# Regression Equations for Estimating Landslide-Triggering Factors Using Soil Characteristics
## 2 Methodology
### Estimation of Landslide-Triggering Factors Using Soil Properties  
The permeability test in landslide studies was conducted to find the permeability coefficient through constant and variable head permeability tests on the unsaturated sample. The shear test, on the other hand, determined the shear characteristics of the slope by obtaining the cohesive force and internal friction angle through a triaxial test, ring shear test, and direct shear test. Furthermore, slope stability decreased sharply when the soil layer was almost saturated with water content and reached the maximum shear stress, which eventually led to a failure. Figure 1: Measurement of the landslide scales through field surveys of landslides in the study area and sampling soil samples using a cylindrical stainless ring sampler (diameter 10 cm, height 6–15 cm) at a depth of about 40–60 cm of the ground after removing the topsoil; (**A**) View of landslide in Yangju, Gyeonggi-do. (**B**) Measurement of landslide length (using tapeline). (**C**) Before sampling soil samples using a cylindrical stainless ring sampler. (**D**) After inserting the cylindrical ring sampler by hitting it with a hammer, sampling the soil sample. Reproducing the permeability coefficient and shear strength characteristics of the soil slope corresponding to the landslide occurrence conditions and different geological materials was difficult. Therefore, studies relied on the characteristics of permeability coefficient at saturation and shear strength obtained at extremely limited shear rates. However, the greatest advantage of the direct shear test was that the shear strength properties of the soil were identified relatively more accurate, quicker, and easier compared to other test methods. As such, the test methods for measuring the permeability coefficient and shear strength were more complicated than the test for the basic physical properties of soil and required expert skills. However, permeability coefficients and shear strength constants of various points were required to understand the soil characteristics and identify the failure mechanism in the landslide areas [42; 43]. Thus, a considerable amount of time and costs were necessary to obtain the results. The permeability of soil was affected by grain size distribution typically described by the equivalent particle diameters D\({}_{10}\) and D\({}_{60}\), which corresponds to 10% and 60% passing by weight, respectively. Here, the descriptive parameter of grain size distribution is the coefficient of uniformity (\(c_{u}\)), which is defined as the ratio of D\({}_{60}\)-D\({}_{10}\). A higher value of \(c_{u}\) is indicative of a well-graded soil that has a lower permeability coefficient compared to uniformly graded soil as the smaller grain fills the voids between larger grains, resulting in less interconnectivity. Several correlations were developed to evaluate the permeability coefficient using the grain size [44; 45; 46; 47; 48]. The most commonly used correlation proposed by [PERSON] [49] is presented below:  
\[k\;\text{(m/s)}=C\,D^{2}{}_{10} \tag{1}\]  
where \(C\) is a constant that varies between 0.1 and 100 [50]. However, the typical values of \(C\) range between 0.4 and 1.2 and are typically taken as 1 [51]. In addition, the permeability coefficient can be raised by increasing the void ratios as particle shape and void arrangements also affect this variable. Hence, soils with angular particles exhibit a lower permeability coefficient compared to more rounded particles. Particle size is one of the most important properties that play dominant roles in the stress, strain, and strength response of the soil. In particular, changes in particle size indicate changes in porosity, particle effective contact area, and the load distribution mechanism of soil particle contact as well [52]. [PERSON] and [PERSON] [53] and [PERSON] and [PERSON] [54] used particle materials for evaluating the effects of particle size and confirmed that maximum porosity lowers while compressibility rises when the particle size increases.