The rapid growth of tourism on Jeju Island has led to an increase in traffic volume, causing accelerated ground subsidence at the intersections between natural caves and roads. Natural phenomena are not caused by a single specific factor, but rather occur through interactions among multiple factors. Therefore, to analyze natural phenomena, it is necessary to consider not only the main effects, but also the interactions among various factors. In this study, the design of experiments was utilized to analyze the vibration-generating mechanism according to the geometrical characteristics of lava tubes, a kind of natural cave. Analysis of variance was used as the main analysis method, and multiple linear regression analysis and decision trees were additionally used. To detect all the interaction effects, multi-way factorial design, which can estimate the effect of any combination of levels, was utilized. The joint orientation, aspect ratio, and cover depth were selected as factors representing the geometrical characteristic of the lava tubes, and vehicle speed was selected as an external influence factor. As a result of the analysis, all the main effects were found to be significant, and the results of the additional two analysis methods were consistent. The two-factor interactions that showed significant results were aspect ratio $\times$ cover depth, joint orientation$\times$ vehicle speed, and joint orientation$\times$ shape ratio. However, it was difficult to analyze the interaction effect using multiple regression analysis and decision tree analysis. Among the two-factor interactions, aspect ratio $\times$ cover depth was found to be the most significant, while the main effect of the two interacting factors was the least significant. The most significant effect at a specific level of aspect ratio and cover depth could be analyzed through an interaction plot. These findings will be useful for evaluating the stability of lava tubes using only geometrical characteristics.

Most geotechnical engineers focus on ground strength and stability. However, when determining stability by analyzing the exact strength of the ground, the failure surface is essential. Nevertheless, limited studies have been conducted on the methods to determine the exact failure surface of the ground. This study shows that the failure surface and plastic area can be analyzed using the slip line method based on the slip line and lower bound analysis. To improve existing studies limited to single ground, we analyzed the failure area of heterogeneous ground conditions. The results of the slip line method were compared and verified through FELM, a finite element analysis method to which a lower limit analysis was applied. As a result, the failure area and maximum internal stress according to the ground properties and the slope angle are presented. In addition, the points of the slip line method and the finite element limit analysis are summarized. Finally, we propose limitations and solutions when applying the slip line method to the slope.