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Since the alarming settlement of transport infrastructures on soft subgrade caused by long-term traffic loading, a method for predicting settlement is of considerable significance in the engineering design. In this study, we proposed a practical and simple predicting method on the settlement of soft subgrade considering traffic loading effects. The model used in this method involves the principal stress rotation and loading frequency, which needs only four parameters with clear meaning obtained by several cyclic triaxial tests. The applicability of the model has been verified by previous results from other researchers. Moreover, the engineering practicality of this method was validated by the field data of a highway. The settlements under low-frequency and high-frequency are the upper limit and lower limit of the traffic load-induced settlements, respectively. With the increasing embankment thickness, the settlements decrease because the cyclic stress ratio decreases and the detrimental effect of the principal stress rotation on the settlement reduces. The vehicle load is a more influential factor in the settlement than the traffic volume.

The equivalent stiffness of a saturated poroelastic halfspace that supports an infinite Euler-Bernoulli beam under a moving point load has been investigated in this paper. The smooth contact condition is assumed for the interface of beam and halfspace, however, with an improved continuity condition, i.e. the continuities of contact normal stress and contact vertical displacements are imposed across the width of the beam. The equivalent stiffness of the halfspace has been evaluated using a contour integration approach such that contributions of the Rayleigh pole and the dispersion branches can be explicitly taken into account. Influences of the continuity condition and the permeability on the equivalent stiffness have been studied. It is found that the imaginary part of the equivalent stiffness is nonzero since the viscous coupling between two phases of the saturated halfspace has been considered. This observation fundamentally differentiates the present paper to the work by Shi and Selvadurai (2016) where an infinite permeability has been assumed for the halfspace, i.e. null viscous coupling.

A truck–pavement–ground coupling model was established to study the dynamic responses of a saturated poroelastic half-space generated by a moving heavy truck on the uneven pavement. The ground was simulated as a fully saturated poroelastic half-space governed by Biot’s theory. The overlying pavement was simplified as a Kirchhoff thin plate. With the assumption of a sinusoidal pavement surface, the dynamic wheel–pavement force was obtained through a linear Hertizian contact model. The numerical results showed that this dynamic load could make considerable contributions to the stress and excess pore water pressure responses in the ground. Furthermore, the effective stress path of the soil unit beneath the pavement caused by the moving truck was firstly calculated and presented. It was found that the differences between the total stress path and the effective stress path became significant as the truck speed increased, thus the effective stress path was more suitable than total stress path to reflect the stress history of soil elements in the saturated ground during the passage of high-speed traffics.

Subgrade soils of traffic infrastructures are subjected to large numbers of load applications at a stress level below their shear strength. It is therefore of great practical relevance to study the deformation behavior of soft clay under long-term cyclic loading. In this study, a series of monotonic triaxial tests and long-term cyclic (50,000 cycles) triaxial tests have been carried out to investigate the undrained deformation behavior of undisturbed soft clay from Wenzhou, China. The stress–strain hysteretic loop, resilient modulus and permanent strain of the tested samples were found significantly dependent on CSR and confining pressure. With an increase of CSR and confining pressure, the resilient modulus decreases more significantly with increasing number of cycles and the accumulation rate of permanent strain increases. Furthermore, the shape of the stress–strain hysteretic loop almost remains unchanged and the resilient modulus tends to a steady value after a large number of cycles. Based on the experimental results, two equations are established for the prediction of long-term resilient modulus and permanent strain. Finally, a new critical value of 0.65 is suggested for CSR . When CSR >0.65, the resilient modulus for large number of cycles is reduced to a so called “asymptotic stiffness” and the accumulation rate of permanent strain significantly increases.

Biot’s theory has been widely employed to study responses of saturated soil under dynamic loads. To simplify the analysis, three simplified formulations based on Biot’s theory have been proposed, including the u–p formulation, fully undrained formulation and fully drained formulation. The u–p formulation is established by neglecting the relative pore fluid acceleration. The fully undrained formulation founds on the assumption of no relative pore fluid displacement. The fully drained formulation supposes an infinite soil permeability. Nevertheless, the successful applications of these simplified formulations are hindered because of their indefinite application scopes. To overcome this, this paper carries out a comparative study of the simplified formulations for modeling a saturated poroelastic half-space subjected to a moving harmonic point load. The three simplified formulations are investigated by comparing with Biot’s u–w formulation. A triple Fourier transform is first used to transform the four formulations into the frequency-wavenumber domain. Then an analytical inverse transform with respect to the frequency is performed to obtain the vertical soil displacement and pore pressure in the time-wavenumber domain. A parameter RΩ defined in the wavenumber domain, which integrates effects of the soil permeability, load oscillating frequency and moving load velocity, is proposed to determine the validity ranges of the three simplified formulations. Some critical values of RΩ are suggested and applied to a model in a previously published paper by Siddharthan et al.

A study is carefully conducted for the rocking response of a rigid circular foundation resting on a poroelastic half-space when subjected to seismic waves under the framework of Biot’s theory. The free-field waves, rigid-body scattering field waves and radiation scattering field waves are introduced to consider the complex behavior of the soil owing to the scattering phenomena caused by the existence of the foundation. The contact surface between the soil and the foundation is supposed to be perfectly bonded and fully permeable. Combining with the divided wave fields, two sets of dual integral equations elaborating the mixed boundary-value conditions are established, and then reduced to Fredholm integral equations. Therefore, with a semi-analytical method, the expressions of the rocking displacements are obtained. The numerical results of the rocking vibration of the foundation for incident P, SV and Rayleigh waves are presented. The influences of certain parameters, such as the permeability of the soil, the incident angle, Poisson’s ratio and the mass of the foundation, on the rocking vibration of the foundation are explored and studied. Different reactions are found when the foundation is excited by different waves.

An analytical approach is used to study the torsional vibrations of a rigid circular foundation resting on saturated soil to obliquely incident SH waves. Biot’s poroelastic dynamic theory is considered to characterize the saturated soil below the foundation, which is solved by Hankel transform later. In order to consider the scattering phenomena caused by the existence of the foundation, the total wave field in soil is classified into free-field, rigid-body scattering field and radiation scattering field. According to the classification of wave field and the mixed boundary-value conditions between the soil and the foundation, torsional vibrations of the foundation are formulated in two sets of dual integral equations. Then, the dual integral equations are reduced to Fredholm integral equation of the second kind to be solved. Combining with the dynamic equilibrium equations of the foundation, the expressions for the torsional vibrations of the foundation are obtained. Numerical results are presented to demonstrate the influence of excitation frequency, incident angle, the torsional inertia moment of the foundation and permeability of the saturated half-space on the torsional vibrations of the foundation.

An analytical approach is used to investigate dynamic responses of a track system and the poroelastic half-space soil medium subjected to a moving point load under three-dimensional condition. The whole system is divided into two separately formulated substructures, the track sub-system and the ground. The ballast supporting rails and sleepers is placed on the surface of the ground. The rail is modeled by introducing the Green function for an infinitely long Euler beam subjected to the action of the moving point load and the reaction of sleepers represented by a continuous mass. Using the double Fourier transform, the governing equations of motion are then solved analytically in the frequency–wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain load velocities. Computed results show that dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.