Table 1 Empirical and semi-empirical...

Table 1

Empirical and semi-empirical approaches of vibration predictions of foundation installation activities, such as piling and vibro-stone column works

Prediction approaches	Expressions for PPV: mm/s
Attewell and Farmer (1973) An empirical model for predicting the PPV due to pile driving by impact hammers and for vibro-floatation.	$P P V = 0.76 \times {(\frac{D}{\sqrt{W_{r}}})}^{- 0.87}$ 1
Wiss (1981) A modified approach to his earlier proposal for driven piles (Wiss, 1967).	$\log (P P V) = \log k - n \times \log (\frac{D}{\sqrt{W_{r}}})$ 2
Attewell et al. (1992a, 1992b) To account for the non-linearity of the scaled distance and PPV correlations, Attewell et al. (1992a, 1992b) proposed the use of a quadratic log–log fit.	$\log (P P V) = k_{1} + k_{2} \times \log (\frac{D}{\sqrt{W_{r}}}) + k_{3} \times \log^{2} (\frac{D}{\sqrt{W_{r}}})$ 3
Ko et al. (1990) A model that includes both geometric and material damping for piling works.	$P P V = 70 \times (\frac{1}{\sqrt{D}}) \times e^{- 0.04 \times (D - 1)}$ 4
Hiller and Crabb (2000) A best-fit curve model developed by the Transport Research Laboratory (UK), considering three case studies where vibro-stone columns were used.	$P P V = \frac{33}{D^{1.4}}$ 5
Achmus et al. (2010) Best-fit prediction models for vibro-replacement and vibro-compaction works based on four different depth vibrators.	$P P V = 1.18 \times {(\frac{D}{\sqrt{W_{r}}})}^{- 1}$ 6

Prediction approaches	Expressions for PPV: mm/s
Attewell and Farmer (1973)An empirical model for predicting the PPV due to pile driving by impact hammers and for vibro-floatation.	1 $P P V = 0.76 \times {(\frac{D}{\sqrt{W_{r}}})}^{- 0.87}$
Wiss (1981)A modified approach to his earlier proposal for driven piles (Wiss, 1967).	2 $\log (P P V) = \log k - n \times \log (\frac{D}{\sqrt{W_{r}}})$
Attewell et al. (1992a, 1992b)To account for the non-linearity of the scaled distance and PPV correlations, Attewell et al. (1992a, 1992b) proposed the use of a quadratic log–log fit.	3 $\log (P P V) = k_{1} + k_{2} \times \log (\frac{D}{\sqrt{W_{r}}}) + k_{3} \times \log^{2} (\frac{D}{\sqrt{W_{r}}})$
Ko et al. (1990)A model that includes both geometric and material damping for piling works.	4 $P P V = 70 \times (\frac{1}{\sqrt{D}}) \times e^{- 0.04 \times (D - 1)}$
Hiller and Crabb (2000)A best-fit curve model developed by the Transport Research Laboratory (UK), considering three case studies where vibro-stone columns were used.	5 $P P V = \frac{33}{D^{1.4}}$
Achmus et al. (2010)Best-fit prediction models for vibro-replacement and vibro-compaction works based on four different depth vibrators.	6 $P P V = 1.18 \times {(\frac{D}{\sqrt{W_{r}}})}^{- 1}$

Note: some of the expressions have been altered for consistency in using the same units for the parameters considered in the expressions (all input in metre, kilogram, second (MKS) units and PPV given in mm/s)

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