# Progressive Formation of Retrogressive Landslide and the Lateral Length of Instability
## 3 Determination of Lateral Length of Traction Instability and Analysis of Influencing Factors
### Analysis of Influence Factors on Lateral Length of Traction Instability  
It can be seen from the above formula that the lateral length of traction instability when the slope is damaged is affected by many factors, including the dip angle of bedding, the friction coefficient, the bonding force, the tensile strength, and so on [57; 58]. Analyzing the influence degree of these factors is helpful to judge the size of the landslide and roughly determine the range of slope instability in practical engineering. Based on this towed landslide, the influence of \(S_{pi}\), \(f_{pi}\), \(c_{pi}\),\(f_{ri}\), and the dip angle of bedding on the lateral length of the slope traction instability is analyzed in detail. Figure 14 shows the later length traction instability as a function of \(S_{pi}\) (equivalent tensile strength of rock masses above the i-th layer that are not affected by excavation). It can be found that the curve is close to a straight line, which is a linear relationship. The influence of \(S_{pi}\) on the lateral length of traction instability is relatively small, and it decreases by 0.8 m for every 100 kPa length increase. When \(S_{pi}\) = 0 kPa, the lateral length of traction instability is the largest, which is 4.65 m. When \(S_{pi}\) = 480 kPa, the slope is in a state of ultimate equilibrium. Figure 15 shows the later length traction instability as a function of \(c_{pi}\) (the cohesion of the bottom surface of the \(i\)-th layer that are not affected by excavation). It can be found that when \(c_{pi}\) < 300 kPa, the curve is linear; when \(c_{pi}\) > 300, the larger the \(c_{pi}\), the faster the lateral length of traction instability decreases, as shown in Figure 15. When \(c_{pi}\) > 400 kPa, the slope tends to be stable. When \(c_{pi}\) = 0 kPa, the lateral length of traction instability is the largest, which is 4.71 m. \(c_{pi}\) is also not the main factor affecting the lateral length of slope traction instability. Figure 14: Influence of \(S_{pi}\) on the lateral length of traction instability. Figure 16 shows the later length traction instability as a function of \(f_{pi}\) (the friction coefficient of the bottom surface of the \(i\)-th layer that are not affected by excavation) [59; 60]. The curve is almost at a right angle, as shown in Figure 16. When \(f_{pi}>0.5\), the curve is relatively flat; when \(f_{pi}<0.5\), the traction instability length increases sharply, and it reaches 73.5 m only when \(f_{pi}=0.47\). This happens because the \(f_{pi}\) is too small, resulting in the direct instability of the slope, and the upper rock mass will slide along with the lower rock mass of the slope without the phenomenon of segmented collapse. The lateral length of traction instability measured at this time is meaningless. Figure 17 shows the later length traction instability as a function of \(f_{pi}\) (the friction coefficient of the bottom surface of the \(i\)-th layer most affected by excavation). The curve can also be divided into two parts, as shown in Figure 17. When \(f_{pi}<0.35\), the two are linear; when \(f_{pi}>0.35\), the larger the \(f_{pi}\), the faster the lateral length of traction instability decreases. It can be seen that the two factors \(f_{pi}\) and \(f_{pi}\) have a great influence on the lateral length of traction instability. Figure 16: Influence of \(f_{pi}\) on the lateral length of traction instability. Figure 15: Influence of \(c_{pi}\) on the lateral length of traction instability. Figure 18 shows the later length traction instability as a function of the dip angle of bedding. It is found that the lateral length of the traction instability increases exponentially as shown in Figure 18. When the dip angle of bedding is less than or equal to 21\({}^{\circ}\), the slope tends to be stable; when the dip angle of bedding is greater than 30\({}^{\circ}\), the slope will be directly unstable, and the upper rock mass will slide together with the lower rock mass of the slope, without the phenomenon of segmented collapse.