We found a recent paper by Keller (Singapore) to be particularly interesting. Here’s a quick summary on this novel work and how we see its potential practical implications for geotechnical engineering applications.
Ground improvement by deep vibro-techniques — vibro-replacement (stone columns) and vibro-compaction — is a routine part of modern geotechnical practice. Both methods use a depth vibrator to densify or reinforce the ground, and both impart significant vibrations into the surrounding soil in the process. When works are carried out near existing structures, the question of how those vibrations attenuate with distance becomes a practical matter of genuine consequence: too conservative an assessment sterilises the working area; too optimistic and you are issuing damage claims.
A paper by Weng et al. (2020), published in Geotechnical Research, addresses this problem directly. Drawing on close to 1000 field measurements across multiple vibro-replacement and vibro-compaction sites in Southeast Asia, the authors evaluate existing predictive models against real data, identify their shortcomings, and develop a semi-empirical approach that better captures the physics of the problem.
The limits of existing models
Most published predictive models for construction vibrations were developed from pile driving data, not vibro-technique data. The widely used scaled-distance approach of Attewell and Farmer (1973) — relating peak particle velocity (PPV) to the ratio of distance to the square root of vibrator energy — was originally calibrated for impact and vibratory pile driving and for early vibro-flotation work. Hiller and Crabb (2000), whose work was incorporated into BS 5228-2, assessed only three vibro-replacement projects in the UK and did not specify the energy ratings of the vibrators used. Achmus et al. (2010) covered a broader range of vibrator energies (700–6000 J), but their dataset was still limited relative to the diversity of equipment and ground conditions encountered in practice.
When Weng et al. (2020) plot their field data against the predictions of these models, the deficiencies become clear. The models either overestimate near-field vibrations and underestimate far-field attenuation, or vice versa, and none adequately accounts for the specific characteristics of the vibrator in use. The quadratic log-log fit of Attewell et al. (1992a, 1992b) performs relatively better across the dataset, but its predictions become physically unrealistic in the far-field — for some vibrator combinations, it predicts higher PPV from a less powerful machine than from a more powerful one, which is clearly wrong.
A physics-informed empirical approach
The authors’ response is to build a prediction framework grounded in the wave propagation physics rather than pure curve-fitting. Starting from the classical attenuation expression of Mintrop (1911), which describes how vibration amplitude decays with distance as a product of geometric spreading and material damping, they derive a normalised PPV expression that explicitly accounts for both the vibrator energy Er and the vibrator mass M. The resulting form is:
PPVR / √(Er/M) = Ψ × D⁻⁰·⁵ × exp(−α × D)
where D is the horizontal distance from the source, Ψ is a proportionality constant capturing vibration transfer efficiency, the geometric damping exponent of 0.5 reflects Rayleigh wave dominance at the surface (consistent with Gutowski and Dym (1976)), and α is the material damping coefficient. Regression against the full dataset of ~980 data points from four vibrator types gives α ≈ 0.030 m⁻¹ — in good agreement with the values reported by Woods and Jedele (1985) for intermediate-strength soils, and physically consistent with the ground types typically treated by these methods.
A notable feature of the normalised plot is that data from all four vibrator types — three for vibro-replacement and one for vibro-compaction, spanning energy ratings from 1000 to 4000 J — cluster together with considerable overlap. This collapse of diverse datasets onto a common trend is precisely what a well-chosen normalisation should achieve, and gives confidence that the underlying physics is correctly captured.
The authors follow Achmus et al. (2010) in recommending the 97.7% confidence level (two standard deviations above the best fit) as the appropriate upper-bound for structural protection assessments, and derive explicit safe working distances for four categories of structure — from heavy framed industrial buildings (PPV threshold 25 mm/s) through to historic monuments and statically indeterminate masonry structures (PPV threshold 5 mm/s). For the largest vibrator considered (VC-A, 4000 J), safe working distances to historic structures are estimated at approximately 40 m at the 97.7% confidence level — considerably more than the ~35 m suggested by Attewell et al. (1992a, 1992b) at the same confidence level, and more consistent with the observed field data.
The paper also notes a practically important feature of deep vibro-techniques that distinguishes them favourably from impact piling: their operating frequencies (30–60 Hz) are well above the resonant frequency range of most soils (10–20 Hz), as established by Massarsch (2002), making soil resonance and consequential structural amplification unlikely. At these higher frequencies, most codes of practice also permit higher limiting PPV values, which is an additional advantage.
What this means in practice
The message for practitioners is straightforward but important. Pre-construction vibration assessments based on pile driving empirical models are likely to be poorly calibrated for vibro-technique work. The semi-empirical approach of Weng et al. (2020) offers a sounder starting point, and the authors make the practical recommendation — which deserves emphasis — that preliminary estimates should be followed by early-stage field monitoring to refine site-specific parameters. A model calibrated on 1000 data points from regional practice is a good prior; actual field measurements from the specific vibrator on the specific site are better still.
References
Achmus, M., Wehr, W. and Spannhoff, T. (2010) Building vibrations due to deep vibro processes. 7th Conference on Ground Improvement Techniques, Seoul, South Korea.
Attewell, P.B. and Farmer, I.W. (1973) Attenuation of ground vibrations from pile driving. Ground Engineering, 63(7), pp. 26–29.
Attewell, P.B., Selby, A.R. and O’Donnell, L. (1992a) Estimation of ground vibration from driven piling based on statistical analyses of recorded data. Geotechnical & Geological Engineering, 10(1), pp. 41–59.
Gutowski, T.G. and Dym, C.L. (1976) Propagation of ground vibration: a review. Journal of Sound and Vibration, 49(2), pp. 179–193.
Hiller, D.M. and Crabb, G.I. (2000) Ground Borne Vibration Caused by Mechanised Construction Works. Report 429. Transport Research Laboratory, Crowthorne, UK.
Massarsch, K.R. (2002) Effects of vibratory compaction. Keynote Lecture, TRANSVIB 2002. Balkema, Lisse, the Netherlands, pp. 33–42.
Mintrop, L. (1911) Über die Ausbreitung der von den Massendrucken einer Großgasmaschine erzeugten Bodenschwingungen. PhD thesis, Georg-August-Universität Göttingen, Germany.
Weng, L.K., Yohannes, M.M. and Chong, W. (2020) Data analysis and prediction of ground vibrations due to deep vibro-techniques. Geotechnical Research, 7(4), pp. 244–257.
Woods, R.D. and Jedele, L.P. (1985) Energy–attenuation relationships from construction vibrations. In Gazetas, G. and Selig, E.T. (eds), Vibration Problems in Geotechnical Engineering. ASCE, New York, pp. 229–246.
