Scouring can reduce the strength and rigidity of the pile–soil system and become one of the major causes for the failure of the structure of the partially-embedded single pile. The stratification of the soil fields has a significant influence on the internal force and deformation of laterally-loaded piles. A dynamic model of the laterally-loaded single pile in layered soil is established employing Hamilton’s principle based on the modified Vlasov foundation model. Then, the finite difference method is used to obtain the numerical matrix containing the control equations of the single pile to achieve accurate modeling of the soil–structure interaction (SSI) system affected by scouring, so as to solve the natural frequencies of the single pile. Green’s function method obtains the analytical solution of the forced vibration of the single pile. The effects of scouring and the layered soil on the dynamic response of the single pile are studied by numerical calculation and parameter analysis. It is shown that the dynamic model of the partially-embedded single pile in layered soil based on the modified Vlasov foundation model can accurately predict the dynamic characteristics of pile foundation affected by scouring. As the scouring degree intensifies, the first-order natural frequencies of the single pile in layered soil decrease significantly. The subgrade reaction coefficient of each layer of soil in the modified Vlasov foundation model decreases, and the shear coefficient increases. The first-order natural frequencies of the single pile at each scour level increase with the increase in the thickness of the underlying soil. When the elastic modulus of the first layer of soil is increased by one time, the first-order natural frequencies of the single pile are increased by about 20%.

In this paper, the thermoelastic behavior of a rod made of an isotropic material under the action of a moving heat source was investigated using a new theory of thermoelasticity related to fractional-order time with two relaxation times. A mathematical model of the one-dimensional thermoelasticity problem was established based on the new thermoelasticity theory. We considered the symmetry of the material, and the fractional-order thermoelasticity control equation was given. Subsequently, the control equations were solved and analyzed using the Laplace transform and its inverse transform. This study examined the effects of fractional-order parameters, time, two thermal relaxation times, and the speed of movement of the heat source on the displacement, temperature, and stress distribution patterns in the rod.

This paper investigates the influence of soil with finite depth on the vibrational behavior of a multi-span continuous beam resting on an elastic foundation. The simplified model of the Timoshenko beam supported on soil with finite depth is established, introducing the foundation displacement decay function. The numerical solution of the continuous beam’s vibration response on the elastic foundation is obtained by using the transfer matrix method (TMM) and fourth-order Runge-Kutta method (RK4). Taking a two-span continuous beam as an illustrative example, the validity of the calculation theory is validated by comparing it with the outcomes obtained from the finite element method (FEM). Utilizing numerical computation and parametric analysis, the vibration response of continuous beams is evaluated in terms of its influence by various factors such as soil thickness, viscous damping coefficient of the soil, subgrade reaction coefficient, and span ratio. The findings indicate that the inertial motion of the soil with a finite depth significantly reduces the continuous beam’s inherent frequency and enhances the structure’s resonance effect. The rise of the subgrade response coefficient increases the system’s resonant frequency while decreasing the displacement response amplitude. The ratio between the adjacent spans determines the effect of beam span vibration energy transfer to adjacent spans. In addition, compared with the span directly excited by a concentrated harmonic load, the impact of soil thickness, subgrade reaction coefficient, and viscous damping, the coefficient of the soil is more significant on the indirect influence span of a continuous beam.

Homogenized micro-crack crushing is a new method of concrete pavement rehabilitation that makes full use of the bearing capacity of the original concrete pavement, whereby the treated pavement can be directly overlaid with hot mixed asphalt concrete. In order to solve the problem of longitudinal crack extension of a cracked core in the weak position of local pavement, the crack propagation mode of concrete slabs under low-velocity impact from different numbers and distributions of impact heads was studied using numerical simulation. Moreover, field tests were also carried out to determine the optimal layout of drop hammer impact heads, and the numerical simulation results were compared with the experimental data. The results show that, when a concrete slab is impacted by a single impact head, the bottom of the slab first cracks and then the crack develops upward until the main crack runs through the concrete slab. However, when the concrete slab is impacted by multiple-impact heads, including three or four impact heads, the concrete slab forms a triangular or quadrilateral fracture core, respectively. The numerical simulation results are in good agreement with the laboratory experiments. Through the optimized arrangement of the hammer’s impact heads, the problem of longitudinal crack extension of a cracked core can be effectively solved, and the probability of reflection cracks can be reduced.