Ground Vibration
Prediction and
Assessment
R.M. Thornely-Taylor
Rupert 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.
3.50E+04
3.00E+04
Magnitude (Ns/m)
2.50E+04
2.00E+04
Female, 56kg
Male, 75kg
1.50E+04
1.00E+04
5.00E+03
0.00E+00
0
5
10
15
20
25
Frequency, Hz
Driving-point impedance (z-axis) of seated human body
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
impedance ratio
100
10
1
0.1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
radius/wavelength
Impedance ratio of spherical source in elastic medium
1.8
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)