## 1 Introduction  
Ground subsidence, potholes, and falling rocks occur in natural caves due to vehicle vibration loads where the road and the natural caves intersect. There are 142 points of intersection between natural caves and roads on Jeju Island [1]. In the past, geological studies have mainly been performed on lava tubes, a kind of natural cave, because they are usually not subjected to special external forces [2; 3; 4]. To explore the mechanism of lava tube formation, a large number of experimental studies have been carried out by investigators [5; 6; 7; 8].  
Lava tubes form as lava flows downward. The surface is hardened by cold air, and the lava flows inside, reducing heat loss at the flow surface and extending the flow up to several kilometers from the vent. These lava tubes have a low cover depth, and there is a high risk of ground subsidence when external force occurs. While most lava tubes collapse within a relatively short period due to their easily weakened geological characteristics immediately after their initial formation, the lava tubes distributed throughout Jeju Island have preserved the surface flow characteristics of the initial lava flows very well for a long period of time [9]. However, the possibility that the geometric value of these lava tubes might also be easily affected by continuous development is being raised.  
The complex action of multiple factors has resulted in the formation of complex structures and structural features in lava tubes. Theoretical and numerical simulations are mainly used to describe these structures [10]. However, it is not easy to explore the interaction effects of the geometrical characteristics of lava tubes only with the results of numerical simulations.  
To resolve these problems, in this study, a dataset was formed using a numerical analysis of the geological and geometrical characteristics of the lava tubes on Jeju Island. The design of experiments (DoE) was used throughout the research process. In addition, the factors (main effects, interaction effects) that affect the occurrence of vibration in the lava tubes were analyzed using multi-way analysis of variance (ANOVA). The design of experiments involves designing ways in which to perform an experiment for a problem in order for it to be solved and how to handle the data, in addition to determining what statistical method should be used to analyze the data obtained through the experiment to obtain the maximum information with minimal effort and cost. The main kinds of data analysis used include ANOVA, regression analysis, etc. In this study, experiments were performed for all combinations of each level of factor, and the full factorial arrangement method, which can estimate all factor effects, was used. For the data analysis, ANOVA was used for interpretation, focusing on the interaction effect. In addition, multiple regression analysis and decision tree analysis were performed to compare the results according to each interpretation method.  
This study is expected to provide a scientific basis for revealing the mechanism of vibration triggered by vehicles passing directly over a lava tube according to its geometric characteristics.