###### Abstract
[25] conducted extensive DC model tests with energy levels, drop distances, masses, and diameters of falling weight as variables, and point out that the combination of the tamping impulse and falling weight diameter is appropriate as the control standard of the final cumulative settlement. As for monitoring the consolidation process, [PERSON] et al. [26] developed an intelligent monitoring method for the number of compaction cycles during DC construction based on machine vision and pattern recognition. Despite the extensive research on the mechanism of ground improvement and evaluation of reinforcement performance, there are relatively few studies on controlling the ground vibrations induced by DC to minimize their impact on the surrounding environment. As engineering construction increasingly focuses on minimizing the environmental impact, further research in this area is needed. Dynamic compaction can generate a series of waves in the soil, such as shock waves, stress waves, and vibration waves. These waves propagate underground and on the surface, which may cause vibrations in nearby structures and pipelines, deformation of surrounding foundations, and even cracking and collapse of structures. Two measures were commonly employed in engineering practice to mitigate the vibrations. One is to move the vibration source away from important structures, while the other is to install vibration reduction facilities between the vibration source and the structures, which restrict the vibration from reaching the structure within the allowable range. The former measure involved studying the propagation attenuation law of vibrations on the ground to determine the allowable distance. [PERSON] et al. [27] investigated the propagation law of waves caused by DC in a full stone foundation and found that the ground vibration response continuously decreases as the distance from the vibration source increases. Moreover, based on extensive measured data of the tamping waves, [PERSON] et al. [28] discovered that the attenuation of ground vibration with horizontal distance follows a negative power relationship. An isolation trench is one of the most common, economical, and convenient vibration reduction facilities. Its vibration isolation effect is mainly achieved through the reserved fissure between the vibration source and the protected object. This fissure surface is perpendicular to the ground surface and becomes a barrier for the vibration wave. The propagation characteristics of the waves mainly depend on the characteristic wave impedance of the medium. When the vibration wave reaches the interface of different media, due to the different wave impedances, the vibration wave will be reflected and transmitted. In particular, when the wave reaches a free surface, there is no transmission, so the vibration of the soil behind the trench is reduced [29]. [PERSON] and [PERSON] [30] conducted vibration tests of DC with vibration isolation trenches that had a width of 1 m and a depth of 3 m to investigate their isolation effect. However, despite the use of these trenches, no significant isolation effect was observed, possibly due to their shallow design. [PERSON] and [PERSON] [31] indicated that the majority of ground vibration energy propagates in the form of Rayleigh waves. Through case tests, they provided evidence that the isolation effect is correlated with the wavelength of Rayleigh waves when the dominant frequency is identified. [PERSON] and [PERSON] [32] and [PERSON] et al. [33] reported that under pulse loads, the isolation effect of the isolation trench is practically unrelated to the width of the trench, while the isolation efficiency of empty trenches exceeds that of trenches filled with concrete. [PERSON] et al. [34] evaluated the safety of underground oil pipelines and discovered that empty trenches exhibit significant isolation effects on vertical and horizontal vibrations, with the isolation effect increasing with trench depth. [PERSON] et al.