Traffic induced vibrations in two-and-a-half dimensional framework

Vibrations induced by road and rail traffic are a growing environmental concern in urban areas because these vibrations might annoy the occupants of roadside/railside buildings and affect the normal operation of vibration-sensitive instruments. The increasing awareness of these consequences has stimulated the need of reliable and efficient models to predict traffic induced vibrations. For this purpose, various models are developed in this thesis, ranging from the simplest beam-foundation models for investigating one dimensional wave propagation in the road or rail to more sophisticated two-and-a-half dimensional (2.5D) models that are capable of incorporating the three dimensional effects of soil-structure interactions. In the beam-foundation models subjected to moving loads, only a few have the closed-form with the beam modeled as a Euler-Bernoulli type. If the beam is modeled as a Timoshenko beam such that shear deformation can be included, it is a challenging task in formulating new closed-form solutions because the characteristic equation of the model, a fourthor fifth-order polynomial with complex coefficients, cannot be solved by radicals except the following three cases: zero speed, elastic foundation and harmonic loads, and elastic foundation and constant loads. The characteristic equation is biquadratic in the first two cases, and becomes quartic with real coefficients only in the third case. The three cases correspond to a Timoshenko beam-viscoelastic foundation model subjected to a non-moving harmonic line load, a Timoshenko beam-elastic foundation model subjected to a moving harmonic line iv load, and a Timoshenko beam-elastic foundation model subjected to a moving quasistatic line load, respectively. The corresponding three new closed-form solutions are successfully deduced. These solutions are verified through comparisons with those calculated from existing analytical and numerical models. For predicting road traffic induced vibrations, a two-step 2.5D finite elementperfectly matched layer (FE-PML) approach is proposed. First, dynamic axle loads of the vehicle are determined by solving the equation of motion of the vehicle at a given road surface unevenness. Next, source-receiver transfer functions in the frequencywavenumber domain are calculated in a way that the road and a portion of the soil are meshed by 2.5D finite elements and the semi-infinite property of the soil is considered by 2.5D PML elements. Finally, the outputs of these two steps are connected through the dynamic Betti-Rayleigh reciprocal theorem to calculate the free field responses to the moving axle loads. The proposed approach is able to obtain the free field responses as accurately as the well-validated 2.5D FE-BEM approach, and is more computationally efficient than the latter in the case of embedded structures in the soil because the proposed approach tends to grow its complexity linearly with the problem size rather than according to the square of the problem size for the 2.5D FEBEM approach. The proposed approach is then applied to investigate the influence of an embedded circular-shaped cylindrical cavity and a concrete pipeline on the free field responses due to dynamic excitations. For predicting railway induced vibrations, the 2.5D FE-PML approach is redeveloped through a subdomain formulation in order to account of both the interaction effects of the vehicle-track and track-soil systems. The dynamic train-track interaction takes place at moving contact points of each axle of the train, and the dynamic track-soil interaction is realized through a massless strip foundation. Three distinct methods are used in the modeling of the subdomains: the train is modeled by a multi-body dynamic system, the track is idealized as a continuum model of six v degrees of freedom, and the soil is discretized by the 2.5D solid and PML elements. The proposed approach is verified through comparison with an existing numerical example studied by the 2.5D FE-BEM approach. The proposed approach is then applied to investigate the influence of an inclined layer and irregular layer of soil on the vibrations induced by the passages of a Thalys high-speed train. Due to the inherit merit of the 2.5D FE-PML approach, the computational efficiency of the proposed approach is greatly improved, as compared to the 2.5D FE-BEM approach, in the case where the problem size is relatively large such as the case of embedded structures. The two-step 2.5D FE-PML approach is verified through a field experiment on a road at Hong Kong, in which the asphalt strains at the bottom of the second layer of the road were measured during the passage of a three-axle Hino truck. Next, the subdomain formulation of the 2.5D FE-PML approach is verified through an existing field test on a stretch of the Portuguese railway network, in which the responses of the track and the free field were simultaneously measured during the passages of an Alpha-Pendular train. The results of these two experiments are fairly satisfied and show that the respective prediction model is capable of capturing the essential physical phenomena.