23rd International Congress on Sound & Vibration
Athens,
Greece
10-14 July 2016
ICSV23
RESEARCH DEVELOPMENT OF SUBWAY VIBRATION
IMPACT ON ENVIRONMENT
Yao Kun
Beijing Municipal Institute of Labour Protection, Beijing 100054, China
email: [email protected]
Yu Hao-wei
Beijing Metstar Radar Co., Ltd, Beijing 100094, China
Wei Dong
Tsinghua University, Beijing 100084, China
With the development of subway in China, the impact induced by subway operation on
environment is more and more seriously concerned. Research work in this field has been carried
out both in China and abroad. This paper simply introduce subway vibration research, and the
research progress of vibration mechanism, trains’ dynamic loads, spread of vibration waves and
vibration control measures. On that basis, the paper indicates that researches on dynamic theory
of vehicle-track interaction, regularity of subway responses to environmental vibration, vehicle
vibration analysis methods and vibration insulation and reduction measures are insufficient.
1.
Introduction
With the development of subway in China, vibration and noise generated from subway operation
impact on communities, sensitive buildings, precise instruments, etc is more and more seriously
concerned.
Since 70s, a lot of research work on vibration theory, numerical simulation, experiments has
been carried out. Because of complexity of vibration source, uncertainty of transmission peculiarity
and diversity of research subjects, study on vibration sources, transmission, effect and vibration
insulation measures, etc haven’t been finished, deeply research on subway vibration for improving
estimate accuracy and controlling vibration influence is meaningful.
This paper introduces advances in subway vibration theory, sources and insulation measures,
combining main methods, hotspots and difficulties of subway induced vibration research, which
could be used for reference for research in China.
2.
Vibration mechanism
2.1 Vibration Sources
Subway induced vibration and noise is mainly from wheel system and train power system, the
factors induced vibration and noise are (1) dynamic vehicle vibration (when train run up and down,
nod, shake, aking, eccentric wheel, wheel tread irregularity), (2) track irregularity (steel rail
irregularity; discrete support of rail joint, sleeper and fastener; transformation of track type;
sub-grade stiffness, etc).
2.2 Vibration Transmission
Moving train makes an impact on track, then the effect passes through the tunnel into the
surrounding soil strata and nearby buildings or structures (both over and underground) to vibrate.
Such vibrations may induce secondary-vibration and noise interior structure [1,8]. According to the
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The 23rd International Congress on Sound and Vibration
subway vibration generation, transmission and effect peculiarities, its impact on the surrounding
environment have three steps [9] (Figure 1): (1) vibration generation-wheel acts on track generates
incentives; (2) vibration transmission-that vibration passes through the track foundation and lining
structure to the surrounding soil and building overground; (3) vibration effect-the vibration affect
on buildings along the ground, and then induces secondary vibration and noise of the building
structure.
Figure 1: Vibration induced by subway track.
2.3 The main factors of subway vibration impact on the surrounding environment
The strength of subway vibration affection on surrounding environment is not only related to the
tunnel structure and stratigraphic characteristics, but also related to the track structure, train types
and acceleration which are the main factors affecting the subway vehicle vibration. (Table 1)
Subway vibration transmission pathway factors can be divided into five sub-systems: vehicle,
track, tunnel structure (track bed and tunnel), stratigraphic and building structure. Current research
on the subway vibration problems briefly by two methods the overall analysis and sub-structure
analysis [8,11]. The former regards five sub-systems as whole, considering subsystems interaction
automatically during calculation, but the difficulty is due to huge computational demand.
Sub-structure analysis breaks down the whole system into several parts, analyzes separately, and
considers the boundary conditions between these parts to obtain the reaction of the whole system,
the difficulty is five sub-system intercoupling makes the research complicated.
Both of theoretic analysis and field measurement are not sufficient to assess and evaluate the
vehicle vibration, various methods must be combined effectively in order to achieve optimum
results.
Table1: Influential factors of subway vibration.
No.
1
2
3
4
5
6
2
Factors
Influence
Speed, load, cabin length, stiffness and damping of vehicle
Vehicle
suspension, wheel surface condition, creep coefficient between
wheel and rail, traction motor, gear, airflow
Rail line curvature, gradient, rail running surface condition, track
Track
mass, stiffness and damping, rail fasteners spacing
Track bed Type, structure, vibration isolation condition
Depth, wall thickness, size and shape of structure, foundation,
Tunnel
lining
Geological Composition, density, elastic modulus, shear coefficient and
conditions damping factor of soil and rock, terrain condition
Distance between lines, building type, structural material
Building
properties, structure size
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The 23rd International Congress on Sound and Vibration
3. Vehicle dynamic load source research
Research on vibration sources supplies load parameter for track-tunnel structure-strata and
building structure dynamics analysis. Vehicle generated vibration is random, thus dynamic load
acting on the track is extremely complicated. Determining vehicle dynamic load is a very important
topic in this field, scholars have made a lot of research [5,8,12-16]. According to multiple vibration
source models, there are approaches of vehicle dynamic load determination: model analysis,
laboratory analysis, empirical analysis.
3.1 Model analysis
Model analysis is building vehicle-track vibration system dynamic model, solving vehicle
dynamic load by analytical method or finite element numerical method. Usually when solving the
basic equations of vehicle-track coupling system, vibration source model is divided into vehicle
subsystem and track subsystem, and the interacting force coupling relationship between the two
subsystems [8]. Vehicle model have been developed from single moving load model to
semi-vehicle and whole-vehicle model considering the interaction of vehicle components; track
model have been developed from initial mathematical model to the lumped parameter model,
continuous elastic foundation beam model and the continuous elastic discrete points supporting
beam models, etc; and various wheel-track contact model considering coupling relationship of
sub-systems to determine contact condition between wheel and track have been developed rapidly
[12].
(1) Vehicle model
Table 2 shows the development of vehicle model [12-16], in Table 2, the first three models don’t
regard vehicle, wheel and track as a joint power system but simply consider vehicle quantity as
single wheel or uniformly distributed load, so the results can’t reflect the practical situation. The
forth model taking sub-systems structure of vehicle into account is more complete.
Table 2:Development of vehicle models.
Vehicle model
Model assumptions
Figure
P0
V
(a) original model, considering the upper
excitation as moving constant force load
(a)
1
Pt = P0 f(t)
V
(b) take force change into account, such as
resonance force load or impact load
(b)
m
V
(c) consider vehicle load as moving mass
2
(c)
M1
3
k
c
m
(d)
ICSV23, Athens (Greece), 10-14 July 2016
V
(d) bond sprung mass with unsprung mass
by springs and dampers, the model takes
inertia force and interaction of two masses
into account
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The 23rd International Congress on Sound and Vibration
Vehicle model
Model assumptions
Figure
(e) newer model, about sprung mass
considering both translation and rotation
inertial force, can simulate vertical
vibration of a two-axis vehicle or bogie
better
M1 J1
k
c k
c
m
m
V
(e)
M2 J2
c′
k′
4
M1 J1
k
1
c′
k′
M1 J1
ck
c k
ck
c
m
m
m
m
V
(f) vehicle-track multi-DOF vibration
system, the model analyzes vibration of
train body, bogies and wheelsets,
furthermore, bonds vehicle model with
track model by springs to reflect
vehicle-track power force interaction
(f)
(2) Track model
For track simulation, there are Timoshenko beam model and Euler beam model [8,12]. The
difference between two models is theory of Timoshenko beam includes shear stiffness and
rotational inertia moment of the beam, which will get more realistic solution. When focusing on the
dynamic properties of the track structure, Timoshenko beam model is better choice, and when
focusing on the vibration of the ground and building nearby, Euler beam model is common choice.
For simulation of support mode, there are continuous supported elastic beam model and discrete
supported elastic beam model [8,12]. The former regards sub-rail foundation as whole foundation
distributing evenly that reflects overall characteristics of track system; the latter describes sub-rail
structure as a series of discrete elasticity-damp support system, which reflects partial influence of
each sleeper support point (e.g. sleeper mass impact on vibration). Discrete support model can be
solved in both frequency and time domains, however, frequency domain solutions are limited to
linear behaviours inside the track’s structure [17].
According to the structural layers under the track, track model can be divided into [18-20]: (1)
one beam (single layer) track model with hypothesis close contact between rails and sleepers; (2)
second beam (double layer) track model that simulates rail-sleeper interaction by spring-damper; (3)
three layers track model which considers track bed in detail makes the model more complicate.
3.2 Test analysis
Test analysis is kind of common and intuitive approach to determine the vehicle dynamic load.
Test analysis is divided into two kinds of approaches in practice: one is vehicle dynamic load test,
which is testing rail dynamic load in field, then converting to vehicle dynamic load; the other is
constant loading method, which is based on the field measurement, gets rail vibration acceleration
expression by spectrum analysis, then establishes motion equation according to simplified vehicle
vibration model to deduce vehicle dynamic load.
Pan Shi-chang and Liu Wei-ning [21] researched responses of vehicle dynamic load in soil
tunnel, and obtained track force expression from the measured data. Liu Wei-ning and Sun
Xiao-jing [12] deduced vehicle dynamic load on the basis of the measured rail acceleration. Pan
Chang-shi, Lee De-wu [22], Xie Zheng-guang, Zhang Yu-e obtained vertical and horizontal
simulated load by using a line, two-line spring-mass system model respectively. Zhang Pu obtained
vertical simulated vehicle load of ShangHai subway by field measurement.
Test analysis can obtain wide vehicle excitation frequency range, meanwhile, considering the
wheels irregularity and track irregularity sufficiently. But test analysis only apply to specific track
and speed, and demands a large number of measured data, these are limits of test analysis in
application.
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3.3 Experience Analysis
When the field measurement and simulation analysis subject to conditions, experience data can
be used to analyze vehicle dynamic load, that’s experience analysis which simulates vehicle
dynamic load with a excitation force function.
Pan Chang-shi [22,25], Liang Bo [26] adopted excitation force function that reflected periodic
characteristic of vehicle load vibration (e.g. irregularity, additional dynamic load and rail surface
corrugation effect) to simulate wheel-track interaction. On this foundation, Zhang Yu-e [23,27]
obtained speed of 350 km/h vehicle vibration load based on British rail irregularity management
value. On the basis of irregularity spectral density function of trunk railway in China, Gan Hui-lin
[28 ] de duced track surface irregularity excitation force function by simulating the
stochastic process of specific spectral density function.
4.
Vehicle vibration impact on tunnel structure and surroundings
4.1 Experiment method
Experiment method is initial method to research subway vibration propagation, is the most direct
and reliable, but experiment is interfered by many factors and need large quantity data to do
statistical analysis, so it’s not common.
In the seventies last century, Lang [29] and Kurzweil [30] proposed simple prediction formula
about the magnitude of the distance. Based on subway vibration test in London, Degrande et al. [31]
studied vibration response of track and tunnel wall, and the correlation between vehicle speed and
ground vibration. Urgar [32] and Kurzweilet et al. [33] proposed correction parameter of existing
subway vibration prediction formula with test data of different train, track, tunnel and building type.
Okumura et al. [34] researched test data of 79 points in Japan, and analyzed effect of distance, rail
structure, train type, speed, train length and background vibration.
Experiment on subway vibration was carried out late in China, and mostly focused on EIA for
subway engineering. Xia He et al. [35] researched multi-storey buildings response to subway
vibration that showed characteristic of vehicle induced vibration on ground and underground is
significantly different, Liu Wei-ning [36] adopted spot test and simulation analysis to research soil
tunnel dynamic response under the influence of vehicle load. Ge Shi-ping [37] analyzed subway
vibration propagation in saturated soft soil based on ground test nearby #1 line in ShangHai.
4.2 Analytical method
Analytical method is establishing theoretical model for research objects, describing vibration by
theoretical derivation of mathematical mechanics. Analytical method is rigorous reasoning, can
provide a powerful reference for the numerical simulation and experiences predictions, but vehicle
vibration propagation in medium such as soil is very complex system problems, often be simplified
when modeling, and accurate analytical method have certain limitations in application.
Jones et al. [38] simplified strata as semi-infinite isotropic elastic domain, layered medium on
elastic foundation and rigid foundation, and simplified load as harmonic pressure within rectangular.
Based on substructure analysis method, Balendra [39] proposed a semi-analytical method to study
on tunnel-strata-building dynamic interaction. Hunt [40] adopted Stochastic theory and substructure
method to establish cross-section model that rigid tunnel and rigid strip foundation is embedded in
viscoelastic half-space, analyzed vibration waves propagation. Hussein [41] studied vibration of
floating slab track model by analytical method. Cao Yan-mei and Xia He et al. [20] proposed a
more complete train-track-soil interaction theoretical model based on the Green function. Liu
Wei-ning et al. [42] transformed infinite domain problem to periodic problem solving, and spectrum
periodic expression of the dynamic response of arbitrary points on space.
4.3 Numerical Method
With the development of computer technology, numerical simulation approaches plays an
increasingly important role in vibration research. At present, numerical simulation methods mainly
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The 23rd International Congress on Sound and Vibration
include: Finite Element Method, Boundary Element Method, coupling method, etc.
FEM is the most in common, which has good adaptability for dynamic analysis with complex
material properties and geometric structure. It should be noted that finite element method needs to
establish the effective artificial boundary, because FEM calculations needs to intercept a limited
area from the infinite medium. Studies show that paraxial boundary and transmitting boundary have
second order accuracy, but calculation is complex; viscous boundary has only one order accuracy, it
is widely used in engineering because the concept is clear and easy to program. Based on the
two-dimensional finite element method, Nelson [43] studied dynamic response of tunnel and
vibration insulation measures. Stuit [44] adopted static model, tack model and dynamic model to
research Netherlands’ subway vibration propagation and analyzed influence of cell size, soil
parameters, damping, boundary conditions, analysis software (e.g. ANSYS, LS-DYNA), etc for
results. In China, researchers [8,12,24] established 2D and 3D numerical model for Shanghai,
Shenzhen and Beijing subway by ANSYS, then obtained dynamic response rule in track foundation,
tunnel lining structure and soil.
Because BEM satisfies far-field radiation condition, when dealing with problems of infinite
domain, BEM has unique advantages. Combination of FEM and BEM is known as coupling method
or hybrid method that divides the field into two parts near-field and far-field and adopts FEM for
near-field, and BEM for far-field. Wang et al. [45] adopted combination of 12 nodes isoparametric
elements, 10 nodes triangular element and unbounded element to predict vehicle induced ground
vibration and propagation. Forrest et al. [46] adopted coupling method for the damping effect of
floating slab track.
5.
Vehicle vibration insulation
Subway vibration mainly spreads in form of waves through tunnel structure and surrounding
strata, so that insulation research includes three aspects [6]: reducing vibration source excitation
intensity, cutting off or reducing vibration transmission and passive isolation measure for objects.
About reducing vibration source excitation intensity, vehicle vibration insulation and track
vibration insulation [6,12]. Vehicle vibration insulation measures include: vehicle weight reduction,
radial bogie, axle configuration optimization, vehicle suspension systems resilient, flexible wheel,
damping wheel, grinding wheel tread, novel rolling stock; track vibration insulation measures
include: rail grinding and oiled, pasting damping materials on rail, seamless rails, elastic fastener.
Cutting off or reducing vibration transmission refers to tunnel and foundation structure damping.
Research shows that due to corners refraction of rectangular tunnel, vibration larger than the
horseshoe-shaped and circular; the tunnel section is bigger, the vibration is stronger; because of
distance, the tunnel is deeper, damping effect is better; likewise thickness of tunnel lining is larger,
damping effect is better. Continuous barrier (e.g. ditch, filled ditch, concrete wall, isolation barriers
combination), non-continuous barrier (piles and holes) and wave isolation block (WIB) can be used
to reduce vibration transmission.
About passive isolation measures, damping effect mainly relates to type and structure of
surrounding buildings [12]. In common, building with better foundation, bigger mass and vibration
isolation measures will have greater vibration attenuation.
6.
Development and outlook of subway vibration research
In summary, the present study on subway vibration has made great progress, but there are still
problems about vehicle-track coupling dynamic mechanism, rules of subway response to vibration,
subway vibration analysis method and damping measures not solved completely:
(1) Vehicle dynamic load simulation
All of existing methods have defects, to obtain precise vehicle dynamic load is impossible. For
example, model analysis method’s loading form of the model is too simple to consider vehicle-track
coupling adequately, and model analysis method consider only finite length track; Test analysis
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needs extensive field measurements which are not available for new lines.
(2) Vibration propagation in soil
Subway vibration propagation is closely related to dynamic characteristics of the soil, subway
passage soil is very complicated in practical engineering, meanwhile, mechanical properties of soil
have strong non-uniformity, dispersion and randomness. Rules of vibration absorption and diffusion
in soil based on wave theory and influence of soil (or stratum) parameters on vibration wave remain
to be further studied.
(3) Vibration waves effect on buildings evaluation
Attenuation, amplification and specific value of subway vibration induced secondary-vibration
and noise of buildings need to be further researched, otherwise, vibration and noise evaluation
objectives are lack of in-depth study.
(4) Analysis and evaluation methods of subway vibration
Until now, comprehensive and reliable method for subway vibration analysis and evaluation is
not available. Field measurement is not applicable because of experimental condition limit and
insufficient test data. Hardware requirements, assumptions of rationality, model parameter
selection,etc are difficulties for numerical simulation method.
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