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Vibration due to train movement has been concerned since the advent of rail transportation systems. Nowadays this subject is more important by increasing the speed of trains and wagon weight and development rail way in urban area. Different methods and techniques have been proposed to reduce these vibrations by researchers. In this study, geotechnical modeling of trench barrier isolators to reduce train vibrations are investigated by numerical modeling. Trench barrier according to location are divided into two categories: active and passive. Active trench is located near the source load but passive trench is located near the structure that needs protections. The main focus of this research is the effects of trench depth on efficiency of passive trench barrier. In advance by considering the wagon weight and distance between the wheels, the load in terms of time domain by calculating Fourier spectra and considered effective frequency range, the load-time function is determined. Then, a series of nonlinear finite-element analyses were carried out to study effect of trench depth. The depths of trench are considered 0 to eight meters in analysis. Viscous damping was considered by means of Rayleigh methods. The coefficient of mass and stiffness matrices are defined by modal analysis. Then, modeling of rail, sleeper, ballast, sub-ballast and soil layers is conducted to analyze wave vibration propagation due to train movement and evaluation of amplitude reduction due to trench barrier. Mohr Coulomb failure criterion is supposed for soil, ballast and sub-ballast layer and a linear elastic behavior was assumed for sleeper. Infinite element boundaries were used at the lateral sides of the finite element mesh for prevention of wave reflection. The dynamic response analysis was based on input time historical wagon load which determined in previous section applied at the sleeper.Thereby the studying of deformations and displacement and particle velocity of the elements of the model, the effects of the trench barrier on before and after trench, are considered. Results indicate that increase in trench depth is effective on vibration reduction. This means that by increasing the depth of the trench, amplitude of deformation becomes more reduced. It also increases the depth of the trench, reduces the dominant wave frequency vibrations. On the other hand, by increasing the depth of the trench, amplitude reduction ratio has a significant decreasing that means increase efficiency trenches. The relationship between depth and amplitude reduction ratio (Arr) was introduced as a quadratic function. For validation of modeling, theory equation of amplitude decreasing is compared with numerical modeling. The result showed that there is a good accordance between numerical model and theory equation at different distance.The minimum depth of the trench should be selected based on different parameters. To define depth of trench should be note that the reduction due to trench should be significantly greater than the decreasing wave amplitude due geometric and material damping. Reducing the required to mitigate the potential damage of protected structures and economic and implementation considerations are important factor in determination of final depth of the trench barrier isolator.

Keywords: Load-time function, Vibration, Train movement, Trench barrier, Depth

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