Piles are widely used to transfer the horizontal load of high-rise buildings, transmission towers, and bridges, especially for superstructures constructed near slopes. This study investigated bearing capacities of single piles under the combined horizontal force (H) and bending moment (M) for the pile in sloping ground. A 3D finite element model was proposed to simulate the non-linear pile–soil interaction and was verified by a model test. A series of numerical tests were conducted to obtain the failure envelope of bearing capacities of single piles under various combinations of H and M. The existence of slopes significantly reduced the bearing capacity of piles, especially when the horizontal and rotational displacements moved to the dip direction of the slope. An oblique ellipse was able to describe the failure envelope of bearing capacities of single piles near slopes in the HM plane. As the pile was installed away from the crest of the slope, both the width and height of the ellipse increased and the center of the ellipse was approaching the origin. The results of this article can provide useful references for designing horizontally loaded piles near slopes.

Single piles are normally used to support the transmission tower in mountain areas. Uplift capacity of piles is a key factor in the engineering design to increase the stability of transmission tower foundation. This study numerically investigated the uplift capacity of single straight and belled piles in the sloping ground which consisted of a clay layer underlain by medium weathered sandstone. A non-linear 3D finite element model was proposed to describe the uplift behavior of single piles and was calibrated against a field test on single piles subjected to uplift loading. A parametric study was conducted to investigate the effect of the slope angle (θ) on the uplift behavior of single piles. The uplift capacity decreased as θ increased for either straight piles or belled piles. Moreover, the range of the equivalent plastic strain was greatest for single piles in the level ground. For piles in the sloping ground, the range of equivalent plastic strain was wider at the position of the downstream slope than that at the position of the upstream slope when the uplift load of single piles reached the maximum. As the expansion angle increased to 30° and 45°, the uplift capacity of belled piles (Ru) was increased by 100% and 180% with respect to that of straight piles, respectively. The increase percentage in Ru was independent of θ. A practical method was proposed to quantify the slope effect on Ru.

Transmission tower structures support high-voltage power lines that carry electricity over long distance and rockfall is one of critical disasters during its safe operation. This paper presented a simplified analytical methodology for lateral dynamic responses of a transmission tower structure due to rockfall impact. At first, the lateral dynamic displacement of a lattice transmission tower structure can be represented by a second-order partial differential equation and half sine wave was used for rockfall impact. Then, the solution can be approximated by a set of specified shape functions multiplied by time-dependent generalized coordinates. And the partial differential equation is discretized into a set of single degree of freedom system. And then the shape function can be determined by solved an eigenvalue function and the fundamental frequency of a transmission tower can was derived based on the energy method and combination synthesis method. Finally, the lateral dynamic displacements can be approximately obtained. A numerical study of a transmission tower was conducted. Parametric study of the effect of impact location height, impact duration, peak impact force, as well as the distribution of cross-arms on dynamic responses were also carried out. And the results show that the discrepancy between the analytical and the computed of fundamental frequency is less than 3%, the error of dynamic displacement is within 10%, and the fundamental frequency of the structure decreases with the increase of the tower top additional mass ratio.