PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Reducing ground borne noise due to railways.
Part II : mitigation measures
Philippe Jean, Catherine Guigou-Carter and Alexandre Jolibois
CSTB 24 rue Joseph Fourier, 38400 Saint Martin-d’Hères FRANCEABSTRACT
The construction of new buildings very close to existing tracks with heavy commuting traffic requires
careful design. Such projects must be accompanied with noise and vibration reduction measures. The
practical case here considered has been analysed by first assessing the existing situation prior toconstruction (type of soil and traffic: results exposed in a companion paper). Here we focus on themitigation measures which have been tested and the expected corresponding vibration and ground-borne
noise levels inside the buildings. A 2.5D FEM/BEM commercial software (Mefissto), developed by CSTB,
has been employed in what is a very challenging numerical context: multi-layered ground, large
multi-levels buildings, large frequency range (10-200 Hz). In every situation the use of an original 2.75D
approach leads to the low frequency noise levels inside the building. As the trackwork cannot be modified
the solutions tested consist in inserting different types of barriers in the ground or in inserting spring-likematerials in the lower part of the structure. Results are compared to target values in terms of vibration andground-borne noise levels selected in order to limit dwellings occupants’ annoyance. Satisfactory results
can only be achieved with the use of the spring-like solution.
Keywords: Ground-Borne noise, train excitation, BEM/FEM

1. INTRODUCTION
In densely populated areas, the rarefication of land leads to the construction of buildings very close torailway tracks. Alternatively, the construction of new lines will impact existing buildings. In both cases,vibration and noise levels in offices, shopping malls or lodgings might be severely impacted by theproximity of passing trains and mitigation measures must be found. The situation here reported is that of an
existing embanked railway line 20 km East of Paris, where buildings are being built right above theembankment, very close to a station. Consequently, as the tracks cannot be modified the mitigation
measures must be taken on the receiver side. The approach here employed mixes measurements prior to theconstruction and numerical calculations for the various scenarios encompassed. The experimental phase of
the project is presented in a companion paper (1) and uses vibrations levels on the ground free surface totune the soil properties by correlating measurements and numerical estimations in order to estimate theforce spectra of passing trains both in the vertical and tangent directions to the rails, at different locations
corresponding to future buildings. In the present paper, we first describe the project and its numerical
implementation and solution. The computations are made with the 2.5D BEM/FEM software mefissto (2)which assumes a 2D description of the geometry while accounting for 3D aspects of both excitation andwave propagation. The mitigation measures tested are twofold: i) insertion of a vertical barrier in theground between tracks and foundations and ii) insertion of a resilient material (hereafter called “springs”)
between ground level (shopping mall) and first level (lodgings)- the parkings are below ground level (y=0),
We compute vibration and noise levels in the volumes (representative of livable spaces) closest to the tracks
for the different solutions tested. Finally, global velocity and pressure levels are given.

3403

2. THE PROBLEM
A global view of the initial project is showed in Figure 1. A 2D representation is displayed since theapproach employed is a 2.5D BEM/FEM model which assumes invariance of the geometry along the z axis
parallel to the tracks. Previous work (2) have showed the adequacy of this approach for the type ofbuildings here considered (i.e. walls and slabs). The ground is composed of 4 layers atop a semi-infinite
limestone sub-ground. The ground properties are listed in Table 1. The value of losses in the ground (8 %)was estimated in (1). The two tracks are modelled as point force in 2D and actual finite incoherent lines in
2.5D with 2 components Fy (vertical) and Fz (parallel to the tracks). The parking’s outer wall are 35-cm
thick by default.

Table 1 - Material properties (building and soil layers)

TypeThickness(m)ConcreteDensity(kg/m3)

E(MPa)

Poissondampingcs(m/s)

2300

30000

0.151%

2300

Embankments

Variable

1800

780

0.308%

408.2

Formation de Brie

Variable

1900

1668

0.458%

550.1

Clay & limestone

7

1900

580

0.458%

324.4

Clay marls and gypsum

19

2000

1015

0.45

8%

418.3

Limestone

infinite

2100

4350

0.458%

845.2

Figure 1 – 2D and extruded view. Two buildings close to a railway embankment.

3. DISCUSSION
Several aspects considering the numerical modelling are first addressed. In the course of this project,many questions were raised, and many parametric aspects were considered and analyzed. A few highlights
are now given. Computations have been done between the 10 and 200 Hz third octave bands.
Mutual influence of both buildings: we have run computations with both buildings modelledsimultaneously and then with only one or the other and found that no noticeable difference could be found,meaning that standing waves between both foundations could be neglected and that computations can bedone with one building at a time.
Embankment: we wanted to estimate the influence of the embankment on the transmitted vibrations inside
the buildings and we compared the velocity with and without embankment where two positions of the flat

3404

free surface are considered (low and high, see Figure 2). The velocity level on the ground floor isrepresented. The excitation is a 100 m incoherent line vertical force along z. Above 30 Hz, the case with theembankment leads to the lowest levels.

Figure 2. Influence of the soil profile between both buildings.
(*) High flat , (O) Embankment (□) Low flat
Number of underground levels: as the project evolved, the number of underground parking levels wasreduced from four to two with the hope that reducing the total height of exposed foundations would lead toa reduction of velocity levels. No significant difference was found. Most of the power is likely to be input
in the top underground levels. In the next paragraph the case with two subterranean levels is studied.
kz decomposition: for each frequency f the 2.5D computations relies on a set of computations carried fora set of kz wavenumbers. For each kz value, the problem solved corresponds to an infinite line excitation
along z which varies as a kz cosine. The Fourier-like integration (3) over kz of any 2D solution V(F,M,f,kz)-with a shift of Δ m along z- will give the 3D velocity for a point source at (xF,yF,zF) and receiver at(xM,yM,zM) separated by Δ=zM-zF

Figure 3 – 2D excitation with wavenumber kzஶܸሺ‫ݔ‬ǡ ‫ݕ‬ǡ ο‫ݖ‬ǡ ݂ሻ ൌ ‫ି׬‬ஶ ܸሺ‫ݔ‬ǡ ‫ݕ‬ǡ ݇௭ ǡ ݂ሻ݁ ି௝௞೥ ο௭ ݀݇௭(1)

A train of finite length Dz is modelled by a set of uncorrelated forces along z (incoherent integration ofresults). The integration over kz must be done carefully with a sufficient discretization in terms of ݀݇௭ andkz,max. Figure 3, shows typical kz responses for 2 cases: surface response without any building and groundfloor velocity for the full situation. The more complex the situation the more complex the kz response, andthe higher the frequency the higher kz,max must be. Automatic kz discretization schemes are employed. Thepicks correspond to the propagating waves either in the ground or/and in the building (building modes).

3405

Figure 4 – V(f,kz) as a function of kz for different values of f. Left/ Right: without/with buildings.
Protection with a barrier: positioning a barrier between and the tracks and the foundations was firsttested with a void (full decoupling). As this is not feasible in practice, point connections were added. As
could be expected, this results in a total loss of the efficiency of the barrier. A more sensible solution
consists in adding a layer of resilient material. The efficiency of the case with a void can be recovered. The‘barrier’ solution thereof refers to the layer+barrier disposition. Different depths of the barrier were tested,and it was found that it should go down below the bottom of the foundations. Deeper barriers gave little
extra reduction in vibration levels in the buildings. The influence of the lateral dimensions could not be
estimated with a 2.5D approach and 3D FEM computations with full FEM were carried for a simple
2-levels buildings with the conclusion that for a force centered on the length (Lz along z) of the building,the barrier needs not be longer than Lz. For non-centered forces the barrier should be longer by a few meters.
Figure 5 shows different barriers and a view of a 3D FEM meshing with a screen that exceeds thebuilding’s length by 4 m on each side.

Figure 5 – (a) Barriers of different depths (b) view of the 3D FEM calculation.
The 3D barrier (Figure 6) shows a reduction of varying amplitude (0 to 15 dB according to frequency).

Figure 6 – 3D barrier: velocity reduction.

3406

Increasing the thickness of the parking wall: since the vibration power mostly enters the buildings
through the parking outer wall we have increased the thickness from 35 cm to 50 cm. Figure 7 shows
the resultant modification of several floors’ average velocity levels. The building is excited by a 100 mlong incoherent line source (vertical excitation). We notice that the reduction (positive values) is not
systematic through the whole spectrum and varies with the building’s levels : at 100 Hz an increase isobserved. Increasing the buried parking outer walls does not seem to be an optimal solution.

Figure 7 - Effect of an increase of the thickness of the parking outer wall on floor vertical velocity(35 cm to 50 cm).

4. Application caseIn (1), excitation force spectra have been estimated for 3 positions along z corresponding to 3 projected
constructions sites. A 200 m-long train is modelled. As these locations are situated in a close proximity to arailway station, the trains are either accelerating (going east) or decelerating (going west). The buildings
north of the tracks have been studied for accelerating trains and the south buildings for decelerating trains(closest excitation). It was found that the tracks are excited both with vertical and tangential forces (seespectra in (1)). The tangent excitation may exceed the vertical component in the higher frequency range.
The buildings here considered only have two subterranean levels.
The acoustic response in volumes is obtained by means of the 2.75D approach, recently published (2).
In 2.5D, volumes are in in fact ducts of infinite length along z from which it possible to extract the velocity
field on grids having a finite length Lz. The velocities on the four finite walls thus defined are coupled bymeans of an integral representation with the 3D green functions of volumes of the same length Lz. Thesefunctions are evaluated with a modal approach for a reasonable cost since computations are done at low
frequencies (usually bellow 300 Hz). Alternatively, a SEA radiation approach can be employed for a
reduced precision (2,5). Figure 8a gives an overview of the central part of the problem in the case ofbarriers with viscoelastic patches. Figure 8b shows the position of viscoelastic materials (“springs”) (leftbuilding) with a cut-of frequency of 5 Hz. Figures 9 and 10 show the Velocity Levels and Sound PressureLevels spectra obtained in one case, at three levels. Note that the ground floor behavior around 50 Hz (seeFig.10) is different from results at other levels: this is related to the height of these volumes.
Global velocity and sound pressure levels have been computed for the 3 buildings (left buildings for the3 sections) with both the vertical and tangent excitations (y & z directions). In each graph, the target value
is displayed: 66 dB and 30 dB(A). Results are given for the reference, barrier and “spring” solution either
considering only the vertical forces (dashed lines) or both vertical and tangent forces (solid lines). The“spring” solution is successful for the velocity levels since above ground level all values obtained are
below the target of 67 dB. For sound pressure levels, the target of 30 dB(A) is more difficult to satisfy evenwith the “spring” solution. If only the vertical force (Fy) is considered the target is mostly satisfied but not
if we take tangential forces (Fz) into account. Therefore, the conclusion is very much related to the validityof the assessment (see (1) of these tangent forces and further research on this poorly documented aspect isneeded. One might probably consider that reality lies somewhere in between both cases (Fy versus Fy + Fz).
Note, also, that the difference between dB(C) and dB(A) always lies between 20 and 30 dB and is little
influenced by the insertion of a barrier or springs, which confirms that this problem is a low frequency
problem.

3407

Figure 8 – a) Buildings with barriers: close-up b) Viscoelastic layers on top of ground floor walls

Figure 9 – LV spectra for 3 situations – dashed lines with vertical force only.
South building, section 3. (*) Reference, (o) Barrier, (□) Spring.

Figure 10 – SPL spectra for 3 situations – dashed lines with vertical force only.
South building, section 3. (*) Reference, (o) Barrier, (□) Spring.

3408

Figure 12 – Global Velocity levels for the 3 sections and both sides (3 buildings)
dashed lines with vertical force only- Target value of 67 dB.
(*) Reference, (o) Barrier (□) Springs

Figure 13 – Global dB(A) levels for the 3 sections and both sides (3 buildings)
dashed lines with vertical force only-Target value of 30 dBA.
(*) Reference, (o) Barrier (□) Springs
3D representations: we plot the vertical velocity in the buildings, top surface, interlayers and a central
vertical plane at 100 Hz for a vertical unit force along y or z for 2 cases: reference (Figure 14), and “springsolution” (Figure 15). These snapshots visually demonstrate the efficiency of the “springs”.

5. CONCLUSIONSThe construction of buildings close to railway lines may lead to high vibration and acoustic levels if nomitigation measure is taken. A real situation is here reported where a numerical analysis has been carried
right from the design stage of the new project, east of Paris, close to a station where trains are either
accelerating or decelerating. First, the existing problem (soil data and track excitation) has been assessed in(1). Here, mitigation measures have been considered with the main conclusion that a decoupling of upper
floors is necessary by means of the insertion of resilient materials. Even then, the target of 30 dB(A) isexceeded in certain cases by a few dB’s if one considers a full model where not only the vertical but also
the tangential forces applied to the soil are considered. Little literature can be found for this problem andthe authors feel that further work is needed; the assessment of both force components was done in a simple
manner which needs be improved. Finally, one might note that another component must be added if thetracks are not straight.

3409

Figure 14 - 100 Hz, reference case Left/Right: Fy/Fz excitation (vert/tangent)

Figure 15- 100 Hz, spring case Left/Right: Fy/Fz excitation (vert/tangent)

ACKNOWLEDGEMENTS
The authors would like to thank LinkCity and Eparmarne, as well as the Caisse des Dépôts etConsignations (Deposit and Consignement Fund) for supporting this work through the “Ecocité 2 –Ville de Demain” program. This national French program involves publ ic and private actors in aterritory to develop disruptive projects to accelerate the energy and ecological transition of cities.

REFERENCES
1. Guigou-Carter C, Coquel G, Jean P, Jolibois A Reducing ground borne noise due to railways. Part I:
assessing the problem. ICA 2019 Aachen
2. Jean P. A 2.75D model for the prediction of noise inside buildings due to train traffic. Acta Acustica
2018; 104:1009-1018
3. Jean P, Guigou-Carter C, Villot M. A 2.5D BEM model for ground structure interaction. BuildingAcoustics 2004;11(3):157-163.
4. Villot M, Jean, P, Grau L, Bailhache S. Predicting railway-induced ground-borne noise from thevibration of radiating elements using power-based building theory Intern. J. of Rail Transp. 20173410