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Shallow slope failure is often induced by rainfall infiltration in a soil mantle overlying a less permeable bedrock. Soil depth is an important input parameter in slope stability analysis. This paper provides the spatial variation of soil depth and the occurrence of slope failure in Sangun mountains area. The spatial pattern of soil depth was simulated by proses based model using airborne laser survey data (LiDAR data) and Geographic Information System (GIS) function. As a function for soil production, we use in the study area a numerical model developed by Dietrich et al. (1995) to predict the local spatial variation of the depth of soil. The soil depth data measured at 20 locations that represent morphological variability are used as a sample data set to test the model results. Furthermore, the soil depth variations are compared to the slope failure distribution in the whole area. Slope failure locations in the study area are identified from interpretation of aerial photographs and field surveys. Fifty-five of slope failures are considered for slope failure hazard analysis. Therefore, the slope failures occur more frequently at soil depth intervals in the ranged from 1.01 m to 1.5 m.

In the Sangun mountain, Fukuoka Prefecture, Japan, abundant slope failures occurred in 2003 [

The soil thickness on hillslope, which often coincides with the failure depth, is a critical parameter in performing a slope-instability analysis, and it is an important factor, such as to the ratio of the saturated depth to the soil thickness [

We have calibrated and validated the model in a study area, Sangun basin located in west part of Sangun mountains, Fukuoka Prefecture, Japan. Furthermore, the soil depth variations are compared to the slope failure distribution at whole area. Slope failure locations in the study area are identified from interpretation of aerial photographs and field surveys. There are fifty-five slope failures which are considered for slope failure hazard analysis.

The Sangun mountains area is located in the north of Kyushu islands, Japan. The study area is the Sangun catchment area (1.67 km^{2}) which is located the west part of Sangun mountains. Morphological characteristics of the study area present slope angle, aspect, and elevation. These characters were produced from DEM. It is characterized by rugged topography and steep slopes where the gradient varies from 10˚ to 70˚, moreover the majority of the aspect direction of slope is ranged from 150˚ to 337˚. The altitude of study area ranges between 290 and 930 m. The geology consists mainly of Mesozoic granitic rock. Granitic rocks are composed of a mixture of quartz, feldspar, micas and ferromagnesium minerals. On July 18-19, 2003, a short duration, high-intensity rainfall event impacted the Sangun city area (

The slope failures and resultant debris flows were the largest and most damaging of these disasters. A moderate-size, 3 - 10 m deep debris avalanche triggered the debris flow which caused casualties. The rainfall intensity was estimated to about 315 mm/day, and the density of slope failure was about 48 points/km^{2}.

In order to create the patch variation in soil depth we use a stochastic soil production and annual soil transport model, building upon earlier work [_{o} and m are empirical constants). In the model, K and ρ_{s} were assumed spatially constant with the soil depth described as a complex, bell-shaped function of h,

where ρ_{r} and ρ_{s} are the bulk density of rock and soil. The soil depth model in the form given in Equation (1) assumes that over the time period sufficient to influence the soil depth, the dominant hillslope transport process can be represented by a slope-dependent transport law.

To apply Equation (1) to Sangun basin, we need to assign the diffusivity (K) value, the production function, and

the bedrock and soil density. The diffusivity is not known, therefore the simulation of soil depth must consider the change of the diffusivity (K) values to get the reasonable value. Here we will use the range 37 - 55 cm^{2}/yr. The production function is based on of the production rate of cosmogenic nuclides concentration. Moreover, the bedrock and soil density were obtained from the literature. We use a 5 m resolution Digital Elevation Model (DEM) prepared using airborne laser survey data (LiDAR data). An inventory of slope failure has been documented. The distribution of the slope failure has been conducted by utilizing Geographic Information System (GIS) function.

The soil depth model simulations were carried out by utilizing Geographic Information System (GIS) function. The soil model, in the form given in Equation (1), assumes that over the time period sufficient to influence the soil depth, the dominant hillslope process can be represented by a slope dependent transport law. The diffusivity (K), the bedrock and soil density, and the production function are uncertainty values. Therefore, we needed guidance for initial values from literature. Dietrich et al. [

Therefore, here we will use 50 cm^{2}/yr. Moreover, for the bedrock and soil density ratio we will use the value proposed by Dietrich, et.al data of about 1.7. Furthermore, the production function is not known, therefore the initial value will be as from Dietrich, et.al data, and we make a range of values to get the best results from simulations. The range value of 0.019 cm/yr to 0.025 cm/yr will be used in the simulation. By fitting an exponential function, _{o} = 0.019 cm/yr and m = 0.05 [

We apply these models to a small catchment in the upper Sangun mountain area. The area is mostly underlain by granite rock. In the investigation, the morphometry aspect was considered to collect measurements of soil depth. We have two profile of soil investigation. A Portable Dinamic Cone-Penetrometer Test (CPT) tool was used in the measurements. The CPT is a valuable method of assessing subsurface stratigraphy associated with soft materials, discontinuous lenses, organic materials (peat), potentially liquefiable materials (silt, sands, and granule gravel), and landslides [

In order to determine the grade of weathering, the classification of granites presented by Hencher and Martin [

This simulation presents a distribution of soil depth. The variables identified as predictors include topographic variables, soil production rate (P_{o}), a density of the rock and soil, and diffusivity (K) value. However, the range of soil production rate (P_{o}) was considered in the simulation such to get a reasonable value of soil depth comparable with soil depth in direct measurements.

We use three P_{o} values, such as 0.019, 0.022, and 0.025 cm/yr. For the purpose of model validation, the time interval of 1000 to 2000 years was used. _{o} value, (a) 0.019 cm/yr, (b) 0.022 cm/yr, and (c) 0.025 cm/yr.

The performance of the process based model can be compared to the field measurements to compute the error between the two data sets. We propose that mean square prediction error close to zero value could indicate a good result from simulation process. Root Mean Square Error (RMSE) (also known as Root Mean Square Deviation) is one of the most widely used statistics in GIS. In a variety of geostatistical applications, RMSE is one method to evaluate the model performance.

Root mean square error takes the difference for each soil depth value based on simulation and surveyed value. We can swap the order of subtraction because the next step is to take the square of the difference. RMSE value is calculated by following Equation (2):

N SPT | Soil Depth (m) | Description | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

(Blow) | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 | S10 | |

30 | 1.6 | 0.5 | 1.35 | 1.55 | 0.35 | 0.35 | 0.1 | 0.25 | 0.45 | 0.6 | Saprolitic soil zone |

50 | 2.4 | 0.72 | 1.44 | 1.75 | 0.35 | 0.35 | 0.1 | 0.25 | 1 | 0.8 | Partially weathered Rockzone |

N SPT | Soil Depth (m) | Description | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

(Blow) | S11 | S12 | S13 | S14 | S15 | S16 | S17 | S18 | S19 | S20 | |

30 | 0.55 | 0.13 | 0.65 | 0.9 | 0.6 | 0.71 | 0.95 | 1.1 | 1 | 1.5 | Saprolitic soil zone |

50 | 1.18 | 0.13 | 0.81 | 1.4 | 0.71 | 0.71 | 2.21 | 2.29 | 1 | 2.15 | Partially weathered Rockzone |

where N: number of observation points; x_{i}: prediction value; y_{i}: observation value. The raster file of soil depth was prepared and sampled at the measuring points. Therefore, we estimate the soil characteristic and compared the observed and predicted soil depth values (

The process based model simulates soil depth at 11 times (1000; 1100; 1200; 1300; 1400; 1500; 1600; 1700; 1800; 1900; and 2000) and have P_{o} values 0.019; 0.022; and 0.025 cm/yr for simulating the influence of soil production rate. Observations were available only for twenty observation points. _{o} = 0.019 cm/yr and time 1500 year are the better RMSE value (0.306) than other P_{o} values.

Furthermore, _{o} = 0.019 cm/yr and time 2000 year have a low RMSE value (0.570). Therefore, the root-mean-square errors (RMSE) reported in

Process based model [

depth observations, soil production rate (P_{o}), and production time (year). In this study, the soil production rate (P_{o}) 0.019 cm/yr, 1500 year, N value 30 (0.1 - 1.6 m) provide the reasonable model for spatial distribution of soil depth. _{o}). The relationship between soil production rate (P_{o}) and the amount of soil depth distribution is not linear. The soil production rate increases for soil depth 0.51 - 1.00 m. Moreover, the soil depths of 0 - 0.5 m, and greater than 1.01 m show the soil production rate (P_{o}) to decrease. In the soil depth model the distribution of soil depth shows a trend with a peak centered on the depth range 0.51 - 1.00 m (_{o} = 0.019 cm/yr, the maximum area of soil depth distribution is 0.875 km^{2} the 1500 years. Secondly, the P_{o} = 0.022 cm/yr shows the peak maximum area is 0.928 km^{2} the 1300 years. And thirdly, the P_{o} = 0.025 cm/yr shows the peak maximum area is 1.011 km^{2} on 1100 years. Furthermore, the area of distribution of soil depth 0.51 - 1.00 m is larger than the other soil depth interval, about 52.23% of the total area.

^{2} with an average slope angle of 36.5˚.

Landslide occurrence in tropical and sub-tropical region is generally associated with weathered rock profile characterized by chemical and mineralogical heterogeneities [

Soil depth (m) | Area of soil depth distribution (km^{2}) | Number of slope failures | Ratio of distribution of slope failures on the area of soil depth distribution; P_{o} = 0.019 (d/a) | ||||||
---|---|---|---|---|---|---|---|---|---|

P_{o} = 0.019 | % (a) | P_{o} = 0.022 | % (b) | P_{o} = 0.025 | % (c) | n | % (d) | ||

0 - 0.5 | 0.46 | 27.67 | 0.43 | 25.68 | 0.41 | 24.56 | 12 | 21.82 | 0.78 |

0.51 - 1.00 | 0.88 | 52.23 | 0.93 | 55.43 | 1.01 | 60.38 | 28 | 50.91 | 0.97 |

1.01- 1.50 | 0.31 | 18.56 | 0.30 | 17.70 | 0.24 | 14.40 | 14 | 25.45 | 1.37 |

1.51 - 2.00 | 0.02 | 1.45 | 0.02 | 1.12 | 0.01 | 0.64 | 1 | 1.82 | 1.26 |

>2.00 | 0.002 | 0.09 | 0.001 | 0.07 | 0.00 | 0.02 | 0 | 0.00 | 0 |

Total | 1.67 | 100 | 1.67 | 100 | 1.67 | 100 | 55 | 100 |

In this study, the spatial distribution of soil depth was estimated using a process based model [_{o}), and a soil production time (year) provided the reasonable model for spatial distribution of soil depth. The results also showed that the soil depth ranged from 0.51 m to 1 m had the largest area of soil distribution, and that the high density of slope failures was occurring at the soil depth ranged from 1 m to 1.5 m. Considering the limited number of soil depth observations, this model appears as an important improvement toward solving the need for distributed soil depth information in the process based modeling.

The authors would like to thank the Indonesian Government, Directorate General of Higher Education for its DIKTI Scholarship. This work was supported by JSPS KAKENHI Grant Number 25350429.

HendraPachri,YasuhiroMitani,HiroIkemi,WenxiaoJiang, (2015) Spatial Variation of Soil Depth and Shallow Slope Failures in Sangun Mountains, Fukuoka Prefecture, Japan. International Journal of Geosciences,06,813-820. doi: 10.4236/ijg.2015.68065