*7.2. Empirical-Statistical Model*

The empirical formula, mainly based on simple geometric relations of landslides (Figure 11), is simple and effective in the prediction of long runout distance. Figure 11 reveals the geometric relationship between the landslide's apparent friction angle (i.e., the angle between the trailing edge of

the landslide and the farthest point of landslide movement), height difference, and motion distance [19]. Based on the concept of the apparent friction angle, Scheidegger proposed an empirical formula called the sled model to calculate the velocity of the sliding body [19]. The specific formula is as follows

$$V = \sqrt{2\mathbf{g}(\mathbf{H} - \mathbf{t} \times \mathbf{L})} \tag{8}$$

where *V* is the velocity of the estimating point (m/s); g is the acceleration of gravity (m/s2); and t is the rake ratio between the highest point of the rear edge and the estimating point of the sliding distance (dimensionless); H is the height difference from the highest point of the rear edge and the calculated velocity point of the sliding distance(m); L is the horizontal distance between the landslide trailing edge and the calculated velocity point (m).

**Figure 11.** Sketch of the Empirical-statistical model (It is modified from [19]).

According to the calculation of the sled model (Figure 12), the maximum speed of the sliding body was 28 m/s, which occurred near the horizontal distance of 250 m. Similar to the calculation results of the DAN model, the sled model showed that the slide velocity increased sharply after the landslide occurred, and the speed decreased significantly when the slide moved to the front of the road and eventually struck the opposite side of the mountain. The maximum speed obtained by the sled model is far greater than that of the DAN-W dynamic model. Instead of taking the dynamic characteristic of the landslide into account, such as erosion and entrainment, the sled model only gives a preliminary description of the process of landslide movement variation. It could be seen that the calculation results of the DAN model are more accurate. While the concept of the sled model and the apparent friction angle tends to be conservative for landslide hazard prediction, they still comprise a qualitative and effective way to predict disasters.

**Figure 12.** Speed contrast diagram of two models of the Panjinbulake landslide.

The landslide under study is located in Piliqinghe Basin, located in the western part of the Loess Plateau and is part of the "Belt and Road" area. The location has many potential loess landslides, all of which pose a threat to agricultural production. It is especially important to research the prediction of potential landslide disasters, which is of great benefit to disaster prevention and devising mitigation measures. During the period 2017–2018, our team carried out field geological survey work in the area and counted 12 loess landslides that occurred. At the same time, the team measured the basic parameters of the landslide, and calculated the apparent friction angle of each landslide (Table 3, Figure 11). The statistical results indicate that the apparent friction angle of the loess landslide in this area is approximately 25◦. Based on the concept of the apparent friction angle, the farthest running distance of the landslide (i.e., Lmax) can thus be calculated by the formula which is as follows

$$\mathcal{L}\_{\text{max}} = \frac{\mathcal{H}\_{\text{max}}}{\tan 25^{\circ}} = 2.15 \mathcal{H}\_{\text{max}} \tag{9}$$

where Hmax is the height difference from the highest point of the rear edge and the farthest point of the sliding distance (m).


**Table 3.** Basic geometry of the loess landslides in the Piliqinghe basin.

The empirical formula and the DAN model can be used to predict and analyze the moving distance of potential landslides from qualitative and quantitative aspects separately.
