## 1 Introduction  
The problem of environmental vibration caused by traffic load has attracted more and more attention with the rapid development of road traffic in recent years. Road traffic accounts for 11.3% of the total complaint rate of environmental vibration pollution and ranks third behind construction and factories, according to relevant statistics [1]. Vibration caused by traffic load may result in the strength decrease and settlement increase of roadbed and foundation. The long-term vibration can cause serious damage to nearby buildings, threaten the comfortability of people's lives, and affect the normal use of precision instruments [2; 3], which must be solved urgently. To solve the vibration pollution caused by trains, [PERSON] et al. [4] presented a model to understand the dynamic behavior of ballasted tracks with mats. It was found that the vibration amplitude could be reduced by placing the mat beneath the subballast. [PERSON] et al. [5] conducted in-site experiments to measure the vibration levels of buried operating natural gas pipelines under the moving traffic. They focused on the assessment of the impact of the traffic-induced vibration and the increased risk on individuals that were affected by such underground natural gas pipelines at road crossings. Based on soil stabilization technology, a novel subgrade material that is silty clay modified by fly ash and crumb rubber was proposed by our research group. It has been proven that the modified soil possesses greater performance in conventional physical properties of strength, deformation, and stability, especially after freeze-thaw cycles [6; 7; 8]. This modified soil is also regarded as a sustainable subgrade material because it disposes and recycles the large amount of industry waste fly ash and rubber products. The great resistance to freeze-thaw cycles contributes to the sustainable performance of the subgrade in seasonally frozen regions. However, many sources show that the anti-vibration performance of soils modified by fly ash is poor, as the liquefaction resistance decreases after multiple vibrations [9; 10]. The research on the anti-vibration of silty clay modified by fly ash and crumb rubber is scarce and worth studying. The influence of vibration on the sustainable performance of buildings can be effectively mitigated by the design and development of more efficient solutions. In road engineering, an isolation layer is effectively adopted against vibrations. Expanded polystyrene foam sheet (EPS) is the most commonly used isolation material, which has the characteristics of ultra-light weight, good compressive property, high strength, good durability, and thermal insulation [11; 12]. [PERSON] et al. [13] proved the significant vibration isolation effect of EPS on soils by the indoor model test. It was found that the closer the EPS board and the vibration generator, the better the vibration isolation effect. [PERSON] et al. [14] studied the viability of EPS as the vibration isolation layer. The effect of barrier depth, thickness, and distance from the vibration source on the vibration isolation of EPS was investigated. XPS is a rigid foam board made of polystyrene resin, other raw materials and polymers, heated, mixed, and injected with the catalyst at the same time, and then extruded and molded. Compared with EPS, XPS (extruded polystyrene) foam sheets have weaker hygroscopicity, lower thermal conductivity, higher compressive strength, and more environmentally friendly characteristics [15; 16]. Furthermore, it has also been used as the functional layer (i.e., thermal insulation, vibration isolation, and so on) beneath the building's foundation. [PERSON] et al. [17] performed laboratory tests to evaluate the performance of XPS board in earthquake engineering and also revealed the failure mechanism of the building structure founded on XPS board subjected to earthquake loading. [PERSON] et al. [18] found that the presence of foam behind the flexible retaining wall could effectively result in a reduction of dynamic pressure and displacement.