Vibrations,induced,by,tunnel,boring,machine,in,urban,areas:,In,situ,measurements,and,methodology,of,analysis

Antoine Rllu,Nicols Berthoz,Simon Chrlemgne,Denis Brnque

a University of Lyon,ENTPE,LTDS -UMR CNRS 5513,CeLyA,Vaulx-en-Velin,France

b French Centre for Tunnel Studies (CETU),Bron,France

Keywords: Ground-borne vibrations Tunnel boring machine (TBM)In situ measurement Dynamic characterization Vibration levels Site spectrum

ABSTRACT Excavation with tunnel boring machine(TBM)can generate vibrations,causing damages to neighbouring buildings and disturbing the residents or the equipment.This problem is particularly challenging in urban areas,where TBMs are increasingly large in diameter and shallow in depth.In response to this problem,four experimental campaigns were carried out in different geotechnical contexts in France.The vibration measurements were acquired on the surface and inside the TBMs.These measurements are also complemented by few data in the literature.An original methodology of signal processing is proposed to characterize the amplitude of the particle velocities,as well as the frequency content of the signals to highlight the most energetic bands.The levels of vibrations are also compared with the thresholds existing in various European regulations concerning the impact on neighbouring structures and the disturbance to local residents.

Vibrations generated during underground excavations have a significant impact on geological structures,equipment and people.This problem is particularly widespread in urban areas,which is a major concern for all parties involved in tunnel construction,for example the owners,designers and contractors.

The prediction of vibrations induced by tunnel boring machine(TBM) in urban areas,whether they are earth pressure balanced shield (EPBS),slurry shield (SS) or,more rarely,open or hard rock TBM,requires the use of analytical or numerical models.The development of this type of model has two issues:characterization of the vibratory source constituted by TBM and characterization of three-dimensional(3D)propagation of the(visco-)elastic waves in the ground.The calibration of these models requires robust experimental data,both close to the vibration source and at the surface,in different geotechnical contexts(inducing different types of machines).

Surface measurements of the vibrations emitted during TBM excavation have already been carried out by some authors:Flanagan (1993) for the Buffalo metro (USA),Hiller and Crabb(2000) for the London JLE metro (UK),Ferrari et al.(2011) for the Lyon metro (France),Lunardi et al.(2015) for the Breschia metro(Italy),Bigot and Farotto(2016) for the Rennes metro(France) and Grund et al.(2016) for the Karlsruhe metro (Germany).To our knowledge,an exhaustive synthesis of all the particle velocity measurements at the surface from the literature has not been conducted to date.

There are few descriptions of the wave spectra measured on the surface.In predominantly rocky terrain,such as shale (Bigot and Farotto,2016) or limestone (Flanagan,1993),the authors suggested the vibration frequency is in the range 30-100 Hz.In sands and gravels,Grund et al.(2016) showed signals mainly at a low frequency range of 1-30 Hz.

Fig.1.The measurement system in Sorgues micro-tunnel: (a) Plan section and (b) Partial longitudinal section.

The information publicly available close to the vibratory source constituted by TBM is even more incomplete in the literature.No measurements were indeed made in the aforementioned projects.Mooney et al.(2014) presented an experiment on an EPBS (i)characterizing experimentally the transfer function between the cutting wheel and the bulkhead under impulsive loads,and (ii)evaluating the influence of geology on the spectrum of accelerometers located on the rigid bulkhead behind the cutting wheel.In that case,the energy of the signals was mainly located in the frequency range of 300-500 Hz,corresponding to the dominant range of the transfer function bulkhead/cutting wheel.It suggests that the vibrations inside the TBM are induced by free vibration response during excavation.However,a strong influence of the rotation speed of cutting wheel on the dominant frequencies (in high frequency range) induced a forced vibration response.The rotation frequency of the cutting wheel was in the range of 0.02-0.04 Hz,only the harmonics greater than five orders of magnitude of this frequency range (300-500 Hz) were measured.Several dynamic analyses (with testbed experimental observations at site scale) of the functioning of hard rock TBMs (without confinement) were performed by Zhang et al.(2010) and Huo et al.(2021).The main aim of their works is to understand the impact of the driving parameters on the dynamic function,in order to reduce failure of the mechanical parts and engines,without decreasing the excavation performance.

To provide some insight into tunneling-induced vibrations and their impacts on urban areas,measurements with 3D velocimeters were performed in four French tunnels or micro-tunnel projects in different geological contexts.The associated particle velocities,close to cutting wheel and ground surface,are presented and supplemented by data from the literature.The frequency content of the measured signals is then discussed.Finally,the mechanical impacts on neighbouring constructions and the inconvenience to local residents caused by the vibrations generated by TBMs are discussed.

In this section,the main characteristics of the four in situ measurement campaigns are presented.The raw data and exact positions of all sensors are available in Rallu and Berthoz (2022).

2.1.Sorgues micro-tunnel

This project has a hydraulic gallery with a diameter of 1.3 m and a length of 108 m using a micro-tunneling machine.The overburden is around 10 m in the area of the measurements.The strata are gravel and sand,with local clayey fringes.The measured pressiometric moduli (EM) are between 5 MPa and 15 MPa.The ground is saturated,with the water table located approximately 7 m above the gallery key.The measurements were carried out in July 2019.

The instrumentation set up includes (see Fig.1): (i) four 3D geophones located inside the micro-tunnel (C3),on the surface above the micro-tunnel(C1),in the arrival shaft(C2),and near the surface pumps and sludge treatment system (C4);(ii) a T-shaped array of 18 vertical one-dimensional (1D) geophones (R1 to R18)located on the ground surface.

The excavation machine of Herrenknecht AVN©micro-tunneler was used in this project.Bentonite was injected into the chamber to ensure face stability and control the hydrostatic pressures.Three rotation speeds for the main components of the micro-tunneling machine were employed: 7 rpm (rotation per minute) for the cutting wheel,1500 rpm for the motor driving the cutting wheel,and 1000 rpm for the mucking pump.

2.2.Lyon subway: line B tunnel - granite section

This project is located in the southern extension of line B of the Lyon subway.Two measurement campaigns were carried out for this project.For the first one,the TBM was excavated in granite stratum(see Fig.2).This measurement was initiated in September 2020,with excavation diameter of 9.8 m.The overburden is composed of approximately 20 m of good granites,topped by 3-5 m weathered granites,and less than 2 m of alluvium (sandy clayey limes).The unweathered granites have a moderate to high uniaxial compressive strength (σc=90 ± 70 MPa),and the rock mass is moderately fractured with rock quality designation (RQD)value between 50% and 75%.

Fig.2.The measurement system in Lyon-granites micro-tunnel: (a) Longitudinal section and (b) Plan section.

The instrumentation set up includes (see Fig.2): (i) two 3D geophones located in two TBM hyperbaric manlocks(C3,see Fig.3,and C4),about 1.5 m above the tunnel axis and about 2 m from the cutting wheel,and (ii) six 3D geophones on the surface above the tunnel axis (i.e.C1,C2,T70,T71,T75 and T76).

The main vibration source in this case is generally from the TBM characterized by variable density pressures(Herrenknecht).During the measurements,the excavation was performed with the cutting chamber full of bentonite (for muck management and hydrostatic pressure balance).The TBM control parameters are the cutting wheel speed of 3 rpm,penetration pitch of 7 mm/revolution(mm/rev),torque of about 3000 kN∙m on the cutting wheel,bentonite face pressure of 180 kPa in the tunnel axis,and wheel/ground contact force of about 15,000 kN.

2.3.Lyon subway: line B tunnel - alluvium section

This second measurement campaign was launched in January 2021 in pre-glacial alluvium(rollers with a sandy-silty matrix)(see Fig.4).The cover is about 20 m thick,which is composed of sandygravelly clays and topped by clayey-sandy silts.The water table is below the tunnel raft.

The 3D geophones installed inside the TBM(C3 and C4)and on the ground surface (C1,C2,T70,T71,T75 and T76) are identical to those described in Section 2.2.This instrumentation was completed by an L-shaped network of eighteen 1D geophones(TR01 to TR18),as shown in Fig.4.

The excavation was also carried out with the cutting chamber full of bentonite.The TBM driving parameters are as follows: a cutting wheel speed of 2 rpm,a penetration pitch of 15 mm/rev,a torque on the cutting wheel of about 1000 kN∙m,a bentonite face pressure of 200 kPa in the tunnel axis,and a wheel/ground contact force of about 3000 kN.

2.4.Grand Paris Express-line 16 tunnel - TULIP research project

This measurement campaign,carried out in July 2020,is part of a research project devoted to the study of the impact of a TBM on piles.This experiment was carried out on line 16 of the Grand Paris Express.The diameter of the excavated tunnel is 9.9 m,and the axis depth is 22.5 m.

Fig.3.Lyon -sensor C3 in one manlock of the TBM.

Fig.4.The measurement system in Lyon-alluvium micro-tunnel: (a) Longitudinal section and (b) Plan section.

Three auger piles with a 500 mm diameter and depths of 15 m and 20 m were constructed in the vicinity of the tunnel,and loaded by steel weights.The load exerted on the head of the piles throughout the experiment is 2060 kN,which is applied by means of jacks between the pile’s heads and the steel weights.A ball joint ensures the connection between the jack and the reaction mass in order to prevent the occurrence of parasitic moments at the head.Measurements carried out during the loading of the piles reveal the Young’s moduli of the piles with the magnitude of 35 GPa-40 GPa at the head,and 45 GPa-50 GPa at the tip.

The lithological succession from top to bottom around the section is shown in Fig.5: backfills constituted of clayey marl and gravels (MG),marly limestones of Saint-Ouen Limestones (SOL),clayey sands of Beauchamp Sand (BS),indurated and fragmented marly limestones of Marls and Stones(MS)and Coarse Limestones(CL).The stable water table is at a depth of 11.5 m.The average pressiometric moduli are 30 MPa(MG),60 MPa(SOL),90 MPa(BS)and 260 MPa(MS),respectively.

The excavation was carried out with a Herrenknecht EPBS.The average values of the machine’s control parameters are as follows:a cutting wheel rotation speed of 1.4 rpm,a torque on the cutting wheel of 4000 kN∙m,an average face pressure of 175 kPa in the tunnel axis,a cutting wheel/ground contact force of 7000 kN,and an average grouting pressure in crown of 175 kPa.Two 3D geophones are positioned in the TBM: the T76 sensor located in a manlock,and the T75 sensor on the 4th ring of segments already installed (17 m behind the cutting wheel).

An electric generator(EG)supplying the pumps to maintain the load imposed on the pile heads and the instrumentation is also presented on site (EG in Fig.5).This generator transmitted significant vibrations into the ground.The 3D geophone T70 is positioned on the ground surface,close to this generator.

Six 3D geophones(i.e.T20,T21,T40,T71,C2,and C4)and fifteen 1D geophones were also distributed on the ground surface.In particular,sensors C2 and C4 were located on the ground close to piles P2 and P3.Sensors C1 and C3 were positioned on the top of the piles (Figs.5 and 6).Note that numerous “quasi-static” measurements were also carried out in the piles to measure quasi-static strains and displacements (topographic targets,optical fibres and vibrating cords) as well as the ground (topographic targets,inclinometers,and extensometers).

2.5.Instrumentation

The dynamic measurement device used in various sites is composed of geophones (speed acquisition) of the Moho brand,comprising 3D TROMINO© sensors (denoted C1,C2,C3,C4,T20,T21,T40,T70,T71,T75 and T76) and 1D Soilspy ROSINA© (noted R01 to R18).All measurements were acquired at a sampling rate of 1024 Hz.This frequency range is wide enough (theorem of Shannon) to investigate ground induced vibrations (f≤40 Hz) and vibro-acoustic vibrations (40 ≤f≤200 Hz).

The TROMINO© sensors are equipped with three highly sensitive orthogonal acquisition channels (X,Y,Z) to measure ambient noise(high-resolution with precision of 10-7mm/s).In the present study,theX-direction represents the tunnel axis,Y-direction the transverse direction,andZ-direction the vertical direction,so that the reference frame(X,Y,Z)is direct.During the measurements,all the TROMINO© are synchronized by global position system (GPS).However,the GPS signal is not always accessible everywhere,especially underground.Therefore,in practice,all sensors are synchronized on the surface at the same location to obtain the GPS time,and then each sensor is moved according to the experimental setup.

Fig.5.The measurement system in TULIP: (a) Longitudinal section and (b) Plan section.

The connection between the TROMINO© and the ground is ensured by three very sharp spikes (Fig.7),allowing to level the instrument and to avoid any parasitic displacement for the weak vibration levels.Indeed,the vertical displacement are inhibited by low acceleration levels(compared to the gravity),and the thinness of the spikes and the heavy weight of the sensors lead to slight penetration into the supports (concrete,ground or painted rough metal) avoiding horizontal displacements.

Fig.6.TULIP: sensors C3 (on the top of pile P3) and C4 (on the ground).In orange a jack between the pile head and the steel weights.

The Soilspy ROSINA© device is made up of vertical 1D geophones,planted or laid on the ground,and physically linked to a computer serving as an acquisition centre.Each sensor is equipped with a speed acquisition channel with an accuracy of about 4 ×10-8mm/s.

2.6.Measurement analysis principle

The pre-processing of the acquisitions consists of (i) the restriction of the time traces to a relevant interval over which the signals can be considered stationary,(ii)the filtering of the signal in the frequency range of 0.05-160 Hz corresponding to the usual frequencies of building engineering,and(iii)imposing a zero-mean value of the time-histories.

Each measurement campaign includes(i)a measurement phase before excavation,under ambient mechanical noise,for example the road and pedestrian traffic,and rotating machines (e.g.the EG of the TULIP project,see Section 2.4),and(ii)a measurement phase during excavation,with synchronous acquisitions between the sensors on the ground surface and in the TBM.The latter is positioned close to the cutting wheel as possible,which is mainly in the TBM’s manlocks,and on the rigid surfaces with natural frequencies much higher than the studied one of 0.05-160 Hz.

The evaluation of the measurements is mainly carried out according to the following three indicators:

(1) As the signal is not perfectly stationary,the peak velocities presented in Fig.8 are not representative of the phenomena involved.For this,a characteristic velocity per channel is defined,representing the absolute velocity value within a 0.5%probability of being exceeded.This value covers the vast majority of the energy of the signals and can remove the peaks that are not representative of the phenomenon.The characteristic velocities of the signals in the tunneling phase on the ground surface and in the TBM(source)are noted as vkand vSk,respectively The characteristic velocity under ambient mechanical noise is noted v0k;

Fig.7.Short and long spikes of TROMINO© (Moho,2020): (a) Short spikes for soft grounds and (b) Long spikes.

(2) The signal-to-noise ratio (SNR) is defined as the dimensionless energetic ratio SNR=and allows the excavation effect to be quantified in relation to the ambient noise;and

(3) The amplitude surface to source velocity ratio (ASSV) characterizes,in each direction,the ratio between the characteristic surface velocity and the characteristic velocity near the TBM source,i.e.ASSV=

3.1.Particle velocities measured in the TBMs

Fig.8 shows an example of a signal measured in one manlock of the TBM.The signal is maintained to allow determining the characteristic velocity.The characteristic velocities measured during the excavation phase in the four TBMs are summarized in Table 1,for each acquisition direction.

For each of the two Lyon sites,the sensors positioned in both TBM manlocks give similar velocities.On the TULIP project,the T76 sensor is in the manlock and the T75 sensor in the invert of the segments,which is 17 m away from the cutting wheel.It can be seen that the measured velocities are also of the same order of magnitude for the horizontal directions.These identical measurements confirm the representativeness of the measurements carried out.

The comparison between the four sites clearly highlights the influence of the geotechnical context on the measured velocities.They are of the magnitude of 0.1-0.2 mm/s in clayey sands(TULIP),1-2 mm/s in gravels and sands (Sorgues and Lyon-alluvium) and 20-25 mm/s in granite,respectively.It is interesting that the two series of measurements carried out in the gravels and sands (Sorgues and Lyon-alluvium) reveal similar speeds,whereas the diameter of the two machines varies from one to eight.

The velocities measured in the three directions of acquisition(X,Y,Z) of a given sensor are similar:

A similar observation can be made with respect to other data on the cutting wheel of TBM in the literature(Huo et al.,2015;Huang et al.,2018;Wu et al.,2021).According to our measurements and the observations in the literature,it is not systematically in the same direction that the vibration amplitude is the highest.This finding is consistent with the TBM excavation mechanism,with a cutting wheel pressing longitudinally on the face and rotating simultaneously.

3.2.Particle velocities measured on the ground surface

The particle velocities measured on the surface have been compared to those measured under ambient mechanical noise.On the Sorgues sites,Lyon-granite and Lyon-alluvium sites,the velocities measured during the excavation phase are significantly higher than those measured under ambient noise.The SNR values are between 10 dB and 20 dB in the gravel and sand (Sorgues and Lyon-alluvium),and even 30 dB and 60 dB in the granite (Lyongranite).Particularly,the SNR values in case of TULIP are close to zero.This has two causes:(i)the velocities measured in the TBM are low(0.2 mm/s),and(ii)the EG presented on the surface during the measurements under ambient noise generates particle velocities of the same order of magnitude as the TBM(approximately 0.1 mm/s in the vicinity of the T70 sensor).

Fig.9 summarizes the velocities measured on the surface for all the sensors of the four sites according to their distance from the cutting wheel of the TBM.As for the TBMs,the surface measurements reveal similar velocities in the three spatial directions.This observation can be observed on the four construction sites.The particle velocities measured on the surface at about 30 m away from the cutting wheel are:

(1) 0.02-0.1 mm/s in clayey sands (TULIP),i.e.the ASSV ratio ranges from 10% to 50%.These ASSV values should be considered in view of the importance of the vibrations generated by the generator set.

(2) 0.03-0.2 mm/s in the gravels and sands(Sorgues and Lyonalluvium),i.e.the ASSV ratio ranges from 1% to 10%,and

(3) 0.1-1 mm/s in the granite (Lyon-granite),i.e.the ASSV ratio ranges from 0.5% to 5%.

The evolution of the velocities measured on the surface is consistent with the magnitude of the vibrations measured in the TBMs:the more vibrations the TBM generates at depth,the greater the amplitude measured at the surface.However,the ASSV ratios measured in granite,and to a lesser extent in gravel and sand,appear surprisingly low (less than 10%) given the short distance(30 m)and stiffness of the overburden.It is likely that only a part of the vibrations measured in the manlocks were transmitted to the ground.

Fig.8.Signals from sensor C3 in the TBM,during Lyon-granites measurements in the three directions(X,Y,Z)from left to right(a) vX (b)vY and(c)vZ∙Horizontal lines represent the relevant source characteristic velocity,vSk.

The TULIP project offers the opportunity to compare the particle velocities on the top of two piles(P2:sensor C1;P3:sensor C3)with those measured on the ground,1 m from the piles (C2 and C4,respectively).Similar velocities are measured at these different points,as displayed in Fig.9d.However,this observation must be considered in view of the low levels measured,the presence of the generator,and the low stiffness of the piles.

For each site,a fitting curve in the form of a power function(Eq.(2) is sought to consider all the sensors installed on the surface in front of the TBM.In the following,PPVsurfaceis the peak particle velocity(PPV)at the surface(mm/s),d(m)is the total distance from the TBM face,and α and β are two coefficients.

Eq.(2)is commonly used in practical engineering to evaluate the vibrations induced at a certain distance from a load(often a blast),see the works of Chapot (1981),Berta (1994),Hiller and Crabb(2000),and Rahman and Orr (2011).The obtained regressions with Eq.(2)on different sites are shown in Fig.10.The parameters(α,β) and the determination coefficient (R2) are summarized in Table 2.The same exercise has been done with the data in the literature,as tabulated in Table 2,except for the correlation coefficient because only fitted curves were available.One can see that the particle velocities measured on the surface are rather low(between 0.01 and 1 mm/s for a distance to the cutting wheel,a distance basically between 10 m and 80 m).

Table 1 Characteristic velocities(for each direction)measured on the four TBMs and micro-TBMs studied.

The influence of the geotechnical context described in the previous paragraphs is confirmed.In rocky grounds,the velocities measured at a distance between 10 m and 30 m from the cuttingwheel axis are 0.1-1 mm/s (Ferrari et al.,2011;Bigot and Farotto,2016).In soft ground (Hiller and Crabb,2000;Grund et al.,2016),these are about 10 times lower (e.g.0.01-0.1 mm/s).

An attenuation of particle velocities with distance is observed for these various sites.The calculated coefficient α varied between 0.6 and 1.4,which reflected a fairly low damping with distance.These values are generally of the same order of magnitude as those provided by other authors for vibrations induced by TBMs: 1.3 by Godio et al.(1992) and 1.05-1.2 by Rahman and Orr (2011).

The accuracy on the statistical coefficient α is estimated to be±10%for the four field measurement campaigns in Table 2.Here,it should be noted that there is some uncertainty as to the calibration of this coefficient because: (i) these regressions are calibrated on fairly scattered point clouds,and (ii) the TBM/sensor distances remain small (<100 m).Feedbacks from blasting with longer distances between the TBM and sensors reveal that the values are more representative.One can for example note the value of 1.5-2 from Chapot(1981),and 1.7 from Berta (1994).

Table 2 Summary of the main characteristics of the projects.

The values of the coefficient β vary between 0.1 and 50.The high values correspond to rocky soils,while the low values to fine soils.Godio et al.(1992)retained a value of this coefficient equal to 180 in rocky soils.The feedback from Nishimatsu(Rahman and Orr,2011)reported a value between 7.4 and 176 without specifying the associated geotechnical context.

This coefficient is a function of the “loads” at the source.In the case of explosive excavation,Chapot (1981) and Berta (1994)expressed it as the ratio of a coefficient linked to the site (nature of the ground,topography),by the unit charge of explosive.In the case of tunneling,this coefficient could depend on the nature of the ground,the diameter of the tunnel excavated,and the operating conditions of the TBM(type of TBM,axial force and torque exerted on the face,consistency of the material present in the working chamber).

Section 3 shows that the temporal analysis of a quasi-stationary signal allows quantification of the characteristic vibratory level of a source or the characteristic vibratory level on the surface.The timefrequency duality allows observation of the same signal in view of a frequency point.In other words,the frequency representation of the signal provides its contribution for each frequency.This phenomenon is commonly described by Fourier analysis.The objectives are: (i) to characterize the frequency of the vibration source,and(ii)to make the link with the frequency representation on the surface.

Fig.9.Representation of the characteristic velocities vk in the three directions of acquisition(X; Y; Z)measured on the surface according to the distance from the cutting wheel:(a)Sorgues,(b) Lyon -granite,(c) Lyon -alluvium;and (d) TULIP.

Firstly,an individual analysis of the signals was performed,and then an analysis method was proposed and conducted on each site,based on the notion of inter-correlation between signals.

4.1.Frequency characterization of the source

4.1.1.Power spectral density

One way to estimate the frequency spectrum of a signal is to compute its power spectral density (PSD),f↦Sxx(f),wherefdefines the frequency.Let us consider a finite time [0;T] (implicitely zero elsewhere),stochastic,stationary,ergodic and zero-mean signalt↦x(t) (trepresents the time andxis the velocity).Thanks to the assumptions of ergodicity and that of zero-mean,the autocorrelation function is defined as

whereE[∙] defines the mathematic expected value,★denotes the convolution product andt↦ˇx(t)=x(-t).The (finite-time)Fourier Transform F applied tot↦x(t),denotedf↦X (f),is defined as

As discussed in Au(2017),for a stochastic stationary signal,the calculation of the frequency spectrum cannot be processed by Fourier Transform or by Fourier series.Because of the nature of this signal,the scaling by 1/---is then necessary to ensure the convergence whenT→+∞.

The PSD is defined as (∙★stands for the complex conjugate):

Then,the Wiener-Khintchine theorem states in particular that the Fourier Transform of the autocorrelation functionRxxyields the PSD (and reciprocally the inverse Fourier Transform of the PSD gives the autocorrelation):

Consequently,computing the square root of the PSD allows an estimation of the amplitude spectrum ofx.Moreover,the Parseval equality ensures that the energy of the signal is identical to the energy of its spectrum.This yields that the square of root mean square(RMS)of the signal corresponds to the area under the PSD:

However,calculating the PSD of the whole time-history yields a very noisy spectrum.To improve this,the Welch method (Welch,1967) is used: (i) the signal is divided innKsegments using a tapering window,(ii) on each segment,the PSD is performed,and(iii) the final PSD is provided by averaging the PSD on all the segments.A 50% overlap between the segments,associated with a Hann tapering window(cosine bell,Blackman and Tukey,1958),is a reasonable choice (Welch,1967;Brincker and Ventura,2015) between accurate estimations of the signal power and not taking too much data into account.

Fig.10.Evolution of the fitted PPVsurface with the distance from the tunnel face.

The Fourier Transform of a tapering window presents sidelobes that generate unwanted noise,which can be measured by the normalized equivalent noise bandwidth (Harris,1987):

where() represent the mean (the variance) of the tapering window of lengthnw.Finally,the scaling is performed by multiplying the PSD by the effective noise bandwidth EBs=(fs/nw)NBs,in whichfsis the sampling frequency of the signal.In the following,all the calculated PSD (also called power spectrum) are scaled and the unit is (mm/s)2.

4.1.2.Spectrum inside a TBM

For the extension of Metro line B in Lyon,two measurement campaigns had been performed in two different geological contexts:a granite hill(“Lyon-granite”,Fig.2)and a gravel-and-sand stratified soil (“Lyon-alluvium”,Fig.4).In both cases,a TBM with variable density pressures was used,and the excavation was carried out with the cutting chamber full of bentonite.Fig.11 presents the PSD of the sensors in the left and right manlocks of the TBM (on the top and bottom of this figure,respectively),for the three directions(X;Y;Z).Left and right measurements show very similar results,ensuring the repeatability of the measurements.The PSD of the TULIP and Sorgues campaigns are also presented in Figs.12 and 13,respectively.

First,observations in all the PSDs reveal that the energy is within wide frequency band of 20 Hz.For each signal,the energetic contribution of different frequency ranges(i.e.0-20 Hz,20-40 Hz,40-80 Hz,80-100 Hz,and 100-160 Hz)is estimated by integration(via the Parseval theorem).This highlights the fact that the ranges(e.g.0-20 Hz and 20-40 Hz) are focusing at least 80% of the total energy of the signals,even if some peaks are presented in the range of 80-100 Hz.This statement is also valid for the campaigns TULIP(Fig.12) and Sorgues (Fig.13),even if this energy distribution is a slightly different in the transverse directionY,with lots of energy accumulated in the frequency band of 40-80 Hz.The frequency band 0-40 Hz is consequently the common relevant band in terms of energy for the three tunnelling technologies studied,namely earth pressure balanced shield,variable density(as a slurry shield),and micro-tunnelling.

Fig.11.In three directions(X;Y;Z),PSD of the sensor C3(C4)in the left(right)manlock of the TBM in Lyon:(a)and(d) X,(b)and(e)Y,(c)and(f) Z.The energetic contribution of each frequency range is printed.

Then,the TBM itself must be seen as a multi-body vibrating source,with several engines,pumps,and jacks,which emit vibrations at different fundamental frequencies (and their harmonics).Actually,the spectrum of a machine presents narrow peaks(consequently with a weak associated energy) at the fundamental frequency and at its harmonics(for example,the 20 Hz orange peak of left sensor inY-direction).These peaks are mainly visible if the effect of boring is of the same order as the solicitations by these machines: this is the case in soft ground(TULIP in Fig.12 or Lyonalluvium in Fig.11-orange),but not for hard rock grounds (Lyongranite in Fig.11-blue).Due to the weak energy associated with these peaks,this effect is less significant compared with the highfrequency ranges.

Secondly,for a given TBM in two different geotechnical contexts(Lyon site),the evolution of PSD in terms of frequency is very similar,with energetic bands in the same frequency ranges.However,the magnitude of the PSD in the granite context is clearly 100 times greater than that in the alluvium context.The square root of this ratio corresponds to the ratio of the characteristic velocities measured in the TBM: around 20 mm/s in granite against around 1.5 mm/s in alluvium.Thirdly,the isotropy observed regarding the characteristic velocities (Table 1,) is globally maintained regarding the frequency spectra.Consequently,the geotechnical context has a strong impact on the amplitude of frequency spectra,but their energetic distribution is globally the same.In order to take into account the minor differences highlighted above,in the following section we proposed a global methodology based on the inter-correlation of the signals to build a representative spectrum.

4.2.Site frequency analysis

4.2.1.Methodology

The large number of sensors make individual spectrum analysis being irrelevant to characterize a site.In order to have a concise representation of all the spectra of several sensors for a given campaign and a given acquisition direction,a methodology based on the inter-correlation of the signals is proposed.This is typically used in operational modal analysis (OMA) under the so-named frequency domain decomposition (Brincker and Ventura,2015).Let us consider a collection ofNSsignals(for example all the sensors on the surface during excavation inZ-direction)satisfying the same assumptions as indicated in Section 4.1.1,e.g.finite time span[0;T],stochastic,stationary,ergodic signalst↦xi(t).These signals are grouped on the vectort(t).Following the Welch method in Section 4.1.1,the method is:

Fig.12.PSD of the sensor inside the TBM in TULIP,in the three directions: (a) X,(b) Y and (c) Z.

With numerical sensors,the time-varying and frequencyvarying functions take discrete values,where the time step is defined as

wherefsis the sampling frequency(here 1024 Hz),andNis the total number of data points.

The frequency step is

The originality of this analysis is the extension of this framework to soil dynamics: the representation of the singular values in function of the frequency highlights the frequency where the sensors are the most correlated.

4.2.2.Representative site spectra

In this study,we proposed a site-spectrum representation.For this purpose,we extracted,at each frequencyfj=j× Δf,the first(that is the largest) singular valuesof spectral density matrices.This extraction is realized for three sets of 3Dsensors.For a given acquisition direction(X;Y;Z):(i)sensors on the surface under mechanical ambient noise before excavation,(ii)sensors on the surface during excavation,and (iii) sensors inside the TBM.This is illustrated on the Lyon-granite site(see Fig.14),in a gravel and sands context(Fig.15)and clayey sands context(Fig.16).

Firstly,whatever the case,the evolution of the first singular value according to the frequency globally decreases,but presents some peaks locally.This means that globally the correlation between the signals is greater at low frequencies rather than at high frequencies.A weak intercorrelation between two signals can be explained on one hand by weak values of one or both signals,or on the other hand by a weak correlation between them.Conversely,two signals having an energetic contribution in the same frequency band lead to a strong intercorrelation in this band.Consequently,the first singular value of the SDM(called site-spectrum)highlights an energetic peak in a frequency band,suggesting that the contribution of all the sensors is strong in this band.

Considering the case of sensors on the surface measuring the mechanical ambient noise,the energetic peaks of the site-spectra represent the frequency bands around the eigenfrequencies of the soil(dotted lines in Fig.14).Then,as in the context of structural dynamics,the response of the soil to a given solicitation will be preferentially around its eigenfrequencies.Thus,the evolution of the site-spectrum during excavation (solid lines) is coherent with the ambient noise site-spectrum and the spectrum of the solicitation (dashed lines).In Fig.14,it shows that.

Fig.13.PSD of the sensors inside the TBM in Sorgues,in the three directions: (a) X,(b) Y and (c) Z.

(1) In the frequency range of 0-20 Hz,the soil (under ambient noise) presents an energetic frequency band (classical soil eigenfrequencies) allowing a strong response,solicited strongly by the TBM,generating an energetic response on the surface;

(2) In the frequency range of 20-40 Hz,although the soil presents a weaker response under ambient noise,thanks to the clear contribution of the TBM,an energetic response of the surface under solicitation is observed;

(3) The results of the frequency range of 40-60 Hz band show the importance of the soil response under ambient noise.Despite a weak contribution of the TBM,the soil presents a significant response capacity,and

(4) Beyond 60 Hz,energy levels are very weak.Consequently,this site-spectrum under ambient noise can be seen as a transfer function: the response on the surface under TBM solicitation corresponds to the convolution between the TBM and the ambient noise.

In terms of amplitude,as shown in Section 4.1.2,the ratio between the square root of the site spectra of the three sets of measurement at a given frequency (for example atf=0 Hz) is consistent with the ratio of the characteristic velocities (see Table 3):

Table 3 Lyon-granite,representative magnitudes of characteristic velocities and PSD for three sets of sensors.

Fig.14.Lyon-granite site-spectrum in the three directions of acquisition for sensors.

This explains why in the site spectra of softer grounds (gravel and sands,Fig.15 and clayey sands,Fig.16),the three sets of measurements are closer than that for the rocky site.In the particular case of TULIP,the presence of the EG emitting vibrations of the same magnitude as the TBM makes the uncoupling between the three sets of measurements more complicated.

Characterization of TBM-induced vibrations with support of four different examples has enabled a description of both the source and the surface responses in terms of amplitude and frequency.It has been shown that,in the manner of other type of works such as vibration drilling,TBM generates vibrations with permanent,stable and stationary features,as opposed to impulsive and isolated or intermittent events produced by shocks or blasting.

Fig.15.Site spectra of gravel and sands sites: (a) Lyon-alluvium and (b) Sorgues.

Fig.16.Site spectrum of TULIP (clayey sand geology).

The impacts on the surroundings have yet to be predicted.The GT16R2A1 recommended by French Tunnelling and Underground Space Association(AFTES)deals with the influence of vibrations in terms of damage to surrounding structures and disruption to exposed residents (AFTES,2018).

5.1.Structural impacts

Considering damages to structures,the characteristics of the building potentially impacted have to be considered: structural integrity,function/use,constitutive materials,geometry,architectural/archaeological/historical value,type of foundations,eigenmodes of vibration and their associated frequencies and shapes,etc.However,the PPV is widely used.Points of measurements differ according to the different norms and regulations,but it is generally recommended to place sensors near the foundations of the structure,and in upper storeys if the building is high enough (three or four storeys and more).

Norms and regulations often suggest approaches that consist in setting vibration thresholds that should not be exceeded.They are usually defined by frequency bands.Obviously,such methods cannot take into consideration all the specifics of each configuration as described above.Several examples are presented in this section in order to give orders of magnitude,starting with standards which define thresholds for structural protection.

Fig.17 plots thresholds extracted from different texts.Here,guideline values for sensitive structures are represented,thus highlighting the lowest thresholds.In references examined,listed monuments,buildings presenting pathologies or structures with high arches are common examples of sensitive structures.In addition to six national standards from Germany (DIN 4150-3,1999),the United Kingdom (BS 5228-4,1992),Austria,Norway,Spain and Switzerland (ITA,2016),three French texts are cited: a French circular (1986) from the Ministry of the Environment relative to mechanical vibrations induced by facilities classified for environmental protection,a French decree(1994)relative to quarry working and the IN 1226 procedure of the French national railway operator SNCF (2009).A schematic representation of the measurements obtained in the Lyon-Granite campaign is also depicted in the figure,considering that the maximum characteristic velocity is 1 mm/s and that the major part of the vibratory energy is contained in the 0-40 Hz band.

For the approaches,almost all standards consider the sensitivity of the structure as a parameter that influences the maximum values to impose.However,only three of them specify the level of damage corresponding to thresholds,which can lead one to believe that when nothing is stated,respecting the threshold should guarantee no damage at all.

Some texts refer to as transient and impulsive vibrations.The thresholds under impulsive vibrations are about twice greater than those for continuous vibrations in French circular(1986).BS 7385-2(1993)also recommends using a factor two when the thresholds for continuous vibrations are not explicitly given.Likewise,only the Austrian standard defines a limit for the resultant velocity vR(t)=,where vX,vYand vZstand for the spatial components of the velocity.In order to compare with thresholds valid for PPV (highest values of the respective maxima of vX;vYand vZ) of the other standards,one can use the following upper and lower limits (see Rallu and Gaillard,2019):

Therefore,in soft ground contexts(Sorgues,Lyon-alluvium and TULIP),the characteristic velocities vkare about one to two orders of magnitude lower than the lowest threshold.We can therefore conclude that,according to the texts referenced above,the TBMinduced vibrations presented in this paper should have no structural impact on the surrounding buildings.However,in rocky grounds(Lyon-granite),the characteristic velocities vkare similar to the lowest threshold.Some cosmetic damage on the most sensitive structures could thus appear,without compromising the integrity of the structure.

Two specific cases must be taken into account: (i) the case of extremely sensitive structures,which are not described in the texts above (for example structures made of mud-brick),and (ii) some infrequent high-level vibrations not considered in the steady-state studied here(for example shocks due to the dynamic impact of rock blocks).

5.2.Disruption to exposed residents

The disruption to local residents can have different causes: (i)the physical perception (apart from acoustic) of vibrations,(ii)movements of furniture(crockery,doors,chandeliers,etc.),and(iii)noise generated by the vibration of structural elements.The last one is excluded from the following analysis.

DIN 4150-2 (1999) proposes an estimation of the disruption to residents based on an energy estimation via the velocities.For each direction of acquisition,velocity signals are filtered in the frequency range of 5.6-80 Hz,and then are used to calculate the maximum weighted vibration severityKBmax,which is defined as

where S is the set of sensors on the surface,and τ=1/8 s.

Table 4 Resident disruption thresholds calculated according to German standard(DIN 4150-2,1999).

Other standards choose acceleration as a reference parameter.For example,NF ISO 2631(2014)uses the RMS acceleration by third octave band,weighted depending on the purpose considered:health,comfort,perception or motion sickness.In contrary to the previous version(ISO 2631-2,1989),in which some thresholds are defined according to different parameters(the nature of the source or the place where the evaluation was realized),the new version of this standard does not give specific limit values,but states for example that 50% of alert people barely detect (perception threshold) a weighted vibration with a maximum magnitude of 0.015 m/s2.

Fig.17.Summary of thresholds of PPV values related to damage to sensitive structures.

Another example of a standard defining thresholds in acceleration is BS 6472-1 (2008): a vibration dose value (VDV=is calculated in horizontal and vertical directions,using two different frequency-weighting curves and depending on the total occurrence period of vibration (T).The calculated values are then compared to tabulated thresholds.

Vibration measurements have been carried out on four French tunnels and micro-tunnel projects.These measurements integrate geophones both on the surface and in the TBMs.The data collected were compared with the limited data available in the literature.The analyses concern the amplitude of the particle velocities,and the frequency content of the signals.The main conclusions are obtained as follows:

(1) The vibrations measured on the surface and in the TBMs are similar in all three spatial directions,both in terms of amplitude and frequency content.

(2) The amplitude of the velocities measured in the TBMs is of the order of 0.1 mm/s in clay soils,1 mm/s in sand and gravel,and 10 mm/s in rocky soils.

(3) On the ground surface,the particle velocities between 10 m and 30 m in front of the cutting face are about 10 times lower than those inside the TBM.The high contrast between velocities measured inside the TBM manlock and on the surface reveals that only a part of the energy measured inside the manlock is transmitted to the ground,

(4) The TULIP experiment also allowed the comparison of the amplitude of the vibrations measured at the head of the foundation piles with those at the ground surface just next to the piles.The particle velocities measured are similar,but this observation must take into account the low velocities measured and the relatively low rigidity of the piles,

(5) The four measurement campaigns carried out in various geotechnical contexts (fine soil,gravelly soil,and rock respectively)revealed that 80%of the energy of the vibration signals measured in the TBMs is in the range 0-40 Hz,and

(6) A representative method of each site-spectrum by extracting the largest singular values of spectral density matrices for all the sensors is proposed.This approach,applied to the measurements carried out under ambient noise,in the operating TBM,and on the surface during the excavation phase,facilitates the interpretation of the ground response to the vibrations induced by the TBM.

A comparison of the vibration thresholds relating to the impact on neighbouring structures and the disruption to local residents(physical perception of vibrations and movements of furniture) in the main European regulations was then carried out.This comparison shows that in soft ground,where pressurised TBMs are used,it is unlikely that the vibrations emitted by a TBM could cause damage or disturbance to neighbouring structures.However,in rocky ground,cosmetic damage or disturbances could occur on the surface because particular velocities are of the same order of magnitude as literature thresholds.

More impacts could be observed in the following cases: (i) a short distance to the TBM,(ii)an extremely sensitive structure,(iii)an amplification of ground-vibrations due to the excitation of inner eigenmodes of the structure,and (iv) infrequent high-level vibrations (not considered here).The impact of noise radiated by local structural elements vibrating is also excluded.This analysis should be completed by other experimental campaigns allowing the study of other geotechnical contexts(for example TBM face composed of highly contrasted grounds mixed face),or other TBM types (for example open-shield TBMs in rocky ground),with measurements in the ground closer to the face.The understanding of these wavepropagating phenomena could be performed by analytical or numerical models calibrated on data presented in this paper.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to thank VALENTIN Environnement et Travaux Publics,IMPLENIA,SYSTRA,the SYTRAL,EIFFAGE Génie Civil Réseaux and the SOCIETE DU GRAND PARIS for allowing them to carry out the measurements presented in this article.The Labex CeLyA is also acknowledged for their support.

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