Keywords: Plaxis, soil models, wave propagation, soil particles vibrations, Rayleigh waves, Rayleigh damping.

The vibrations generated by a passing railroad propagated in soil, to a nearby building involve an oscillatory process [1]. In this paper, the problem of soil vibration induced by railway traffic is studied and presented. This research was done using the dynamic modulus defined in the finite-element program Plaxis-8v (developed at Delft University) as a tool for practical analysis in geotechnical engineering [2]. The object studied represented a railway embankment with the superstructure and a contact soil mass. The geometry is simulated by means of an axisymmetrical model with fifteen node elements in which the centre of symmetry is positioned at the midpoint between rails. Force action and kinematic action include: prescribed displacements on the superstructure; force action which is harmonically pulsating, prescribed displacement which are harmonic, and considered frequencies from 5 to 100 Hz. The force from the wagon with an axis static load of 230 kN is taken into account, but the dynamic load is assumed to be 30% more.

The character of the propagation of the vibrations in both cases is identical; however the force action more precisely reflects the true behaviour. In the case of the force loading the "deformation pit" is elastic soil bending deflection where a maximum deflection of 4-5 mm under the track is observed. This deformation extends in the transversal direction from 20 to30 m. The vibrations of the soil particles occur relative to a line of elastic deflection, the amplitude of the fluctuations depends on the frequency of the force. However with increasing frequency the amplitude decreases, whereas the velocity of vibration increases.

Moving away from a source of the vibrations the amplitudes of the steady-state vibrations also reduce. The greatest vibrations of the soil particles take place in a vertical direction, movement in a horizontal direction is less. By comparison of the various soil models accessible in Plaxis it is possible to draw a conclusion that the most appropriate is the linear-elastic body soil model. For the Mohr-Coulomb soil model similar results are obtained because of the stress from dynamic loadings do not exceed a limit of elasticity of the ground and the elastic-plastic model of the Mohr-Coulomb works in the linear area [3].

The nonlinear model of an isotropic hardening soil shows slightly different results. This is connected with the uncertainty of the soil parameters and the absence of experimental data to confirm them. Comparison of results of the calculation with the existing measurements of soil particle vibrations parameters at different distances from the tracks confirms the possibility of the Plaxis-v8 program being used to provide an estimation of the parameters of the soil vibration caused by the movement of trains [4].

1

D. Thompson, "Railway noise and Vibration. Mechanism, Modelling and Means of Control", Elsevier Ltd, 2009.

2

Plaxis 2D-v8, Plaxis b.v. Delft, the Netherlands, 2007.

3

N.A. Tzitovich, "Soil Mechanics", Moscow, 1983.

4

E.K. Borisov, S.G. Alimov, A.G. Usov et al., "Experimental structural dynamics. Transport vibration monitoring", Monograph, Petropavlovsk-Kamchatsky, KamchatGTU, 2007.

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