Arab J Geosci (2017) 10:513 https://doi.org/10.1007/s12517-017-3279-3

REVIEW

Vibration screening by trench barriers, a review Ehsan Mahdavisefat 1 & Aliakbar Heshmati 1 & Hossein Salehzadeh 1 & Hamed Bahmani 1 & Mohsen Sabermahani 1

Received: 10 November 2016 / Accepted: 3 November 2017 # Saudi Society for Geosciences 2017

Abstract This paper provides a review of various investigations concerned with vibration isolation using trench barriers and factors affecting their performance, also extracts design recommendations, because there is no exact conclusion of researches in this field. Vibrations induced by different sources can be seriously harmful to structures and occupants. Geometrical parameters, soil characteristics, and filling material properties can affect a barrier’s performance. Investigators have applied analytical approach, finite element, boundary element, experimental, and field studies to identify relevant factors. Various geometrical parameters affecting trench’s isolation level were examined, among which depth of trench was found to be the most important, but in most cases, the width of the trench and source-barrier distance have a low effect. Shear-wave velocity ratio of filling material and surrounding soil has the most significant role of all material properties. Using high-energy-absorbing materials can lead to better isolation. The majority of studies consider soil and filling material’s behavior to be elastic, so changes in loading amplitude have no effect on vibration reduction. Finally, among special cases in vibration isolation by trenches, non-rectangular and multiple ones found to be economically satisfying and wellisolating barriers.

Keywords Trench barrier . Vibration isolation . Open and infilled trench . Ground borne vibrations

* Ehsan Mahdavisefat [email protected]

1

Iran University of science and technology, Tehran, Iran

Nomenclature λR is the Rayleigh wavelength. Ar is the vibration amplification reduction factor. Arh is the horizontal velocity amplitude reduction factor. Arv is the vertical velocity amplitude reduction factor. Vs is the shear-wave velocity. Dd or d is the normalized depth of trench. Wd is the normalized width of trench. L is the normalized source-barrier distance. Vb/Vs is the shear-wave velocity ratio of infill material to surrounding soil. Eb/Es is Young’s modulus ratio of barrier to surrounding soil. β is the maximum acceleration reduction. VRMS − is the root mean square of vertical velocity component with presence of trench. TR VRMS − is the root mean square of vertical velocity component without presence of trench. NTR

Introduction Vibrations induced by heavy vehicles, blasts, railway, traffic, and other construction-related activities have become a significant concern of major cities during the few recent years, which, depending on their source and the distance to where they are originated can disturb both occupants and constructions containing sensitive equipment. Also, construction noise and vibration at the preconstruction phase have environmental costs (Hong et al. 2014). Therefore, isolating vibrations demand considerable attention, especially when vibration source is close to sensitive constructions and establishments and when it is inside or near densely populated urban cities.

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Too much vibration distorts sensitive instrument functions, damages constructions, and disturbs residents. Among isolation techniques applied to reduce the unfavorable vibrations, active wave barriers (located close to the source of vibrations) and passive ones (more distant from the source of vibrations) are of great interest (Woods 1968). These barriers include trenches (either open or infilled with an especial material such as bentonite, water, Geo-foam, concrete,…), heavy mass technology, sheet piles, wave-impeding blocks, soil grouting, gas-filled cushion, groups of piles, or scrap-tire isolation walls. Due to easy and economical construction procedure and good performance, trench barriers (open or infilled) are common ones. Wave-barrier performance is influenced by various factors, including wave and soil characteristics, as well as geometrical parameters. Released energy during mentioned activities propagates in forms of surface waves (Rayleigh waves) and body waves (including pressure (P) and shear (S) waves). Most of the energy (nearly twothird) generated by vibrations is released in the form of Rayleigh waves (Miller and Pursey 1955; Sánchez-Sesma et al. 2011). Thus, we can measure barrier effectiveness through the amount of Rayleigh waves reflected, diffracted, or scattered (Jain and Soni 2007). Alterations in the amplitude of Rayleigh waves’ components with depth are directly affected by the source of vibrations and dynamic features of the soil. To address vibration isolation using trench barriers, numerous analytical approaches (White 1958; Knopoff 1959a; Knopoff 1959b; Mal and Knopoff 1965; Thau and Pao 1966; Lee 1982; Avilés and Sanchez-Sesma 1983), two and three-dimensional investigations using finite element method (FEM) (Saikia and Das 2014; Younesian and Sadri 2014; Esmaeili et al. 2013; Zakeri et al. 2014; Yang and Hung 1997; Bo et al. 2014; Liyanapathirana and Ekanayake 2016; Jesmani et al. 2012; Jesmani et al. 2011; Jesmani et al. 2008; Hamdan et al. 2015; François et al. 2012; Shrivastava and Rao 2002), boundary element method (BEM) (Al-Hussaini and Ahmad 1996; AlHussaini and Ahmad 1991; Ahmad and Al-Hussaini 1991; Leung et al. 1991; Dasgupta et al. 1990), and other numerical methods (Sivakumar Babu et al. 2010), as well as laboratory and field studies (Murillo et al. 2009; Ulgen and Toygar 2015; Xiong and Li 2013; Coulier et al. 2014; Alzawi and El Naggar 2011; Connolly 2013; Çelebi et al. 2009), have been conducted on both open and infilled trenches. Laboratory and field studies are limited; thus, investigations employing numerical methods are most frequently utilized. Open trenches bear the probability of instability, therefore requiring constant maintenance and care; whereas for infilled trenches, this is not the case. Trench effectiveness is measured by the reduction in horizontal and

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vertical components of surface displacements. Factors influencing the measurement include soil characteristics, trench geometry, and infill material properties. Many researches have been conducted on vibration isolation using trench barriers, but there is no exact conclusion of them, so we tried to provide a conclusion of these investigations and also extract design recommendations for engineers. This review paper focuses on various factors affecting vibration isolation using trench barriers (including geometrical parameters, loading parameters, and filling material characteristics) based on a range of studies. In order to add more depth to the discussion, we also consider special cases concerning isolation by means of trenches.

Mechanisms of elastic wave propagation through trenches In the analysis of seismic wave propagation, it is common to assume that earth can be simulated by homogenous isotropic elastic half-space. This assumption is made frequently in seismology and in many soil mechanic problems. The elastic half-space theory defines two basic types of waves, body waves and surface waves. Two important body waves are compression and shear wave, and one surface wave is Rayleigh wave. The energy is transmitted to the soil by compression, shear, and Rayleigh waves. All the waves encounter an increasingly larger volume of material as they travel outward; thus the energy density in each wave decreases with distance from the source. This decrease is called geometrical damping. The distribution of energy among these waves has been computed by Miller and Pursey (1955) for the case of an elastic half-space having a Poisson’s ratio of 0.25, exited by a vertically oscillating circular disk. The basic features of wave propagation in a half space and Miller and Pursey’s energy partition calculation are shown in Fig. 1. The distribution of total input energy among the three elastic waves was determined to be the following: 67% Rayleigh wave, 26% shear wave, and 7% compression wave. So the Rayleigh wave is of primary concern for vibration isolation problems. In order to discretize the P-wave, S-wave, and Rayleigh in records, we can use the difference between these waves’ velocity and calculate the arrival time of them to the record point. The P-wave velocity is more than S-wave, and Swave is more than Rayleigh wave. So first the P-wave, then the S-wave and then the Rayleigh wave arrives at the recording point. In an isotropic homogeneous medium, these arrival times can be calculated and the waves can be discretized. The velocity of waves can be calculated from Eqs. 1 to 3 below. After that, the arrival time for each

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Fig. 1 Distribution of elastic waves in homogeneous, isotropic, elastic half-space (Miller and Pursey 1955)

elastic wave (tP, tS, and tR) is calculated by having the distance of the point and velocity of the corresponding elastic wave at hand. After the calculation of these arrival times, they can be determined on displacement, velocity, or acceleration time histories to discretize the different elastic waves. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ð1−υÞ VP ¼ ð1Þ ρð1 þ υÞð1−2υÞ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E VS ¼ ð2Þ 2ρð1 þ υÞ VR ¼

0:87 þ 1:12υ VS 1þυ

ð3Þ

In a research, Bo et al. (2014) did the abovementioned procedure in their numerical models in order to discretize the waves arriving at a predetermined point. The results of their study are presented in Fig. 3 below. It should be mentioned that tP, tS, and tR are the P-wave, S-wave, and Rayleigh wave arrival times, respectively. The calculated arrival times are shown in Fig. 2a, b, and c. As we know most of the propagated wave’s energy (nearly two-third) transfers through Rayleigh wave. This can be seen in Fig. 2 by arriving Rayleigh wave the amplitude of displacement, velocity, and acceleration increase drastically. Therefore, for the case of isotropic homogeneous elastic medium, this procedure can be followed in order to discretize the propagated P-wave, S-wave, and Rayleigh wave. The concept of isolation by trenches is dependent on the interception, scattering, and diffraction of surface waves by a barrier. Placing a trench (open or filled) means creating a finite geometric or material discontinuity in the half space. Figure 3 shows the Rayleigh wave incident on a trench

(open or filled). After incidence on the trench, it changes into reflected Rayleigh wave, transmitted Rayleigh wave, and body waves that radiate outward from the trench. The energy contained within the transmitted Rayleigh and body waves causes the ground vibration beyond the trench. The phenomenon of conversion of Rayleigh wave energy to other forms (body waves) due to the presence of a wave barrier is known as mode conversion. Different ways have been used to study the trench barrier’s performance on vibration screening. Field and laboratory tests as one of the most reliable methods for investigating such phenomenon have been conducted. But the problem is that due to the difficulty, expensiveness, and implementation restrictions, this type of research has not gained much attention. This method also is not widely used because of the complexity of the solution, and it is just limited to some simple examples. However, numerical investigations (2D or 3D modeling using FEM, FDM, and BEM) due to their capabilities and easy application are most frequently utilized. A planar P-wave or Sv-wave hitting the boundary between two layers will produce both P- and SV-reflected transmitted waves. This is called mode conversion. The angles of the incident reflected and transmitted rays are related by Snell’s law as follows (Subsurfwiki.org 2017): p¼

sin θ1 sinθ2 sin φ1 sin φ2 ¼ ¼ ¼ V P1 V P2 V S1 V S2

ð4Þ

where p is called the ray parameter and Vp1, Vs1, Vp2, and Vs2 are P-wave and S-wave velocity in the first and second medium. Also, θ and φ angles are shown in Fig. 4. Zoeppritz (1919) derived the particle motion amplitudes of the reflected and transmitted waves using the conservation of stress and displacement across the interface, which yields four equations with four unknowns:

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Fig. 2 The motion of a point in homogeneous isotropic and elastic soil medium without damping. a Displacement of point. b Velocity of point. c Acceleration of point (Bo et al. 2014)

2

−sinθ1 6 cosθ Rp 1 6 6 6 RS 7 6 7 ¼ 6 sin2θ1 6 4 TP 5 6 4 TS −cos2φ1 2

3

−cosφ1 −sinφ1 V P1 cos2φ1 V S1 V S1 sin2φ1 V P1

sinθ2 cosθ2 ρ2 V 2S2 V P1 cos2φ1 ρ1 V 2S1 V P2 ρ2 V P2 cos2φ2 ρ1 V P1

RP, RS, TP, and TS, are the reflected P, reflected S, transmitted P, and transmitted S-wave amplitude coefficients, respectively and ρ1, ρ2 are the density of the first and second medium. Inverting the matrix form of the Zoeppritz equations gives the coefficients as a function of angle.

3−1 cosφ2 7 −sinφ2 7 7 ρ2 V S2 V P1 7 cos2φ 27 2 ρ1 V S1 7 5 ρ2 V s2 sin2φ2 ρ1 V P1

2

3 sinθ1 6 cosθ1 7 6 7 4 sin2θ1 5 cos2φ1

ð5Þ

Snell's law (also known as Snell–Descartes law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic medium, such as water, glass, or air. When waves incidents to the boundary of two isotropic elastic

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Fig. 3 Waves generated due to incident Rayleigh wave on trench (Ahmad and Al-Hussaini 1991)

medium a portion of wave reflect and a portion pass through the boundary. The reflection or passing behavior is dependent on material properties at the sides of discontinuity surface. One important property is the impedance of the material. If the wave with an amplitude of A1 incidents the boundary of another medium with the wave amplitude of A2 the amplitude of reflected wave (Ar) and passed wave in the second medium (A2) is expressed as: Ar ¼

Z 1 −Z 2 A1 Z1 þ Z2

ð6Þ

A2 ¼

2Z 1 A1 Z1 þ Z2

ð7Þ

where z1 and z2 are the impedance of first and second medium respectively (also, z=ρ.Vs).

Geometrical parameter effect Normalized trench depth Researchers often normalize geometrical characteristics (trenches’ depth, width, and distance to the source of vibrations) in their studies with respect to Rayleigh wavelength in

order to provide dimensionless studies so anywhere normalized is used in this paper it means normalized to Rayleigh wavelength. Trench depth is recognized as the most important factor affecting trench performance in the majority of studies (AlHussaini and Ahmad 1991; Ahmad and Al-Hussaini 1991; Haupt 1981; Bo et al. 2014; Saikia and Das 2014; Saikia 2014). In a research, Bo et al. (2014) (Fig. 5) demonstrated that in not excessively thin trenches (with relatively small width to depth ratio), adding more depth to trenches strengthens vibration amplitude reduction; this proved to be right especially when dealing with vertical vibrations. On the other hand, wide shallow (superficial) trenches exhibit unfavorable results and actually magnify vibrations. So in an average range of width, by increasing the depth of trench, its performance becomes better. Also, Emad and Manolis (1985) investigated shallow trenches and mentioned that presence of shallow trenches results in an amplification along the surface of half-space up to 200%. Increasing the normalized depth (Dd), however, slows vibrations down until they eventually reach a rather steady value where the further addition to depth yields no considerable effect on amplitude reduction. One reason explaining the finite reduction effect resulted by deepening the trenches could be a drastic decrease in Rayleigh wave amplitude with depth. Richart et al. (1970) have mentioned Rayleigh wave components’ amplitude fall by 90% in 1.5λR deep. Saikia and Das (2014) mentioned that the trench depth can decrease both vertical and horizontal vibrations. For instance, in an open passive trench (with the source to barrier normalized distance, L = 5) with a normalized width of 0.2, vertical vibrations reduction factor falls from 0.62 to 0.14 when normalized depth (d) rises from 0.3 to 1.5. A deeper trench reflects waves of greater depth, resulting in a better isolation. Regarding multiple trenches, Saikia (2014) studies demonstrated that deepening the trenches improves their performance against vibrations, especially vertical ones. In this case, normalized depths further than 0.6 λR yield

Fig. 4 Transmitted and reflected waves at discontinuities: compression wave (a), vertical shear wave (b), and horizontal shear wave (c) (Resende et al. 2010)

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Fig. 5 Effect of depth on vibration reduction: a normalized width = 0.1, b normalized width = 1.0 (Bo et al. 2014)

no more considerable improvements in performance. It must be noted that this is not the same as the 1.5 λR value proposed by Bo et al. (2014), since here utilized multiple trenches. We will discuss the issue in greater details later on. Investigations mentioned above and other researches are nearly consistent and show that the trench depth is a key parameter which affects vibration amplitude reduction factor. Also when designing trenches, we can consider the depth of 1.5 λR as the upper bound of depth. Normalized trench width The majority of studies indicate little amplitude reduction effect for normalized trench width. For example, Saikia (2014) pointed out that obtaining specific results from amplitude reduction with respect to normalized width is rather difficult (see Fig. 6), because actually no clear trend can be extracted, however, given a shear-wave velocity ratio (the ratio of shearwave velocity of barrier to the surrounding soil) in range of 0.1–0.2, which is the recommended scope for practical purposes, the effect is relatively small and can be neglected.

Research conducted by Saikia and Das (2014) shows excessive normalized width values (over 0.6) for active trenches that are relatively shallow (with normalized depth values smaller than 0.6) result in unfavorable effects (see Fig. 7). Adding depth and distance from the source can diminish these effects, however. Yang and Hung (1997) also observed that for shallow trenches, the wider trench performed worse but as the trench becomes deeper, varying the width of the trench does not make much difference. We can say the explanation behind the issue is that when a trench is located near the source of vibration, body waves play a more dominant role with respect to surface waves, and thus a shallow trench would allow greater amounts of body waves to underpass the trench. A wider trench, however, provides a greater free surface that converts body waves to surface ones, yielding unfavorable outcome. As we move further away from the source of vibration, surface waves gain dominance over body ones, this, in turn, explains the reason for rather less unfavorable effects that shallow passive trenches with greater width have. Finally, when the trench is deep enough, most surface waves will be reflected by the trench and effect of width becomes minor.

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Fig. 6 Variation of average amplitude reduction factors in y and x direction (Amy and Amx) versus shear-wave velocity ratio (Vb/Vs) for different normalized widths (Wd) at normalized depth (Dd) of a 0.3, b 0.4, and c 0.6 (Saikia 2014)

Centrifuge model tests conducted by Murillo et al. (2009) also supported the idea that width effect is more considerable in shallow trenches, and it decreases as depth increases. Having studied a wide range of the normalized trench width (stretched from 0.1 to 2.0), Bo et al. (2014) concluded that expanding the trench width to some specific extent can yield improved performance; however, further expansion results in an undesired outcome. Trenches with width values greater than depth are actually another breed of wave barriers known as wave-impeding block whose behavior varies and have not received much attention yet. Briefly, the results obtained from the most of the researches insist on the negligible effects of width, some researches, for active trenches that are relatively shallow, show that excessive normalized width results in vibration amplification. To diminish these effects, depth and distance from the source should be added. So when designing active trenches to prevent undesired performance, the minimum normalized depth should be 0.6. Fig. 7 Variation of average amplitude reduction factors in y and x direction (Amy and Amx) versus normalized source-barrier distance (L) and normalized width (W) (Saikia and Das 2014)

2.3. Source-barrier distance (L) Most of the researchers reported the negligible effect of this parameter in trench performance. In their centrifuge experiments, Murillo et al. (2009) found no considerable traces of the effects caused by source-barrier distance. However, results indicated that at normalized distances below 0.5, some subtle magnification is observed in front of the trenches, which was due to wave reflection. In numerical studies, also the amplification before the trench was seen. There is no clear trend towards trench distance from the vibration source in investigations conducted by Bo et al. (2014) (see Fig. 8). Not much influence on amplitude reduction coefficient is observed with changes in distance, and no certain pattern can be extracted for the alterations. Moreover, authors have not mentioned any details on trench width or depth in this scenario. In parametric studies conducted by Saikia (2014) on multiple trenches (Fig. 9), which supports the fact that with normalized depths of 0.5 and widths of 0.3, trench distance to

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Fig. 8 Effect of normalized distance from the vibratory source to the barrier on the vibration isolation effectiveness (Bo et al. 2014)

vibration source is rather a trivial factor towards trench performance. Yang and Hung (1997) reported no significant effect of changes in the source-barrier distance on trench performance. It can be concluded from various researches mentioned above that the source-barrier distance has a low effect on barrier’s performance except in shallow trenches. So in practice based on the type of construction to be protected, source of vibration, and other conditions, active or passive isolation can be employed. For example, when a reduction in a machine vibration is the problem, active isolation can be used or when a sensitive structure or equipment is placed near the railway, passive isolation is a better and more economical solution.

Loading parameters Frequency Geometrical parameters in studies concerned with wavebarrier trenches are generally expressed as ratios of Rayleigh

wavelength; therefore, the frequency influences trench performance indirectly. Briefly, with an increase in frequency, the wavelength decreases and the normalized dimension of the trench will increase, so this will result in improvement of trench performance. The generated wave frequencies in different investigations are variant. According to Table 1, the frequency range of the most of the environmental and civil construction vibrations is below 100 Hz. Therefore, most of the researchers conducted their investigations in the frequency range of below 100 Hz. In addition, the resonant frequency of domain is variant too, because the properties of the domain are not constant in different investigations. However, the point is the presence of the trench in the domain does not make a noticeable change in the resonant frequency; value and models with and without the trench have almost the same resonant frequency. On the other hand, the efficiency of the trench barrier is determined by Ar (amplification reduction ratio), which is the ratio of particle velocity in the presence of the trench to that of without the trench. So the effect of the resonant phenomenon is omitted because it has almost the same effect on models with and without the trench. Loading amplitude As the majority of studies consider soil and filling material’s behavior to be elastic, and as they are based on the assumption Table 1 1990)

Fig. 9 Effect of trench locations on vibration attenuation (Saikia 2014)

Typical characteristics of man-made vibration sources (ISO

Source

Type of excitation

Frequency range (Hz)

Traffic Blasting Pile driving Machinery (outside) Machinery (inside)

Continuous/transient Transient Transient (intermittent) Continuous/transient Continuous/transient

1 to 80 1 to 300 1 to 100 1 to 300 1 to 100

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that soil and filling material are tied to each other, without any interruptions, one might, therefore, expect increases in loading amplitude to have no effect on vibration reduction in the range of elastic strain. Bo et al. (2014) for example, investigated the issue in their parametric study and not surprisingly, results indicated no relevance to the dynamic loading amplitude. However, when loading cause plastic strains more accurate, modeling of the contact surface between the filling material and the surrounding soil is required, as is more careful consideration of soil’s dynamic behavior. These can be addressed in further studies.

Filling material characteristics Shear-wave velocity Infill material used in trenches plays a significant role in the vibration amplitude reduction and trenches performance. The majority of studies insist that declines in shear-wave velocity of infill material entail a reduction in vibration amplitude and thus improve trench performance. As we observed earlier (Fig. 6), smaller values of shear-wave velocity in filling material compared to that of the surrounding soil mean superior trench performance. Note that not any decline in the shear-wave velocity ratio necessarily returns improved performance. There is a limit where further reductions will actually result in inferior trench performance. For shallow trenches (with a normalized depth of 0.5 and below), the threshold for shear-wave velocity ratio, which yields optimum trench performance, is from 0.15 to 0.2. For deeper trenches, the range is from 0.1 to 0.15. Overall, one can conclude that a shear-wave velocity ratio between 0.1 and 0.2 provides ultimate trench performance. Moreover, falls in shear-wave velocity of filling material strongly affect vertical vibration reduction compared with horizontal ones (Saikia and Das 2014).

Fig. 10 Effect of barrier Young’s modulus ratio on the vibration isolation effectiveness (Bo et al. 2014)

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A study conducted by Bo et al. (2014) (see Fig. 10) considers the parameter in the form of filling material elasticity (because the material was assumed to be elastic). Knowing that shear-wave velocity directly corresponds with the square root of Young’s modulus to density (√(E/ρ)), one obviously concludes that changes in elastic modulus represent changes in shea-wave velocity. In this study, the ratio of filling material elastic modulus to that of the surrounding soil (Eb/Es) was in the range of 0.03 to 25. Both vertical and horizontal vibrations were suitably reduced as long as the ratio was below 0.2, which was very similar to the case of open trenches. Performance levels keep falling until Young’s modulus ratio reaches 2.5; no further changes in performance are witnessed thereafter for horizontal vibrations. In the case of vertical vibrations, little improvement in trench performance is observed. From the results reported, one can say that difference between shear-wave velocity of filling material and surrounding soil (i.e., shear-wave velocity ratio) is a key parameter in the scattering mechanism of vibration amplitude reduction. Also, shear-wave velocity ratio about 0.1–0.2 can be considered for design purposes. Material damping As mentioned earlier, when working on vibration amplitude reduction using trenches, wave reflection is one of the usual approaches. It has been shown that higher impedance difference between the two mediums results in greater amounts of reflected waves, which in turn implies superior trench performance. Another approach towards amplitude reduction is absorbing wave energy using the medium through which a wave spreads. Mediums with higher absorption capabilities (i.e., higher damping) perform a more satisfactory amplitude reduction and clearly more favorable trench performance. Therefore, it can be concluded using infill material with higher energy absorption and damping capability that results in better

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application of high-energy absorptive infill material in wavebarrier trenches, especially to investigate their damping performance. In our opinion, in the range of plastic strains, damping can be a more effective parameter due to high values of damping in that range.

Type of filling material

Fig. 11 Effect of open and geofoam-filled trench on vibration reduction at 2.5 and 5 m distance to vibration sources (Alzawi and El Naggar 2011)

isolation performance for trenches. So we expect more satisfying trench performance, which results in a greater amplitude reduction of the input waves and a more reliable level of isolation. Further studies are required, in order to address the Table 2

Various filling materials, including water, bentonite, soilbentonite mixture, concrete, and geofoam have been investigated in order to identify the effects of them on the trench performance (Beskos et al. 1986; Ahmad and Al-Hussaini 1991; Ulgen and Toygar 2015; Ju and Li 2011; Majumder and Ghosh 2016). Ulgen and Toygar (2015) attempted field experiments to observe trench performance. They studied open trenches, water-filled, and geofoam-filled ones, with a careful examination of the soil in the area which was characterized by its layered structure. Results showed better performance for open and geofoam-filled trenches compared to the ones filled with water. The geofoam trench, on the other hand, performed relatively satisfactory, suggesting the possibility of utilizing it as filling material since open trenches are facing stability challenges. Water-filled trenches, however, transmit compression waves and are therefore not as effective as geofoam when used to isolate the vibrations generated nearby. Also, Alzawi and El-Naggar (2011) reported acceptable performance of geofoam-filled trenches based on field experiment observations. Figure 11 illustrates open and geofoamfilled trenches’ role in reducing particles’ vertical velocity components. The range they experimented resulted up to 68% reduction in vibration amplitude, which is a satisfying performance. Table 2 compares performance level of different filling materials investigated by several researchers.

Comparison of performance of different filling materials

Reference

Filling material

Normalized depth

Reduction percentage

Impedance ratio Excitation frequency (Hz) Investigation method

Open Water Geofoam Garinei et al. (2014) Open with concrete walls Celebi et al. (2009) Open Concrete Alzawi and El-Naggar (2011) Open Geofoam Murillo et al. (2009) Geofoam

1.48 1.48 1.48 2m 0.64 0.94 0.6–0.8 0.6–0.8 1–2

70% 60% 75% 40% 79% 36% 85% 70% 60%

– – 0.01 – – 17.57 – 0.04 0.023

Saikia (2014) Yang and Hung (1997) Bo et al. (2014)

0.6 1.5

80% 70–80% 65%

0.1–0.15 IR < 0.2 0.17

Ulgen and Toygar (2015)

Soft elastic material Soft elastic material Soft elastic material

25, 50, 70

Field test

No harmonic excitation 10 to 100

Field test Field test

15 to 58.84

Field test

150 to 2000 (in model) 3 to 50 (in prototype) 31 31 50

Centrifuge test Numerical Numerical Numerical

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Fig. 12 Influence of ratio of density of barrier to that of soil (Al-Hussaini and Ahmad 1991)

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Fig. 14 Schematic view of multiple trenches (Saikia 2014)

According to Table 2, among the materials examined in different investigations, geofoam has been found to be one of the best, but it has low-shear strength parameters. However, the numbers of materials tested are limited and further investigations concerned with the discovery of a highperformance filling material are required.

studied a wide range of density ratio from 0.005 to 5. It was observed that the higher value of density ratio results in better isolation of vibrations. However, it should be mentioned that material with too large density is probably unavailable in practice.

Filling material density ratio

Special cases

Figure 12 below shows the effect of density ratio (density of barrier to that of the soil) on the screening effectiveness of wave barriers with different normalized cross-sectional areas (A), in a research conducted by (Al-Hussaini and Ahmad 1991). The value of density ratio varies from 0.75 to 1.5 that covers the range of values for practical purposes. It should be mentioned that all other parameters were kept constant. From Fig. 12, it can be concluded the increase in density ratio results in the improved screening of vibrations and its effect cannot be neglected. Also, Bo et al. 2014 studied the effect of density ratio on vibration isolation by trench barriers (Fig. 13). They

Using multiple trenches

Fig. 13 Effect of barrier density on the vibration isolation effectiveness (Bo et al. 2014)

Figure 14 shows a schematic view of multiple trenches investigated by Saikia (2014). Employing such barriers, especially when dealing with severe vibrations, has recently considered. As mentioned earlier, nowadays, railways are one of major ground-borne vibration sources (Connolly 2013; Chiang and Tsai 2014; Zoccali et al. 2015; Barbosa et al. 2015; Garcia-Bennett et al. 2012). An investigation of reducing the vibrations caused by train movement at different speeds using multiple trenches was conducted by Younesian and Sadri (2014). In order to

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evaluate trench performance and the level of vibration pass through the trench, they used a W parameter measured in decibel, which was obtained by Eq. 8:   V RMS−TR w ¼ 20 log ð8Þ V RMS−NTR where VRMS − NTR and VRMS − TR are root mean square of vertical velocity components with and without the presence of trenches, respectively. They concluded a multiple-trench system that yields better performance levels compared to a single one (both in active and passive cases) and reduces vibrations’ amplitude more effectively. It is also mentioned that changes in the distance between the trenches in range of 5 to 13 m resulted in no significant performance variation. Another research by Saikia (2014) has also focused on comparing multiple-trench performance to that of the single trench, which also supports the better performance of multiple trenches. Much less depth is required for multipletrench systems to attain specific performance levels than what is required for single-trench systems. For instance, a double trench with a normalized depth of 0.5 has reduced vertical vibrations by 80% and horizontal vibrations by 63%, while a single trench would require a normalized depth of nearly 1 for the same value of the vibration reduction. Hence, when the single trench is not feasible due to depth restrictions, a suitable alternative can be a dual trench. For example, when a high-isolation level is needed or when loading frequency is low, the trench should be very deep. In these cases, in order to achieve the needed isolation levels, we need to use multiple trenches instead of a deep-single trench. Non-rectangular trench This type of trench majorly corresponds with the pattern for Rayleigh wave reduction in depth. As shown in Fig. 15, Rayleigh wave’s amplitude reduces with increasing depth sharply. Therefore, employing a trench which reflects the trend mentioned (Fig. 16) can yield maximum performance. Zakeri et al. (2014) conducted an examination of rectangular and step-shaped trenches in both open and filled forms which were similar in depth and cross-sectional area. Trench dimensions were chosen such that W = W1 − W2 , so the step shaped and rectangular trench have the same cross sectional area. Trench depth was considered to be 3 m, also d1 = d2 = 1.5. Results show that the maximum amplitude reduction ratio for a step-shaped open trench is smaller than that of an openrectangular trench by about 21%. In addition, the maximum amplitude reduction ratio for an infilled step-shaped trench is smaller than that for a rectangular infilled trench by about 26.2%.

Fig. 15 Variation of the amplitude of vibration of the horizontal and vertical components of Rayleigh waves with depth (Das and Luo 2016)

Knowing that excavating V-shaped trenches is rather difficult in practice, in order to investigate the performance of such trenches, Esmaeili et al. (2013) considered a V-shaped trench with depth and cross-sectional area equal to a rectangular one, and vibration reduction factors were compared. Results show that V-shaped trench performs better in terms of lower amplification reduction ratio, Ar . Comparison of the Ar values for the V-shaped and rectangular trenches is presented in Table 3. It is shown that the V-shaped trench reduced the Ar value by approximately 36.62% (from 0.688 to 0.436).

Fig. 16 Cross section of rectangular, step-shaped, and V-shaped trenches (Zakeri et al. 2014; Esmaeili et al. 2013)

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Table 3 Comparison of the Ar values for v-shaped and rectangular trenches (Esmaeili et al. 2013) Trench shape

Trench dimensions (m) d

Ar

W

Rectangular

3

1

0.688

V-shaped

3

2

0.436

–

Non-rectangular trenches seem to be economically satisfying and well-isolating ones, but researches are limited in this case especially that there is a lack of field tests to investigate such barriers.

Conclusion This paper focuses on various investigations concerned with wave-barrier trenches and factors affecting them. To identify relevant factors such as geometric parameters, soil characteristics, and filling material accurately, investigators have applied a variety of methods including analytical approach, finite element, finite boundary, experimental studies, and field studies. What follows is an outline of the results obtained through this study: –

–

–

–

Various geometrical parameters affecting trench performance were examined, among them trench depth was found to be the most important. Also when designing trenches, we can consider depth of 1.5 λR as the upper bound of depth. Results obtained from the most of the researches insist on negligible effects of the width. On the other hand, in case of active trenches that are relatively shallow, some researches show that excessive normalized width results in vibration amplification. So when designing active trenches to prevent undesired performance, the minimum normalized depth should be 0.6. The source-barrier distance has low effect on barrier’s performance. Therefore, in practice based on the type of construction to be protected, source of vibration, and other conditions, one can consider employing either active or passive isolation. Of all material factors that influence trench performance, shear-wave velocity in filling material to that of the surrounding soil has the most significant role. In order to determine exact trench behavior and performance, when loading causes plastic strains more accurate modeling of the contact surface between filling material and the surrounding, soil is required, as is more careful consideration of soil’s dynamic behavior. This enables more careful and more accurate design of such barrier systems. Also using

–

a material with high-energy absorption and damping capabilities, we expect more satisfying trench performance, which results in greater amplitude reduction of the input waves and a more reliable level of isolation. The effect of using such materials in different excitation frequencies is investigated by authors and will be published in the future. Although open trenches exhibit more favorable performance levels, their stability is their challenges. Therefore, there is a need to infilled trenches whose filling material allows for optimum performance. In that case, geofoam trench has been found to be a relatively satisfactory alternative to open trench but it has low-shear strength parameters. The numbers of materials tested, however, are very limited, and further investigations are required in order to find a high-performance filling material. Multiple trenches are known to be very effective and require considerably lower depth values to provide the same amplitude reduction factor compared to singletrench systems. Thus, situations demanding very deep single-trench-barrier systems can use multiple trenches as suitable alternatives. Also, trenches that employ improved non-rectangular cross-sectional forms perform better than their rectangular counterparts; they benefit from stability advantages as well.

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