Progress in Civil and Structural Engineering Computing
Chapter 12 D. Le Houédec+, G. Lefeuve Mesgouez* and B. Picoux+
+Laboratory of Mechanics and Materials, Ecole Centrale of Nantes, France *Laboratory of Complex Hydrodynamics, Sciences Faculty, University of Avignon and Vaucluse Country, Avignon, France Keywords: soil-structure interaction, wave propagation, moving loads, railway traffic, numerical simulation. The problem of determining the response of a soil medium under the action of moving loads has received considerable attention in the past. Work in this area has been motivated by the need to determine the vibratory motion on the ground surface and at depth caused by moving vehicles. Moreover, high-speed trains are becoming increasingly popular and freight trains increasingly heavier. Combined with this fact and the observation that Rayleigh wave speeds are slower in soft soils, we see that the study of moving loads is important for environmental and geotechnical engineers. A lot of models are possible for the simulation of propagation phenomena. First, we can consider the case of a two-dimensional problem involving a moving harmonic strip load. The results derived by Fourirer transform are valid for any frequency and load speed. For moving loads, to choose a suitable damping model, an original modified hysteretic damping is employed. Also, it is possible to investigate the transmission of vibrations due to a moving harmonic train of rectangular loads rigidly attached to an elastic multilayered ground. In this case, the previous damping model is used, combined with a dynamic stiffness matrix approach. In the spatial wavenumber domain, the dominant features encountered in a spectral decomposition corresponding to compression, shear and Rayleigh waves are illustrated. Also, results of the model at certain critical load speeds can be presented in dimensionless parameters. For 3D problems, a three-dimensional semi-analytic model of ground vibration due to a moving harmonic rectangular load can be developed. The model consists of a half-space, an elastic layer over a rigid foundation, or a multilayered soil, excited by an uniform harmonic surface load moving with constant velocity. The displacements are obtained in a wave number domain after a double Fourier transform for the equations of motion. Actual displacements are then calculated using a FFT algorithm. Numerical results can be presented in the wave number and actual domains, showing the existence of different regimes (sub-Rayleigh and super- Rayleigh) depending on the load speed. Besides, for multilayered soils, we have to construct a global stiffness matrix using the same assembly process as in finite element analysis. A more complete study needs to take into account the railway track. In this case, a railway track model lying on a layered ground and submitted to a moving train can be developed and the resolution method uses the formalism of Fourier transform for a semi-analytical resolution in the wave number domain. It includes all elements of the track (rails, pads, sleepers and ballast) and allows a parametric analysis of its different elements and evaluation of vertical displacements according to the speed, the weight and the composition of the trains. The handwriting of the stiffness matrix for a layered ground with the help of a fitted phase angle of Helmotz functions provides a fast numerical approach of the problem. Then Mach cones for the super-Rayleigh regime can be obtained near the track involving very high displacements on waves front. In the continuation of these numerical results, in situ measurements can be performed with a view to the validation of the model. These studies allow the construction of an available data basis for a possible development of models. | ||||||||||
