The pile-anchor supporting structure is widely used in foundation pit engineering, it is particularly necessary for calculating lateral displacement of the pile-anchor supporting structure. The soil stress state is transformed by the additional stress caused by the prestress, thus the lateral displacement can be decreased own to pile-anchor supporting structure bearing active earth pressure had changed. Prestress as a concentrated force is decomposed into the horizontal component and vertical component, calculating the additional stress caused by the prestress and getting the formula of active earth pressure of considering the additional stress, setting up calculation model of the pile-anchor supporting structure. For typical examples of foundation pit engineering, the parameters are substituted into a program written based on derived formulas, and the elastic deformation superposition method is used to calculate the horizontal displacement of the pile anchor support structure. The comparison and verification is carried out by Finite element analysis. The influence of cohesion and friction angle on pile displacement, bending moment, and shear force has been studied. This study found that cohesion and friction angle have a significant impact on the displacement of pile anchor support structures.

This note presents an analytical solution to investigate the dynamic behavior of pile groups of embedded rock due to rock burst, which takes into account the interaction between piles. The energy generated by the rock burst propagates through the soil in the form of stress waves. It is transmitted to the pile foundation through the interaction between the soil around the pile and the pile. For rock-socketed piles, the condition of pile tip fixing is considered. The horizontal dynamic response calculation model of the pile group is established, and the analytical forms of the pile group stiffness and pile group interaction factor are obtained. In addition, the effect of saturated soil parameters on the dynamic response of pile groups are discussed.

Based on the wave theory of saturated frozen porous media, this study investigates the effects of soil-skeleton viscosity and thermal processes. By employing the Kelvin-Voigt linear viscoelastic model and generalized thermoelastic theory, the governing wave equations for a thermo-viscoelastic saturated frozen soil medium under thermo-hydro-mechanical coupling are established. Analytical solutions for the reflectivities and energy ratios of waves reflected from the free surface are then derived under plane SV1-wave incidence. The analytical solutions are validated through model reduction, and the effects of viscosity and thermal processes on reflection behavior and energy distribution are further analyzed. The results show that skeleton viscosity and thermal processes significantly alter the reflection characteristics and energy distribution of the reflected waves. Increasing the relaxation time weakens the reflected P1 wave while enhancing the other reflected waves. Thermal conductivity mainly affects the thermal wave, whereas the thermal expansion coefficient has a stronger influence on compressional waves. For each 1×10−4 K−1 increase in the thermal expansion coefficient, the reflectivity and energy ratio of the reflected P1 wave increase by approximately 0.54% and 54.27%, respectively. Increasing frequency generally reduces the reflectivities and energy ratios of all reflected waves. In addition, increasing the specific heat of the solid phase markedly suppresses thermal-wave propagation. For each 200 J/(kg⋅K) increase in the solid-phase specific heat, the reflectivity and energy ratio of the reflected T wave decrease by approximately 17.08% and 17.11%, respectively.