Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)
ISSN: 2311-9020; ISBN: 978-972-752-165-4
Prediction model for train induced vibration and structural noise in buildings
1
H. Gjelstrup1, J. Andersen1, A Larsen1, J. Sandreid2
COWI A/S, Parallelvej 2, 2800 Kongens Lyngby, Denmark. Parallelvej 2, 2800 Kongens Lyngby, Denmark.
2
Banedanmark, Vasbygade 10, 2450 København SV, Denmark.
email: [email protected], [email protected], [email protected], [email protected]
ABSTRACT: A general model for prediction of ground borne vibrations and structural noise in buildings in relations to passing
trains is introduced. The model is intended for estimation of vibration and structural noise levels in buildings from nearby rail
lines and for assessment of human discomfort in relation to existing well established comfort boundaries. The human comfort
part of the prediction model is based on transfer functions between ground, foundation and floor structures, whereas the
structural noise part is based on a correlation between measurements made on the floor in the same room as the noise was
recorded. The transfer functions, which are used in the model is derived from measurements of several train types and at several
geographical locations, representing most of the rail systems used in Denmark. Apart from Danish locations, data from Austria
is also included in deriving the model. The structural noise part of the model is based on measurements in 26 different houses,
where the rooms were chosen based on minimizing external sound sources. Comparisons of predicted and measured values are
presented in conjunction with theoretical expression used in the prediction model. The model show good results in predicting
human comfort levels, whereas the prediction of the noise level leads to the need for a more in depth analysis of the measured
data.
KEY WORDS: Prediction; Train induced vibrations; Human comfort; Structural noise.
1
INTRODUCTION
A general model for prediction of ground borne vibrations and
structural noise in buildings in relations to passing trains is
introduced.
The model is intended for estimation of vibration and
structural noise levels in buildings from nearby rail lines and
for assessment of human comfort in relation to existing well
established comfort boundaries. The model is based upon
classical empirical assumptions leading to adding up
frequency dependent transmission loss functions from source
to receiver in order to estimate vibration levels from passing
trains within a building.
The model is derived from measurements of several train
types and at several geographical locations, representing most
of the rail systems used in Denmark. Apart from Danish
locations, data from Austria is also included in deriving the
model. The collection of the experimental data was carried
out using two main measurements campaigns. The first part
was based on finding geological damping and transmission
loss functions for vibration from passing trains to houses,
whereas the second part was based on expanding the
transmission loss functions database from ground to the house
and finding a relationship between measured vibration level
on the floor and sound pressured in the same room.
2
and at some locations only vibrations at the rail line or in the
building has been measured.
2.1
Part one
The
generic
instrumentation
setup
consisted
of
accelerometers, microphones, temperature sensors and ultrasonic distance sensors for determination of train speed and
length. Vibrations were measured by accelerometers at the
rail, sleeper, ballast and 7.5m, 15m, 30m from the rail center.
Furthermore a microphone was placed a 7.5m from the rail
center and inside one family houses, where vibrations also
were measured by accelerometers.
Figure 1 show the geographical locations in Denmark where
data has been measured. Apart from these locations, data from
measurements carried out in Austria, are also included in the
model. For the Kværkeby location ( ) a setup involving 72
geophones was placed in groups of 4 with ½ m spacing
perpendicular to the track.
SELECTED MEASUREMENT LOCATIONS AND
SETUP
The following section describe the measurement setup used
during the two main part of the measurement campaign. The
measurement setup for the two parts of the campaign was
generally carried out with the same measurement setup.
However some minor variation occurs due to local limitations
Figure 1. Measurement locations in Denmark, from where
data is included in the model. Each bullet represents several
local positions.
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Hammer blows on the surface and rail as well as vibrations
from passing trains was recorded in order to conduct a seismic
survey and thereby understand the wave propagation in the
geology (boulder clay on top of lime stone, typical Danish
situation). A list of typical sensor locations is shown in Table
1
Table 1. Sensors and positions used as generic setup.
was a straight line between the vibrator the 5m point and the
point on the foundation. Table 2 show a list of the used
sensors and their location in the measurement setup
Table 2. Sensors and positions used in the second part.
Sensor
Position
accelerometer
5m from house foundation
accelerometer
At the house foundation
Sensor
Position
Sensor
Position
accelerometer
Ground floor
Thermometer
Rail
accelerometer
At building
accelerometer
foundation
microphone
accelerometer
Rail
accelerometer
Ground floor
accelerometer
Sleeper
accelerometer
1. floor
accelerometer
Ballast
Microphone
Ground floor,
accelerometer
3
the floor
7.5m from
Ultra-sonic
At sleeper
center of
microphone
10m down
nearest
from rail
track
accelerometer
7.5m from
Ultra-sonic
At sleeper
center of
10m up from
nearest
rail
track and
accelerometer
3.1
Model composition
The model is based upon classical empirical assumptions
leading to adding up frequency dependent transmission loss
functions from source to receiver in order to estimate
vibration levels from passing trains within a building [1] &
[2]. The acceleration level is measured in m/s2 and converted
into 1/3-octave spectrum in dB with a reference of 10-6 m/s2.
1,2m over
Laj  Lak  Lh  TLg  TLb  TLe  
rail level
accelerometer
20m from
On the floor under the microphone
MODEL FOR PREDICTING HUMAN DISCOMFORT
IN RELATION TO VIBRATIONS FROM PASSING
TRAINS
1.2m over
accelerometer
1st floor
A room with no ventilation and no windows if possible
Thermometer
7.5m from
center of
center of
nearest
nearest track
track and
in shadow
where:
Laj
(1)
Vibration spectrum in the building (1/3-octav
spectrum).
5m from
building
foundation
A more detail description can be found in [3].
2.2
Second part
The second part of the measurement campaign was perform in
26 houses located as shown in Figure 2
j
is the location.
Lak  Lh Vibrations source from the train (1/3-octav
spectrum).
Correction for the train speed (1/3-octav spectrum).
Lh
TLg
Damping relation to vibrations transmission
through the ground (1/3-octav spectrum).
TLb
Damping relation the vibrations transmission from
ground to
spectrum).
TLe

building
foundation
(1/3-octav
Damping in relation to vibrations transmission
through the different building levels (1/3-octav
spectrum).
Error on the calculation.
Figure 3 show a sketch of the model, and how the different
terms relates to the different position from the vibrations
source (the train) to the house.
Figure 2. Measurement locations for the second part of the
measurement campaign.
For the second part the instrumentation setup consisted of
accelerometers and one microphone. The accelerometer was
place at 5m, from the house foundation, on the foundation, at
the ground floor and at the 1st floor if possible. The vibration
source for theses measurement was a seismic vibrator which
was place 5 to 10 from the 5m point and was lined up so there
820
TLe
Lak  Lh
TLg
Figure 3. Sketch of model.
TLb
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
The new feature is to base the statistical calculations behind
the model upon a very large set of input data, detailed analysis
of train speed effects and soil/distance damping by analytical
1 or 2 layer models based upon input from geotechnical
borings. The assumption that the individual 1/3 bins are
normal distributed is based on a "Chi-Square Goodness of Fit
Test" on the dataset of each 1/3-octave bin.
Using the above mention assumption it is possible to rewrite
equation (1) into the following expression of a normal
distribution.

 
 
 
N TL ,  TL   N TL ,  TL 

N  Laj ,  Laj  N  Lak ,  Lak  N  Lh ,  Lh  N TLg ,  TLg 
b
b
e
(2)
e
where:
 Laj   Lak   Lh  TLg  TLb  TLe
Figure 4. Number of trains, by type and measurement
location.
The two locations is Bedstedvej 16 and Kongstedvej 15
located in Kværkeby, which was marked by in Figure 1.
2
2
2
 Laj   L2ak   2L   TL
  TL
  TL
g
b
e
h
It is assumed that the correction for the train speed and the
damping in the ground is deterministic functions, why:
2
 0 . This leads to a simplify expression:
 2L  0 ,  TL
g
h

 
N  Laj , Laj  N  Lak , Lak
Corr  N TL , TL  N TL , TL 
b
b
Where the data used for determining
e

e
N  Lak , Lak
(3)
Corr is
corrected for the train speed and then for the damping in the
ground.
The model works by choosing a set of six parameters which
defined the vibration case which is to be studied. The six
parameters are:
 Rail track type.
 Rail track level in relation to the surroundings.
 Train type.
 House type.
 Floor level.
 Eigenfrequency of the floor (4 frequency intervals).
For a more detail description of the human comfort model,
please see [3].
4
4.1
MEASURMENT RESULTS
Figure 5. Two selected locations in Kværkeby:
Bedstedvej 16, = Kongstedvej 15.
=
Figure 5 show the two locations and how the alignment of
rail track is between the two locations.
In order to make a comparison between the two locations,
all trains measured at Kongstedvej 15 was also measured at
Bedstedvej. The difference in the number of measured trains,
which is seen in Figure 4, is due to the fact that the
measurements started at Bedstedvej 16 before Kongstedvej
15.
Figure 6 show the distribution of the train speeds of the
measured trains at Bedstedvej 16. This particular part of the
rail track is has a max speed of 180 km/t which the measured
results also indicates.
Results from passing trains
In the following part selected result from part one of the
measuring campaign is shown.
Figure 4 show the distributions of the measured trains for
two locations which is about 2 km apart. It is seen that there at
two main types of trains namely IC3 and ER. These two train
types are more or the same except IC3 is powered by fossil
fuel and ER is electrified. In the following the results from the
IC3 trains is shown in greater detail.
Figure 6. Train speeds measured at Bedstedvej 16, by train
type.
Figure 7 (top) shows the measured source strength 7.5 m
from the track center at Bedstedvej 16. A dominant frequency
is identified in the range 60-80 Hz. Figure 7 (bottom) shows
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
houses are significantly different from the other house which
was measured.
Transmission loss
the measured source strength 7.5 m from the track center at
Kongstedvej 15. There is again a dominant frequency range
60-80 Hz. It is also seen that the levels are approx. 10 dB
lower than at Bedstedvej 16.
Hz
Figure 8. Transmission loss from 5m to foundation. Bold line
is showing the mean curve.
Transmission losses
This section presents only data from part two of the
measurement campaign. In part two of the measurement
campaign, where the vibrations source was a seismic vibrator,
measurements in 26 houses was preformed, in order to
identify the transmission loss from ground to house
foundation, from house foundation to the ground floor and
from the house foundation to the 1st floor.
Figure 8 show the transmission loss from 5m from the house
and to the house foundation. The transmission loss is defined
as measurements at the house foundation divided by the
measurements at the 5m point, within a 1/3 octave spectrum.
It seen there is a quit large difference in the results between
the individual measurements. It seems like there are two sets
of measurements which fall outside the grouping of the other.
The reason to this difference has not been found, but it is
believed that the geology or the foundation of for these two
822
Transmission loss
4.2.1
Results from seismic vibrator
Hz
Hz
Transmission loss
4.2
Transmission loss
Train speed was measured for each train passage at both
Bedstedvej 16 and Kongstedvej 15 and significant difference
was found in the in the speed of the same train at both sites.
Based on this observation, it is assumed that the differences
seen between the two sets of curves shown above may come
from a difference in reaction forces on the track and/or
differences in ground conditions.
The biggest difference is seen in the frequency bands
between 1.25 and approx. 90 Hz, where the level
measurements are approx. 10 dB higher for Bedstedvej 16
than for Kongstedvej 15. The variations in the individual
curves in the top and bottom of the figure are due the different
speed of the measured trains.
Transmission loss
Figure 7. Source strengths from IC3 trains at Bedstedvej
16(top) and Kongstedvej 15(bottom), measured 7.5 m from
the centre of the track.
Figure 9 and Figure 10 show obtained transmission loss from
the house foundation and to the ground floor and the 1st. floor
respectively. The values presented in the figures are
amplifications factors to the individual 1/3 octaves in linear
scale. The results are sorted into the four frequency intervals
namely, 0-20Hz, 20-40Hz, 40-65Hz and 65-110Hz.
The reason for sorting the transmission losses into theses
interval is bases on already obtained data which have been
analyses. This analyse showed that the transmission losses
tended to fall in the four frequency intervals as noted above.
Furthermore it shows that the amplification was link to the
eigenfrequency of the floor.
In comparison to the transmission loss from the ground to
the foundation, then the result found for the transmission loss
from the foundation to the different floors are nicely group in
three frequency intervals, namely 20-40Hz, 40-65Hz and 65110Hz. From the Figure 9 and Figure 10 it's seen that none of
the measured transmission losses falls within the 0-20Hz
interval.
Hz
Hz
Figure 9. Transmission loss from foundation to ground floor,
sorted after amplification in 4 pre-set frequency intervals.
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Hz
Hz
LAeq/Afloorarea
SoundPress(A)/floor
25,00
Transmission loss
Transmission loss
Floor; Concrete
20,00
15,00
10,00
5,00
0,00
Hz
Hz
For the ground floor it seems that most of the measured
transmission losses falls within the 65-110Hz interval, see
Figure 9, whereas for the 1st. floor there seems that the
measured transmission losses is mainly distributed in the 4065Hz interval, whereas the rest is distributed between 2040Hz and 65-110Hz.
Looking at the distribution of transmission losses within
these intervals, it is seen that even though there is some
deviation from the mean, then there is a definite trend within
the groups shown in Figure 9 and Figure 10.
Structural noise
Structural noise was also measured during the measuring of
the above shown transmission losses.
As mentioned above the instrumentation setup was a
microphone placed 1.2m above an accelerometer which was
placed on the floor.
The data from the both sensors was analyses and converted
into 1/3 octaves running from 10Hz to 160Hz, in dB, which is
the range defining the structural sound in Denmark, Erro! A
origem da referência não foi encontrada..
The data recorded by the microphone have been A-weighted
and the data from the accelerometer have been KB-weighted.
Figure 11 and Figure 12 shows the relationship between the
structural noise and the measured vibration level on the floor,
which was found for a concrete floor and at wooded floor
respectively.
The plots show the weighted total band power which have
been normalized with the floor area of the room in which the
measurements was obtained.
The total band power(LAeq and Law) used for producing
Figure 11 and Figure 12 is calculated by: 20Log10x / 1e  6
n
where x is given by

10,0
15,0
20,0
25,0
30,0
Figure 11. Relation between acceleration and sound pressure
measured on a concrete floor
Figure 10. Transmission loss from foundation to 1st. floor,
sorted after amplification in 4 pre-set frequency intervals.
4.2.2
5,0
Acc band power(KB)/floor
Law/Afloor area
Making a linear fit to the data found on a concrete floor,
which is presented in Figure 11, result in the expression for
predicting the A-weighted sound pressure as a function of the
KB-weighted acceleration and the rooms floor area, see
equation (4).
LAeq  0.8136 Law  0.7666 Afloor
(4)
Floor; wood
16,00
LAeq/Afloorarea
SoundPress(A)/floor
Transmission loss
Transmission loss
0,0
14,00
12,00
10,00
8,00
6,00
4,00
2,00
0,00
0,0
5,0
10,0
15,0
20,0
25,0
Acc band power(KB)/floor
Law/Afloor area
Figure 12. Relation between acceleration and sound pressure
measured on a floor made out of wood.
The distribution and the of number data points for the wood
floor makes it difficult to say anything certain about the
relationship, but under the assumption that it following the
same trend as for the concrete floor the following has been
found. Making a linear fit to the data found on a wooded
floor, which is presented in Figure 12, result in the following
expression for predicting the A-weighted sound pressure as a
function of the KB- weighted acceleration and the rooms floor
area, see equation (5).
.
LAeq  0.5847 Law  0.4061 Afloor
(5)
Octave i2 , were i is the Octave bin
i 1
running from 10Hz to 160Hz and the octaves is either Aweighted or KB-weighted.
Looking at the measurement in a combined plot yields the
result shown in Figure 13 and equation (6).
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
5.3
Floor; Concrete and wood
LAeq/Afloor area
SoundPress(A)/floor
25,00
For the presented case we have a good agreement between the
measured and the predicted human comfort level. The
differences for the two floors were found to be:
20,00
15,00
•
•
10,00
5,00
0,00
0,0
5,0
10,0
15,0
20,0
25,0
30,0
Acc band power(KB)/floor
area
Law/Afloor
Figure 13. Relation between acceleration and sound pressure
measured on floors made out of wood and concrete.
LAeq  0.7707 Law  0.3709 Afloor
(6)
More measurements in room with floors made of wood
needs to be performed in order to say if there are different
expressions as shown in equation (4) and (5) for different
floor types or if a combined expression can be made as shown
in equation (6).
Ground floor:
1st floor:
5.4
1.2 dB
-1.1 dB
Structural noise level bases on measurements.
Using a passing train as the vibration source the following
noise and floor vibrations was measured in the same room.
The room has a concrete floor with an area of 5.95m2. The
room was empty but has a door leading outside with a large
window, which was cover with Rockwool to minimize
airborne sound.
•
•
Floor vibration level:
Noise level:
5.5
58.29 dB(KB)
34.27 dB(A)
Structural noise level bases on model predictions
Using equation (4) and the floor vibration level mention above
result in the following prediction of the structural noise.
•
5
Comparison of measured and predicted human
comfort
Predicted noise level:
42.9 dB(A)
MODEL PREDICTIONS
In the following a presentation of measured and model
predicted Human comfort levels and structural noise is given.
5.1
Human comfort level bases on measurements.
Looking at measurements performed at a house located about
30 meters from the rail track; the following human comfort
level is calculated from measured data obtained in the ground
floor and at the 1st floor. The measurements were performed
during the fall of 2012 and the values are given as a 95%
confidence interval.
•
•
Ground floor:
1st floor:
72.9 dB(KB)
76.5 dB(KB)
5.6
Comparison of measured and predicted noise level
Looking at the measured and predicted noise level, it's found
that there is a relative large difference of about 9 dB in over
estimating the measured value.
Looking at the measurements which was used in deriving
the model in compassion to the measurements used in
prediction the noise level shows a discrepancy which seems to
be the reason to the offset in the predicted value, see Figure 14
and Figure 15.
3,50E-04
3,00E-04
2,50E-04
The house is a single family house and the first mode for both
floors falls within the interval of 20 Hz to 40 Hz. The data
used to calculate the human comfort level originates from
passing train of the type MF, also called IC3, and the rail track
itself was situated about one meter above the surrounding
landscape.
5.2
Human comfort level bases on model predictions
Using the model and inputting parameters which corresponds
to the case described above yields the following results, also
presented in a 95% confidence interval:
•
•
824
Ground floor:
1st floor:
71.7 dB(KB)
77.6 dB(KB)
2,00E-04
Accelerometer
1,50E-04
Microphone
1,00E-04
5,00E-05
0,00E+00
10
100
Hz
Figure 14. Measurements used in deriving the prediction
model.
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
5,00E-03
4,50E-03
4,00E-03
3,50E-03
3,00E-03
2,50E-03
Accelerometer
2,00E-03
Microphone
1,50E-03
1,00E-03
5,00E-04
0,00E+00
10
100
Hz
Figure 15. Measurements used in predicting the noise level.
A deeper analysis of is discrepancy is still ongoing.
6
CONCLUSION
Using a general empirical model for vibration transferring
from a source to a location, the human comfort level is
calculated in a 95% confidence interval. Furthermore a linear
relationship between the structural noise and the vibration on
the floor has been presented.
A comparison between the values obtained from a calculated
95% confidence interval and the measured values shows a
good agreement between the model and measured values. The
difference is within ±1.2 dB for the case presented in this
paper.
A comparison of measured noise level and predicted noise
levels has shown a relative large discrepancy. A deeper
analysis of why discrepancy is found is still ongoing.
ACKNOWLEDGMENTS
I would acknowledge Rail Net Denmark for giver us this
opportunity for make this model and letting us perform this
extensive measurement campaign.
REFERENCES
[1]
[2]
[3]
[4]
VIBRA-1-2-3: A software package for ground borne vibration and noise
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Ingenieure USIC, Asylstrasse 41, CH-8032 Zürich
C. Madshus, B. Bessason and L. Harvik, Prediction model for low
frequency vibration from high speed railways on soft ground, Journal of
Sound and Vibration (1996) 193(1), 195-203.
H. Gjelstrup, A. Larsen, J. Andersen, H.B. Kock and J. Sandreid, New
approach to calculated human discomfort affected by vibrations from
passing trains. Proceedings from IWRN11
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9/1997
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