## 4 Discussion
### Comparative Analysis of the PPAs
\[A_{r}=A_{0}\sqrt{\frac{r_{0}}{r}}\mathrm{exp}[-\alpha(r-r_{0})],\ \mathrm{mm/s^{2}}, \tag{1}\]  
where:  
\(A_{r}\)--peak acceleration attenuation of the recorded motions in the \"\(r\)\" point, mm/s\({}^{2}\),  
\(A_{0}\)--peak ground acceleration value [mm/s\({}^{2}\)] at a distance \(r_{0}\), mm/s\({}^{2}\),  
\(r\), \(r_{0}\)--distances of points \"\(r\)\" and \"0\" respectively, from the source of vibration, m,  
\(\alpha\)--coefficient related to material damping, 1/m. The present case concerns (and not only in the direction z) a much lower attenuation and absorption of the surface vibration acceleration propagated in the ground medium, which is more linear (in some cases with the local intensification of vibration acceleration) than exponential. For this reason, it must be concluded that the vibrations generated in heterogeneous-made grounds located in the immediate vicinity of various types of buildings, will propagate at greater distances than what would result from the theoretical relationships describing this phenomenon. As an alternative to the simplified methodology based on dependence (1), it is possible to carry out numerical simulations using software based on the Finite Element Method (FEM)--similar to the works [19; 20; 21]. In this work, due to the considerable heterogeneity of the ground, no such numerical analyses have been carried out. The focus is on the analysis of the results of vibration acceleration measurements on a real object in a natural scale. By comparing PPA distribution (see Tables 2 and 3) at the second (MP2, L2 = 2.5 m), the third (MP3, L3 = 5.0 m), and the fourth (MP4, L4 = 7.5 m) measurement points in the first and second stages of the study, it can be observed that PPAs may be subject to a significant intensification with the increase of distance from the vibration source (see Table 2: direction x--MTS V8 compactor in X1 and X2 operating modes, direction y--X1, X2, and X3 operating modes, direction z--X3 operating mode, and also Table 3: direction y--practically all operating modes of MTS V8, direction z--plate compactor). To a slightly lesser extent, a similar effect can be observed also in the third stage of research (source of vibration at a distance Ls = 5 m from the building's front wall)--especially in the case of surface vibrations of the ground propagated in the longitudinal direction (x) and the work of the hydraulic compactor in X1 mode and plate compactor (see Figure 4 and Table 4)--which is most probably related to the very complex wave process occurring in the ground medium, and as a result, to the amplification of vibration, due to the reflection and the refraction of waves from the boundary surfaces of made ground, natural ground, walls of excavation, a building, or other types of local inhomogeneities and inclusions in the ground medium. It is unlikely that the intensification of ground surface vibrations observed at the measuring points MP2 and MP3 has any relationship with the natural vibrations of the soil medium, because they are far below the operating frequencies of both devices. Further analysis of PPAs indicates that in the case of direction x, the most essential, from the point of view of the possible influence of vibrations propagated from the ground to the structure (see Tables 2-4) and the vertical direction z (see Tables 2-4), the most intense vibrations recorded on the ground surface along the adopted measuring profile are generated during operation of hydraulic compactors in mode of operation X1 (operating frequency 38 Hz, centrifugal force of 90 kN). Significantly lower vibration level is generated by the MTS V8 hydraulic compactor in X2 mode (45 Hz, 50 kN)--except for the horizontal direction x in the second stage of study. The lowest vibration level is generated by the MTS compactor in X3 mode (60 Hz, 90 kN).