https://orcid.org/0000-0002-9990-0468
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ABSTRACT
The attenuation response from a series of block vibration tests performed on a model square machine foundation at a site near IIT Kanpur, India, is reported in this paper. The dynamic response at different locations from the vibration source is measured for a wide range of frequencies. The observed attenuation response is compared with the analytical and the finite element (FE) solutions to bolster the experimental findings. A parametric study is conducted utilising the FE analysis to predict the surface wave mitigation characteristics in various soils. It can be observed that the surface waves dominate the attenuation characteristics at the far-field locations and attenuate at a faster rate in soft soils compared to stiff soils. The material and the geometric damping characteristics of the surface waves influence the attenuation characteristics of horizontal and vertical vibrations at the far-field pick-up points. The attenuation characteristics of horizontal and vertical amplitude responses are found to differ significantly. Curve fitting and regression analyses are also performed to develop simplified design expressions to predict the attenuation response of horizontal and vertical vibrations. The proposed design expressions compare well with the values reported in the literature and can be utilised by practicing engineers.
Symbols and Notations
| a | = | Attenuation coefficient |
| ao | = | Frequency-independent coefficient of attenuation |
| AC | = | Alternating current |
| BEM | = | Boundary element method |
| c | = | Damping coefficient of soil |
| D | = | Damping ratio of soil |
| Da | = | Absolute damping of soil |
| DAQ | = | Data acquisition system |
| e | = | Distance between the centre of the shaft and the unbalanced masses |
| f | = | Input frequency |
| fmr | = | Resonant frequency of the soil-foundation system |
| fn | = | Natural frequency of the soil-foundation system |
| F0 | = | Force amplitude applied by the mechanical oscillator |
| FE | = | Finite element |
| g | = | Acceleration due to gravity |
| k | = | Soil stiffness |
| m | = | Mass of the vibrating system |
| me | = | Unbalanced rotating masses in the oscillator |
| MSD | = | Mass-spring-dashpot |
| n | = | Geometric damping coefficient |
| r1,2 | = | Pick-up point distance from the source of vibration |
| USCS | = | Unified soil classification system |
| uy | = | Vertical displacement |
| uz | = | Horizontal displacement |
| Vs | = | Shear wave velocity in soil |
| VR | = | Rayleigh wave velocity in soil |
| SPT (N) | = | Standard penetration test resistance |
| w1 | = | Measured displacement |
| w2 | = | Unknown displacement |
| ∆x | = | Distance between measurements |
| z | = | Displacement in MSD analytical solution |
| = | Velocity in MSD analytical solution | |
| = | Acceleration in MSD analytical solution | |
| zr | = | Peak vertical displacement at resonance |
| = | Spectral ratio | |
| λR | = | Rayleigh wavelength |
| ν | = | Poisson’s ratio |
| ρ | = | Bulk density of soil |
| ω | = | Operating angular frequency |
| θ | = | Angle between the central shaft and the eccentric masses |
Acknowledgments
The authors would like to acknowledge the financial support provided by the Council of Scientific and Industrial Research, India, to carry out the present work through a sponsored research project (Ref No. 22(0731)/17/EMR-II).
Disclosure statement
No potential conflict of interest was reported by the author(s).