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Physical modeling of the vibration mitigation by an isolating screen
Modélisation physique de l'atténuation des vibrations par un écran isolant
Masoumi H., Vanhonacker P.
D2S international, Leuven, Belgium
ABSTRACT: The vibrations generated by railway traffic in urban area can be mitigated using the isolating screens. Both
experimental and numerical simulations have been used by authors to realize the vibration transmission through the ground and the
soil-barrier interaction. Since a full-scale test is usually expensive and has some difficulties and limitations in terms of the soil
conditions and the cost of screen construction, a physical modeling of the problem in small-scale has been proposed. In frame of an
European project, a test bench consisting of a soil container and an isolating screen has been fabricated. The container is filled with a
very fine sand using the pluviation technique to guarantee the uniformity of the soil conditions and the repeatability of the test. A
small foundation excited by a shaker at different frequency ranges is used as the vibration source. The soil responses are measured by
accelerometers placed on the soil surface at different distances from the source. The isolating efficiency of a concrete screen has been
examined. Results of experimental measurements show a reasonable agreement with those obtained by the numerical modeling.
RÉSUMÉ : Les vibrations générées par le trafic ferroviaire dans les zones urbaines peuvent être atténuées par un écran antivibratoire.
Les simulations expérimentales ou numériques ont été utilisées par les auteurs pour réaliser la transmission des vibrations par le sol
ainsi que l'interaction sol-écran. Tandis qu'un essai à grande échelle est généralement cher et difficile à réaliser en termes de
conditions du sol et de coût de construction, une modélisation physique du problème en échelle réduite a été proposée. Dans la cadre
d'un projet européen, un banc d'essai constitué d'un conteneur de sol et un écran isolant a été fabriqué. Le conteneur est rempli par un
sable très fin en utilisant la technique de pluviation afin de garantir l'uniformité des conditions du sol et la répétabilité de l'essai. Une
petite fondation excitée par un excitateur à différentes gammes de fréquences a été utilisée comme source de vibrations. Les réponses
du sol sont mesurées par des accéléromètres placés sur la surface du sol à différentes distances de la source. L'efficacité d'isolation
d’un écran en béton a été examinée. Les résultats des mesures expérimentales montrent un accord raisonnable avec ceux obtenus par
la modélisation numérique.
KEYWORDS: Small-scale test, pluviation, soil-structure interaction, vibration mitigation, isolating screen.
1 INTRODUCTION
To assess the efficiency of isolating screens, besides several
numerical computations presented and discussed in the
literature (Adam and von Estorff 2005 , François et al. 2010), a
few researchers have been focused on experimental tests (Celebi
et al. 2010). Since a full-scale test is usually expensive and has
some difficulties and limitations in terms of the soil conditions
and isolating screen construction, small-scale tests with their
flexibility for selecting different soil conditions and screen
properties are more relevant. A major difficulty facing the
physical modeling of vibration problems in the soil is the
repeatability of the test and the replication of the in-situ stress
field. Other difficulties for realizing the boundary conditions in
the infinity where there are no reflections, may be resolved by
selecting an appropriate scale factor or a relevant size for the
soil container.
The similarity of the conditions between the model (small-
scale) and the prototype (full-scale) is guaranteed by the scaling
factors. The scaling factor is defined to extrapolate the relation
between the results of the small-scale testing to those of the
prototype. These relations represent the effects of the geometric
and the stress scale. Three different scale factors between the
small-scale model and the prototype can be defined as follows
(Altaee and Fellenius 1994), where the subscripts “m” and “p”
denote to the model and the prototype, respectively:
(1) the geometric scale ratio N = L
p
/L
m
, that represents a
linear relation between the corresponding dimensions in the
full-scale prototype and the small-scale model,
(2) the effective stress scale ratio n =
σ′
p
/
σ′
m
, that represents
the ratio of the effective stress at a certain depth in the prototype
to that at the corresponding depth in the model,
(3) the effective stress gradient ratio I =
′
p
/
′
m
, that is the
rate of change of stress with depth to that of the prototype. In a
conventional physical testing, and for the normal gravity
condition (1g model), the product of the stress-gradient ratio (I)
and the geometric scale ratio (N) is equal to unity when n = 1.
However, in a dry soil, the effective stress is equal to
γz
, and
the scaling factor n is related to the geometrical scaling factor N
such that n = N(
/
), where
and
are the unit weights
of the soil in the prototype and the model.
In a wave propagation problem (as a dynamic problem), an
additional scaling factor should also be considered for the time
or the frequency to guarantee the similarity of the stress wave
transmissibility in the model and the prototype. In a low strain
dynamic problem (a linear problem) where the influence of the
soil stress condition in the soil behavior can be neglected, the
dimensionless frequency ratio (
/
) must be identical in
both small and full scale test, where
is the excitation
frequency, and
is the wave velocity. Therefore, it can be
written that
(
/
)
p
=(
/
)
m
(1)
This results in the frequency scaling factor
/
=
(
/
)/
, and for identical wave velocity in model and in the
prototype, the frequency scaling factor is equal to the inverse of
the geometrical factor N. In table 1, the prototype to model
ratio’s for different physical units are presented where identical
soil properties (E,
ρ
,
ν
) in both model and prototype are
assumed. E,
ρ
, and
ν
are the Young’s modulus, the density and
the Poisson’s ratio, respectively.
