Effects of Geometrical Properties of Rectangular Trenches Intended for Passive Isolation in Sandy Soils

Wave barriers are placed actively and passively in the ground to reduce the transmission of vibration produced by industry, traffic, train, etc. They include open trenches, in-filled trenches and sheet piles, etc. In most recent studies, the researchers have worked on parameters such as depth, width, length of trenches and also, the distance between the source of vibration and trench in cohesive soils. Most researches are evaluation on screening induced by shallow foundation. In this study the passive isolation has been investigated with the help of open trenches screening against the vibration produced by deep foundations in sandy soils, and the effect of trench angle and radius have been studied. Moreover, the reasons for amplitude increasing before open trenches have been evaluated. Three dimensional finite element analyses (FEM) with ANSYS software are used to achieve an exact parametric study on passive screening. The assumed strains are less than 10so the bilinear Elasto-Plastic behavior has been utilized.


Introduction
It is obvious that vibration occurred by machines, structures, and dynamic systems is destructive; Firstly, because of their inculcating stresses and vibrations which can cause failure or fatigue on nearby structures and, Secondly because of the aggravating effect of vibration on the performance of vibration producer.So isolating structures against vibration created by traffic jam, machine foundations, explosion and earthquake has become an undeniable subject in engineering science.
Wave barrier is one of the solutions for this problem.Installing wave barriers near the sensitive structures is called passive isolation.Regarding to the literature of vibrations (Barkan, 1962) conducted an open trench screen to isolate a building against vibrations created by vehicle traffic and reported that screening is not a workable system for mitigating vibrations.In addition, he mentioned that open trench dimensions are related to the wavelength of the surface motion.Woods (1967Woods ( -1970) ) investigated the screening performance of trench's different parameters by conducting a series of field tests in active and passive isolation.Woods used rectangular open trenches for his research and also defined amplitude Reduction ratio (Arr).Furthermore, his research concluded that the thickness of the passive open trenches has an unimportant effect on their workability.In addition, Woods reported that effective trenches have a depth between to times of the Rayleigh wavelength.Wass (1972) presented that amplitude is reduced by screening when the frequency is high.Aboudi (1973) worked on the ground surface response of wave barriers affected by time-dependent loading in an elastic half-space with the help of finite difference method (FDM).Woods et al. (1974) evaluated the screening efficiency of hollow cylindrical piles as a passive system in a half-space model.Haupt (1977) and G. Segol et al. (1978) investigated the effect of shape and trench dimension on amplitude reduction by the help of finite element method (FEM).Liao and Sangrey (1978) examined the effect of piles as a wave barrier against Raleigh waves with high wavelength.They announced that in the case of impractical trenches, piles are the best choice for reducing the wave amplitude.In addition, Fuykui and Matsumoto (1980) considered the open trench efficiency on reduction of Rayleigh, P, SV and SH waves amplitude by using a two-dimensional method through finite difference method (FDM).May and Bolt (1982) contemplated on the utilization of open trenches against compression and shear waves under the assumption of plane strain condition.Beskos et al. (1985Beskos et al. ( -1991) ) worked on a complete series of numerical models which contains in-filled and open trenches isolation in continuously homogeneous and non-homogenous soils under the assumption of plane strain condition and by using boundary element method (BEM).They reported that if the depth of soil layer be less than 2.5 times that of Raleigh wavelength, the depth of trench must be at least2 times that of layer thickness.Ahmad andAl-Hussaini (1991-2000) examined the effectiveness of active and passive isolation of circular open trenches.Besides, they investigated the effect of depth, width and location of the trenches by the usage of BEM method.Yeh et al. (1997) assessed the efficiency of open and in-filled trenches on reducing the vibration induced by train movement.This research showed that using trench barriers against vibration with low frequency is useless.Kattis et al. (1999) examined the isolation of open trenches, in-filled trenches and pile barriers against the vibration produced by machinery foundations.Moreover, Shirvasta et al. (2002) explored the efficiency of open and in-filled trenches for screening Rayleigh waves by using 3D FE model.Shen-Haw and Hung-Ta (2004) worked on the open and in-filled trenches as barriers for vibrations occurred by train movement.The results show that the adjacent building foundations have an important effect on vibration reduction.Adam and Estroff (2005) deliberated the efficiency of open and in-filled trenches in reducing the six-storey building vibrations due to passing trains by using a two-dimensional FEM analysis.The results show that these barriers could reduce 80 percent of the vibrations.Also, they reported that open trenches are more effective in vibration reduction than in-filled trenches.El Nagger and Chehab (2005) conducted a numerical research using two-dimensional model to evaluate the screening effectiveness of open and in-filled trenches on reducing the pulse-induced waves of shallow foundations resting on an elastic half-space.Celebi et al. (2006) with the help of finite element method (FEM) showed that using an open trench has an important effect on reduction of vibration amplitudes induced by passing trains.In addition, they presented two mathematical models and numerical techniques for solving problems related to wave propagation.Gaoet al. (2006) inspected the effect of pile barriers designed in rows as a passive screening by a three-dimensional model.The results show that piles with small diameter act like open trenches in reducing vibrations.Furthermore, they show that the distances between piles in a row are more important than the distances between rows of piles.Karlstorm and Bostrom (2007) investigated the opus of open trenches on reduction of wave amplitude induced by trains.They located these trenches in the both side of a railway and reported that these trenches could noticeably reduce the vibration amplitude especially at frequencies in the range of 2-8 Hertz.Tsai et al. (2007) worked on active isolation provided by pile barriers against vibration induced by shallow foundations under vertical loading.They investigated the effect of pile dimensions, pile distances, pile materials and screening location.They reported that steel pipe is generally better than other solid piles, and a concrete hollow pile barrier can be ineffective because of its stiffness.Jesmani et al. (2008) studied the effect of geometrical properties of an open trench intended for active isolation of deep foundations resting on a homogenous half-space cohesive soil by using a three-dimensional finite element method (FEM).In addition, Jesmani et al. (2011) conducted a research to evaluate the effect of geometrical properties of an open trench intended for passive isolation of deep foundation in sandy soils.Moreover, in this research the effect of soil properties and loading time has been investigated by using two-dimensional model in finite element method (FEM).
From the above review, most researches have focused on in-filled and open trenches as an active barrier against vibrations induced by shallow foundations.In addition, the effect of geometrical properties of trenches has been investigated such as depth, width, location, etc.
In this study, the ground passive isolation of deep foundations have been studied by open trenches in sandy soils and also the effect of two important parameters; trench radius and trench angle, have been evaluated.

Propagation and Attenuation Characteristics of Deep Foundation
The form of wave propagation is different in shallow foundations and deep foundations.Attewell and Farmer (1973)   The foundation is assumed to be restrained against horizontal movement and the soil is under assumption of being isotropic and homogenous with linear soil behavior for low deformation.

Geomet
For reduct been built been taken

Finite E
The most stiffness a applied to (

The Evaluation of Amplitude Increasing before Trench
As it can be seen in Figures 11 through 13, near the trench there is a dramatic increase in Arr.This result is caused by the following reasons: 1) When waves approach to an open trench which has an impedance coefficient equal to zero, they will be reflected with the same amplitude.This will emphasize the wave concentration near trench.
2) Excavating and removing the material from an open trench in actual situation causes a free movement for unrestrained trench edges because of its low stiffness.In conclusion, the wave amplitude near the trench edges increases in comparison with a model without open trench (Arr>1) (Jesmani et al., 2011).
In addition, as it can be seen in the Figures11 through 13, by increasing the trench angle, Arr increases.This issue is the result of increasing free nodes because of increase in trench dimension which increments the quantity of reflected waves.

The Effect of Open Trench Angle
The effect of trench angle on Aarr is demonstrated in Figures14 through 16 for L= R, 2R and 3R middle distances.Generally, increasing the trench angle leads a decrease in Aarr.It also observed that the reduction rate in every curve decreases from the trench angle bigger than  = 150°.Thus  = 150° is highly recommended for the optimal open trench angles.Theequations that have been presented near curves (because of the low coefficient of ) approximately show a linear behavior between Aarr and trench angle.In addition, it is noticeable that increasing the trench angle has the most effect on the rate reduction of studied points in the distance of 2R from the vertex of the trench.However, this fact is in its lower value in the distance of R.

The Effect of Open Trench Radius
The effect of trench radius on Aarr is illustrated in Figures 17 through 20 for L=R, 2R and 3R middle distances.
As it can be seen in these figures, in a constant trench angle, increasing trench radius doesn't have an important effect on Aarr.Actually, in accordance with normalized distances by trench radius, the effect of trench radius increasing has been omitted.It can also be inferred that by increasing the trench radius, longer length of wave path will be protected.

Conclusions
A three-dimensional finite element analysis of a vibration of deep foundation has been taken in this research to evaluate the effects of passive isolation on the reduction of wave amplitude and the following conclusions can be extracted. Increasing the trench radius has a direct effect on the protected area.Hence, by increasing the trench radius a bigger area will be protected.


By keeping the trench angle unchangeable, increasing in trench radius doesn't have a significant effect on wave amplitude reduction.Therefore, it is better to investigate the interaction of trench radius and angle simultaneously and put the responsibility of wave reduction to the height and geometric properties of trench related to the trench length. Generally, increase in trench angle cause a decrease in average amplitude reduction ratio (Aarr).


Trench angle =150° is highly recommended for the optimal open trench angles.


The behavior of wave amplitude reduction versus the increase of trench angle is approximately linear.

Figure 2 .
Figure 2. Problem definition -Section of passive isolation by open trench Fig Fig Figure 8

Table 2 .
Static properties of the sandy soil

Table 3 .
Dynamic properties of the sandy soil

Table 4 .
Geometric properties of the trench and deep foundation