Jet-Grouted Columns of Soft and Lightweight
Geomaterials as Vibration Isolation Barriers
M. Kholmyansky(&) and Kh. Dzhantimirov
NIIOSP Research Institute, Research Centre “Civil Engineering”,
2nd Institutskaya, 6, 109428 Moscow, Russian Federation
mlkholmyansky@yandex.ru
Abstract. Analytical method is applied to investigate the influence of material
parameters and thickness of vibration isolation barriers on its efficiency. Jetgrouted columns of lightweight and soft geomaterials are shown to be the most
effective. The fact is confirmed by 2D modelling with finite element method.
Keywords: Vibration isolation barriers Jet-grouted columns
geomaterials Lightweight geomaterials
Soft
1 Introduction
In urban conditions, the proximity of sources of vibration and residential buildings
imposes severe restrictions on vibration. One of the principal vibration reducing
technologies is installation of barriers in soil to prevent wave propagation.
Many designs of vibration isolation barriers were proposed, including open trenches (Barkan 1962, Woods 1968, Haupt 1981) and wells (Aleshin et al. 2006), trenches
filled with water, bentonite slurry or concrete (Çelebi et al. 2009), gas-filled cushions
(Massarsch 2005), rows of piles (Liao and Sangrey 1978). There are proposals of using
of GeoFoam polystyrene foam laid in preliminary dug trenches (Alzawi and El Naggar
2011).
The simplest type of vibration isolation barriers are open trenches and wells, but
their depth and durability are limited. Trenches filled with bentonite slurry and gasfilled cushions are quite promising, but their design and maintenance during long-term
operation are difficult. Laying blocks of expanded polystyrene foam and other prefabricated elements in trenches requires a large amount of earthwork. The design and
operation of barriers with increased stiffness in the form of rows of piles and trench
walls cause fewer problems, but they are considerably more expensive and their efficiency is lower. Woods (1968), Haupt (1981) and other authors conducted field tests,
analytical studies and laboratory model experiments to study the screening performance
of open trenches and concrete walls.
In this regard, various vibration isolation barriers of reduced stiffness and density
created directly in the soil were proposed. A barrier made of columns of artificial
geomaterials manufactured using standard equipment for jet grouting technology
(Croce et al. 2014) was proposed (Dzhantimirov et al. 2008). There are proposals by
Uretek on the use of inclusions of polyurethane foam (PUF) in the soil and of vibration
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
M. Barla et al. (Eds.): IACMAG 2021, LNCE 126, pp. 621–628, 2021.
https://doi.org/10.1007/978-3-030-64518-2_73
622
M. Kholmyansky and Kh. Dzhantimirov
isolation barriers of aerated soil with reduced stiffness (Minaev 2014). If a soft infill
material is used, the behaviour of a filled trench resembles that of an open trench
(Coulier et al. 2013).
In all cases, the barrier material is characterized by a decrease not only in stiffness,
but also in density (compared to soil). At the same time, the strength, and therefore the
stability of the soil mass, is also reduced.
In this paper, vibration isolation barriers in the soil and made of jet-grouted columns (JGC) with low density and stiffness are considered. Using calculations with
analytical formulas for the one-dimensional case it is shown that a decrease in the
density of the barrier material with respect to the surrounding soil can give a significant
attenuation of vibrations along the path of their propagation. The result is confirmed by
numerical calculations for the two-dimensional case, taking into account the uneven
wave field in the soil.
2 1D Vibration Transmission for Vibration Isolation Barrier
Consider the effect of barrier parameters on the effectiveness of its vibration protection.
In (Massarsch 2005), when analyzing the effectiveness of barriers, the ratio of impedances Z = cq of soil (Z1) and vibration isolation barriers (Z2) is considered; here c is
the wave propagation velocity; q is the density. The energy transmission coefficient Te
is used (Massarsch 2005):
Te ¼
4Z1 Z2
ðZ1 þ Z2 Þ2
ð1Þ
This coefficient corresponds to the normal incidence of the wave at the interface
between two media and does not take into account the presence of two interfaces
between the soil and the barrier. Therefore, the energy transmission coefficient does not
depend on the angular frequency of vibration x and the barrier thickness d. Moreover,
this coefficient refers to the vibrations of the barrier itself, and not the soil behind it.
Absorption in materials here and hereinafter is not taken into account.
Wave propagation in layered media is described by Brekhovskikh (1980), where a
general formula is given for the transmission coefficient for the normal incidence of a
wave on a layer between media with different properties. In the case of a soil mass with
a vibration isolation barrier (a layer separating media with the same properties), it
follows from this formula that the absolute value of the displacement transmission
coefficient
1
T ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
cos2 a þ a2 sin2 a
ð2Þ
where a = xd/c2; a = (1/2) (Z2/Z1 + Z1/Z2).
The minimum value of the transmission coefficient T = 1/a = 2/ (Z2/Z1 + Z1/Z2); in
this case, the effect of increasing and decreasing the impedance of the barrier material is
Jet-Grouted Columns of Soft and Lightweight Geomaterials
623
the same. The transmission coefficient is maximum and equal to unity when the
impedances of the barrier material and the soil are equal.
Consider the various parameters of the barrier material and soil (see Table 1). The
wave velocity for JGC with low stiffness and density is equal to soil wave velocity, and
its density is 0.4 tonne/m3 — minimum value for lightweight concrete (Kana and
Demirboğa 2007). JGC very low stiffness and density is suggested having the same
wave velocity and half density.
Table 1. Soil and barrier material parameters
Material
Soil (loam)
Concrete (with fine aggregates)
PUF
JGC
JGC with low stiffness
JGC with low stiffness and density
JGC with very low stiffness and density
q, tonne/m3
1.8
2.2
0.3
1.8
1.8
0.4
0.2
C2, m/s
200
1500
400
1200
60
180
180
Z2/Z1
1
9.17
0.333
6
0.3
0.2
0.1
A
1
4.64
1.67
3.08
1.82
2.60
5.05
Fig. 1. Transmission factors for vibration isolation barriers 1 m thick
As was expected, the best results are achieved either for the materials with higher
stiffness and density (concrete, JGC), or for JGC with low and very low stiffness and
density.
624
M. Kholmyansky and Kh. Dzhantimirov
The transmission coefficient varies periodically depending on the parameter a —
phase incursion in the vibration isolation barrier (and, accordingly, on the frequency
and on the barrier thickness). It reaches the desired minimum when barrier thickness is
equal to a quarter of the wavelength. Figure 1 shows the dependence of the transmission coefficient on the frequency f for various materials and for barrier thickness of
1 m. The effectiveness of screening for vibration isolation barrier materials with high
wave velocities is achieved only for the high frequency range. In the frequency range of
20… 70 Hz, which is practically important for the conditions of megacities (where the
most intense effects are caused by the subway) the best results are shown by a barrier of
JGC with very low stiffness and density.
3 Simulation of Vibration Screening in 2D
The results obtained need further verification due to the existence of two types of
waves (longitudinal and transverse), the possibility of their oblique incidence on the
barrier, etc. The propagation of vibrations with a frequency of 50 Hz typical for
subway effects is considered in the presence of a vibration isolation barrier 1 m thick
and 5 m deep of JGC with very low stiffness and density. The soil is supposed linearly
elastic (q = 1.8 tonne/m3; cS = 200 m/s; m = 0.35) and so is the barrier (q = 0.2
tonne/m3; cS = 180 m/s; m = 0.2). Sinusoidal vertical unit load is applied to the surface
(see Fig. 2).
Finite element method and COMSOL Multiphysics software package were used
with quadratic Lagrange elements. To avoid unnatural reflections from the sides and
the bottom of the model special boundary conditions were introduced (Lysmer and
Kuhlemeyer 1969). The finite element sizes were not greater than LS/nre, where LS is
shear wave length, nres = 20. The common practice was to choose minimum element
length equal to LS/nres (nres = 6…10) (Ihlenburg 1998, Langer et al. 2017). Later
research showed that at least nres = 20 quadratic elements per wave provide error of
less than 1% (Langer et al. 2017). The resulting number of degrees of freedom is
129542 (see Fig. 3).
The results for wave propagation in case of no barrier are shown (Fig. 4) to be
compared with the case of barrier. The amplitudes of displacement vector are shown at
phases of 0 and 90 degrees to provide the complete information on sinusoidal vibration.
The wave patterns show no unnatural reflections from the sides and the bottom of the
model so the domain size and boundary conditions are chosen in a satisfactory way.
Figure 5 shows the analogous results for the barrier. The scales for Fig. 4 and
Fig. 5 are identical. The wave patterns again show no unnatural reflections from the
artificial boundaries.
Jet-Grouted Columns of Soft and Lightweight Geomaterials
625
Fig. 2. Vibration isolation barrier (2D model)
Fig. 3. Finite element mesh (the central part)
The protective influence is visible for both the surface and the interior of the
ground. On the other hand the vibration level to the opposite side of the applied load
increases. This fact may be explained by the constructive interference of the waves
reflected from the barrier.
To assess the influence of the barrier more clearly Fig. 6 plots the amplitudes of
surface total displacements. The displacement values at all points behind the barrier
(further than 1 m) are 3 or more times less than in case of absence of the vibration
protection barrier. The rise of vibration level on the opposite side (up to 1.8 times) is
shown again.
In the case considered the barrier depth ratio to Rayleigh wavelength is equal to
5/3.74 = 1.34 is very close to 1.33 to the minimum recommended value (Woods 1968).
626
M. Kholmyansky and Kh. Dzhantimirov
Fig. 4. Propagation of waves without vibration isolation barrier at phases 0°(a) and 90°(b)
Fig. 5. Propagation of waves in the presence of a vibration isolation barrier made of JGC with
very low stiffness and density at phases 0°(a) and 90°(b)
Jet-Grouted Columns of Soft and Lightweight Geomaterials
627
Fig. 6. Amplitudes of total displacements of the surface
4 Conclusions
The results obtained show the effectiveness of the considered vibration protection
technique by vibration screening using jet-grouted columns of soft and lightweight
materials. It is also relatively inexpensive and durable. Currently, the research of the of
vibration isolation barriers of jet-grouted columns of soft and lightweight material and
other geomaterials is beginning.
References
Aleshin, A.S., Osipov, V.I., Filimonov, S.D.: Method of building protection against vibration:
Patent 2298614, Russian Federation. Application# 2006105280/03 of 21.02.2006. Published
10.05.2007. (2006). (in Russian)
Alzawi, A., El Naggar, M.H.: Full scale experimental study on vibration scattering using open
and in-filled (GeoFoam) wave barriers. Soil Dyn. Earthq. Eng. 31(3), 306–317 (2011)
Barkan, D.D.: Dynamics of Bases and Foundations. McGrow-Hill, New York (1962)
Brekhovskikh, L.M.: Waves in Layered Media (2nd ed.). Academic Press, New York (1980)
Çelebi, E., Firat, S., Beyhan, G., Çankaya, İ., Vural, İ., Kirtel, O.: Field experiments on wave
propagation and vibration isolation by using wave barriers. Soil Dyn. Earthq. Eng. 29(5),
824–833 (2009)
Coulier, P., François, S., Degrande, G., Lombaert, G.: Subgrade stiffening next to the track as a
wave impeding barrier for railway induced vibrations. Soil Dyn. Earthq. Eng. 48, 119–131
(2013)
Croce, P., Flora, A., Modoni, G.: Jet Grouting. Technology, Design and Control. Boca Raton,
Taylor & Francis (2014)
Dzhantimirov, Kh., et al.: Structure for building protection against vibration and method of its
installation:
Patent
2365710
Russian
Federation.
Application# 2006105280/03# 2008113030/03 of 07.04.08. Published 27.08.08 (2008). (in
Russian)
628
M. Kholmyansky and Kh. Dzhantimirov
Haupt, W.A.: Model test on screening of surface waves. In: Proceedings of the 10th International
Conference on Soil Mechanics and Foundation Engineering: Stockholm, vol. 3, pp. 215–222
(1981)
Ihlenburg, F.: Finite Element Analysis of Acoustic Scattering. Springer, New York (1998)
Kana, A., Demirboğa, R.: Effect of cement and EPS beads ratios on compressive strength and
density of lightweight concrete. Indian J. Eng. Mater. Sci. 14(2), 158–162 (2007)
Langer, P., et al.: More than six elements per wavelength: the practical use of structural finite
element models and their accuracy in comparison with experimental results. J. Comput.
Acoust. 25(4), 1750025 1-1750025 23 (2017)
Liao, S., Sangrey, D.A.: Use of piles as isolation barriers. Proc. ASCE 104(GT9), 1139–1152
(1978)
Lysmer, J., Kuhlemeyer, R.L.: Finite dynamic model for infinite media. Proc. ASCE 95(EM4),
859–878 (1969)
Massarsch, K.R.: Vibration isolation using gas-filled cushions. In: Soil Dynamics Symposium to
Honor Professor Richard D. Woods. Geo-Frontiers, Austin, Texas (2005)
Minaev, O.P.: An effective technique of building protection against vibrational and dynamical
effects in course of soil compaction at nearby sites. Sci. Tech. Bull. St. Petersburg State
Polytech. Univers. 4(207), 81–91 (2014). (in Russian)
Orr, T.L.L., Rahman, M.E.: Using trenches to reduce tunnelling vibrations. Geotech. Eng. 161
(5), 227–233 (2008)
uretekworldwide.com
Woods, R.D.: Screening of surface wave in soils. Proc. ASCE 94(SM4), 951–979 (1968)