Improved analysis method for frame beams with prestressed cables in slopes based on inclined foundation stiffness

The frame beam with prestressed cables is a reinforcement structure to stabilize slopes or landslides, where the frame beam is placed on the slope face. Since the inclined foundation for the beam is different from the level one, it is crucial to determine reasonable normal stiffness of slope foundations to analyze mechanical responses of the frame beam under the cable tensioning forces. According to the upper-bound limit analysis theory, an analysis method for the ultimate bearing capacity of strip foundation on the slope face is provided based on a bilateral failure mechanism. The inclined foundation stiffness is accordingly expressed as the level one multiplied by the ratio of the inclined over the level bearing capacity. Further, a calculation method for the frame beam is established based on static equilibrium and deformation compatibility of the intersected elements in the frame as beams on the inclined elastic foundation. Some in-situ tests indicate the proposed inclined foundation stiffness is about 16 % smaller than the observed result. Compared with the classic level-foundation method for the frame beam, the improved method is closer to the numerical simulations. The ratio of the inclined over the level foundation stiffness is nonlinearly decreasing clearly from 1 as the slope angle increases from 0°. The stiffness ratio reduces with the increase of the soil unit weight, internal friction angle, and beam width, while increases with the cohesion and beam-soil friction angle. The mid-span bending moment and deflection of each element in the frame increases nonlinearly with the slope angle, whereas the shear force is faintly influenced by the slope angle.