Finite element analysis of ground borne vibrations in sensitive buildings using inputs from free field measurements

T.N. Tuan Chik

1, J.M.W. Brownjohn

2, M. Petkovski

3

1,2,3 University of Sheffield, Department of Civil and Structural Engineering

Sir Frederick Mappin Building, Mappin Street, Sheffield, S1 3JD, United Kingdom

Email: tn.chik@sheffield.ac.uk, james.brownjohn@sheffield.ac.uk, m.petkovski@sheffield.ac.uk

Abstract The development in modern fabs manufacturing of micro-electronics components like chip processors and

laboratories fully equipped with high resolution devices requires very low level of vibration due to small

allowable tolerances of the size of the equipment. As a result, the generated vibration level at the site is

critical for estimating and providing suitable conditions for vibration sensitive facilities. For this purpose,

ground borne vibration levels at specified locations are considered as input for the simulation analysis

which is used in assessing the response of the structure in time domain and also in one third octave band

frequency domain. This paper investigates the transmission of the amplitude of ground borne vibrations

generated by external sources, into low rise structures housing sensitive facilities. Finite element analyses

of the structure are used to predict the dynamic response of the structure, which is then compared with the

free field measurements (input). The results of FE analyses are checked against the generic vibration

criteria guidelines for vibration sensitive equipment. The results show that prediction based on dynamic

response analysis can be used for selecting and designing an effective foundation system. The effect of the

foundation system will provide guidelines for designing new vibration sensitive facilities.

1 Introduction

The modern laboratories producing integrated circuits consisting of smaller, more tightly packaged and

high-tech elements require greater precision and stability in micro-electronics manufacturing and

evaluation equipment. There is a need for a better understanding of the effects of environmental low level

vibrations on this type of equipment, in order to enable microelectronics facility designers to provide a

suitable condition without costly overdesign of the structure. Manufacturers provide vibration

specification for some, but not all sensitive equipment. With a few exceptions, the information provided is

incomplete. In these cases further analyses have to be carried out to ensure that the equipment follows the

existing guidelines.

In this paper, the state of the art of low level ground borne vibration with a focus on vibration criteria for

sensitive facilities and dynamic response of the buildings is assessed. Ground borne vibration induced by

external sources such as moving traffic like trucks, trams, trains etc. can produce unacceptable vibration to

humans and especially to buildings which accommodate very sensitive equipment [1]. The vibrations

propagate through the ground and into buildings often causing vibrations at the resonant frequencies of

various components of the building, such as floors and walls. Predicting the transmission of ground borne

vibration waves to a structure is one of the problems that need to be taken into account when designing the

building. The potential sites for advanced technology buildings are limited by varying degrees of ground

borne vibrations from a variety of potential sources [2].

The vibration sensitive equipment has been investigated by Gordon [3] and his colleagues since 1980s, for

various vibration sources, including ground borne vibration. There are several significant research

contributions with theoretical and experimental studies related to vibration sensitive equipment. Gendreau

et al. [4] investigated a desirable vibration environment at a site may be degraded by ground borne

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propagation of waves from a variety of external sources as well. They proposed that a site vibration

evaluation is needed for all facilities requiring the equivalent of VC-D or more stringent as shown in

Figure 1 and described in Table 1. Because of poor performance of several types of equipment, Gordon

[2] found that some vendors had inadequate vibration control, where their tool specification was either did

not satisfy the standard or was not reliable for facility design. He also introduced the generic vibration

criteria with Ungar [5]. Kim and Amick, Bayat and Davis and Bessasson et al. [6-8] have the same issues

with sensitive equipment. They proposed several methods of active vibration control to reduce excessive

vibration. They also used specific vibration criteria for equipment designing tools as shown in Figure 1.

1.1 Generic vibration criteria

Generic vibration criteria are essential in this study as a guideline when designing facilities for research,

microelectronics manufacturing and other similar activities. They were introduced by Ungar and Gordon

[5][9]. The criteria are specified as a set of one third octave band velocity spectra levels, from VC-A (least

severe) to VC-E (most severe). This criteria were upgraded several years later by Amick et al. [10] to VC-

G with the smallest value 0.78µm/s as shown in Figure 1(b). The application and range of the VC limits

including ISO criteria for humans is described in Table 1. The amplitude of velocity is measured in one

third octave frequency band over the frequency range of 8 to 80 Hz for VC-A and VC-B or 1 to 80 Hz for

VC-C to VC-G. The detail size of the equipment is referred to line width in the case of microelectronics

fabrication, the particle (cell) size in the case of medical and pharmaceutical research, etc. These criteria

curves are used in this study to evaluate the simulated response of the structures. Gordon [3]

recommended these criterion curves as a means of evaluating the performance of the floor that supported

vibration sensitive equipment.

(a)

(b)

Figure 1: Generic vibration criterion (VC) curves for vibration-sensitive equipment, showing also the ISO

guidelines for people in building. (a) Ungar and Gordon version [5] (b) Amick et al version [10]

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Vibration Curve Amplitude,

µm/s

Detail size,

µm

Application and experience

Workshop (ISO) 800 N/A Distinctly perceptible vibration. Appropriate to workshops and

no sensitive areas.

Office (ISO) 400 N/A Perceptible vibration. Appropriate to offices and no sensitive

areas.

Residential day

(ISO)

200 75 Barely perceptible vibration. Appropriate to sleep areas in most

instances. Usually adequate for computer equipment, hospital

recovery rooms, semiconductor probe test equipment, and

microscopes less than 40X.

Operating theatre

(ISO)

100

25 Vibration not perceptible. Suitable in most instances for surgical

suites, microscopes to 100X and other equipment of low

sensitivity.

VC-A 50 8 Adequate in most instances for optical microscope to 400X,

microbalances, optical balances, proximity and projection

aligners, etc.

VC-B 25 3 Appropriate for inspection and lithography equipment

(including steppers) to 3 µm line widths.

VC-C 12.5 1 - 3 Appropriate standard for optical microscopes to 1000X,

lithography and inspection equipment (including moderately

sensitive electron microscopes) to 1 µm line widths. TFT-LCD

stepper/scanner processes.

VC-D 6.25 0.1 – 0.3 Suitable in most instances for demanding equipment, including

electron microscopes (TEMs and SEMs) and E-Beam systems.

VC-E 3.12 < 0.1 A difficult criterion to achieve in most instances. Assumed to be

adequate for the most demanding of sensitive systems including

long path, laser-based, small target systems, E-Beam

lithography systems working at nanometer scales and other

systems requiring extraordinary dynamic stability.

VC-F 1.56 N/A Appropriate for extremely quiet research spaces, generally

difficult to achieve in most instances, especially cleanrooms.

Not recommended for use as a design criterion, only for

evaluation.

VC-G 0.78 N/A Appropriate for extremely quiet research spaces, generally

difficult to achieve in most instances, especially cleanrooms.

Not recommended for use as a design criterion, only for

evaluation.

Table 1: Application and range of the vibration criteria curve of Figure 1[10]

2 Finite element modeling techniques

Finite element modelling is a default norm for determining the dynamic performance of structures by

saving valuable design time and money in construction. In this study, the numerical simulation of

vibration response of typical building housing sensitive equipment was carried out by using ANSYS [11],

general purpose FE package and MATLAB software. ANSYS is finite element analysis software which

enables the researcher to develop models of structures, products, components or systems. It can apply

operating loads or other design performance conditions and also can optimise a design early in the

development process to reduce production costs, whilst MATLAB is a high-level programming language

and interactive environment that enables the researcher to perform computationally intensive tasks faster

than with traditional programming languages. All the relevant outputs from ANSYS were processed by

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means of MATLAB programmes, developed to determine the absolute response of the structure, and to

compare the structural performance with generic vibration criteria. The flow of the whole FE analysis for

this study is shown in Figure 2, showing the useful link of using ANSYS and MATLAB. ANSYS will

analyse the model (structure) to obtain dynamic response (output). MATLAB will continue the process of

analysis by calculating the obtained response (output) with the generic desired criteria values. If there any

errors occurred or the output over the criteria limits, the model need to be analysed again by performing

structural optimisation with several design variables changed. The further section will explain all required

analysis related to this study.

Figure 2: The structural vibration analysis process

2.1 Response to base excitation

The response analysis for a multi storey frame subjected to base acceleration, as in the case of earthquake,

is similar to the analysis of systems subjected to external force. From dynamic equilibrium, the equations

of motion for free (unforced) vibration are:

0)( tftftf kcI (1)

Where If = ( )mx t is inertia force, ( ( ) ( ))c gf c x t x t is damping force and ( ( ) ( ))k gf k x t x t is

elastic spring force (positive when gx x ), gx and gx are ground displacement and velocity respectively.

By substituting for kf etc. and dropping the (t),

0)()( xxkxxcxm gg (2)

Adding gxm (where gx is ground acceleration) to both sides of equation (2) gives:

gggg xmxxkxxcxxm )()()( (3)

It is the relative movement that gives rise to spring and damper forces; hence the relative displacement of

the mass with respect to the foundation can be defined as

gxxv (4)

Replacing (4) in (3) gives:

gmv cv kv mx (5)

Equation (5) can be used for determining the relative response to any base excitation. The absolute

response can be found by adding the base response.

ANSYS

YS

MATLAB

BAB

Excitation

(input)

Desired

criteria

Structure Response

(output)

Compare with

criteria values

Error, if any

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2.2 Modal analysis

The modal analysis was used to determine the dynamic properties (natural frequencies and mode shapes)

of the structure considered in this study. In this analysis, a Block Lanczos Eigen solver is used as a

solution method. This is an efficient algorithm which is suitable for modal analysis of large models. The

dynamic properties provide insight into the possible causes for vibration problems and therefore they can

be used as a basis for quality assurance in the design analysis. As a quick way to determine structural

flexibility, it can be used for prediction of structural performance under given vibration inputs. Also, the

model analysis is used as the first step in the more detailed dynamic analyses, such as a transient dynamic

analysis which is performed by using the mode superposition technique.

2.3 Transient analysis

Further analysis is the transient (time history) analysis which is a linear analysis technique used to

determine the dynamic response of a structure under the action of any general time-dependent loads. It is

used to determine the time-varying displacements, strains, stresses, and forces in a structure as it responds

to any combination of static and time varying loads while simultaneously considering the effects of inertia

or damping [12].

Transient analysis can be carried out using three methods; namely full method, reduced method and mode

superposition method [13]. The full method is the easiest way to use, does not reduce the dimension of the

considered problem since original matrices are used to compute the solution. All kinds of nonlinearities

may be specified, automatic time stepping is available, all kinds of loads may be specified, masses are not

assumed to be concentrated at the nodes and finally all results are computed in a single calculation. The

main disadvantage is the fact that the required solution time will increase with the size of the considered

model.

The reduced method will reduce the system matrices to only consider the Master Degree of Freedom

(MDOFs) to solve the transient problem. The calculations are much quicker than full method. However,

automatic time stepping is not possible. Consequently, this method is not very popular any more since all

its disadvantages do not really compensate the advantage of lower costs in solution time.

The mode superposition method is a very powerful method to reduce the number of unknowns in a

dynamic response analysis. This method requires a preliminary modal analysis, as factored mode shapes

are summed to calculate the structure's response. It is the quickest of the three methods, but it requires a

good deal of understanding of the problem at hand. It reduces the dimension of the original problem as the

transient analysis is finally performed in the modal subspace which has the dimension of the number of

mode shapes used for the superposition, thus reducing the solution time. The accuracy of the solution

depends only on the number of mode used for the modal superposition. The results of this analysis give

the relative response to which the input motion should be added in order to obtain the absolute response of

the structure.

2.4 Dynamic response by mode superposition

It is usually necessary to determine the dynamic response of a structure to applied forcing functions. This

amounts to finding the solution to the equation of motion of the equivalent multi degree of freedom as

given by:

fkxxcxm (6)

The solution for the displacements x can be used to calculate internal forces and stresses at any instant of

time [14]. In this analysis, direct numerical integration is used to solve equation (6) by mode superposition

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method, which is generally more efficient for linear structures. Mode superposition is based upon the fact

that the deflected shape of the structure is expressed as a linear combination of all the modes:

N

n

nnNN YYYYYx1

332211 ... (7)

The coefficients nY are the modal amplitudes, which vary with time, and n are the mode shapes.

Equation (7) may be written in the more compact matrix notation:

Yu (8)

Where the modal matrix is whose columns are the mode shapes, and Y is a vector of the modal

amplitudes:

N ...321 (9)

Nn

T YYYYYY ......321 (10)

The modal amplitudes, nY are often referred to as generalized coordinates which may be contrasted with

the natural coordinates x. Modal analysis is a process of decomposing (6), using generalized coordinates,

so as to obtain a set of differential equations that are uncoupled, each of which may be analyzed as a

single degree of freedom.

Mode superposition is an efficient method of analysis because of the modal summation, given by (7), is

usually dominated by the lower modes of vibration, allowing higher modes to be excluded from the

analysis without significant error.

3 Structure characteristics and materials properties

The FE model was developed based on a particular three story industrial building in South East Asia. The

building has dimensions of 29mx20m in plan and a total height of 17m. The basic structure consists of a

reinforced concrete frame comprising columns and beams with various cross sectional dimensions without

a pile system. This frame structure supports slabs with three different thicknesses: 300mm at first floor,

160mm at second and third floor and 225mm at the roof level. Figure 3 shows the 3D FE model of this

building. The structural material used for columns and beams is concrete with density of =2400 kg/m3,

Young’s Modulus, E=38GPa, and Poisson ratio, =0.2. The modal damping ratio was assumed to be

=2%. The beam and column elements were modeled in ANSYS by using BEAM4 element, while the

slab was modeled using SHELL63 element. The base slab is fixed to the ground.

The response of the building was assessed by means of transient analysis of the response to free field input

signal (acceleration) as shown in Figure 4. One third octave band for the acceleration input with the

vibration criteria curve (VC-D) is shown in Figure 5. The structural velocity response was checked against

the VC-D curve to determine whether it velocity was over the limits or not.

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Figure 3: Finite element mesh of the industrial building

Figure 4: Acceleration input, time history (top) and frequency (bottom)

Figure 5: One third octave velocity spectra with vibration criteria curve (VC-D)

3.1 The structural response with rigid base foundation

The FE Model developed in ANSYS shows that the lowest mode of the superstructure with a rigid body

(sway) mode occurs at 2.58 Hz (mode 1) as shown in Figure 6(a). A few other modes are also shown in

the same figure. For example, the third floor has a vertical deformation at 11.33 Hz (mode 16), the first

mode where floor response significantly. The second floor similarly has a vertical deformation at 19.31

Hz. The FE model predicts about 50 modes of the structure falling under 20 Hz. These low frequency

modes display mostly global horizontal bending modes and global torsional modes of the whole building.

The remaining mode above 20 Hz indicates global horizontal bending of the whole building and the

columns.

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(a) Mode 1, 2.58 Hz

(b) Mode 16, 11.33 Hz

(c) Mode 50, 19.31Hz

Figure 6: Mode shapes and natural frequencies for selected modes

Figure 7 shows the responses from transient analysis both the time histories and frequency contents for

velocity responses for the investigated floors. The first floor was not considered as it is a fixed base onto

the ground. The maximum instantaneous velocity responses of the second and third floor were 2µm/s and

4µm/s, respectively. The peak amplitude is similar for both floors at about 7 Hz. The ground vibrations

above 20 Hz are not transmitted to both floors, which is a consequence structural damping.

Figure 8 shows one third octave velocity spectra for both floors. The structural responses are checked with

the design vibration criteria whether they lie within the acceptable limits or not. It shows both investigated

floors are not exceeding the limit VC-D (input signal). It is VC-B for the second floor, which is most

suitable for vibration sensitive equipment, for example an inspection and lithography equipment

(including steppers) to 3 µm line widths for the size of microns. For the third floor, the analysis shows

VC-A is adequate in most instances for optical microscope up to 400X, microbalances, optical balances,

proximity and projection aligners, etc up to the size of 8 microns.

These analyses demonstrate that the three stories of the structure fall within the limit of the design

vibration criteria. These predictions on dynamic response analysis will be used for selecting and designing

an effective pile foundation system. The effect of the foundation system to the same structure will be

investigated whether it still follows the limitation or not.

(a)

(b)

Figure 7: Time history and frequency content of the vertical structural velocity in the middle of (a) second

floor and (b) third floor

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Figure 8: One third octave band spectra with the vibration criteria curve for second floor (top, VC-B) and

third floor (bottom, VC-A)

3.2 The structural response with pile foundation

Further analysis is done by applied the similar structure with the piles as a foundation system to support

the structure. The foundation system in this analysis are comprises 15 piles with 7.5m length. The material

properties of piles with radius r= 0.3m and the wall thickness is 0.15m [15]. Bending stiffness is

=0.34GPam4, axial stiffness is =11GPam

4, Young’s modulus of piles is E=28GPa and density

=2667kg/m3. The properties of the soil are Young’s modulus, E=0.28GPa, density =2000kg/m

3, Poisson

ratio, =0.4 and damping loss factor=0.02. The piles were simulated in ANSYS by using elastic BEAM

element [16].

The effects of the piles to the structure were evaluated by comparing the results with the results obtained

for building with rigid base foundation. Figure 9 shows selected vibration modes which include

deformation of the piles. The first mode increased from 2.58 Hz (rigid base) to 3.66 Hz (pile foundation).

Mode 1 and Mode 2 show a global torsional and bending mode for the columns as shown in Figure 9(a)

and 9(b). The vertical deformations of the floors (third floor and roof) occur at 11.27 Hz (mode 13).

Figure 9(d) shows vertical bending modes in all floors at a frequency of 12.04 Hz. The other vibration

modes mostly show global horizontal bending of the whole structure. The pile does not affect significantly

the behavior of the superstructure at all obtained frequencies.

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(a) Mode 1, 3.66 Hz

(b) Mode 2, 5.37 Hz

(c) Mode 13, 11.27 Hz

(d) Mode 19, 12.04 Hz

Figure 9: Selected mode shapes and natural frequencies of the structure supported on pile foundation

Time histories analysis and frequencies content for structure is shown in Figure 10. For the second floor,

its maximum velocity response is 0.02µm/s and the peak amplitude occurs at 9 Hz. Significant vibration

amplification can be seen between 5 to 10 Hz for the second floor (Figure 10 (a)). The ground vibrations

are not transmitted to the second floor after 10 Hz, but different response occurred with the third floor

until 20 Hz. Third floors has a similar response with the previous analysis, which is the piles did not

influence too much for the floor behavior.

According to the design vibration criteria analysis, it can be found that for both floors, they have same

criteria curve which are VC-A as shown in Figure 11. Second floor shows the significant changed from

VC-B to VC-A after analyzed with the piles foundation. These analyses also shows the whole structures

are acceptable within the limits of generic vibration criteria for sensitive facilities guidelines.

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(a)

(b)

Figure 10: Time history and frequency content of the vertical structural velocity in the middle of the floor

structure with pile foundation system, (a) second floor and (b) third floor

Figure 11: One third octave velocity spectra for second floor (top, VC-A) and third floor (bottom,

VC-A); structure with pile foundation system

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3.3 Comparisons results with vibration criteria (VC) curve

The comparison of the results of two analyses (rigid base and pile) with design vibration criteria is

presented in Table 2. It shows that the vibration criteria for sensitive equipment for the structure are

achieved; the response vibrations are not over the limit from the input signal. Pile foundation system does

not affect performances of the structure due to transmission of ground vibration into the observed floor.

However, it increases the detail size of the sensitive equipment from 3 microns to 8 microns (VC-B to

VC-A) for second floor. The performance of the third floor is not affected by the foundations system. The

response was the same for a structure fixed at the base or supported on pile foundation.

Observed

floors

Foundation

system

Maximum

velocity

Peak

amplitude

Design

criteria,

VC

Comparison with

input, VC-D

Second floor Rigid base 2 µm/s 7 Hz VC-B OK

Piles 0.02 µm/s 9 Hz VC-A OK

Third floor Rigid base 4 µm/s 7 Hz VC-A OK

piles 4 µm/s 7 Hz VC-A OK

Table 2: Comparing results with design vibration criteria for both floors

4 Conclusions

The main aim of this study was to assess the feasibility and rationality of a method of low level vibration

simulation analysis based on free field measurement, in which the boundary condition of the simulation

model is defined by the acceleration time history of finite points obtained through site measurement. The

work was carried out as a stage-by-stage design procedure using a combination of site vibration

measurement and numerical simulation analysis. The results of the analyses were compared with design

criteria for vibration sensitive facilities and showed that, for the given structure and site vibration

conditions, the stringent micro-vibration criteria were satisfied.

The following conclusions can be drawn from this study:

1. The results of numerical simulations agree with on-site measurements of response.

2. The vibration response of the building with rigid base foundation predicted by the finite element

analysis, which was verified by the free field measurement, provides reference for the next design

(building with pile foundation system).

3. The compared results of finite element analysis shown that the applied methodology is rational

and feasible.

Acknowledgements

This research is fully funded by Ministry of Higher Education Malaysia (KPTM) and Universiti Tun

Hussein Onn Malaysia (UTHM). Their financial support is gratefully acknowledged.

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References

[1] G. A. Athanasopoulos, P. C. Pelekis, Ground Vibrations from Sheetpile Driving in Urban

Environment: Measurements, Analysis and Effects on Buildings and Occupants, Soil Dynamics

and Earthquake Engineering, (2000), 19, pp. 371-387.

[2] M. Gendreau, C. H. Amick, T. Xu, The Effects of Ground Vibrations on Nanotechnology

Research Facilities, Proceedings of the 11th International Conference on Soil Dynamics &

Earthquake Engineering (11th ICSDEE) & the 3rd International Conference on Earthquake

Geotechnical Engineering (3rd ICEGE), Berkeley, California (2004).

[3] C. G. Gordon, E. E. Ungar. Vibration Criteria for Microelectronics Manufacturing Equipment,

International Conference on Noise and Vibration. R. Lawrence (1998).

[4] C. G. Gordon, Dynamics of Advanced Technology Facilities: A Historical Perspective,

Proceedings of 12th ASCE Engineering Mechanics Conference, La Jolla, California (1998).

[5] E. E. Ungar, D. H. Sturz, C. H. Amick, Vibration Control Design of High Technology Facilities,

Sound and Vibration, (1990).

[6] J. J. Kim, C. H. Amick, Active Vibration Control in Fabs, Semiconductor International, (1997).

[7] A. Bayat, J. B. Davis, Converting Semiconductor Fabs: The Vibration Design Perspective,

Journal of the IEST, 48 (1):161-168, (2005).

[8] B. Bessason, C. Madshus, H. A. Froystein, H. Kolbjornsen, Vibration Criteria for Metrology

Laboratories, Measurement Science Technology, 10:1009-1014, (1999).

[9] C. G. Gordon, Generic Criteria for Vibration-Sensitive Equipment, International Society for

Optical Engineering (SPIE), Proceedings of the SPIE, (1991), pp.71-85.

[10] C. H. Amick, M. Gendreau, T. Busch, C. G. Gordon, Evolving Criteria For Research Facilities: I

– Vibration, SPIE Conference 5933: Buildings for Nanoscale Research and Beyond. San Diego,

California ( 2005).

[11] ANSYS, ANSYS Operation Guide, ANSYS 6.1 Edition, ANSYS Incorporated, (2002).

[12] J. M. W. Brownjohn. Vibration Control of Sensitive Manufacturing Facilities. Proceedings,

EVACES 2005, 2005 October 26-28, Bordeaux, France, (2005).

[13] E. Wang, T. Nelson, Structural Dynamic Capabilities of ANSYS. CADFEM GmbH, Munich,

Germany.

[14] J. W. Smith. Vibration of Structures, London, UK:Chapman and Hall, (1988), 275 pages.

[15] J. P. Talbot, H. E. M. Hunt, Isolation of Buildings from Rail-Tunnel Vibration: a Review,

Building Acoustics, 10 (3):177-192, (2003).

[16] S.M. Huang, J.Y. Yue, C. Zhou, W. Li, Design and Practice of Micro-Vibration Control for the

Pile Foundation of a Special Sensitive Facility on Soft Subsoi,. Proceeding of ISEV2009-

Environmental Vibrations: Prediction, Monitoring, Mitigation and Evaluation, China, (2009),pp.

299-307.

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