A_55_Isolation of Buildings from Ground Vibration

14 Pages·01.254 MB·English

39
Isolation of buildings from ground vibration: a review
of recent progress
D E Newland, MA, ScD, FEng, FIMechE, FIEE and H E M Hunt, PhD, CEng, MIMechE
Department of Engineering, University of Cambridge
Many buildings near railways are mounted on rubber springs to isolate them from ground vibration. This paper reviews the theory o f
resiliently mounted buildings and discusses recent calculations of the effects of (a) diffkent damping models and (b) piled foundations.
The paper also describes site measurements in London and laboratory tests in Cambridge which are being made to support new
analytical work.
1 PREAMBLE station booking hall); secondly, the vibration measuring
equipment available at the time was relatively primitive.
One of the authors (DEN) was an undergraduate at
No narrow-band analyses were made and there are no
Cambridge when Dick Bishop was a lecturer here and
more recent measurements at this site known to the
subsequently came to know Dick well in several capac-
authors.
ities, but particularly as a fellow member of the Edi-
In the twenty-year period that has elasped since
torial Panel of this Journal for many years; the other
Albany Court was built, very much bigger buildings
(HEMH) now lectures in Dick’s old department on the
have been mounted on springs and methods of vibra-
same subjects. It is an honour to have this opportunity
tion measurement and analysis have become much
to contribute to his memorial issue. In doing so the
more sophisticated. As a result there has been a growing
authors offer their sincere tribute to Professor Bishop’s
realization that a resiliently mounted building is a
remarkable achievements in vibration engineering.
complex dynamical system in which the properties of
Others have recorded his many accomplishments, but
the foundation, the method of isolation, and the flex-
one particular quality was his encouragement of col-
ibility and damping of the building all contribute to the
leagues. This short review paper is offered as a mark of
overall dynamic response. It is now recognized that this
respect and gratitude for that encouragement and for all
response cannot be described by a simple model of a
his work. This includes many papers on the vibration of
mass on a spring. However, the alternative has not yet
beams, plates and structures which are subjects close to
been agreed in the sense that there is no generally
the authors’ present one of building vibration.
accepted model for calculating the effectiveness of vibra-
tion isolation measures for buildings.
In this paper recent progress towards that objective is
2 INTRODUCTION
described. A first impression might be that the large-
In the United Kingdom, the six-storey Albany Court scale finite element computer programs now available
building in London was the first to be isolated against would make the necessary calculations straightforward
ground-transmitted vibration from an underground in principle (if complex in setting up the detailed
railway (1). Underneath the building, the railway had a geometry required). It turns out that the problem is
set of switch points; the vibrations generated in a pre- much more complicated than this because of lack of
vious building on the same site were said to be ‘fairly knowledge about how damping should be described
perceptible’ with r.m.s. vibration levels up to 1 mm/s. and about how it is distributed throughout a building
The new building was mounted on laminated rubber and because of the complex soil/structure interaction
springs which were designed to give a vertical fre- that occurs at the foundation of the building.
quency of 7 Hz. According to measurements taken
shortly after its completion, the vibration environment
in the sprung building was reported to be in the range 3 THEORETICAL PREDICTIONS OF
VIBRATION TRANSMISSION
0.16-0.25 mm/s for a bandwidth of 3-30 Hz. Waller (2)
recorded that ‘The (Albany Court) building was behav- For a rigid mass on a flexible foundation, the transmis-
ing substantially as a rigid body’. This conclusion, that sibility of harmonic vibration from the ground has the
the behaviour of buildings on springs could be well-known form shown as the solid line in Fig. I.
explained by the motion of a rigid body on a damped Transmissibility is defined as the ratio of the amplitude
elastic spring, became conventional wisdom which has of response of the supported mass to the amplitude of
only been challenged relatively recently. There are two excitation of the ground. The high-frequency response
explanations for this. Firstly, the Albany Court building decays at a rate of 20 dB/decade and the width of the
was a small building (a block of seven flats over the resonant peak depends upon the damping ratio of the
resilient support. This dynamical model assumes linear
viscous damping, linear elasticity and only vertical exci-
The MS was received on 17 September 1990 and was accepted for publication on 6
February 1991 tation.
COS390 @I IMechE 1991 09S4-4062/91 $2.00 + .OS Proc Instn Mech Engrs Vol 205
D E NEWLAND AND H E M HUNT
Fig. 2, and for which the response is calculated at z = 0,
immediately above the pad. The properties of the
resilient pad are such that, for a rigid column of the
same mass as the flexible column, the undamped
natural frequency of the suspension would be 9 Hz and
- ?i
..-- its damping ratio would be 0.1. The material of the
-0 *;
.9 % -10 column has the density and elasticity of concrete (see
E Appendix 2) and there are two different damping
2
E assumptions. Damping assumption A (dashed) is one
-20
for which all the column modes have the same band-
I: width. Damping assumption B (chained) is one for
!!ii II<'' 12: It I: which the modal bandwidth increases in proportion to
5
I the square of the mode's natural frequency. The two
I
damping assumptions may be combined in any propor-
0 20 40 60 80 100 120 140 160 180 200
tion; however, all the results in this paper are shown for
Frequency
pure damping A or pure damping B as indicated. The
Hz
physical models which these damping assumptions
Fig. 1 Transmissibility curves for a 30 m elastic column
describe are (A) distributed viscous damping to ground
resting on a 9 Hz resilient foundation at its base:
and (B) internal distributed viscous damping [see refer-
dashed curve, column damping assumption A;
ence (3), Fig. 12.201. Numerical data are given in
chained curve, column damping assumption B; solid
Appendix 2.
curve, a rigid column of the same total mass.
(Displacement excitation below base of resilient pad Similar results are given by Grootenhuis (4) using a
at h = 0; displacement response measured imme- third damping assumption that the modal bandwidth
diately above pad at z = 0, see Fig. 2) increases in proportion to frequency (not frequency
squared). This is the consequence of using a complex
3.1 Response of a single column elastic modulus for the column with a constant ratio of
real part to imaginary part.
For the theoretical case of a flexible elastic column
All these response calculations use the exact theory
(with damping) supported vertically on a resilient pad,
for the longitudinal vibration of a continuous elastic
the transmissibility for vertical displacement excitation
column. The resilient isolation pad is modelled by a
at ground level (that is on top of the pile in Fig. 2) and
linear, massless spring with viscous damping in our cal-
displacement response at height z is given in Newland
culations (Fig. l) and by a linear, massless spring with
(3) for a number of different cases. Exact results have
hysteretic damping in the calculations by Grootenhuis
been calculated by solving the partial differential
(4).
equation in Appendix 1. Two of these cases are shown as
Figure 1 illustrates the importance of modelling a
the dashed and chained curve,s in Fig. 1. They app ly for
building as a flexible structure. Local resonances of the
a damped elastic column of 30 m height which is
supported assembly greatly modify the transmissibility
mounted on a damped resilient pad at its base, h = 0 in
and the form of the transmissibility curve depends on
the elasticity of the building and the damping mecha-
Flexible column
nism. The role of different damping models is clearly
important in determining overall response levels. At
present there is little fundamental knowledge about the
30 m mechanisms of energy dissipation in large buildings and
Dibplacement rebponse
research is in progress to try to obtain more informa-
,at position z (metres)
tion.
above ground level
Ir
3.2 Response of a column on a pile
Resilient pad The column calculations described above determine the
at position h (metres) ratio of the vibration level on the column above the
above ground level isolation pad to that below the isolation pad. In prac-
tice, the isolation pad will rest upon the building's foun-
dations which are generally piles embedded in the
I ground. Therefore it is important to calculate the trans-
'i mission of vibration from the surroundings through a
building's foundation in order to determine the level of
vibration likely to occur below the isolation pad.
A dynamical system has been studied consisting of a
vertical elastic column mounted on a single vertical pile,
both with and without an intermediate resilient iso-
lation pad. Both the column and the pile have the same
dimensions and material properties as those for the cal-
culations shown in Fig. l, with damping assumption A
Fig. 2 Damped eiastic column with resilient pad: model for (constant modal bandwidth). The modified response of
vertical vibration analysis the column-pile system is shown in Fig. 3a to d, as cal-
Part C : Journal of Mechanical Engineering Science 0 IMechE 1991
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42 D E NEWLAND AND H E M HUNT
important practical consequences in the building’s
design. For example, the location of isolation pads
could then be chosen so as to minimize vibration at a
particularly sensitive location such as an operating
theatre in a hospital.
3.3 Response of more complicated structures-the
finite element method
The theoretical results discussed above are for the longi-
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approximate model for the soil is used. For more com-
Frequency plicated cases, involving assemblies of columns and
Hz beams, an exact vibration analysis of the ‘building is‘no
longer practicable and various attempts have been
made to devise ad hoc. models of particular buildings.
Swallow (8) uses a lumped parameter model of a single
vertical column with additional masses and springs
attached to represent the action of connected floors.
The soil/foundation interaction is modelled by a mass
and spring, subject only to vertical excitation. Damping
is included by assuming complex stiffnesses. The author
concludes that the standard of isolation achieved
depends markedly on structural features and suggests
that good isolation relies upon tuning a building to its
specific site.
Willford (9) uses a somewhat similar model for prac-
Frequency tical calculations. This also consists of a single vertical
HZ column, but the connected floors are modelled by finite
element idealizations, each floor having four elements.
(a) Transmissibility curve for response at the top of The soil model is a frequency-dependent spring and
the column (z = 30 m) and excitation at the pile cap dashpot whose parameter values depend on foundation
for a column resting on a pile, with an isolation pad size and the estimated shear wave velocity in the soil.
located at h = 0 m (solid line), 10 m (dashed), 20 m Willford’s model has been used to analyse several build-
(chained) and 29.75 m (dotted) from the base of the ings in London, and apparently achieved good agree-
column. The three-dimensional figure (b) shows the ment with site measurements.
variation of transmissibility with pad position chang-
We have modelled a two-dimensional frame structure
ing continuously from 0 to 30 m
having two columns and two connecting floors using a
finite element model. In order to determine how many
nearly at the top). The stiffness of the pad is calculated elements to include in this model, the response of a
at each location to give a rigid-body resonant frequency single column was first calculated by finite element
of 9 Hz, so that the pad stiffness reduces linearly with analysis to compare with the exact results described
its position up the column. The equivalent damping above. The results quoted below were computed by
coefficient is also adjusted so that the damping ratio Bhaskar (lo), using his own finite element program.
remains at 0.1 for all pad positions. From Fig. 4a, it is They have been compared with similar results obtained
clear that, for response measured at the top of the by Wilson (11) using the MARC-K2 program. There are
column (z = 30 m) and excitation measured at the base some detailed differences between the results obtained,
(z = 0), the position of the isolation pad significantly due we believe to differences in the way in which
influences transmissibility. When the pad is at the top of damping is included in the finite element models. Figure
the column (dotted curve), the transmissibility becomes 5a and b shows Bhaskar’s results for the response of the
close to that for the rigid mass shown in Fig. 1, because same elastic column as in Fig. 1. They show transmis-
the small piece of column remaining is very stiff com- sibility measured across the resilient pad when this is
pared with the stiffness of the isolation pad; the reson- located at the base of the column, h = 0. Calculations
ance peaks that are still observable arise from the are compared with the known exact solution for both
motion of the part of the column below the pad. An damping assumptions A (Fig. 5a) and B (Fig. 5b). Four
overall picture of the variation of transmissibility with finite elements represent the column and a discrete
pad position is shown in Fig. 4b. spring and viscous damper model the isolation pad. In
These results show that quite simple elastic models the MARC-K2 program, it is difficult to select a discrete
have vibration amplitudes that vary widely with posi- damper as an element so that the pad is represented by
tion and frequency. Similar variations occur in real an additional (fifth) element with its own stiffness and
buildings. Advance knowledge of the distribution of damping. In both graphs, the exact solution is shown as
vibrational energy within a large building may have the solid line for comparison with the results computed
Part C: Journal of Mechanical Engineering Science Q IMechE 1991
ISOLATION OF BUILDINGS FROM GROUND VIBRATION: A REVIEW OF RECENT PROGRESS 43
30 m
t t t
a a 2
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lot
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0m
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-40 I I
0 20 40 60 80 100 120 140 160 180 200
Freauencv $i
Hz
(a) For damping assumption A
20 I I
0 Pinnedjoint Rigidjoint
Fig. 6 Finite element model of two-dimensional frame struc-
ture with ground excitation at one point
sixteen elements (excluding the two pads) and sixteen
nodes each with three degrees of freedom. The bearings
beneath both feet are modelled by parallel springs and
viscous dampers. The left-hand bearing is on a fixed
foundation but the right-hand bearing is subjected to
vertical displacement excitation x at its base. The foot
of the left-hand column is constrained horizontally to
prevent rigid-body motion. Each finite element has two
Frequency nodes, one at each end, and each node has three degrees
Hz of freedom which are the axial and transverse displace-
(b) For damping assumption B ments and the in-plane rotation of the element at the
Fig. 5 Transmissibility measured across the resilient pad in node. The distribution of displacement along each
Fig. 2 when this is at the base of the column, h = 0. element is assumed to be linear in the axial direction
Finite element results are shown as the chained line (constant axial strain) and cubic in the transverse direc-
(constant-strain element) and the dashed line (linear- tion (corresponding to the deflection equation of an
strain elements). For comparison, the exact solution is
Euler beam).
shown as the solid line
The (transmissibility) response at the base of the
right-hand column in Fig. 6 (point 1) is shown in Fig. 7a
with constant-strain finite elements (the chained line) and at the top of the same column (point 2) in Fig. 7b
and with linear-strain elements (the dashed line). for damping assumption A. In each case, the dashed line
It can be seen that there is good agreement between gives the response of the complete structure when mod-
the exact and finite element solutions for the first few elled by 16 elements. The corresponding response for
modes of vibration but that, for modes four and above, the four-element linear-strain model of the column
there is increasing divergence between the exact and alone is shown as the chained line for comparison in
finite element results. As expected, the linear-strain ele- each case. There are clearly gross differences in detail
ments give more accurate results than the constant- between the response of the column alone and the same
strain elements, but at the expense of greater complexity column when part of a framework, although some of
and longer computation time. If the number of elements the features of column response are discernible in the
is increased, accuracy is improved and we have investi- frame response. This is partly because of the dynamic
gated this for a different model. effect of the connected floors and partly because the
A single elastic column is limited in its representation linear axial-strain elements used for the column model
of a real physical system. For example, the floorspans of (which have three nodes per element, one at its centre)
a multi-storey structure exert bending moments on the are more accurate than the constant axial-strain ele-
supporting columns, causing bending resonances in ments used for the frame model. To investigate the
these columns as well as in the floorspans themselves. latter point, the same calculations have been made with
Figure 6 shows a two-dimensional frame structure with a 64-element model of the frame (the same as in Fig. 6,
ground excitation at one point. The representation of but with four times as many elements each one quarter
this structure by a finite element model is discussed in as long). These responses are shown as the solid lines in
Newland and Bhaskar (12). In Fig. 6, the model has Fig. 7a and b. It is clear that the sixteen-element model
@ IMechE 1991 Proc Instn Mech Engrs Vol 205
44 D E NEWLAND AND H E M HUNT
..
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0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200
Frequency Frequency
H7 Hz
(a) For point 1 (a) For damping assumption A
--
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0 20 40 60 80 100 120 140 160 180 I 0 20 40 60 80 100 120 140 160 180
Frequency Frequency
Hz Hz
(b) For point 2
(b) For damping assumption B
Fig. 7 Transmissibility curves for the frame in Fig. 6. The
solid curve in each case is for the 64-element model, Fig. 8 Transmissibility curves for a portal frame calculated
the dashed for the 16-element model and the chained for point 3 of the frame in Fig. 6. The solid curve in
gives for comparison the response of a single column each case shows the response calculated with the 64-
with four linear-strain elements. Damping assumption element model, dashed for the 16-element model and
A chained gives for comparison the response at the top
of a single column with four linear-strain elements
begins to fail above about 100 Hz, and that the two
models differ in detail above about 50 Hz.
3.4 Unified models that include sources of vibration
Generally the floor structures of a building are sub-
structures with low natural frequencies. Therefore they In order to model a complete building accurately, or
interact, particularly with the column modes which even part of a building, there is much further work to
have low natural frequencies. These features can be do. A reliable representation of the foundation is neces-
observed in the frame transmissibility curves of Fig. 8a sary, and there has been a considerable amount of work
for damping assumption A and Fig. 8b for damping on the dynamic properties of foundations [see, for
assumption B. The response at mid-span of the top example, reference (13)]. Although there have been spe-
floor, point 3 in Fig. 6, is compared with the response at cific calculations on the dynamics of rigid foundation
the top of a column alone. As in Fig. 7, the response of blocks on a semi-infinite elastic medium [for example
the 16-element frame model is given by the dashed line, reference (14)] and of the vibration of piles (7), there
the 64-element frame model by the solid line, and the have been very few attempts [reference (15), for
four-element column model by the chained line. We example] to bring these theories together to calculate
observe that the two frame response curves diverge after how the design of a building's foundation affects the
about 20 Hz. This, of course, is the limitation of the transmission of vibration into the building. None is sup-
finite element technique; for accuracy at the higher fre- ported by site measurements. Although there has been
quencies of multi-modal systems, it is necessary to use a much work on the response of buildings and their foun-
very large number of elements. There is also the ques- dations to earthquake loading, this concentrates on the
tion of damping, and it is clear from the differences very low frequency (below 2 Hz) shear response of the
between Fig. 8a and b that the correct choice of building, not on its response to typical ground vibration
damping model is as important as the correct choice of frequencies.
element size. As a next step, it is intended to combine the pile
Part C: Journal of Mechanical Engineering Science @ IMechE 1991
ISOLATION OF BUILDINGS FROM GROUND VIBRATION: A REVIEW OF RECENT PROGRESS 45
model described in Section 3.2 with a finite element correspond to the vehicle bounce and wheel hop fre-
model of part of a building in order to study the quencies respectively. The attenuation with distance of
response of the combined system. In addition, it is the higher frequency measured vibration is larger than
hoped that the representation of damping in the finite predicted, probably because material damping in the
element model will be improved by introducing the soil is higher than that included in the theoretical model
results of the experimental work described below. The at these frequencies.
overall objective is to describe quantitatively the com-
plete process of vibration transmission from roads and
4 FIELD MEASUREMENTS
railways. There are three main stages : (a) determination
of the excitation by analysis of vehicle response to road Although there have been many ad hoc measurements
or rail roughness, (b) transmission of vibration through of building vibration, the authors are not aware of
the road or rail system and the surrounding ground and many detailed publications in the literature. Swallow (8)
finally (c) the combined response of pile, isolation pad gives some limited data for an isolated building and
and building. Jakobsen (21, 22) gives some measurements for houses
Work on the ground transmission problem is already close to a railway line. In nine reports by the Office for
well advanced. It is possible to estimate the levels of Research and Experiments of the International Union
ground vibration transmitted from roads and railways of Railways (23), a variety of railway vibration data and
in certain circumstances, using a combination of site analysis is assembled.
measurements and theory. Some studies are based on One reason for the lack of published data may be the
traditional wave propagation theory [for example, refer- difficulty of obtaining accurate and repeatable results.
ence (16)] while others make use of substantial finite The authors’ experience is that successful site measure-
element calculations [see, for instance, references (17) ments of structural and ground vibration necessarily
and (lS)]. require sophisticated electronic equipment. It is desir-
In a recent study by Hunt (19, 20) random process able to have two, but preferably more, high-sensitivity
theory has been incorporated into a conventional visco- accelerometers which can be placed at strategic points
elastic half-space model of the ground so that the for simultaneous data collection. This needs a central
roadway may be treated as an infinite line of random data logger and calls for a number of long data cables
loading. For busy roads, when many vehicles are con- and remote amplifiers which can transmit data long dis-
tributing to ground vibration measured at a given point tances without picking up extraneous noise. Digital
near the road, a statistical treatment of vehicle rather than analogue recording eliminates tape recorder
dynamics makes it possible to predict ground vibration noise, and the time consuming step of digitizing data at
levels in a green field site (20). This model applies for a later stage is avoided. It is also possible to perform
vibration measurements at distances further from the some data analysis on site if the data logger is con-
roadway than the mean vehicle spacing. The model has nected to a computer. Digitized data amount to several
been validated by comparison with field tests at two tens of megabytes after a day of collecting vibration
sites where dynamic properties of the ground (including data, so a fast digital tape storage device is useful.
damping) were obtained by impulse testing. Measured Practical difficulties on construction sites may include
ground vibration spectra are shown in Fig. 9 (as the the absence of mains power, adverse weather conditions
broken lines) and compared with the results of calcu- and hazards posed by normal construction activities.
lations based on this statistical theory, the details of These are particularly troublesome when long cable
which are given briefly in Appendix 1. There are two runs traverse busy passageways. Communication is
peaks, one at about 2-3 Hz and the other at about 7- greatly hindered on large, and often noisy, building sites
15 Hz. in the calculated and measured responses which so a two-way radio is invaluable.
4.1 Instrumentation
The instrumentation that has been used to collect build-
ing vibration data for the work described later in this
section is shown in Fig. 10. The principal components
are a bank of six B&K8318 high-sensitivity acceler-
ometers and their corresponding line-drive supply
amplifiers which allow low-level vibration data to be
transmitted over distances up to 1 km. A CED sixteen-
channel data logger driven by a PC allows data to be
collected easily and transferred directly to a tape-
streamer.
4.2 Impulse response techniques
5 10 15 20 25 30 35 40
Frequency If a known input excitation is used, it is possible to use
measured response data to make quantitative estimates
Hz
of the dynamic characteristics of ground, foundation
Fig. 9 Calculated vibration levels at distances of 100, 200
and 300 m from a busy roadway near Cambridge and building. In order to produce measurable levels of
compared with vibration levels measured at distances vibration in a large structure, a large impulse is
of 200 m (dashed line) and 300 m (chained) required. We have found that sufficient excitation may
@ IMechE 1991 Proc Instn Mech Engrs Vol 205
46 D E NEWLAND AND H E M HUNT
I
16-channel
I data logger/
Line drive supplies
Ac-c elerometers
B & K 2813
I, ~,
-
Accelerometer
I
DJB 302 Al03lW lll11111111lll1
Charge amplifiers
B & K 251 I
IBM PClAT Tecrnar
tape-strearner
.
Impulse hammer
Fig. 10 Schematic of instrumentation used to measure vibration in large
buildings
be provided by dropping a 20 kg mass from a height of Each measured vibration signal is divided into two
2 m. The mass is attached to a pivoted hammer arm parts. During the first part, train vibration is clearly
because this is convenient to transport and to set up. dominant while the signal measured in the second part
The hammer head is fitted with a 50 kN force trans- is largely due to ambient noise as the train passes into
ducer and an accelerometer. The accelerometer allows the distance. The power-spectral densities of these two
the measured force to be corrected for the inertial parts of the measured data are calculated and plotted
loading of the mass in front of the force transducer. The on the same graph. Comparison between them makes it
magnitude of each applied impulse is very repeatable possible to determine which facets of the vibration spec-
and therefore impulse testing can be carried out while trum are apparently due to the passing train and which
other noisy activities are in progress. When a number of are components of the ambient noise. An example of
impulse responses are averaged together, extraneous this is shown in Fig. 12.
uncorrelated noise is largely eliminated. Transmissibility functions may be estimated from the
measured data. They are calculated from the first part
of the signal, which is dominated by train vibration. The
4.3 Analysis of field data estimation is complicated because of the many path-
ways for transmission that may exist. Suppose that it is
In a very short time, an enormous quantity of field data
required to estimate the transmissibility across a
can be collected, both from impulse response tests and
resilient isolation pad in the column of a building.
from measurements of ambient vibration.
Assume that transducers on either side of the pad have
The quantity of impulse test data can be reduced
recorded the local vertical accelerations (for example)
quickly by averaging all impulses for one given configu-
while a train is passing. Since the vibration transmitted
ration. Frequency-response functions may then be cal-
across the pad will be correlated with that below the
culated by discrete Fourier transformation. An example
pad, the transmissibility can be estimated from the
of such impulse response data is shown in Fig. 11 for
formula (24)
the case of the impulse response of a pile.
For vibration data generated, for example, by passing
trains, it is more difficult to reduce the quantity of data,
largely because each train input is different. The authors
have found the following procedure to be satisfactory. where index 1 denotes the transducer below the pad,
Part C: Journal of Mechanical Engineering Science @ IMechE 1991
ISOLATION OF BUILDINGS FROM GROUND VIBRATION: A REVIEW OF RECENT PROGRESS 41
shown in Fig. 12e. 7;ota,(w) is plotted as the solid line
and Girec,(w)a s the dashed line.
There are a number of ways of dealing with the
problem of incoherent data when calculating transmis-
sibilities; some of these are described by Bendat and
-60 L 1 Piersol (25). The calculation of coherence for multi-
0 0.02 0.04 0.06 0.08 0.I input systems is complex and that for distributed inputs,
Time
(a) Applied impulse such as road or railway excitation, even more so. If all
the inputs to a system are measured, then the multiple-
- coherence functions will approach unity, provided that
.-
the system is behaving linearly and that there is no
3 2 noise in the instrumentation. Since it is impractical to
- 0
2 measure all inputs to a building, poor coherence is inev-
itable.
T-ime
s 4.4 Measurements at Gloucester Park
(b) Pile cap response, demonstrating repeatability
A combined residential and retail complex is under con-
struction above the Gloucester Road underground
railway station in London. The station serves two
underground lines, the three surface tracks of the Dis-
trict and Circle Line and the two deeper tracks of the
Piccadilly Line. A single-storey retail block is being
built on top of a concrete raft which spans the three
surface tracks and the station platform. The residential
Frequency
block, a ten-storey structure adjacent to the retail block,
Hz
is supported on piles that pass within a few metres of
Magnitude of corresponding frequency-response function,
the Piccadilly Line. It is anticipated that the retail block
calculated from measured data (solid line) and from theory
will be influenced more strongly by vibrations from
(dashed line)
surface trains than from those of the Piccadilly Line,
but the residential block will be influenced by vibrations
from both.
Vibrations transmitted into the residential block are
being monitored throughout the various stages of con-
struction of the building. Some preliminary measure-
ments were made when the site was bare and again later
I 1
0 20 40 60 80 100 120 140 160 180 200 after the piles had been placed and these have been
Frequency compared with subsequent measurements made as the
Hz building progresses. As described above, both impulse
(d) Phase of the frequency-response function, calculated from response and train vibration data are being collected.
measured data (solid line) and from theory (dashed line) In the first instance, vibration measured above and
below an isolation pad is shown in Fig. 12a and b
Fig. 11 Impulse response of a pile measured at Gloucester
Park during the passage of a train. It can be seen in the time
traces that, after the train had departed, there is still a
significant amount of ambient noise. The power spec-
index 2 the transducer above the pad and S(w) the spec-
trum of the vibration measured above and below the
tral density at angular frequency w. This formula incor-
pad has been computed both from train-generated and
porates the cross-spectral density function S,l (w) and is
ambient vibration. The line shown between the two
close to a true estimate of the transmissibility provided
phases ‘train’ and ‘ambient’ is determined approx-
that only a small amount of the correlated vibration at
imately by eye from the signal below the pad; the same
2 arrives by paths other than through the pad. An alter-
dividing line is used for the signal above the pad (where
native calculation of the transmissibility
the two phases are less distinct). In each case, it can be
seen from Fig. 12c and d that ambient noise is
responsible for some of the spectral peaks in the vibra-
tion spectrum that occurs during the passage of a train.
includes the total response above the pad, regardless of The transmissibility function GireCt(aon) d Total(w)a re
the transmission path and regardless of its correlation shown in Fig. 12e and the difference between them indi-
with vibration below the pad. Tdirsehcou,l d be used to cates that there is a large amount of vibration reaching
estimate the true transmissibility but the occupants of a the floor above the pad which is not correlated with
building do not distinguish between correlated and vibration below the pad. The direct transmissibility
uncorrelated vibration, and so will be interested in shows greater peakiness which is more characteristic of
rota,
Total.E stimates of do not require simultaneous the theoretical column response than the smoother total
measurement of vibration at 1 and 2 since the cross- transmissibility.
spectrum is not required. An example of transmissibility Impulse testing has produced a clear picture of the
estimates determined from the above two formulae is way in which the piles respond to vibration applied
@ IMechE 1991 Proc lnstn Mech Engrs Vol 205
48 D E NEWLAND AND H E M HUNT
10 1
:t
4
.E- 2
;- N;
0
o”E
2 -2
-
-6
-
-8 Train Ambient
I
-10- 10-4
0 20 40 60 80 100 120 140 160 180 200
Frequency
H7
(d) Power spectra below the pad
1 1
I
-8 Time Ambient
-101 I -40 I
0 0.5 I 1.5 2 2.5 3 3.5 4 4.5 5 0 20 40 60 80 100 120 140 160 180 200
Time Frequency
s Hz
(b) Vibration below the pad (e) Transmissibility curves
E
2
I
g g e2,
m <m
5 0.6
.- r
--% 2E 6
e,- 0.4
2
10-4
1
. . . . . .
10-51 , , ,
0 20 40 60 80 100 120 140 160 180 200
Frequency Frequency
Hz Hz
(c) Power spectra above the pad (f) Coherence between signals
Fig. 12 Measurement of transmissibility across an isolation pad: (a) shows
vibration measured above and (b) below the pad, divided into two
parts marked ‘train’ and ‘ambient’; (c) shows the corresponding
power spectra above the pad and (d) below the pad, calculated
separately for ‘train’ (solid line) and ‘ambient’ (dashed) vibration; (e)
shows transmissibility curves Tota,(m) (solid line) and ?&,(m)
(dashed) for train vibration only; (0 shows coherence between
signals in (a) and (b) for the duration when a train can be detected
Part C: Journal of Mechanical Engineering Science Q IMechE 1991