Ground Vibration Prediction and

Assessment

R.M. Thornely-TaylorRupert Taylor Ltd

Noise:

SOURCE PATH RECEIVER

Vibration:

SOURCE PATH RECEIVER

• Source term - dependent on excitation, source impedance, mounting impedance, foundation impedance and surrounding lithology

• Transmission characteristics - dependent on geometry of source, geological characteristics (Lamé constants, loss factor, layering, water tables)

• Building response - consisting of coupling between foundations and the ground and the dynamic response of the building, and, in the case of re-radiated groundborne noise, the receiving room characteristics

• Receiver and support impedance. Receiver attitude.

Driving-point impedance (z-axis) of seated human body

0.00E+00

5.00E+03

1.00E+04

1.50E+04

2.00E+04

2.50E+04

3.00E+04

3.50E+04

0 5 10 15 20 25

Frequency, Hz

Mag

nitu

de (N

s/m

)

Female, 56kg

Male, 75kg

Receiver Issues• Foundation coupling

• transfer functions• piled foundations• Structure response

• Power transmission through/up building• transmission line• floor impedances

– vary with location

• Receiver impedance• axes • support

– standing– chair– bed

Propagation Issues• Soil parameters

• on-site measurement• bore-hole tests• impedance of spherical source in an elastic

medium– departs from inverse-square law for velocity

• pressure and strain dependence of dynamic moduli

• Uncertainties– unknown features in lithology

• perched water tables• boulders/limestone layers

0.1

1

10

100

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

radius/wavelength

impe

danc

e ra

tio

Impedance ratio of spherical source in elastic medium

Seismic measurement of P-wave and S-wave velocities

Propagation Issues• Many wave types

• body waves (dilatational)• shear waves• Rayleigh waves• Stoneley waves• Lamb waves• two-phase propagation

– liquid in a porous medium

– Wave conversion at interfaces• SV P• one layer may attenuate• several layers may increase propagation at eigenfrequencies• progressive change in soil may bend propagation path

Correct Source Data

• Source power– dependent on

– source impedance – source mounting/support

» resilient elements» dynamic stiffness - frequency dependence» loss factor - frequency dependence

• Source signal

Modelling• Empirical

– Extrapolating measurements from similar case– Statistical treatment of large numbers of measurements from many

cases• empirical methods of correcting for changes in parameters

• Algebraic– Isolator transmissibility– Simple distance function

• Numerical– Finite element (FEM)– Finite difference (FDM)– Boundary Element (BEM)– Hybrid (FEM/BEM)