Modeling a building response to railway vibration

671
Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011
Leuven, Belgium, 4-6 July 2011
G. De Roeck, G. Degrande, G. Lombaert, G. M¨uller (eds.)
ISBN 978-90-760-1931-4
Modeling a building response to railway vibration using a source-receiver approach
1
Michel VILLOT1, Pierre ROPARS1, Philippe JEAN1
Department of Acoustics and Lighting, CSTB, rue Joseph Fourier 24, 38400 Saint Martin d’Hères, France
e-mail: [email protected], [email protected], [email protected]
ABSTRACT: Railway lines are a very common source of environmental vibration often leading to human exposure to vibration
in buildings. There is a need for methods to understand and predict the building response to such ground borne vibration
sources. The method proposed is based on a source-receiver approach, where the“source” includes the excited surrounding ground
and the building foundations, and the “receiver” is the building upper structure. The approach is applied to a 2D ground building
configuration, where the “source” (ground and building foundations) is modeled in 2D½in order to get correct ground propagation
and foundation vibration levels, using a FEM BEM ground/structure model. The building upper structure response is estimated
using different models, all purely structural: FEM model, analytical beam model, and simplified model combining wave
approach and SEA. The results presented in this paper show that the source-receiver method allows connecting the “source” to
different model types of the building upper structure and gives rather comparable results except for the simplified model. The
source receiver approach allows separating bending and longitudinal excitations, which shows the dominance of longitudinal
excitation in the vibration propagation to the upper floors of the multi storey building considered.
KEY WORDS: Building response to railway vibration; Source receiver method
1
INTRODUCTION
Railway vibration is a very common source of environmental
vibration often leading to human exposure to vibration in
buildings. There is a need for methods to understand and
estimate the building response to such ground borne vibration
sources.
CSTB has developed a ground structure vibration interaction
model in 2D and in 2D½ (MEFISSTO software; see [1, 2]).
This model is more time consuming than a purely structural
model and only very simplified building structures, often in
2D, can be easily studied. More recently CSTB has proposed
a source-receiver approach, where the “source” includes the
excited surrounding ground and the building foundations, and
the “receiver” is the (disconnected) building upper structure [4,
5]. Using this approach, the “receiver” can be studied separately,
using a common purely structural model; moreover, the
“source”, studied in terms of free velocity and mobility, can be
connected to any type of building, whatever the model of the
building upper structure is.
In this paper, the approach is applied to a 2D ground building
configuration, but the “source” (ground and building
foundations) is modeled in 2D½in order to get correct ground
propagation and foundation vibration levels. This mixed 2D /
2D ½ method has been already experimentally validated [6],
showing that even a 2D model of the building can lead to
rather acceptable vibration levels of the building structure.
The upper structure of the multi storey building considered is
modeled using different approaches: a 2D purely structural
FEM software used as reference model, an analytical beam
model and a simplified (also purely structural) model
combining wave approach and SEA, more practical to
understand the physical behavior of the upper structure. The
capacity of the models to estimate the floor vibration levels in
the building is shown by comparing the results obtained to the
FEM calculation.
The paper starts with a short description of the source-receiver
approach applied to a 2D ground building configuration
(section 2). Then, the source is studied first (section 3),
followed by a description of the models used for estimating
the vibration response of the building upper structure (section
4). Comparisons between the different results are finally
presented (section 5).
2
2.1
SOURCE RECEIVER APPROACH
Ground building configuration studied
The 2D ground building configuration studied, shown in
Figure 1a, can be split into the source-receiver system shown
in Figure 1b.
a)
b)
source
receiver
Figure 1: 2D ground building configuration studied
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Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011
2.2
Source-receiver parameters
Because of the low frequency range (usually below 150 Hz)
of railway vibration, the source-receiver system shown in
Figure 1b can be considered as having two contact points
between source and receiver with 3 degrees of freedom each
(vertical and horizontal velocities as well as angular velocity).
The source is characterized by (i) a free velocity vector (vf)
with 6 components (the three degrees of freedom mentioned
above for each contact point) and (ii) a 6x6 source mobility
matrix [YS] including transfer mobility terms from one contact
point to the other (mobility is the ratio between velocity
response and force applied).
The receiver is as well characterized by a 6x6 receiver
mobility matrix [YR].
Contact forces (fC) and contact velocities (vC) as well as the
power Π flowing from source to receiver can then be
estimated from the parameters above using the following
expressions [8]:
( f C )  ([ YS ]  [ YR ])1 ( v L )
(1)
( vC )  [ YR ]([ YS ]  [ YR ])1 ( v L )
(2)

(3)
  1 / 2 Re ( f C )T ( vC )*

All the quantities used in equations (1) to (3) are complex and
can be expressed in terms of amplitude and phase. It should be
noted that contact forces and velocities as well as the power
can be separately calculated for each contact point and for
each wave type (longitudinal and bending, bending combining
horizontal and angular components).
3
SOURCE CHARACTERIZATION
The source parameters have been calculated using the FEM
BEM ground structure vibration interaction model
MEFISSTO developed at CSTB.
3.1
Source free velocity
Lv1
a) 2D ½ free field ground
Lv2
applied to the configurations shown in Figure 2a and 2b where
the railway tracks are considered as an uncorrelated line
source (1N/m/Hz). The model can then be calibrated from free
field ground vibration levels measured near railway tracks.
3.2
Source mobility
The source mobility matrix terms are calculated using
MEFISSTO applied to the source 2D configuration shown in
Figure 1b; any force applied to contact point #1 will lead to 3
velocity components at this (excited) point and 3 velocity
components at contact point #2. Practically, the three force
distributions shown in Figure 3 are applied to the 2D section
of each contact “point”; the resulting vertical and horizontal
velocities are estimated from the velocity at the contact
section center and the angular velocity estimated from two
points in the contact section.
3a
3b
3c
Figure 3: Force distribution used to calculate the source
mobilities: longitudinal (3a), transversal/bending (3b) and
angular/bending (3c)
4
RESPONSE OF THE BUILDING
The building upper structure can be modeled using any type
of approach: in this paper, the receiver mobilities are
estimated from a purely structural 2D FEM approach and the
building response estimated using 3 different approaches: the
2D FEM model (considered as reference model), an analytical
beam model and a simplified model combining wave
approach and SEA.
4.1
Receiver mobilities
The receiver mobility matrix terms are calculated using a 2D
FEM model of the building. As for the source, a force applied
to one contact point will lead to 3 velocity components at this
(excited) point and 3 velocity components at the other contact.
The same force distribution as before (see Figure 3) is used
for the upper structure and the resulting velocities at each
contact point are also estimated in the same way.
4.2
Response using the FEM model
The (isolated) 2D building upper structure (see Figure 1b) is
modeled using a FEM model; the contact velocities calculated
using equation (2) from the source free velocities estimated
and calibrated in 2D½as explained in section 3.1, are imposed
at the two contact points and spatial averaged velocity levels
calculated for each floor.
b) 2D ½ ground + building foundations
4.3
Figure 2: 2D½configurations used to model and calibrate the
source
In order to get correct ground propagation and foundation
vibration levels, the 2D½version of MEFISSTO has been used:
free field ground velocity and foundation free velocity
(receiver disconnected) are calculated using MEFISSTO
Response using the analytical beam model
The 2D building upper structure is now modeled analytically
as an assembly of beams, taking into account longitudinal and
bending waves in the beams (thin beam assumption) and in
the coupling between them. Such a model has been used by
Talbot and Hunt [9]. The contact velocities are imposed at the
contact points and the floor velocity levels calculated as in
4.2.
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Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011
4.4
Response using the simplified model
When using equations (1), (2) and (3), longitudinal and
bending excitations can easily be separated.
In this simplified model, bending wave propagation in the
building has been estimated using SEA; CSTB has worked on
SEA in the past [10], showing that SEA can give acceptable
results down to 50 Hz in the case of bending excitation. The
bending power, obtained from equation (3) has been used as
input power of an SEA model of the building structure, in 3D
(as shown in Figure 4) in order to get correct plate modal
densities; the floor spatial averaged velocity levels are readily
obtained using SEA. Calculations have been performed using
the SEA based CATRAS software developed at CSTB, where
both bending and in-plane waves are taken into account in the
energy balance at plate junctions. The depth of the building is
6m; so a bending power 6 times higher than in 2D has been
injected in order to get 3D floor velocities comparable to the
velocities obtained with the 2D models.
Πinj1
the tracks. All the results are calibrated (see section 3.1) from
a free field ground vertical velocity 1/3 octave spectrum
measured at 4m from the tracks (traffic: freight train at 70
km/h) as shown in Figure 7.
#5
#4
#3
#2
#1
4m
Figure 6: Five storey building studied
Πinj2
Figure 4: 3D configuration of the building used in the SEA
model (bending excitation only)
Longitudinal wave propagation in the building has been
modeled using a 2D simplified model combining wave
approach for the vertical façade wall and SEA for the different
floors, as shown in Figure 5.
Wave approach
SEA approach
Figure 5: 2D model combining wave approach and SEA
Only longitudinal waves are considered in the façade wall.
Floors are characterized by their SEA parameters and taken
into account in the wave propagation in the façade through
their (semi infinite beam) input mobility. Such a model has
been used by Hassan [7]. A contact longitudinal velocity is
imposed at the (only) contact point and the floor spatial
averaged velocity levels readily obtained using SEA. Two
calculations are performed successively for the two contact
points and the resulting velocities added energetically for each
floor.
5
RESULTS
The source receiver approach has been applied to studying
wave propagation through the five storey building shown in
Figure 6; the building is supposed to be located at 4m from
Figure 7: Free field ground vertical velocity level in dB (ref. 5
10-8 m/s) measured at 4m from the tracks (freight train)
The results are expressed in terms of 1/3 octave spatial
averaged velocity levels of the different floors in dB (ref. 5
10-8 m/s); two graphs are given: (i) top graph: floor velocity
spectra obtained by the 3 different models: FEM, analytical
beam model and simplified model (combining wave approach
and SEA), (ii) bottom graph: for the 3 models, difference in
dB between the velocity level of the floor considered and the
first floor
The results are given in Figures 8 and 9 for floor #1 and floor
#5 respectively.
Figure 8 shows that FEM and analytical beam models of the
building upper structure lead to similar results (upper graph),
as the simplified model overestimate floor #1 velocity.
Figure 9 shows that (i) FEM model and analytical beam
approach still give relatively similar results as the simplified
model underestimates the upper floor levels (upper graph),
and (ii) the bottom graph clearly shows at frequencies below
80 Hz an amplification of the upper floor velocity levels
(compared to floor #1), as the simplified model shows the
opposite (an attenuation).
Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011
Figure 8: Top graph: velocity levels in dB (ref. 5 10-8 m/s) for
floor #1; bottom graph: difference in dB between floor
considered and first floor
674
Figure 10: Relative contributions of bending and longitudinal
excitation for floor #1 in terms of velocity levels in dB (ref. 5
10-8 m/s); top graph: simplified model; bottom graph: beam
model
In Figure 10, the beam model shows similar contributions of
bending and longitudinal excitation in floor #1; it should be
noted that the floor response obtained with the complete
excitation (bending and longitudinal components correlated)
is at certain frequencies lower than the response obtained with
the separated (and therefore uncorrelated) bending or
longitudinal excitation. Also in Figure 10, the simplified
model shows a correct bending contribution (obtained using
the SEA model) and an very underestimated longitudinal
contribution (obtained using the combined wave approach
SEA model)..
Figure 9: Top graph: velocity levels in dB (ref. 5 10-8 m/s) for
floor #5; bottom graph: difference in dB between floor
considered and first floor
In order to have a better understanding of the relative
contributions of bending and in plane (longitudinal) excitation
to the floor responses, the detailed results given by the
simplified model are presented (two separate calculations, one
for bending and one for longitudinal excitation, are performed
as shown in section 4.4). Moreover, and in order to confirm
the relative contributions given by the simplified model, two
separate calculations using the analytical beam model have
also been performed: one with only the longitudinal contact
velocity imposed at the contact points of the receiver, and one
with both horizontal and angular velocities imposed. The
detailed results obtained by the two models (simplified and
analytical) are given in Figures 10 and 11 for floor #1 and
floor #5 respectively.
Figure 11: Relative contributions of bending and longitudinal
excitation for floor #5 in terms of velocity levels in dB (ref. 5
10-8 m/s); top graph: simplified model; bottom graph: beam
model
In Figure 11, the dominant longitudinal excitation
contribution given by the beam model on floor #5 shows that
longitudinal waves propagate better to the upper floors; this
result is not well shown by the simplified model since the
longitudinal wave contribution was underestimated on floor
Proceedings of the 8th International Conference on Structural Dynamics, EURODYN 2011
#1; however, the propagation to the upper floors seems
correctly modeled.
6
CONCLUSION
A source-receiver mobility approach has been applied to a
ground-building configuration in order to study the building
response to a railway ground excitation. The source (ground +
building foundations) is represented by a 2D ½ BEM FEM
model, the railway excitation being taken into account as an
uncorrelated line source. The receiver (building upper
structure) is represented by different models, all purely
structural and 2D: FEM model, analytical beam model, and
simplified model combining wave approach and SEA. Source
and receiver mobilities are estimated in 2D.
The results show that (i) this source-receiver mobility
approach allows connecting the source to different model
types of the building, (ii) the results given by the FEM and the
analytical beam models in terms of floor velocity levels are
comparable; it should be noticed that the beam model is much
faster than the FEM model, (iii) the source receiver approach
allows separating bending and longitudinal excitations, which
shows the dominance of longitudinal excitation in the
vibration propagation to the upper floors of the building, (iv)
the results given by the simplified model show a correct
estimation of bending contribution using SEA, but a
underestimated longitudinal contribution given by the very
simplified combined wave approach SEA model.
ACKNOWLEDGMENTS
This study is part of a PhD work financially supported by
CSTB and the French National Agency for Research.
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