Identifying boundary between near field and far field in ground vibration caused by surface loading

The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves. It is closely related to the type of vibration source and the soil properties. Based on the solutions of the Lamb＇s problem, the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space. Particularly, the variation of the boundary with the material damping was investigated for both cases. The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region, but significantly reduces the vibrations in the region that is at some distance away from the source. When taking the material damping into consideration, the boundary between the near and far fields tends to move towards the vibration source. Compared with the vibrations caused by a concentrated load, the vibrations induced by an infinite line load can affect a larger range of the surrounding environment, and they attenuate more slowly. This means the boundary between the near field and far field should move fitrther away from the source. Finally, the boundaries are defined in terms of R-wave length （2R） and Poisson ratio of the ground （o）. For the case of a point load, the boundary is located at the distance of （5.0-6.0）2R for v≤0.30 and at the distance of （2.0--3.0）2R for v≥0.35. For the case of an infinite line load, the boundary is located at the distance （5.5-6.5）2rt for v≤0.30 and at the distance （2.5--3.5）2R for v≥0.35.

The boundary between the near and far fields is generally defined as the distance from the vibration source beyond which ground vibrations are mainly dominated by Rayleigh waves.It is closely related to the type of vibration source and the soil properties.Based on the solutions of the Lamb's problem,the boundary at the surface between the near and far fields of ground vibration was investigated for a harmonic vertical concentrated load and an infinite line load at the surface of a visco-elastic half-space.Particularly,the variation of the boundary with the material damping was investigated for both cases.The results indicate that the material damping slightly contributes to the attenuation of vibrations in the near-source region,but significantly reduces the vibrations in the region that is at some distance away from the source.When taking the material damping into consideration,the boundary between the near and far fields tends to move towards the vibration source.Compared with the vibrations caused by a concentrated load,the vibrations induced by an infinite line load can affect a larger range of the surrounding environment,and they attenuate more slowly.This means the boundary between the near field and far field should move further away from the source.Finally,the boundaries are defined in terms of R-wave length(λR) and Poisson ratio of the ground(υ).For the case of a point load,the boundary is located at the distance of(5.0-6.0)λR for υ≤0.30 and at the distance of(2.0-3.0)λR for υ≥0.35.For the case of an infinite line load,the boundary is located at the distance(5.5-6.5)λR for υ≤0.30 and at the distance(2.5-3.5)λR for υ≥0.35.