## 5 Results and Discussion
### Relationships between Total Soil Thrust and Slip Ratio  
Figures 6-11 show the relationship between the total soil thrust and the slip ratio of the off-road tracked vehicle operating on the soil exhibiting hardening behavior, softening behavior and hump behaviors, respectively. The weight and size of an off-road tracked vehicle only affect the magnitude of the soil thrust, and the trend of the soil thrust and slip ratio relationship (difference between the soil thrusts and slip ratio relationships evaluated using the proposed method and the existing theory) was not affected. Therefore, in the case of EC380E, the result of using a grouser with a height of 70 mm is representatively shown. As can be seen from Figures 6-11, the total soil thrust developed at a specific slip ratio increases with attached grousers, meaning that the tractive performance of the off-road vehicle is improved. This is because the grouser converts the shear between the material of the track and the soil into shear between the soils, increasing the shear force. In addition, the grouser generates additional soil thrust on the side of the track (i.e., side thrust). In both methods, the total soil thrust increased as the shear strength parameters of soil (i.e., \(c\) and \(\phi\)) and the grouser height increased, showing good agreement with [PERSON] et al. [28]. EC380E weighed more and had larger continuous tracks than EC145E, so EC380E produced a greater soil thrust under the same conditions (soil and grouser conditions). This is because the vertical stress (\(\sigma_{v}\)) and the shear area (\(l\) and \(w\)) of the soil-track interface increase with the weight of the vehicle and the size of the continuous track, respectively. The relationship between total soil thrust and slip ratio differed between the existing and proposed method. In all three types of soils, the existing method exhibited a greater maximum soil thrust at a lower slip ratio than the proposed method. After the peak value (i.e., the maximum soil thrust of the soil exhibiting softening behavior and hump behavior), the soil thrust decreased dramatically in the existing method, whereas the soil thrust slightly decreased in the proposed method. Figure 6: Soil thrust and slip displacement curves in soils exhibiting hardening behavior (\(c\) = 0.96 kPa, \(\phi=27.3^{\circ}\), \(K\) = 1.14): EC145E with a grouser height of (a) 25 mm, (b) 50 mm (c) 70 mm: (d) EC380E with 70 mm grouser height. Figure 7: Soil thrust and slip displacement curves in soils exhibiting hardening behavior (\(c\) = 1.39 kPa, \(\phi=30.6^{\circ}\), \(K\) = 1.13): EC145E with a grouser height of (a) 25 mm, (b) 50 mm (c) 70 mm: (d) EC380E with 70 mm grouser height. Figure 8: Soil thrust and slip displacement curves in soils exhibiting softening behavior (\(c\) = 3.3 kPa, \(\phi=33.7^{\circ}\), \(K_{W}=9.3\), \(K_{r}=0.835\)): EC145E with a grouser height of (a) 25 mm (b) 50 mm (c) 70 mm: (d) EC380E with 70 mm grouser height. Figure 9: Soil thrust and slip displacement curves in soils exhibiting softening behavior (\(c\) = 2.2 kPa, \(\phi=39.4^{\circ}\), \(K_{W}=6.1\), \(K_{r}=0.659\)): EC145E with a grouser height of (a) 25 mm (b) 50 mm (c) 70 mm: (d) EC380E with 70 mm grouser height. where the largest slip displacement (and the largest soil thrust) is generated; whereas the proposed method considers the difference in the slip displacement and soil thrust according to the location of the soil-track interface. For example, when calculating the total soil thrust, the existing method considers the first grouser (see Figure 2) from the direction the vehicle travels. However, since the slip displacement (and the soil thrust) at the first grouser is zero, the proposed method does not consider the first grouser. On the other hand, when the soil shows softening behavior or hump behavior, the total soil thrust predicted by the existing method is greater than that calculated by the proposed method until a specific slip ratio, after which the latter becomes greater (Figures 8-11).