ABSTRACT: Vibrations induced by the circulation of trains in urban surface and underground rail transportation systems may give rise to annoyance to people living and working inside existing buildings and to structural damage. The aim of this work is to illustrate a methodology for the prediction of the vibration levels produced by the railway traffic based on experimental measurements and FE modeling capable of taking into account complex soil conditions and time-varying excitation source. The proposed approach has been applied for the evaluation of the vibrations induced by a new railway line in the city of Palermo, in southern Italy and for the design of suitable countermeasures for the reduction of vibration effects to tolerable levels.

KEY WORDS: Railway; Vibrations; Mitigation; Archeological site.

1 INTRODUCTION

The circulation of trains in urban underground railway lines produces vibrations which, propagating through the surrounding soil mass as deformation waves, reach the ground surface and may give rise to annoyance to people living and working inside existing buildings and, possibly, to significant structural damage.

The difficulties associated to the quantitative evaluation of the effects induced by the vibrations caused by underground railway traffic are mainly due to the multidisciplinary character of the problem, which involves different skills from mechanical, geotechnical and structural engineering.

Several empirical and closed-form solutions have been developed in recent years [1, 2].

Nevertheless, some hypotheses could not always be met in general situations, especially for the geometrical configuration of the layered soil. In this cases finite elements (FE) and boundary elements (BE) formulations, such as those proposed by Gupta et al. [3] can be more efficiently used.

In this work a methodology, based on a FE model tuned by means of experimental measures, capable of taking into account the effective situation of soil, load and structural configuration is illustrated. The proposed approach has been adopted for the comparisons of the vibration levels of two different design solutions for the construction of a new railway line in the city of Palermo, in southern Italy, in the proximity of existing underground caverns hosting the Catacombs of Porta d’Ossuna, an archeological site of relevant interest. The analysis also allowed the design of suitable countermeasures for the reduction of vibration effects to tolerable levels.

2 OVERVIEW OF THE METHODOLOGY

The methodology is made up of two parts, an experimental one and a numerical one. The experimental part consists of recording on site and analyzing acceleration measurements to form a set of data for the calibration of a FE model but also to

determine the discomfort that is currently being produced inside the Catacombs by the vibrations caused by underground existing railway traffic. In the second part of the methodology the tuned FE model has been used to predict and compare the vibrations that could arise from the traffic in the new railway line.

The approach adopted in this work is thus composed of the following main phases: design and implementation of an experimental campaign

for the measurement of ambient vibrations in the area interested by the new underground line;

setup and calibration of a 2D FE model for the analysis of the wave propagation processes induced by the train circulation in the surrounding soil mass based on the result obtained in the previous step;

assessment of the expected annoyance levels and structural damage associated with the vibration levels predicted for the new underground line;

judgment on the need of possible countermeasures for the reduction of the vibration intensity to tolerable levels and evaluation of their effectiveness.

A deeper description of this approach is reported in the following, while its application to a real case study is presented.

3 APPLICATION TO THE CASE STUDY

The proposed methodology has been applied to a real case study. The occasion has been found in the works for the doubling of the railway line in Palermo, Italy. During the execution of the works the possibility of change the original path of the new line to avoid major discomfort to the city inhabitants and possible damage to the existing buildings has been investigated. Nevertheless the new path will pass close to an existing archeological site of relevant interest - the Catacombs of Porta d’Ossuna. The investigation was aimed at comparing the vibration levels inside the archeological site achievable with the two different design proposals and to

Vibrations induced by the new underground railway line in Palermo, Italy Experimental measurements and FE modeling

M. Breccolotti, A.L Materazzi, D. Salciarini, C. Tamagnini, F. Ubertini

Department of Civil and Environmental Engineering, University of Perugia, via G. Duranti, 93, 06125 Perugia, Italy email: breccolotti@strutture.unipg.it, materazzi@unipg.it, diana@unipg.it, tamag@unipg.it, filippo.ubertini@strutture.unipg.it

individuate, if necessary, possible countermeasures to reduce the vibration levels to acceptable values.

4 EXPERIMENTAL MEASUREMENTS

4.1 Description of the site

The site under investigation is represented by the ancient Catacombs of Porta d’Ossuna in the heart of Palermo, Italy (see Figure 1). The Catacombs, built between the 4th and the 5th century A.D., are composed by a complex system of burrows and tunnels that are located approximately 6 m below the street plane (see Figure 2).

The site under investigation is currently interested by the vibrations induced by the underground railway traffic along the line from the station “Palermo Centrale” to Brancaccio - Carini. This line runs inside a tunnel which is located at a depth of about 5 m below the street of Via Imera at a distance of approximately 100 m from the Catacombs.

The construction of a second tunnel closer to the Catacombs, which will host the doubling of the railway line, is currently under development. According to the originally approved design, the second tunnel would have passed at a distance of approximately 40 m from the Catacombs.

During the drafting of the final design an alternative path for the new line has been proposed to avoid the excavation of the tunnel underneath many existing buildings and the passage of this latter close to a hospital clinic with surgery rooms. In this alternative the future tunnel will pass below the Catacombs themselves at a depth of approximately 7 m thus moving the problems due to the vibration from the existing buildings to the archeological site. Nevertheless this alternative has been considered feasible and preferred to the original one since it concentrates the shortcomings due to the vibration induced by the railways traffic in a single small site.

The layouts of the existing railway line and of the doubling lines, in both original and variant projects, are shown in Figure 1 (plan view) and in Figure 2 (cross section).

4.2 Field measurements

The vibration monitoring system adopted for this study consisted of nine PCB 393C seismic accelerometers. These sensors were connected to a ROGADAQ-16 analog / digital converter, also serving as power supply, with a resolution of 16 bits. The converter was driven by a dedicated electronic computer, which also serves as memory storage.

The accelerometers have been arranged in tri-axial configurations for each monitored point and have been connected, using magnets, to heavy steel bases. A single tri-axial base thus allowed to measure the vertical acceleration component and two mutually orthogonal horizontal components.

The field measurements have been continuously recorded for the duration of about 1 hour which has been chosen in order to record the passage of several trains. The sampling frequency for all acquisition channels has been set to 1250 Hz, which is sufficiently large to account for the Nyquist sampling theorem and for the maximum frequency of interest for the evaluation of the discomfort to people (80 Hz).

Figure 1. General plan of the area with existing line, originally designed new line and proposed new line.

Figure 2. Vertical section of the area with existing line, originally designed new line and proposed new line.

Figure 3. Sensors configuration in the Via Imera site.

Figure 4. Sensors configuration in the Catacomb site.

4.3 Site of Via Imera

Two measurement sites have been considered in this study. The first measurement site, here called “Via Imera”, is

located along a nameless street which begins from the catacombs and orthogonally crosses the adjacent Via Imera. This latter is a major street which runs parallel and above the existing railway line. The measurement site of Via Imera has been selected as it permits to measure the surface vibrations currently produced by underground railway traffic and to evaluate how these vibrations propagate along the line of minimal distance with the Catacombs.

Three tri-axial accelerometric bases have been installed along a line orthogonal to Via Imera, as shown in the outline of Figure 3. The nearest point to Via Imera has been denoted as 1, whilst the remaining points have been denoted as 2 (intermediate point) and 3 (farthermost point from via Imera). The three channels associated to the three accelerometers placed in point 1 have been numbered in the following order: 0 (vertical component, z), 1 (horizontal component x, directed as the measurement line), 2 (horizontal component y, orthogonal to the measurement line). In the same order channels 3, 4, 5 (point 2) and 6, 7, 8 (point 3), have also been numbered.

The data recorded from the Imera site were essentially used, together with those recorded inside the Catacombs, to verify the FE modelling shown in the next paragraph.

4.4 Site of Porta d’Ossuna

The second site is located inside the Catacombs of Porta d’Ossuna themselves (Figure 5). In this location records of the vibrations currently produced inside the Catacombs by the railway traffic in the existing tunnel have been taken.

Three tri-axial accelerometric bases have been installed in three points dislocated along a line inside the Catacombs, which is approximately orthogonal to the future railway line, as shown in the outline of Figure 4. The closest point to the existing railway line has been indicated by 1, while the remaining two points have been indicated by 2 (intermediate point) and 3 (farthermost point from the railway line). Point number 2, in particular, was referred as the one in which the most significant vibrations are currently felt. Such a point is also very close to the axis of the future railway line, as evidenced in Figure 4. The three channels associated to the three accelerometers located at point 1 have been numbered as already done for the experimental measurements taken at the site of Via Imera: 0 (vertical component, z), 1 (horizontal component x, directed as the measurement line), 2 (horizontal component y, orthogonal to the measurement line). In the same order channels 3, 4, 5 (point 2) and 6, 7, 8 (point 3), have also been numbered.

5 FE MODELLING

5.1 Characteristics of the FE models

A series of FE analyses, performed with the FE code Plaxis v.8.2, has been carried out to assess the possible effects of vibrations associated with train circulation in the planned underground railway lines. To keep the model as simple as possible, also considering the complexity of the stratigraphy in the area under examination, the simulations have been performed assuming plane strain conditions.

Figure 5. Picture of the “Catacomebe di Porta d’Ossuna”.

Figure 6. Assumed soil profile in the section considered.

a)

b)

c)

Figure 7. FE models of the soil condition: a) FE-n1 actual condition with a single tunnel; b) FE-n2 model of the project

hypothesis n. 1, with a planned circular tunnel, on the left side of the Catacombs area; c) FE-n3 model of the project

hypothesis n. 2, with a planned polycentric tunnel, located under the Catacombs area.

The assumed soil profile is shown in Figure 6. The different soil layers, identified from top to bottom with the labels T1-T6, have been modeled as isotropic, linear elastic materials. This is considered to be appropriate due to the very low strain levels induced in the soil by the train circulation. The values of the material constants assigned to each soil layer are summarized in Table 1.

In the dynamic stages of the simulations, the response of fine-grained soil T6 has been analyzed under the hypothesis of undrained conditions, assuming an appropriate value of the

bulk modulus of the pore water ( /wK n = 2.5e6 kPa).

In the numerical simulations, three different FE discretizations have been used, as shown in Figure 7. The bottom layer (T6) has been extended up to an average depth of about 50 m from ground level, which has been considered a reasonable estimate of the extent of the significant soil volume in the vertical direction.

Given the small size of the cavities of the catacombs, and considering that their axes are parallel to the plane of the section, they weren’t included directly in any of the three models.

The first FE model (FE-n1, Figure 7a) refers to the current situation, in which only a single tunnel is present. The second model refers to the design hypothesis n. 1 (original design), with a shallow circular tunnel to be driven on the left side of the catacombs area (FE-n2, Figure 7b). The third model refers to the design hypothesis n. 2 (proposed modified design), with a deeper polycentric gallery to be driven under the catacombs area (FE-n3, Figure 7c).

For all the spatial discretizations, 6-nodes plane strain elements with quadratic interpolation for displacements have been used. To model the tunnel lining, 3-nodes beam elements with quadratic interpolation for displacements have been adopted. The physical and mechanical properties of the lining elements are shown in Table 2.

To avoid spurious reflections of the elastic waves produced by the dynamic loads simulating the circulation of the trains inside the tunnels, special adsorbing elements [4] have been applied at the lateral boundaries of the three FE models.

The initial pore pressure regime has been derived from available piezometric measurements. In the FE-n3 model, the boundary of the deep polycentric tunnel has been considered as a drainage boundary, and the initial pore pressure distribution has been derived from the solution of the corresponding seepage problem. The geostatic stress state has been determined by solving equilibrium equations under drained conditions, starting from an initial guess obtained by means of the K0 coefficients given in Table 1, derived from the Jaky’s empirical relation.

The numerical simulations have been conducted in the following four stages:

1. evaluation of the initial pore pressure regime; 2. evaluation the geostatic stress state; 3. excavation of the tunnels in drained conditions, and

activation of the lining elements; 4. simulation of train circulation within one of the tunnels,

assuming undrained conditions in the fine-grained layer T6.

Table 1. Physical and mechanical characteristics of the soil types.

Soil type (kN/m3)

E’ (kPa)

’ (-)

K0 (-)

R (-)

T1 – cover 18 1.50e4 0.3 0.69 11.42 T2 – limestone 1 24 4.75e5 0.2 0.38 5.71 T3 – limestone 2 19 1.05e5 0.2 0.47 5.71 T4 – limestone 3 24 4.75e5 0.2 0.38 5.71 T5 – limestone 4 19 1.05e5 0.2 0.47 5.71

T6 – clay 20 6.00e4 0.2 0.61 11.42

Table 2. Physical and mechanical characteristics of the tunnel lining.

FE modelA

(m2/m) J

(m4/m) EA

(kN/m) EJ

(kNm2/m)w

(kN/m/m)FE-n1 0.80 4.27e-2 2.40e7 1.28e6 20.0 FE-n2 0.41 5.74e-3 1.23e7 1.72e5 10.0 FE-n3 0.60 1.80e-2 1.80e7 5.40e5 15.0

For the integration of the semi-discrete equations of motion in the dynamic phase (stage 4) the Newmark algorithm has been used, with α = 0.3025 and β = 0.60. To take into account the dissipative characteristics of the materials, a Rayleigh damping matrix has been introduced, proportional to the mass matrix (βR = 0). The αR values used for each material are shown in Table 1. With such values, the damping coefficient is less than 2% for harmonics with frequency higher than 20 Hz for layers T2-T5, and less than 5% for harmonics with frequency higher than 20 Hz for layers T1 and T6.

5.2 Two-dimensional simulation of train circulation

To simulate the effects of the trains travelling within one of the tunnels, the procedure developed by Risitano et al. [5], based on the approach originally proposed by Balli et al. [6] has been adopted.

According to this procedure, the load kP acting on the

generic k -axis of the train, which moves along the track with

the train velocity TV , transmits to each track a load kF equal

to:

1

( ) ( )2 2

kk

PF t ty

l= (1)

where:

1

44( )bEJ

KBl

ì üï ïï ï= í ýï ïï ïî þ (2)

is the characteristic length of the track, considered as a beam

on a Winkler foundation with stiffness K ; ( )bEJ is the

bending stiffness of the track; B is the width of the train sleepers; and the function ( )ty is given by:

{ }| | | |

( ) exp cos sink k kk

r r rr ty

l l l

æ ö é æ ö æ öù÷ ÷ ÷ç ç çê ú÷ ÷ ÷= - +ç ç ç÷ ÷ ÷ç ç çê ú÷ ÷ ÷ç ç çè ø è ø è øë û (3)

0( ) ( )k k Tr t d L V t= - + + (4)

being kL is the distance of a generic k -axis from the first

axis of the convoy and 0d is the distance of the first axis from

the considered section at t = 0. Based on the available

information, in all the simulations, we assumed ( )bEJ =

12.76e3 kNm2; K = 250.0e3 kN/m3; B = 2.5 m; 0d = 30.0 m.

To take account of the vibrations produced by spurious phenomena such as: (i) surface irregularities of the wheels; (ii) surface irregularities of the track; (iii) winding, and (iv) environmental noise, a white noise modulated in time according to a Gaussian curve, centered at the position of the

generic k -axis, has been added to the kF load for each axis.

This signal has been obtained by the superimposition of harmonics with frequencies distributed between 2 and 100 Hz in regular steps of 0.01 Hz and random phases uniformly distributed between 0 and 2π.

In particular, for the generic k -axis, we assumed:

1

1( ) ( )sin(2 )

2 2

mk

k k j jj

PF t G r fp j

l =

D = +å (5)

2

2( ) exp

2k

k

rG r

ì üï ïï ï= -í ýï ïï ïî þ (6)

0( ) ( )k k Tr t d L V t= - + + (7)

where is a characteristic length that defines the extent of the influence zone for spurious vibrations with respect to the current position of the axis, set equal to 15.0 m, and the

quantities jj are randomly generated phase angles.

Superimposing all the contributions arising from eqs. (1)-(7) for all the convoy axes, the load-time history representing the applied load on each track is obtained:

{ }tot1

( ) ( ) ( )n

k kk

F t F t F t=

= + D =å

{ }1 1

1( ) ( ) sin(2 )

2 2

n mk

k j jk j

Pt G r t fy p j

l = =

ì üï ïï ï= + +í ýï ïï ïî þå å (8)

Figure 8. Minuetto - Alstom’s Coradia convoy.

Figure 9. Variation of the force tot ( )F t versus time t .

Table 3. Data on axis loads and on their locations Lk.

Pk (kN) 80 80 80 80 80 80 80 80 Lk (m) 0.0 2.4 14.5 17.2 28.15 30.85 42.8 45.2

Table 4. Limiting values of vibration levels (from UNI 9614).

Z axis (dB) Other axis (dB) Critical areas 74 71

Houses (night) 77 74 Houses (day) 80 77

Offices 86 83 Facilities 92 89

In the FE analyses, the load expressed by eq. (8) has been

applied, in the vertical downward direction, at the nodes located on the tracks. In all the simulations, a specific train composition (the so-called “Minuetto” train produced by

Alstom), running at a speed TV = 50 km/h, has been

considered. This unusual low speed of the convoy is required by the local railways authorities that imposed a speed limit for the train circulation to take into account the presence of close stations and the tortuous path. While the low speed of the convoy reduces the energy content at higher frequency, it produces sensible discomfort in the lower frequency range where the human body is more sensible.

Table 5. Weighted-in-frequency vibration levels after the calibration.

Lwz (dB) Lwxy (dB) Recorded 71.02 59.03 Predicted 73.27 63.50

Data on the axis loads and on their locations kL for the

Minuetto train are summarized in Table 3. A sample of the

time-history of the track force tot ( )F t obtained from these

data is shown in Figure 9.

6 CALIBRATION OF THE FE MODEL

The calibration of the FE model has been carried out taking as reference the values of the weighted-in-frequency vibration

levels ,expwzL and ,expwxyL recorded in the point 2 inside the

Catacombs in the horizontal direction (Ch. 4). The mechanical properties E’ and the damping parameters αR of each soil layer considered in the numerical model have been adjusted to

make estimates of the levels wzL and wxyL supplied by the FE

analysis as close as possible to the measured values. The comparison between the recorded and the predicted vibration levels after the calibration of the FE model is reported in the Table 5. Predicted values higher than those recorded have been accepted to take into account that the actual mass of the real convoy is lower than that of the fully loaded Minuetto train considered in the analysis.

7 ASSESSMENT OF ANNOYANCE

7.1 Reference standards

Vibration levels have been evaluated applying the Italian Code UNI 9614 [7].

Table 6. Comparison between the acceleration levels obtained from the numerical simulations FE-n1 and FE-n3.

Lw (dB) Lwz (dB)

FE-n3 FE-n1 FE-n3 FE-n1

Ch 00 104.7 82.2 22.5 92.4 75.5 17.0

Ch 01 102.1 83.3 18.8 88.0 73.4 14.6

Ch 03 105.9 83.1 22.8 92.7 77.1 15.6

Ch 04 102.5 82.2 20.3 88.7 73.3 15.5

Ch 06 106.3 85.1 21.2 91.3 75.1 16.2

Ch 07 105.4 84.9 20.5 89.2 75.1 14.1

Lwxy (dB) Lwnn (dB)

FE-n3 FE-n1 FE-n3 FE-n1

Ch 00 82.4 67.9 14.5 89.8 73.4 16.3

Ch 01 76.0 63.3 12.7 85.0 70.8 14.2

Ch 03 82.6 68.8 13.9 90.0 74.9 15.1

Ch 04 76.7 63.5 13.2 85.7 70.7 15.0

Ch 06 81.2 65.8 15.5 88.6 72.6 16.0

Ch 07 77.2 65.5 11.7 86.2 72.6 13.6

This standard provides indication for the measurements and annoyance evaluation of vibration in buildings. The choice of using as reference criteria the annoyance on the inhabitants rather than the damage to the buildings, as done for instance by UNI 9916 [8], is due to the fact that, generally, the requirements for the fulfillment of the criteria on inhabitants’ discomfort are more severe than those related to the damage of buildings. Following the UNI 9614 the measured signals as well as those generated by means of the FE model were submitted to frequency analysis carried out by digital filtering with a bank of third-octave band filters. The frequency range considered, as usually done in this analysis, was between 1 and 80 Hz.

The RMS acceleration within each frequency band was computed using a time integration length of 1 second zero-padding the acceleration signal to obtain the required resolution [9], [10].

The intensity of the acceleration within each band is expressed by the following level L , expressed in decibel:

( )2010 logL a a= (9)

being 0a = 10-6 m/s2.

The sensitivity of human beings to ambient vibration has been properly taken into account in each frequency band. The attenuations suggested by the UNI 9614 have been applied to

each calculated acceleration level iL . The overall level of the

frequency-weighted acceleration ( wL ) was evaluated as:

,0.110 log 10 w iLw

i

L = å (10)

where ,w iL are the equivalent levels of the 1/3 octave bands

after having been weighted in frequency.

Table 7. Comparison between the acceleration levels obtained from the numerical simulations FE-n2 and FE-n3.

Lw (dB) Lwz (dB)

FE-n3 FE-n2 FE-n3 FE-n2

Ch 00 104.7 94.3 10.4 92.4 82.4 10.0

Ch 01 102.1 96.1 6.0 88.0 83.5 4.5

Ch 03 105.9 100.3 5.7 92.7 88.0 4.7

Ch 04 102.5 97.9 4.7 88.7 84.1 4.6

Ch 06 106.3 99.1 7.2 91.3 90.7 0.6

Ch 07 105.4 99.0 6.3 89.2 86.4 2.8

Lwxy (dB) Lwnn (dB)

FE-n3 FE-n2 FE-n3 FE-n2

Ch 00 82.4 72.2 10.1 89.8 79.7 10.0

Ch 01 76.0 71.8 4.2 85.0 80.6 4.4

Ch 03 82.6 78.3 4.4 90.0 85.5 4.6

Ch 04 76.7 72.3 4.4 85.7 81.2 4.6

Ch 06 81.2 82.1 -0.8 88.6 88.5 0.2

Ch 07 77.2 75.1 2.1 86.2 83.5 2.7

a)

b)

c)

Figure 10. Acceleration time history recorded inside the Catacombs, channel 4, during the passage of the Minuetto

convoy (a), 1/3 octave band filters frequency analysis of the recorded signal before (b) and after (c) the application of the

FST attenuation.

Table 8. Comparison of the vibration level in the new design proposal with and without FST.

Lw (dB) Lwz (dB)

without with without with

Ch 00 66.1 49.9 16.3 48.3 49.8 -1.5

Ch 01 81.4 51.4 30.0 63.4 51.0 12.4

Ch 03 68.3 46.6 21.8 49.1 46.5 2.7

Ch 04 89.3 49.3 40.0 71.0 43.5 27.6

Ch 06 60.5 47.5 13.0 43.7 47.4 -3.7

Ch 07 62.4 44.9 17.5 45.0 44.8 0.2

Lwxy (dB) Lwnn (dB)

without with without with

Ch 00

Ch 01

Ch 03

Ch 04

Ch 06

Ch 07

Since both vertical and horizontal vibrations can affect the

investigated site and since is not known the posture of the human body, reference to the filtering values for unknown direction has been made.

The limiting values of the vibration levels suggested by the UNI 9614 (see Table 4) has been taken as reference.

7.2 Results of the FE simulations

The results of the FE simulations have been analyzed and compared in terms of total levels of frequency-weighted acceleration for the three different conditions considered, namely FE-n1, FE-n2, and FE-n3. All the acceleration data are relative to a point inside the Catacombs at the floor level placed on the vertical axis of the tunnel of the design hypothesis n. 2.

Table 6 shows the comparison of the acceleration levels predicted with the FE-n3 model (new polycentric tunnel) and with the FE-n1 model (existing tunnel). Table 7 shows the comparison of the acceleration levels predicted with the FE-n3 model (new polycentric tunnel) and with the FE-n2 model (new circular tunnel).

From the results obtained, it can be observed that:

1. the comparison between the current situation (FE-n1) and the design hypothesis n. 2 (FE-n3) shows that the passage of a train in the new polycentric tunnel would produce an increase in the frequency-weighted acceleration level within the Catacombs of 17.0 dB;

2. the comparison between the design hypothesis n.1 (FE-n2) and the design hypothesis n. 2 (FE-n3) indicates that the passage of a train in the polycentric tunnel located under the Catacombs would produce an increase in the frequency-weighted acceleration level within the Catacombs of 10.1 dB.

3. the aforementioned results indicate that, as expected, the design hypothesis n. 2 is worse than the design hypothesis n. 1 in terms of vibration impact on ground surface. Thus

Time (s)

1/3 octave band central frequency (Hz) (s)

1/3 octave band central frequency (Hz) (s)

Acc

eler

atio

n (m

/s2 )

Un-

wei

ghte

d ac

cele

rati

on le

vels

(dB

), r

ef. 1

mic

ro m

/s2

Un-

wei

ghte

d ac

cele

rati

on le

vels

(dB

), r

ef. 1

mic

ro m

/s2

some additional countermeasures are required to insulate the tracks from the tunnel lining, in order to reduce the magnitude of the vibrations transmitted to the soil.

8 CHARACTERISTICS OF THE MITIGATION SYSTEM

Several technical alternatives are available to reduce the annoyance and damage caused by railways vibration. There exist technical solutions that mitigate the vibrations level at the point where it is generated, such as rail pads or base plate pads made of resilient materials [11]. More efficient solutions can be achieved through the use of ballast mats [12] placed between the base concrete slab and the ballast. For critical areas more sophisticated techniques, based on the uncoupling of the motion of the track slab from the underneath soil, are available. These techniques foresee the use of floating slab tracks (FST) [13] that can be realized by means of steel springs or resilient elements. Other strategies can be followed to modify the propagation of the mechanical waves in the soil, such as open or filled trenches [14] and soil replacement [15].

For this specific case the use of floating slab tracks has been considered as the only feasible way to properly reduce the level of the vibration inside the Catacombs produced by the railway traffic in the new tunnel.

A FST with natural frequency 0f equal to 6 Hz and relative

damping x of 0.02 has been assumed in the following. The

low value of the frequency has been obtained increasing the mass of the concrete slab and inserting a ballast layer above the slab. The transmissibility of the FST can be expressed as [16]:

( )

( )( ) ( )

2

0

22 2

0 0

1 2( )

1 2

f fT f

f f f f

x

x

+=

- +

(11)

The attenuations of the vibration levels achievable with the FST for each central frequency of the filters are evident from the comparison between Figure 10(c) and Figure 10(b).

The original design already foresaw a mitigation system similar to a floating slab track called “Sistema massivo”, produced by Coopsette, composed by concrete slabs and continuous strips made of resilient elements placed below the concrete slab. The dynamical behavior of this system is characterized by an eigenfrequency in the range 18-20 Hz. This figure has been considered inadequate to reduce in a significant way the low frequency vibrations produced by the passage of the Minuetto convoy at the velocity of 50 km/h.

9 CONCLUSION

In the present paper a methodology based on experimental measurements and FE modeling to foreseen the vibration levels caused by railway tracks has been proposed. The combination of these two aspects, along with a calibration procedure of the FE model, allows to take into account complex underground stratigraphies and short-duration vibration effects.

The proposed methodology has been applied to the case study of the Catacombs of Porta d’Ossuna, in Palermo (Italy), where a new underground line of the railways network is

under construction. In the study two design solutions, which differ in terms of path and tunnel lining, have been compared.

Finally, a proposal for a mitigation system has been formulated in order to suitably reduce the vibration levels inside the Catacombs.

ACKNOWLEDGMENTS

The Authors gratefully acknowledge the support of the consulting firm SINTAGMA Srl of Perugia, Italy, and of the General contractor NdP “Nodo di Palermo” ScpA.

REFERENCES [1] C. With, M. Bahrekazemib, A. Bodare, Validation of an empirical

model for prediction of train-induced ground vibrations, Soil Dynamics and Earthquake Engineering 26 (2006): 983-990.

[2] Auersch L., Ground vibration due to railway traffic – the calculation of the effects of moving static loads and their experimental verification. Journal of Sound and Vibration 293 (2006): 599-610.

[3] S. Gupta, H. Van den Berghe, G. Lombaert, G. Degrande, Numerical modeling of vibrations from a Thalys high speed train in the Groene Hart tunnel, Soil Dynamics and Earthquake Engineering 30 (2010): 82-97.

[4] J. Lysmer, R.L Kuhlemeyer, Finite dynamic model for infinite media, Journal of the Engineering Mechanics Division, ASCE, 95 (1969): 859-877.

[5] G. Risitano, 2008. Metodo per la mitigazione degli effetti delle vibrazioni indotte dal traffico Ferroviario tramite barriere assorbenti, PhD Thesis, University of Perugia (2008).

[6] R. Balli, A. Garinei, E. Pucci. Modello per lo studio delle vibrazioni del terreno indotte da treni ad alta velocità, Proceedings Workshop Problemi di vibrazioni nelle strutture civili e nelle costruzioni meccaniche, Perugia, Giugno 2004, pp. 61-71. ISBN 8860740215.

[7] Ente Nazionale Italiano di Unificazione, UNI 9614 - Vibration measurements in buildings and annoyance evaluation (in Italian) (1990).

[8] Ente Nazionale Italiano di Unificazione, UNI 9916 - Criteria for measuring and assessing the effects of vibration on buildings (in italian) (2004).

[9] A.L. Materazzi and M. Breccolotti, Ambient vibration effects on buildings, Proceedings EURODYN 2002, Munich, Germany, ISBN 905809510X, 2002.

[10] M. Breccolotti and A.L. Materazzi, Ambient vibration analysis and mitigation in the site of Villa Ruffo in Rome, Proceedings EURODYN 2005, Millpress, Rotterdam, Holland, ISBN 9059660331, 2005.

[11] G. Lombaert and G. Degrande, The isolation of railway induced vibrations by means of resilient track elements, Proceedings EURODYN 2005, Millpress, Rotterdam, The Netherlands, ISBN 9059660331, 2005.

[12] R. Wettschureck, U.J. Kurze, Einfügungsdämmaß von Unterschottermatten, Acustica 58 (1985): 177-182.

[13] S. Gupta, and G. Degrande, Modelling of continuous and discontinuous floating slab tracks in a tunnel using a periodic approach, Journal of Sound and Vibration 329 (2010): 1101-1125.

[14] M. Adam, O. von Estorff, Reduction of train-induced building vibrations by using open and filled trenches, Computers and Structures 83 (2005): 11–24.

[15] F. Kirzhner, G. Rosenhouse, Y. Zimmels, Attenuation of noise and vibration caused by underground trains using soil replacement, Tunnelling and Underground Space Technology 21 (2006): 561–567.

[16] Den Hartog J.P., 1985. Mechanical Vibrations, Dover Publications.