Three simplified models for the analytic determination of the dynamic response of a crossanisotropic poroelastic half-plane to a load moving with constant speed on its surface are presented and compared against the corresponding exact model. The method of analysis of the exact and approximate models uses complex Fourier series to expand the load and the displacement responses along the horizontal direction of the steady-state motion and thus reduces the partial differential equations of the problem to ordinary ones, which are easily solved. The three simplified models are characterized by reasonable simplifying assumptions, which reduce the complexity of the exact model and facilitate the solution. In the first simplified model all the terms of the equations of motion associated with fluid acceleration are neglected. In the second simplified model, solid displacements are assumed to be equal to the corresponding fluid ones, while the third simplified model is the second one corrected with respect to the fluid pressure at the free boundary (top) layer. All three simplified models are compared with respect to their accuracy against the exact model and the appropriate range of values of the various significant parameters of the problem, like porosity, permeability, anisotropy indices, or load speed, for obtaining approximate solutions as close to the exact solution as possible is thoroughly discussed.

This work proposes a novel plastic damage model to capture the post elastic flow-controlled damages in pavement-soil systems prescribed by the vibrations of moving load. Initially, the pavement structure has been modelled as a single-layer system resting on a spring-dashpot system representing soil mass. Then, multilayer modelling was adopted to analyze the post-elastic dynamic response in supporting plastic flow-controlled layers of geomaterial. Three mechanistic zones namely, elastic recoverable, transition, and post elastic zone have been conceptualized to identify the damage. The nonlinearity in stress and equivalent plastic strain has been observed for the set of selected velocities and load intensities specified in codal provisions. The variation in equivalent plastic strain is observed in the range of 10-16 to 10-3% in the granular base layer and 10-16 to 10-4% in the subgrade soil layer. The findings show that the equivalent plastic strain due to plastic flow prescribed by the vibrations of moving action of vehicular load at varied velocities is one of the root causes of permanent deformations. The propagation of dynamic load vibrations from the uppermost layer of pavement induces the generation of stress waves within distinct sub-layers of geomaterial. Hence, the observed behaviour leads to the generation of nonlinear stress waves prescribed by a vibrational mechanism of stress transfer (VMST). Therefore, the evaluation of the nonlinearities causing damage in pavement structure supported by flow controlled geomaterials has the potential to predict permanent deformations and its implications in the design of pavements supporting the transportation network.

This article proposes an analytical layer element methodology for transversely isotropic (TI) laminated water-saturated subsoils to a harmonically moving load over the media surface. Biot's elastodynamic equation is decoupled by the double Fourier transform combined with the Heaviside step function of the load source. Exact 3D dynamical stiffness matrices of the soil layer element and the TI saturated half-space are established based on the derived displacement and stress components in the transform domain. Assembling the stiffness matrices of the discrete layer elements and underlying half-space yields the total 3D dynamical stiffness matrices. Considering the element boundary conditions, the analytical layer-element solutions in the wavenumber domain are obtained. The space domain result is retrieved by the inverse Fourier transformation. The results have a good consistency with the current solutions. The effects of the soft soil layer thickness, the material anisotropy, stratification characteristics, the load frequency, and the load moving velocity are analyzed.

This study establishes a coupled thermo-hydro-mechanical dynamic model(THMD) for saturated porous sediments under the eccentric motion of a deep-sea mining vehicle, considering the characteristics of deep-sea sediments. We applied the method of complex Fourier series expansion to simplify the coupled equations into ordinary differential equations and obtained the complex Fourier series expansion forms of various physical quantities of sediments during the eccentric movement of the mining vehicle. The undetermined constants are determined based on boundary conditions, yielding a series representation of the solution for THMD of deep-sea sediments. Subsequently, the solution was utilized to investigate the influence of mining vehicle parameters on the dynamic response of deep-sea sediments. This study demonstrates that the vertical displacement, vertical stress, and excess pore water pressure of sediments increase as the speed of the mining vehicle increases. Furthermore, the vertical displacement, vertical stress, and excess pore water pressure increase with the increment of load amplitude, and the differences in the curves at different eccentricities gradually become larger as the load amplitude increases. The proposed model can be applied to geotechnical engineering problems in saturated porous foundations, providing a necessary theoretical basis and analytical approach.

Transport systems such as highways and railways are constructed on earthworks that experience fluctuating levels of saturation. This can range from dry to fully saturated, however most commonly they are in a state of partial saturation. When numerically modelling such problems, it is important to capture the response of the solid, liquid and gas phases in the material. However, multi-physics solutions are computationally demanding and as a solution this paper presents a finite element approach for the dynamic analysis of unsaturated porous media in a moving coordinate system. The first novelty of the work is the development of a principle of relative motion for a three-phase medium, where the moving load is at rest while the unsaturated porous medium moves relative to the load. This makes it particularly efficient for moving load problems such as transport. The second novelty is a parametric investigation of the three-phase response of a partially saturated medium subject to a moving load. The paper starts by presenting the time domain model in terms of its constitutive relationships and equations for mass and momentum conservation. Next the model is validated using three case studies: the consolidation of a saturated soil column, the dynamics of an unsaturated soil column and finally the response of a saturated foundation to a moving load. It is then used to study a moving 2D plane strain load problem and its performance is compared to that of a standard FEM solution which does not employ a moving coordinate system. Similar accuracy is obtained while computational efficiency is improved by a factor of ten. Finally, the model is used to investigate the effect of degree of saturation and moving load speed on the response of an unsaturated porous medium. It is found that both variables have a significant impact on the dynamic response.

The aim of this paper is to propose a two-stage theory-based analytical method for the dynamic performance of pile groups in layered poroelastic saturated cross-anisotropic soils induced by moving loadings. Among them, the free-field vibrational analysis of saturated soils is performed by the analytical element-layer approach (ALEA) and Fourier transformation. Based on the free-field response, the boundary element (BE) solution for the soil resistance at the soil-pile interface is derived utilizing the two-stage theory. Simultaneously, the finite element (FE) solutions for the pile shaft resistance and deformation of pile groups are derived based on the Timoshenko beam theory. Finally, the FE-BE coupled dynamic equation for deformations and internal loadings of the soil-pile system is obtained. Thereafter, the reliability of the proposed method is validated by comparing with existing solutions and FE data from ABAQUS. Based on the derived solutions, a comprehensive parametric study is performed to examine the effects of loading amplitude, force speed, soft soil-layer stiffness, soil anisotropy, and pile length on the dynamic responses of pile groups.

In-service masonry arch road bridges, mainly realised before the first half of the last century, represent a wide portion of the entire worldwide infrastructural asset. Given their age, during their service life these structures could have experienced damage due to anthropic (i.e. traffic) and natural (i.e. earthquakes, soil settlements, degradation, etc.) actions which may have inevitably affected their load-bearing capacity. The present study addresses the problem of the residual capacity estimation of damaged bridges by investigating the impact of previous loading on the actual strength of the structure. In particular, reference to a past experimental activity retrieved from the literature on reduced-scale bridges subjected to concentrated vertical loads has been made to calibrate a reliable detailed finite element model in Abaqus software. Then, damage of different extent has been introduced by simulating the transit of vehicles of various weights on the structure and the residual capacities of the bridge have been assessed and compared against the undamaged configuration. The results confirm that preexisting damage due to traffic loading may significantly influence the capacity of such structures, with peak load reductions up to 60% estimated through the proposed methodology.

The soil layer of the roadbed is an uneven unsaturated soil layer in practical engineering. The goal of this article is to consider the uneven gradient distribution of soil particle compression modulus and soil skeleton compression modulus along the depth of unsaturated roadbed soil. Introducing an uneven gradient factor is to propose a power function continuous variation model for the soil particle compression modulus and soil skeleton compression modulus of the roadbed soil along the depth of the soil layer. Then, the model is coupled with Biot's theory of unsaturated porous media to establish a dynamic response model for non-uniform unsaturated soil layer roadbed under uniform moving loads, and provided a method for using Fourier series to solve the model. Analysis the influence of soil particle compression modulus and soil skeleton compression modulus on the dynamic response of unsaturated soil layers under uniform moving loads. The results indicate that the deformation displacement is positively correlated with the non-uniform gradient factor of modulus. The deeper the depth, the weaker the influence of the non-uniform gradient factor on the peak pore water pressure. At the same location from the vibration source, the influence of the non-uniform gradient factor of soil particle compression modulus on the peak pore water pressure is not significantly different from the influence of soil skeleton compression modulus on the peak pore water pressure. However, the gradient factor of soil particle compression modulus has a greater impact on the peak deformation displacement than the factor of skeleton compression modulus. Thus, clarified the influence of the non-uniform gradient factor of soil particle compression modulus and soil skeleton compression modulus along depth on the dynamic response of the non-uniform unsaturated soil layer roadbed under uniform moving load.

Based on the basic control equations of orthotropic anisotropic half-space under moving harmonic loads, the transfer matrix solution of a single-layer foundation is derived by introducing the moving coordinate system, Fourier integral transform, and Cayley-Hamilton theorem. The three-dimensional (3D) dynamic mechanical model of layered orthotropic anisotropic foundation under the rectangular coordinate system is established. The dynamic response of the layered foundation along the depth direction in the frequency domain is derived by using the transfer matrix method, combining boundary conditions, interlayer contact conditions, and continuity conditions. The analytical expressions of the displacements and stresses in the layered foundation are obtained by using Fourier inverse transformation. Based on the derived theoretical method, degradation verification, and corresponding calculation program are prepared for numerical calculation, and numerical example parameter analysis was carried out in combination with the finite element analysis software ABAQUS to study the influence law of the stratification characteristics, load moving speed, load vibration frequency and orthotropic anisotropic properties on the dynamic response of layered foundation. The 3D dynamic characteristics of layered orthotropic anisotropic foundations under the moving load are revealed. The results show that the stratification characteristics of the foundation have a significant effect on the vertical displacement of the surface, and the changes in elastic modulus and shear modulus parameters of the first layer of soil have a greater effect on the displacement dynamic response than that of the subsoil. Within a certain range, the vertical displacement of the foundation surface increases with the increase of load moving speed and decreases with the increase of load vibration frequency. Compared with isotropy, the orthogonal anisotropy of the surface foundation has an obvious influence on the vertical displacement of the foundation surface. In practical engineering, the orthogonal anisotropy of the foundation should be considered in order to obtain more accurate results.

The following objects have been analysed by frequency response functions and moving load responses. A simple modal analysis which is based on the transformed and weighted system equations has been tested for an automotive test car and for many floors in many buildings to get some rules for their natural frequency and damping. Moreover, six neighboured equal, weakly coupled, wooden floors in a castle have been measured by ambient and hammer excitation, and a special method to extract the different mode shapes of the closely spaced natural frequencies has been developed and tested. Different foundations, for which the soil-structure interaction is generally important, have been measured and compared with finite-element boundary-element models of varying soil properties. Similarly by FEBEM calculations, damages in railway tracks have been identified from flexibility functions (frequency response functions) and from the movingload responses to normal train operation. Rail and foot bridges have been measured during train passages and by quasi-static tests with moving vehicles. The repeatability of the inclinometer measurements has been checked for different passages, passage directions, and measurement campaigns at a six-span foot bridge. Two rail bridges at the Hanover-Wurzburg high-speed line have been measured and evaluated for integrity and for the train- and speed-dependent bridge resonances. The relation between the multi-axle and the single-axle excitation can be solved in frequency domain by the axle-sequence spectrum of the vehicle or the whole train. The single axle response has been used to identify track and bridge damages in laboratory and in situ.