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.

Currently, Lamb problems of many engineering foundations investigated are still assuming that foundation soils are two-phase homogeneous saturated porous m

Currently, the Euler–Bernoulli beam nonlocal theory does not fully consider the effects of foundation deformation and axial force on the beams, and cannot accurately reflect the real mechanical properties of nanobeams. The primary objective of this study is to introduce a novel computational method designed for an enhanced characterization of the vibrational behavior of nanobeams. Initially, this method incorporates the influence of foundation deformation on beam bending, accounts for the effects of axial forces, integrates Eringen's nonlocal theory and establishes a modified Euler–Bernoulli beam theory model for the first time, accompanied by a degradation validation of the model. Subsequently, the Laplace transform and Hasselman's complex mode synthesis method are utilized to solve the model, providing the first derivation of the state-space transfer function for the nanobeam vibration model based on the modified Euler–Bernoulli beam theory. Lastly, the study elucidates the impact of nonlocal factors and various parameters on the vibration characteristics of nanobeams. The results show that the order n increases, and the peak frequency value moves in the direction where the nonlocal factor tends to zero. At the same order, the beam length increases, and the peak frequency moves in the direction of increasing nonlocal factor. The modified geometric parameters and the foundation beam stiffness parameters have a greater effect on the peak of the beam's vibration mode in the higher order case and a lesser effect in the lower order case. The larger the nonlocal factor, the larger the peak of the vibration mode.

The porosity and shear modulus, permeability coefficient of pore water pressure and permeability coefficient of pore gas pressure of unsaturated foundation

This study aims to scientifically and reasonably assess the damage caused by randomly induced vibrations from construction vehicles driving on gravel roads