Study on Elevation Effect of Vibration Velocity by Dynamic Compaction on Loess High Slope Based on Dimensional Analysis Method

To solve the problem where the prediction formula for vibration velocity by dynamic compaction cannot fully reflect the elevation amplification effect, the elevation amplification effect of vibration velocity by dynamic compaction was studied theoretically, and the factors that influence the elevation amplification effect of vibration velocity by dynamic compaction were systematically analyzed in this paper. The elevation amplification effect of a loess high slope under dynamic compaction is coformed by the refraction and reflection superposition effect of dynamic compaction vibration waves at the soil layer interface and the diffraction effect of dynamic compaction vibration waves. The propagation path of dynamic compaction vibration waves in soil was analyzed, and the elevation amplification effect was verified theoretically. The related physical quantities that affected the dynamic compaction vibration velocity of a loess high slope were analyzed based on the dimensional analysis method, and the calculation and improved calculation formulas that considered the elevation amplification effect of dynamic compaction vibration velocity were obtained. The multiple regression analysis of the calculation and improved calculation formula that considered the elevation amplification effect of the dynamic compaction vibration velocity was carried out using MATLAB with engineering examples. The results show that the relative error of the two formulas is small when the elevation difference is small; when the elevation difference is large, the calculation accuracy of the improved calculation formula that considered the elevation difference is higher, and it is more in line with the actual situation. Finally, according to the selected maximum allowable value of the slope particle velocity (e.g., 1.5, 2.0, and 2.5 cm/s), the allowable safe distance for dynamic compaction on a loess high slope is proposed area of northern Shaanxi Province, China. The results of this paper could provide a reliable basis for predicting vibration velocity by dynamic compaction in the Loess Plateau area of northern Shaanxi Province, China. They might have a reference value for dynamic compaction vibration control under similar terrain environments with large elevation differences and provide a safe guide for a dynamic compaction construction site in the Loess Plateau area of northern Shaanxi Province, China.