“…In light of this, the layered properties of both the outer and inner soils should be considered simultaneously when establishing the corresponding solutions. On the other hand, the soil would be disturbed during pile installation, making it inhomogeneous in the radial direction [5,15,18,19,24,28,52,53]. Previous studies have shown that this ubiquitous phenomenon, commonly known as construction disturbance, displays a noteworthy influence on the vibration of solid piles [9,22,49,58].…”