and a few meters long by a few slope angle is considered as the topographical factor in meters wide. Some of these triggered debris flows (see most stability models (Talebi et al. 2008). Slope angle is Fig. 1, Yu et al. 2016). The groundwater level is lower probably the main factor for stability as it affects the than the lower boundary because the slips were triggered magnitude of both normal stress (determining the mobi- in the middle or up part of the slopes, and the ground- lized shear resistance) and the driving shear stress on water level is in the bottom part of the slopes. the potential surface of failure. Therefore almost all The Dayi catchment is located in the upstream area of statistical models include slope angle as a topographical the Wangmo River. The Wangmo River is a main tribu- factor (Baeza and Corominas 2001). However, slope tary of the Nanpanjiang River, which is a tributary of the angle is not the only topographical factor for the initi- Zhujiang River, the third largest river in China. The ation of shallow landslides. Take for example the pos- Wangmo River flows in a North- South direction. The ition on a slope: the further upslope from the base of a lowest elevation in the Dayi catchment is 710 m, and the hillslope, the faster a site will drain. Likewise, slope sites highest peaks in the catchment have altitudes between with hollows usually drain much more slowly than sites 1500 and 1600 m. The hill slope gradients in the catch- on ridges. The free-face of a slope is also an important ment are very large, most of them are larger than 20 factor because it provides an open and immediate outlet degrees. These are suitable topographic conditions for of the landslide. triggering shallow landslides. O'Loughlin (1986) and Montgomery and Dietrich Only two lithological units are exposed in the study area: (1994) developed a physical model for the topographic hard siltstone interbedded with thin mudstone. The thick- control on shallow landsliding. The model divides a ness ratio of siltstone and mudstone is 3 – 4to1.There is catchment into topographic elements defined by the no faulting in the study area. The shallow landslides intersection of contours and flow tube boundaries occurred in soil material on the slopes. The geological con- orthogonal to the contours. The slope gradient and the ditions for the triggering of shallow landslides in the study upslope contributing area of a shallow landslide were area are almost identical. considered as the topographical factors in their model. The average annual rainfall lies in the range between Montgomery and Dietrich (1994) pointed out that steep 1190 and 1320 mm, and the average annual temperature slopes and topographic hollows which concentrate the varies between 14.4 and 16 °C. Figure 2 shows the rainfall surface and subsurface water to the outlet are the most data of the Dayi and Xintun (13.1 km south of Dayi) susceptible to failure. Baeza and Corominas (2001) meteorological stations, before and after the occurrence of pointed to the important influence of a cross-section the shallow landslides on June 5 and 6, 2011. The rainfall perpendicular to the slope gradient, on the initiation of started at 22:00 h, June 5, at the Dayi station, but there shallow landslides. The cross-section of the slope (lateral was almost no rainfall at the Xintun station until 01:00 h, convexity or concavity) shows the ability of the topog- June 6. The maximum rainfall intensity in 1 h was raphy to disperse or concentrate water at a certain 105.9 mm at the Dayi station from 23:00 to 24:00, June 5 location, which has a large effect on the susceptibility to landsliding. Based on the findings mentioned above Baeza and Corominas (2001) used the slope, the upslope contribut- ing area and the cross-section of the slope, for the assessment of shallow landslide susceptibility. However, the influence of the presence of a free-face at the toe of a (potential) landslide may also play an important role. In this study, we focus on the shallow landslides occurred in soil (also called shallow soil slips). These shallow landslides provided an unprecedented amount of data to obtain a combined topographical factor. By focusing on the process mechanisms our aim was to find a significant and probably more general relationships between the likelyhood of shallow landsliding and one Fig. 1 Shallow landslides near Dayi, Guizhou Province, on June 6, 2011 single combined topographic factor. Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 3 of 17 (see Fig. 2). The debris flows were triggered between 23:00, June 5 and 04:00, June 6 and the shallow landslides may be triggered also in this period (Yu et al. 2016). Because the rainfall of June 5 - 6 showed a variation from north to south, the study area was divided into 4 sub-areas from north to south. The triggering times of debris flows caused by shallow landslides were between 1:00 and 2:00 o’clock in the sub-areas 1 and 2, between 3:00 and 4:00 o’clock in sub-area 3, and between 4:00 and 5:00 o’clock in sub-area 4 (Fig. 3). Field investigations were conducted upstream and downstream of Dayi town. The topographical factors were investigated for 230 shallow landslides, and 138 Fig. 2 Rainfall in the Dayi area on June 5 and 6, 2011 potential unstable slopes. These potential unstable slopes have a large slope gradient or a gentle upslope gradient in the longitudinal section, or a large degree in lateral concavity or a free-face of slope in the longitudinal Fig. 3 The shallow landslides and potential unstable slopes with the investigated sub-areas in the Dayi area, Guizhou Province Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 4 of 17 section, or a combination of two or more out of four of rainfall conditions are assumed to be uniform for the these characteristics. Figure 3 shows the location of the slopes within that sub-area. Therefore we can assume 230 shallow landslides, and 138 potential unstable that only the topography is the dominant factor for the slopes. The drainage areas of sub-area 1, 2, 3, and 4 are triggering of shallow landslides within each sub-area. 2 2 2 2 16.9 km , 30.3 km , 11.5 km , and 27.6 km , respectively. The most important topographic factor which plays a The percentage of the slope which the slope gradient role in controlling the stability of shallow landslides is the between 20 degree and 50 degrees are 72.7%, 64.1%, slope angle (Mulder 1991). Figure 4 shows the other major 80.3%, and 66.6%, respectively. The slope is very steep in important topographic factors: the upslope gradient in the the right bank in sub-area 2. The percentage of the slope longitudinal section, the sides of the hollow in the cross- which the slope gradient more than 50 degrees is 32.5% section, and the free-face of the slope also in the longitu- in the right bank of sub-area 2. But the percentage of dinal section (O'Loughlin 1986; Montgomery and Dietrich the slope which the slope gradient more than 50 degrees 1994; Baeza and Corominas 2001). is only 4.1% in the left bank of sub-area 2. The slope gra- It is easy to find and measure the parameters in Fig. 4 dient is too large to keep the soil in the right bank of for existing landslides. But for the potential landslides, sub-area 2. So there is no soil slip in the right bank of one must firstly detect the body of the potential land- sub-area 2. The topographical characteristics of the 368 slide. According to the important topographical factors slopes without and with shallow landslide triggered on mentioned above, the largest slope gradient, gentle June 6, 2011 in the Dayi area were obtained from the upslope gradient in the longitudinal section, the hollow field investigations. The investigations in the sub-area 1 in the cross-section, and the free-face of the slope in the were only conducted along the river banks or less than 500 m along the channel in the catchments because these is no way to go into the upstream of catchments. There are 37 gullies were found gully-type debris flows cause by shallow landslides (Yu et al. 2016). According to Yu et al. (2016), the major topographic factors related with the occurrence of debris flows by shallow landslides are the gradient of the stream channels, the area ratio of the catchment with terrain slope angles between 25 degree and 45 degree, and the size of the catchments. The role of the terrain slope angles is far more import- ant than the role of the size of the catchment, and the role of the average gradient of the stream channels. The probability of debris flow formation caused by shallow landslides increases with increasing of the topographical factor which is a combination of the factors of the gradi- ent of the stream channels, the terrain slope angles, and the size of the catchments (Yu et al. 2016). In these gullies with debris flows cause by shallow landslides, 112 shallow landslides were found. The average value of shallow land- slide in the debris flows is 3.03. But the average value of shallow landslide in the 63 catchments without debris flow is 1.87. The average percentage of the slope which the slope gradient between 25 and 45 degrees is 66.4% for the 37 gullies, but the average percentage of the slope which the slope gradient between 25 and 45 degrees is 48.3% for the other gullies without debris flows in Fig. 3. The aver- age topographical factor is 0.338 for the 37 gullies, but the average topographical factor is 0.237 for the other gullies without debris flows in Fig. 3. Methods Fig. 4 The topographical schematic sketch of a potential shallow landslide and surrounding topography. a. top view of a potential In Fig. 3, the maximun N-S width is about 4 km in each shallow landslide and its surrounding area; b. longitudinal cross sub-aera. Due to the relative small size of each sub-area, sectional view; c. lateral cross sectional view and the same triggering time of shallow landslides, the Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 5 of 17 longitudinal section are the key points to detect poten- shallow landslides are triggered on slopes between 20 and 40 tial shallow landslides. To identify a potential shallow degrees (Wang 1999). If the slope gradient is too large (more landslide one can start with the selection in the longitu- than 45 degrees), less shallow landslides will be triggered dinal section of a large slope gradient. Then one can because the soil thickness is too thin (Montgomery and connect this section with a gentler upslope gradient, or Dietrich 1994). If the slope gradient is less than 20 degrees, with a hollow in a cross-section, or a free-face of the less shallow landslides will be triggered because the slope is slope in the longitudinal section, or a combination of too gentle (Godt et al. 2008). The slope angle factor S can be two, or three of these important topographical factors. defined as: Some slopes without a large slope gradient, but with the presence of a gentler upslope gradient in the longitu- S ¼ tanα ð1Þ dinal section, or hollows in a cross-section, or a free-face of the slope in the longitudinal section are also chosen in which α is the slope angle of the shallow landslide as potential shallow landslides. (Fig. 4). In Fig. 1, a slope with cross-section a hollow (lateral concavity) may be first selected as a potential shallow Upslope factor landslide. The top boundary of A is the knick point with The the upslope contributing area draining towards the the gentler upslope. If there is no knick point with the shallow landslide (Fig. 4) were considered as topographical gentler upslope, the top boundary of A is the top end of factors in the model of O'Loughlin (1986), Montgomery the hollow in cross-section. The bottom boundary of A and Dietrich (1994). Wieczorek et al. (2007) indicated that is the knick point with the free-face of the slope. If there an upslope drainage area with a gentler slope gradient is no knick point of the free-face of the slope, the triggered more shallow landslides because drainage is bottom boundary of A is the end of the hollow in cross- slower than on steeper slopes. This will increases the section. The left side and right side boundaries of A are groundwater water storage in the potential landslide area the boundaries of the flat part between the hollows in and hence the probability of failure. Also a larger up- cross-section (see Fig. 1). The top boundary of Au is the stream drainage area increases the chance for slope failure knick point of the gentler upslope or the top of the for the same reason. The upslope drainage factor can be slope. The left side and right side boundaries of Au are defined as: the edges of the upstream contributing area which in- duced convergence of subsurface water flow (see Fig. 1). U ¼ tanðÞ α−β ð2Þ The bottom boundaries of A and A are at the same R L A level of the bottom boundary of A. The top boundaries of A and A are the edges of the lateral concavity which In which: U is the upslope drainage factor; A is the area R L u induced convergence of subsurface water flow. The left of upslope drainage area (m); A is the area of a (potential) boundary of A or the right boundary of A is the out- shallow landslide, A is referred to the source area only; β L R side edge of the hollow (see Fig. 1). is the slope angle of an upslope drainage area. The differences between the gully and a slope corre- The upslope factor U reflects also the role of a gentler sponding to a landslide area in Fig. 1 include the follow- upslope gradient on the triggering of shallow landslides. If ing: a) The slope angle of shallow landslides have larger the upslope angle β is larger than the slope angle α,the gradients, while the slope angles of gullies may be more slope drains much faster, and the effect of the upslope gentle in most sections (see Fig. 1). b) The shallow land- drainage area on shallow landsliding is much lower than slides are a few meters long and a few meters wide, but the effect of a gentler upslope gadient. To simplify our the gullies may be up to 1 km long and tens of meters in research, the upslope factor U is set to 0 if the upslope width (see Fig. 1). c) The shallow landslides may occur angle β is larger than the slope angle α. This simplification at the heads of the first-order gullies (Montgomery and does not mean that there is no contribution of a steep Dietrich 1994). At these heads the gullies may have the upstream area to slope failure, but the contribution is less. same topography as the slopes corresponding to the landslide areas with large slope angles, a few meters in Cross-section factor length and a few meters in width. The cross-section of the slope shows the ability of the top- ography to disperse or concentrate water to the potential Slope angle factor landslide area, which can become less or more susceptible The slope angle of a shallow landslide is one of the most im- to landsliding (Baeza and Corominas 2001). Montgomery portant triggering factors because it provides the driving and Dietrich (1994) indicated that the lower end of topo- force of a slide. That is why all models include slope angle as graphic hollows is predicted to be susceptible to failure. a topographical factor (Baeza and Corominas 2001). Most The sites of the hollows usually drain much more slowly Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 6 of 17 than sites on ridges because the hollows can concentrate sub-area 1, 2, 3, and 4. No shalllow landslide will be water. The cross section factor can be defined as: triggered below these minimum S threshold values irre- spective of the value of U. By separating the data with A A shallow landslides and without shallow landslides, a fac- L R C ¼ tanθ þ tanθ ð3Þ 1 2 tor T , which is a measure for the possibility of shallow A A landsliding in Fig. 5 can be obtained: in which: C is the cross section factor; A is the area of the left side (m); A is the area of right side (m); θ is T ¼ S þ 1:8U≥C ð4Þ 1 r1 R 1 the slope angle of the left side in cross-section; θ is the slope angle of right side in cross-section (Fig. 4). in which T is the factor; C is the critical value for 1 r1 The cross section factor C represents the effect of a triggering shallow landslides. lateral concavity or hollow on the triggering of shallow The critical value C is 0.60, 0.65, 0.70, and 0.73, respect- r1 landslides. When the slope angle θ or (and) θ is (are) ivelyinsub-area1,2,3,and 4. To triggera shallowland- 1 2 less than zero, in other words: in case of a lateral slide, the slope angle factor S must be large or equal to convexity of the slope, the ratio of A /A or (and) A /A is 0.33, 0.36, 0.39, and 0.41, respectively in sub-area 1, 2, 3, L R (are) set to zero. In this way we reduce the effect of and 4. The reason for an increase of the critical value C r1 lateral concavity to zero. and the minimum slope angle S from north to south is the rainfall which was decreasing from north to south. Con- Free-face factor versely we can imagine that for large rainfalls, the critical The free-face is the necessary condition for the initiation value and the minimum slope angle for triggering shallow of a rock slide. For the shallow soil slides, the free-face is landslides are reducing. not necessary because the toe of the slide may shear out Figure 5 shows that the threshold line S + 1.8 U = C r1 from the soil layer as a so called slope failure. However a can separate slopes with shallow landslides from slopes free-face (like a road cut) makes the slope more suscep- without shallow landslides exactly. The triggering prob- tible to failure but is not a prerequisite for shallow soil ability of shallow landslides increases with increasing T - failure. When the downslope angle γ in Fig. 4 is larger values in each sub-area. than slope angle α, there is a free-face. If γ > α, then the free-face factor F will be taken into account: F >0, The relationship between the slope angle S and cross-section C otherwise F = 0. The value of F is determined by field To obtain the relationship between the slope angle investigations (see below). factor S and the cross-section factor C, we compared shallow landslides and stable slopes with the same value Results: the topographical factors in the study of the upslope factor and free-face factor. The topo- area, and their role in the triggering of shallow graphical data with U = 0, and F > 0 (free-face is avail- landslides able) is satisfying this condition. In Fig. 6 a. - d. a scatter To obtain the topographical factor of shallow landslides plot of landslides and stable slopes is now made in a S-C with the sub-factors S, U, C,and F,the mutual relationships field for each sub-area. between these facors have to be established first. All figures show again the posive effect of a larger slope angle factor S and cross-section factor C on the The relationship between the slope angle S and upslope possibility of triggering shallow landslides. Minimum factor U values for S below which no landslides can occur at all To obtain the relationship between the slope angle are: 0.33, 0.36, 0.39, and 0.41, respectively in sub-area 1, factor S and the upslope factor U, a comparison between 2, 3, and 4. By separating the data with shallow land- shallow landslides and stable slopes is needed with the slides and without shallow landslides in the S-C field, a same value of the cross-section factor C and free-face factor T from Fig. 6 can be obtained: factor F. The topographic data in which C = 0, and F >0 (free-face is available) is satisfying this condition. And T ¼ S þ 0:8C≥C ð5Þ 2 r2 the comparison should be in one sub-area because the rainfall condition is almost the same in each sub-area. in which T is the factor; C is the critical value for trig- 2 r2 Figure 5 a. to d. shows the relationship between the gering shallow landslides. slope angle factor S and the upslope factor U in sub-area The critical value C is 0.60, 0.65, 0.70, and 0.73, r2 1 to 4 of Fig. 3. Generally all figures show that with respectively in sub-area 1, 2, 3, and 4. To trigger a shal- increasing value of S and U the chance of shallow land- low landslide, the slope angle factor S must be large or slide failure also increases. But there are minimum equal to 0.33, 0.36, 0.39, and 0.41, respectively in sub- values for S: 0.33, 0.36, 0.39, and 0.41, respectively in area 1, 2, 3, and 4. Here again we see the effect of the Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 7 of 17 Fig. 5 The relationship between the slope angle factor S and upslope factor U. a. Sub-area 1; b. Sub-area 2; c. Sub-area 3; d. Sub-area 4 decreasing rainfall from North to South on the increase whatever the value of G are: 0.33, 0.36, 0.39, and 0.41, of the C and S values. respectively in sub-area 1, 2, 3, and 4 with or without r2 Figure 6 shows that the line S +0.8C = C can com- the free-face factor F. The critical value C is 0.60, 0.65, r2 r3 pletely separate slopes with shallow landslides from slopes 0.70, and 0.74, respectively in sub-area 1, 2, 3, and 4 for without shallow landslides. The probability of shallow a free-face (F > 0) and 0.73, 0.78, 0.83, and 0.87 for sites landsliding increases with increasing T -values in each without a free-face (F = 0) (Fig. 7a-d). So larger T - 2 3 sub-area. The role of the slope angle factor S seems to be values are needed to trigger shallow landslides in case of more important than the role of the cross-section factor C. the absence of a free-face. The role of the free-face factor is the difference of the critical values with and The role of the free-face without a free-face factor. One can obtain the free-face From Eqs. 4 and 5, one can combine the relationship of factor: F = 0.13 in case of a free-face, and F = 0 in case the slope angle factor S, the upslope factor U, and the of absence of a free-face. cross-section factor C. A factor T for triggering shallow landslides can be obtained: The topographical factor T The slope gradient may be too large to trigger shallow T ¼ S þ G ¼ S þ 1:8U þ 0:8C≥C ð6Þ landslides because there is almost no soil (Montgomery 3 r3 and Dietrich 1994). Frattini et al. (2009) indicated that in which T is the factor; G is the factor combining the slopes are unconditionally stable if the gradient is larger role of the upslope factor U, and the cross-section factor than 52.5 (S = 1.3). In the study area, the maximum C; C is the critical value for triggering shallow S-value for shallow landsliding is 1.07 (47 ). The max- r3 landslides. imum S-value may be larger than 1.07 in case of larger To analyze the role of the free-face factor F, all investi- rainfall amounts and soil material more prone to shallow gated landslide and stable slope sites were were plotted landsliding than the soils in this study. In accordance for the sub-area 1 to 4 in Fig. 7 a. - d., with as horizontal with Frattini et al. (2009), the maximum slope gradient axis the slope angle factor S and as vertical axix the for landsliding is set at 1.3. combined factor G. As we can expect increasing values Slope angle should be more important than the of S and the the combined factor G has a positive effect upslope factor U and cross-section factor C, or the on the probability of shallow landslide failure. Minimum combined factor G. Based on our data base the max- values for S below which no landslides can occur imum G-value is as large as 1.6 (Fig. 7 c), while the Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 8 of 17 maximum S-value is only 1.07 in Fig. 7. Shallow land- slides will not be triggered if the slope angle factor S is less than its minimum value regardless the value of the com- bined factor G in each sub-area. So the G-value has a limited role for the triggering of a shallow landslide. A limitation for the G factor is needed for the topographical factor. The points of intersection of the critical line of no free-face and the minimum slope angle factor S are 0.39, 0.42, 0.44, and 0.46 for the G-value (Fig. 7). If the G- value is larger than these intersection points and the slope angle factor S is less than the minimum value in each sub-area, the G-value plays no role because there is still no shallow landslide triggered. To simplify the topo- graphical factor G, a fixed maximum value for G may be used which is the maximum value of the intersection points of the 4 sub-area: 0.46 (Fig. 7 d). If the maximum G-value is obtained from the critical line of the “free- face landslides” instead of the critical line of “no free- face landslides” the limited G-value in that case is 0.33. To simplify the research work, the limited value for the combined factor (G + F) is chosen as 0.46. Then the modified topographical factor can be obtained as: T ¼ S þ G þ F ¼ S þ 1:8U þ 0:8C þ F≥C ð7Þ G þ F ¼ 1:8U þ 0:8C þ F≤0:46 ð8Þ F = 0, when free-face is absent F ¼ 0:13; when free‐face is present ð9Þ S≤1:3 ð10Þ in which T is the topographical factor for shallow soil slides; C is the critical value for triggering these slides. For sub-area 1 to 4 in Fig. 7, the critical value C is 0.73, 0.78, 0.83, and 0.87, respectively. The Eq. 7 shows the U is the most sensitive factor and C is less sensitive. This may because the slope gradient is large, and the landslide is in a few meters long. These result more runoff on the surface during a rainfall event, and less subsurface water converged by the lateral concavity to increase ground- water height, which is more important to decrease the slope stability. Fig. 8 a.- d. shows the relationship of slope angle factor S and combined factor G+F (upslope factor U and cross- section factor C) using the topographical factor with Eq. 7- 10.InFig.8, the free-face factor F is included in the data. In Fig. 7 it is difficult to predict the triggering of a shallow land- slide without the introduction of the minimum slope angle S at a particular site and for a particular rainfall. In Eq. 7 - 10, there is no minimum slope angle for assessing the stability of a slope. With the introduction of a limited value of G + F Fig. 6 The relationship between the slope angle factor S and cross-section (0.46), the minimum slope angle is not needed. The thresh- factor C. a. Sub-area 1; b. Sub-area 2; c. Sub-area 3; d. Sub-area 4 old can be described using only the linear function: S +1.8 U +0.8C + F = C (Fig. 8). However these threshold r Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 9 of 17 a c Shallow landslide, F=0 1.60 Shallow landslide, F=0.13 1.60 Shallow landslide, F=0 Shallow landslide, F=0 1.40 Stable slope, F=0.13 Stable slope, F=0.13 1.40 Stable, F=0 Stable slope, F=0 S+G=0.6 1.20 1.20 S+G=0.7 S+G=0.73 S+G=0.83 1.00 S=0.33 1.00 S=0.39 G 0.80 G 0.80 0.60 0.60 0.40 0.40 0.20 0.20 0.00 0.00 0.2 0.4 0.6 0.8 1 Shallow landslide, F=0.13 b d 1.60 Shallow landslide, F=0 1.60 Stable slope, F=0.13 1.40 Stable,F=0 1.40 S+G=0.65 1.20 1.20 S+G=0.78 S=0.36 1.00 1.00 0.80 0.80 0.60 0.60 0.40 0.40 0.20 0.20 0.00 0.00 Fig. 7 The role of the free-face factor F. a. Sub-area 1; b. Sub-area 2; c. Sub-area 3; d. Sub-area 4 Fig. 8 The topographical factor T and its range. a. Sub-area 1; b. Sub-area 2; c. Sub-area 3; d. Sub-area 4 Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 10 of 17 functions do not separate completely in all cases landslide sites from stable sites except in sub-area 4 (Fig. 8d). In sub- area 1, 2, and 3, a few data predicted wrongly stable slopes. The prediction may fail also at some sites with large critical value (C > 0.87). Nevertheless it is easy to assess the topo- graphical factor T with Eqs. 7-10 and to predict the stability of the slope without the use of the minimum slope angle. Sub-area 1, 2 and 3 show that there is only a small chance for a miss classification. Validation Many shallow landslides are triggered worldwide each year. Validation areas were selected only on the basis of availability of high-resolution digital elevation models in areas suceptable for shallow soil slides. The scale of the map for the field work or indoor analysis is depended the scale of landslides. For example, for the shallow landslides of Dayi area, the slips are a few meters long by a few meters wide. The better contour interval of map is 2 m, and the better scale of the map is 1: 2000. Previous field work in these areas allows us to obtain the topographical factors for these landslides. To test the topographical model, some stable slopes which are shallow landslide-prone were selected. Fig. 9 shows the boundaries for A, Au, A , A for potential landslide area R L for given contour lines. For given contour lines, the definition of the boundaries for A, Au, A ,and A for R L potential landslide area as follow: 1) One can select a Fig. 9 The topographical schematic sketch of a potential shallow large slope gradient in the longitudinal section, and landslide and its surrounding topography for given contour lines connect this section with a gentler upslope gradient, or with a hollow in a cross-section, or a free-face of the slope in the longitudinal section, or a combination of boundaries of Au are the edges of the upstream contrib- two, or three of these important topographical factors. uting area which induced convergence of subsurface 2) Then the boundaries for A is needed to determine. water flow (see Fig. 9). 4) The bottom lines of A and A R L The top boundary of A is the contour line before the are the same level of the bottom line of A. The top lines distance of contour lines increasing (see Fig. 9). If there of A and A are the edges of the lateral concavity which R L is no gentler upslope gradient, i.e. the distance of con- induced convergence of subsurface water flow. The left tour lines of upslope is the same with or less than the boundary of A or the right boundary of A is the out- L R distance of contour lines of A, the top boundary of A is side edge of the hollow (see Fig. 9). the same level of the top contour line of a hollow in a Constant rainfall and geological conditions within one cross-section. The bottom boundary of A is the contour area are assumed because these study areas are relativly line before the distance of contour lines decresing (see small. So the only factor for triggering shallow landslide Fig. 9). If there is no free-face of the slope, i.e. the is the topographical factor given by Eqs. 7-10. distance of contour lines of downslope is the same with or more than the distance of contour lines of A, the Validation in Tennessee Valley, Marin County, California, bottom boundary of A is the same level of the bottom USA contour line of a hollow in a cross-section. The left side The Marin County catchment covers 1.2 km in the Ten- and right side boundaries of A are the boundaries of flat nessee Valley area of the Marin Headlands just north of San part between the hollows in cross-section (see Fig. 9). If Francisco, California. The catchment is underlain by there is only one hollow or no hollow, the left side and stacked thrust sheets composed of Cretaceous greenstone, right side boundaries of A are just below the left side greywacke, and cherts of the Franciscan Complex. The area and right side boundaries of Au. 3) The top boundary of has a Mediterranean climate with a mean annual rainfall of Au is the contour line before the distance of contour about 760 mm. Landslidings is an important sediment lines increasing (see Fig. 9). The left side and right side transport process on steeper slopes and in topographical Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 11 of 17 hollows, and overland flow and seepage erosion dominate Table 1 The numbers and percentages of shallow landslide (SL) and no shallow landslide (no SL) in the three classes in on lower-gradient slopes. Aerial photography and field Tennessee Valley inspection identified 43 landslide scars, most of which Number and percentage Number Percentage Number Percentage occurred during or since the storms in 1974. The max- of SL or no SL of SL of SL (%) of no SL of no SL (%) imum scar size is roughly 10 m wide; the slides have a T ≤ 0.51 0 0 6 50 length of around 20 m and a depth around 1 m. Most of 0.51 < T ≤ 0.67 14 34.1 5 41.7 the shallow landslides occurred in soil and some scoured until the bedrock. Almost all scars were located at steep T > 0.67 27 65.9 1 8.4 parts of the catchment. The digital elevation data set has contours with an interval of 5 m. Soil thickness varies from 0.1 to 0.5 m on topographic noses to depths until 4.0 m in landslides are located in the domain T > 0.51. Almost all topographic hollows (Montgomery and Dietrich 1994). the points (91.6%) without shallow landslides are located Form the digital elevation data (Fig. 4a) provided by in the domain T ≤ 0.67, and more than half of these points Montgomery and Dietrich (1994), only 41 shallow land- (50%) are located in the domain T ≤ 0.51. The topograph- slides could be detected. The topographical factors of 41 ical factor in three classes is applicable in Tennessee Valley. shallow landslides and 12 potential sites without shallow landslides were determined using the digital elevation Validation in Mettman ridge, Oregon, USA data. Generally the T-value of shallow landslides was The Mettman Ridge occupies 0.3 km in the Coast larger than the T-value of stable slopes. Because the Range just north of Coos Bay, Oregon. The area is highly triggered rainfalls for these landslides were different, the dissected and characterized by narrow ridge-tops and critical C values are different. Two critical values were steep slopes, which is typical in the Oregon Coast Range. proposed for separating the shallow landslide sites and Bedrocks consist of gently dipping Eocene sandstone. stable slope sites (see Fig. 10): C = 0.51, C = 0.67. The area has a maritime climate, and receives approxi- ra rb The threshold lines with these critical values were con- mately 1500 mm of precipitation annually. Nineteen structed as follows: below the line T = 0.67 lie all the shallow landslides occurred in the Mettman Ridge catch- “no landslides” (except one). Above the T = 0.51 line lie ment in the period between forest clearance in 1987 and all the landslides. When T ≤ 0.51, the possibility of the summer of 1992. Typical dimensions of the shallow shallow landslide is low; When 0.51 < T ≤ 0.67, the pos- landslides are in the order of 5 m by 10 m with a depth sibility of shallow landslide is medium; When T > 0.67, of about 1.5 m. Digital elevation data were generated the possibility of shallow landslide is high. The critical from a 1 : 4800 scale topographical map of the catch- value C is 31.3% higher than the critical value C , ment with a 5-m contour interval. The soil in this area rb ra which shows a moderate performance of the validated is silty sand and ranges in thickness from roughly 0.1 to model. Table 1 shows the numbers and percentages of 0.5 m on topographic noses to depths until 2 m in topo- shallow landslides and no shallow landslides in three graphic hollows (Montgomery and Dietrich 1994). classes. All the points with T > 0.67 are shallow land- The topographical factors of 19 shallow landslides and slides except one point. All the points with shallow 10 landslide-prone sites, were obtained by the digital elevation data. Generally the T-value of shallow land- slides is larger than the T-value of stable slopes. Because the triggering rainfalls were different in 1987 and 1992, the critical values (C ; in Eq. 7) were different. Two critical values were proposed for separating the sites with shallow landslides and the sites susceptible to sliding (see Fig. 11): C = 0.56, C = 0.73. Below the line rc rd T = 0.73 lie all the “no landslides” (except one). Above the T = 0.56 line lie all the landslides (except one). The possibility for shallow landsliding are low, medium or high for respectively T ≤ 0.56; 0.56 < T ≤ 0.73; T > 0.73. The critical value C is 30.4% higher than the critical rd value C , which shows a moderate performance of the rc validated model. Table 2 shows the numbers and percentages of shallow landslides and no shallow land- slides for the three classes. Fig. 10 The validation in Tennessee Valley Map showing shallow All the points beyond the line of T > 0.73 are shallow landslides and the probability landslides except one point. Almost all the points Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 12 of 17 The topographical factors of 9 shallow landslides and 10 potential sites were determined using the digital ele- vation data. Generally the T-values of shallow landslides calculated with Eq. 7 are larger than the T-values of stable but vulnerable slopes. Because the triggering rain- falls for these landslides were different, the critical values (C ) were different. Two critical values were proposed for separating the shallow landslides and actual stable but susceptible slopes (see Fig. 12): C =0.66, C =0.86. re rf Below the line T =0.86 lie all the “no landslides” (except one). Above the T = 0.66 line lie all the landslides. The possibility for shallow landsliding are low, medium or high for respectively T ≤ 0.66; 0.66 < T ≤ 0.86; T >0.86. The critical value C is 30.3% higher than the critical value C , rf re Fig. 11 The validation in Mettman Ridge which shows a moderate performance of the validation model. Table 3 shows the numbers and percentages of (94.7%) with shallow landslides are located in the shallow landslides and no shallow landslides in three domain T > 0.56. Most of the points (80%) without shal- probability classes. All the points beyond the line of low landslides are located in the domain T ≤ 0.73, and T > 0.86 are shallow landslides except one point. All the 10% of these points are located in the domain T ≤ 0.56. points with shallow landslides are located in the domain The topographical factor is a failrly good indicator for T > 0.66. Almost all the points (90%) without shallow the assessment of landslide probability in three classes in landslides are located in the domain T ≤ 0.86, and half of Mettman Ridge. these points are located in the domain T ≤ 0.66. The topo- graphical factorT is a usefull indicator to predict the possi- bility of shallow landsliding in Split Creek. Validation in Split Creek, Washington, USA The Split Creek occupies 0.6 km of the north flank of Validation in Hofu, Japan the Huelsdonk Ridge on the South Fork of the Hoh The catchment occupies 0.18 km in the Hofu city area River in the Olympic Peninsula. The area is character- in Japan. The soils consist of weathered granites. The ized by steep, unglaciated tributaries that drain into a soil thickness is between 0.06 to 5.4 m (Akiyama et al. wide glaciated valley filled with glacial outwash and 2014). Digital elevation data with a 5-m contour interval Holocenc alluvial sediments. Huelsdonk Ridge is under- is available. Akiyama et al. (2014) searched for the shal- lain by steeply dipping, folded and faulted Oligocene to low landslides in an area of 0.064 km and found eight upper Eocene sandstones. The area receives 4000 to shallow landslides. There were 16 shallow landslides in 5000 mm/yr. of rainfall annually. The soils, which oc- the area of 0.18 km detected in this study with the photos curred on these sandstones in this area consist of silty provided by Akiyama et al. (2014). A heavy rainfall hap- sands. Soil thickness averages about 1 m, although soils pened in July 20 – 21, 2009. The total precipitation was are shallower on topographic noses and thicker in hol- lows. Digital elevation data with a 5-m contour interval were generated from color aerial photographs using a stereo-digitizer. Landslides visible on color aerial photo- graphs flown in 1990 were drawn on this base map. In the west fork of Split Creek, nine shallow landslides were mapped by Montgomery and Dietrich (1994). Table 2 The numbers and percentages of shallow landslide (SL) and no shallow landslide (no SL) in the three classes in Mettman Ridge Number and percentage Number Percentage Number Percentage of SL or no SL of SL of SL (%) of no SL of no SL (%) T ≤ 0.56 1 5.3 1 10 0.56 < T ≤ 0.73 5 26.3 7 70 T > 0.73 13 68.4 2 20 Fig. 12 The validation in Split Creek Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 13 of 17 Table 3 The numbers and percentages of shallow landslide (SL) Table 4 The numbers and percentages of shallow landslide (SL) and no shallow landslide (no SL) in the three classes in Split and no shallow landslide (no SL) in the three classes in Hofu Creek Number and percentage Number Percentage Number Percentage of SL of no SL of SL of SL (%) of no SL of no SL (%) Number and percentage Number Percentage Number Percentage of SL or no SL of SL of SL (%) of no SL of no SL (%) T ≤ 0.55 0 0 3 33.3 T ≤ 0.66 0 0 5 50 0.55 < T ≤ 0.71 6 37.5 4 44.4 0.66 < T ≤ 0.86 3 33.3 4 40 T > 0.71 10 62.5 2 22.2 T > 0.86 6 66.7 1 10 On the other hand, the validation fails to predict 330 mm in 2 days. Some shallow landslides were triggered shallow landslides in pyroclastic fall deposits in the during this period (Akiyama et al. 2014). Fukushima area, Japan, which were triggered during a The topographical factors of 16 shallow landslides and rainstorm of Sep. 10 to 11, 1998 (Chigira et al. 2004). 9 sites without shallow landslides but landslide-prone This is because the the shallow landslides in the pyro- were obtained from the digital elevation data. Generally clastic fall deposits area has no relationship with any the T-value of shallow landslides is larger than the T- topographic factor (Chigira 2015). value of the selected stable slopes. Because the triggered rainfalls for these landslides were different, the critical Quick and primary assessment values C are different. Two critical values were pro- The occurrence of landslides is controlled by various spatial posed for separating the shallow landslides and stable and climatic factors, such as geology, topography, hydro- slopes (see Fig. 13): C = 0.55, C = 0.71. Below the line geological conditions, vegetation and rainfall (Park et al. rg rk T = 0.71 lie all the “no landslides” (except two). Above 2013). The critical values C to assess this topographical the T = 0.55 line lie all the landslides. The possibility for factor appeared to be different in our test area and the vari- shallow landsliding are low, medium or high for respect- ous validation areas in the USA and Japan because of the ively T ≤ 0.55; 0.55 < T ≤ 0.71; T > 0.71. The critical difference in geological conditions and rainfall conditions. value C is 29.1% higher than the critical value C , So does the slope angle factor S. However the critical values rk rg which shows a moderate performance of the validated differ not too much in the investigated areas. From the model. Table 4 shows the numbers and percentages of critical values in the Dayi area and the critical values of C , r1 shallow landslides and no shallow landslides in three C , C , C , C ,and C , C , C , C , C in USA and ra rc re rg r2 rb rd rf rk probability classes. All the points beyond the line of Japan, one can conclude that shallow landslides have a low T > 0.71 are shallow landslides except two points. All probability to be triggered when the topographical factor is the points with shallow landslides are located in the less than 0.51 and high trigger probability when the topo- domain T > 0.55. Most of the points (77.8%) without graphical factor is larger than 0.86. So in the range of shallow landslides are located in the domain T ≤ 0.71, 0.51 < T < 0.86 is the domain where most shallow land- and 33.3% of these points are located in the domain slides may occur in these areas. When we include other T ≤ 0.55. The topographical factorT is a usefull indicator areas we probably have to extent the limits of probability of to predict the possibility of shallow landsliding in Hofu. shallow landsliding due to a large variation in geological conditions and rainfall. A minmum value of C =0.5,and rL amaxmumvalue of C = 0.9 may be a good choise for a rH quick and primary assessment of the possibility of shallow landsliding, ignoring the variation in geological and rainfall conditions. Because the range 0.5 < T < 0.9 is large, three critical values to calculate the T factor are proposed: C =0.5, C =0.7,and C =0.9.When T ≤ 0.5, the rL rM rH possibility of shallow landslide is very low; When 0.5 < T ≤ 0.7, the possibility of shallow landslide is low; When 0.7 < T ≤ 0.9, the possibility of shallow landslide is medium; When T > 0.9, the possibility of shallow landslid- ing is high. The critical value C is 80% higher than the rH critical value C ,and the criticalvalue C is 40% higher rL rM than the critical value C , which shows a moderate per- rL formance of the assessment model. Table 5 shows the num- bers and percentages of shallow landslides and no shallow Fig. 13 The validation in Hofu landslides in four classes for the Dayi area and the USA Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 14 of 17 Table 5 The numbers and percentages of shallow landslide (SL) areas. Almost all sites (99.7%) beyond the line of T >0.5 are and no shallow landslide (no SL) in the four classes shallow landslides except one point, and most sites (90.2%) T ≤ 0.5 0.5 < T ≤ 0.7 0.7 < T ≤ 0.9 T > 0.9 Total with shallow landslides are located in the domain T >0.7. Almost all sites (98.3%) without shallow landslides are Possibility Very Low Medium High low located in the domain T ≤ 0.9, and more than half of these Numbers of SL 0 0 69 161 230 points (57.6%) are located in the domain T ≤ 0.7. The topo- in Dayi graphical factor subdivided in four classes is a good indica- Percentages of 0 0 30 70 100 tor in these areas. SL in Dayi (%) Numbers of no 9 65640 138 Rainfall factor in the shallow soil slips SL in Dayi Rainfall is the major threshold for triggering shallow Percentages of no 6.5 47.1 46.4 0 100 landslides. Unfortunately, there is no detailed rainfall in- SL in Dayi (%) formation corresponding to shallow landslides triggered Numbers of SL 0 18176 41 in the validation areas. In the Dayi area, we were able in TV for one event on June 5 and 6, 2011, using two available Percentages of 0 43.9 41.5 14.6 100 meteorological stations, to distinguish four sub-areas SL in TV (%) with different rainfall amounts leading to different Numbers of no 5 610 12 critical values C . This delivered a primary study on the SL in TV r effect of rainfall on the topographical factor T. Percentages of 41.7 50 8.3 0 100 The landslides in question are most commonly triggered no SL in TV (%) by climatic events, such as high intensity rainstorms or Numbers of SL 1 4410 19 in MR the succession of medium intensity rainstorms in a wet season (Hennrich and Crozier 2004). In some research Percentages of 5.3 21 21 52.7 100 SL in MR (%) work, the duration of rainfall is used as one rainfall factor (Caine 1980, Godt et al. 2008, Baum et al. 2005). These Numbers of no 1 531 10 SL in MR authors use another rainfall factor: the mean rainfall Percentages of no 10 50 30 10 100 intensity in the rainfall intensity–duration model to pre- SL in MR (%) dict the occurrence of shallow landslides. Godt et al. Numbers of SL 0 234 9 (2008) pointed out that rainfall of high intensity and short in SC duration has a limited effect on landslides triggered in Percentages of 0 22.2 33.3 44.4 100 thicker soil mantles. In the study area of Dayi, most shal- SL in SC (%) low landslides have a thickness of less than 1 m. In that Numbers of no 0 631 10 case the rainfall of high intensity and short duration does SL in SC have an effect on the triggering of shallow landslides. In Percentages of 0 603010 100 this paper, the intensity and the cumulative rainfall are no SL in SC (%) chosen as factors for the threshold value of shallow Numbers of SL 0 637 16 landsliding. Yu et al. (2016) used the 1 h intensity and the in Hofu cumulative rainfall before a debris flow event to predict Percentages of 0 37.5 18.7 43.8 100 the triggering of debris flows during the events of June 6, SL in Hofu (%) 2011 in the Dayi area. Since these debris flows are trig- Numbers of no 0 621 9 gered in most cases by shallow landslides (Fig. 1), the rain- SL in Hofu fall threshold proposed by Yu et al. (2016) can be Percentages of no 0 66.7 22.2 11.1 100 introduced for shallow landslides in the study area: SL in Hofu (%) Numbers of SL 1 30 96 188 315 in Total R ¼ ¼ðÞ B þ 5:5I =R ð11Þ Percentages of 0.3 9.5 30.5 59.7 100 SL in Total (%) in which R is the rainfall factor; R* is the critical rainfall Numbers of no 15 88 73 3 179 SL in Total (in mm); R is the annual precipitation of the site (mm); Percentages of no 8.4 49.2 40.8 1.7 100 B is the cumulative precipitation in the period before SL in Total (%) the triggering of the shallow landslide (in mm); I is the TV Tennessee Valley rainfall in 1 h before the start of the shallow landslide MR Mettman Ridge (in mm). The annual precipitation R for each shallow SC Split Creek SL Shallow landslide landslide is obtained from the spatial distribution of Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 15 of 17 annual rainfall in the study area. The R is introduced to Table 6 The numbers and percentages of shallow landslide (SL) and no shallow landslide (no SL) assessment by P factor in the normalize the rainfall threshold (Aleotti 2004). three classes in Dayi The rainfall data of the area downstream of Dayi, such Number and percentage Number Percentage Number Percentage as the rainfall intensity I, and the cumulative rainfall B, of SL of no SL of SL of SL (%) of no SL of no SL (%) was interpolated between the rainfall data of Dayi and P < 0.27 0 0 84 87.5 Xintun (Fig. 2). The rainfall intensity and total accumu- 0.27 ≤ P < 0.30 24 14.8 12 12.5 lated rainfall during June 5 – 6 were generally increasing from south to north. The rainfall intensity and total P ≥ 0.30 138 85.2 0 0 accumulated rainfall in sub-area 1 may be larger than the values measured in Dayi town, which makes it diffi- cult to estimate I and B in sub-area 1. Therefore this 0.30, and most of the points (87.5%) with no shallow area is excluded for the study of the rainfall factor R. landslides are located in the zone P < 0.27 (see Table 6). Fig. 14 shows the relationship between the topograph- The critical values in Eq. 12 only apply to the Dayi area ical factor T and the rainfall factor R in the area down- because of its local geological conditions. The rainfall stream of Dayi. Without the data in the sub-area 1, only factor R has almost the same importance as the topo- 162 points with shallow landslides and 96 points with graphical factor T for the susceptibility for landsliding stable slopes in sub-area 2, 3, and 4 were plotted in Fig. 14. (P). The critical value C is 11.1% higher than the crit- Ra One can define the relationship between the T-factor and ical value C (Eq. 12), which shows a moderate per- Rb the R-factor in the determination of presence or absence formance of the prediction model. of shallow landslides in the Dayi area as follows: Discussion 1:2 P¼RT Montgomery and Dietrich (1994) indicated that slope ≥C ð12Þ gadient calculations using low-resolution data tend to pro- in which P is the primary prediction factor, and C is the duce too low values. Acquisition of high-quality, high- critical value for the triggering of debris flows. resolution digital elevation data is important to allow the There are two critical values in Fig. 14: C = 0.27, identification of potential shallow landslide source areas. Ra C = 0.30. The two lines divide the figure into 3 do- The digital elevation data used in the validation process Rb mains: P < 0.27; 0.27 ≤ P < 0.30; P ≥ 0.30 with respect- has a reasonable high-quality, but the 5-m contour inter- ively low, medium and high possibility of occurrence of val may cause errors for the upslope factor and especially shallow landslides. Table 6 shows the distributions of for the cross-section factor. Digital Elevation Models with shallow landslides and no landslides in the 3 domains. Contour intervals of 2 m or even 1 m, will give a more All the points beyond the line of P ≥ 0.30 are shallow accurate assessment but are costly for larger areas. landslides and all the points under the line of P < 0.27 A maximum value of 0.46 for the combined factor are no landslides. All the points with shallow landslides (G + F) is chosen to simplify the assessment of the topo- are located in the zone P ≥ 0.27, and most of the points graphical factor T. But it may lead to more misclassifica- (85.2%) are located in the zone P ≥ 0.30. All the points tions because the presence of a minimum slope angle without shallow landslides are located in the zone P < for shallow landslides in this simplified assessment is disgarded. More research should be conducted on this issue to revise the topographical factor to obtain better Shallow landslide 0.48 results in the future. Stable slope 0.46 A lots of shallow landslides were triggered in a small RT^1.2=0.27 RT^1.2=0.30 0.44 area provided an unprecedented amount of data to establish a topographical factor for the assessment of 0.42 shallow landslides in soil material (soil slips). These shal- 0.4 low landslides have a typical length and width of several R 0.38 meters and a depth of about 1 m. The susceptibility of 0.36 this kind of shallow landslides may be determined by the 0.34 topographical factor T proposed in this study, because 0.32 (1): the critical water level for failure will be reached 0.3 relatively fast in these shallow soils (around 1 m) compared 0.28 to more deeper soils. As a result, the upslope and cross- section factor (hollow) have a larger effect. (2): The lateral friction of the sides of the slides in these shallow soils are Fig. 14 The relationship of T factor and R factor less, making the effect of the free-face of a topographical Yu et al. Geoenvironmental Disasters (2017) 4:24 Page 16 of 17 nose unimportant. The depths of shallow landslides in USA factor, the upslope factor, the cross-section factor, and Japan used for the validations process are in the range and the free-face factor. The topographical factor T of 0.5 to 5 m, but characteristic depths are less than 2 m. is a combination of these factors. The probability of This may be the reason for the satisfactory validations in shallow landslides increases with increasing T-values. these areas. More research is needed to validate the topo- (2)The role of the slope angles is more important than graphical factor T as a predictor for shallow landslides with the role of the upslope factor, the cross-section factor, adepth of 2to5m. and the free-face factor. The major rainfall factors The soils in this study occurred on siltstones and related with the occurrence of shallow landslides are mudstones (Dayi), greenstones, greywackes, and cherts the cumulative rainfall and the rainfall in 1 h before (Tennessee Valley), sandstones (Mettman Ridge), sand- the shallow landslide. The probability of shallow stones (Split Creek), granites (Hofu), so in general silty landsliding increases with increasing R-values. to sandy soils. More work should be conducted for other (3)The probability of shallow landsliding increases with types of soil to find the suitable values for the topo- increasing P-values, where P is a combination of the graphical factor T and rainfall factor R. T factor and the R factor. The topographical factor T In this study an intensity-cumulative rainfall model was has almost the same influence than the rainfall used for the rainfall factor instead of an intensity–duration factor R on the probability of shallow landsliding. model. However most studies on the influence of rainfall Acknowledgements on triggering of shallow landslides are based on an inten- This work was supported by by the Funds for Creative Research Groups of sity–duration model (Caine 1980, Godt et al. 2008, Baum China (Grant No. 41521002), the National Natural Science Foundation of et al. 2005). More work should be done to prove the valid- China (NSFC, contract number: 41672341) and the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Foundation (contract ity of this intensity-cumulative rainfall model. number: SKLGP2014Z012). We are grateful to Dr. Theo van Asch for having The rainfall parameter R may affect the landslide area provided a very helpful review of the manuscript, and for help on the A, which in turns will affect the topographical parame- English editing of the manuscript. ters U, C, and T, respectively according to Eqs. (2) to (7). Authors’ contributions When the rainfall factor R is large, the landslide area A BY conceived of the study, and participated in its design and coordination may increase, resulting the decreasing of the parameters and drafted the manuscript. YZ carried out the field investigation and the U, C, and T. For this case, the primary prediction factor data analysis, participated in the design of the study and performed the statistical analysis. YL carried out the field investigation and the data analysis. P may still large enough to predict the triggering of shal- All authors read and approved the final manuscript. low landslide because the increasing of R is more, and the decreasing of T is less according to Eqs. (7) and (12). Competing interests The authors declare that they have no competing interests. Conclusions The large number of shallow landslide events in the Dayi Publisher’sNote area, Guizhou, China, triggered by a large rainfall event in Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. June 2011, provided a good opportunity to study the influ- ence of topographical factors on the triggering of shallow Received: 23 September 2016 Accepted: 19 October 2017 landslides. 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Geoenvironmental Disasters – Springer Journals
Published: Dec 1, 2017
Keywords: Environment, general; Earth Sciences, general; Geography, general; Geoecology/Natural Processes; Natural Hazards; Environmental Science and Engineering
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