P-Y Curves of Laterally Loaded Piles Near Earth Slopes

Design of piles under lateral loads using numerical analysis is a time-consuming process, requiring competent geotechnical engineers who can accurately model the soil profile and construction sequence. Therefore, most engineers have resorted to the p-y method that is a less time-consuming process in both the modeling and running time. Contrary to the numerical analysis method, the p-y method doesn’t require the burden of constructing a complicated 3D model. This method simply uses the relation between the soil resistance per unit length (p) and the lateral deformation (y) to deduce the straining actions on the pile, bending moment, and shear forces, which govern the structural design. However, the simplicity of this method comes with its shortcomings. The p-y method, for instance, cannot directly take into account the effect of earth slopes on the laterally loaded piles, and its results are somewhat approximate. A well-instrumented case study from the Caltrans site at Oregan State University is analyzed in this research. The studied case consists of a laterally loaded single vertical pile embedded in a cohesive soil layer near an earth slope of 2H:1V. A three dimensional numerical model of the case study is constructed, utilizing the finite element code, Plaxis 3D 2020. The p-y curves of the loaded piles were back-calculated from the numerical model using the elastic beam theory by performing the differentiation of the shear force acting on the pile along the full height of the earth slope. Normalized p-y curves were obtained to determine the p-multiplier, a factor that helps convert the p-y relation of a pile in leveled ground to that of a pile near earth slopes. Overall, it was found that the p-multiplier ranges between (0.4-0.8), (0.6-0.83), (0.8-0.95), and (0.98-1) for piles located at a distance of 0D, 2D, 4D, and 8D respectively from the crest of the earth slope, for various target depths. A parametric study for the effect of the distance of the pile from the crest of the slope, as well as the slope inclination, on the p-y curves was conducted. The curves were constructed for a single pile located at distances of 0D,2D,4D, and 8D from the crest of the earth slope. The performed study revealed that the p-multiplier, at a target depth of 1m, measured from the top of the pile, for the studied slope inclinations, ranges between (0.3-0.45) for the pile at a distance of 0D, (0.76-0.8) at a distance of 2D, (0.82-0.93) at a distance of 4D and (0.98-1) at a distance 8D. Analysis results showed that the effect of slope inclination diminishes when the pile is placed at a distance 8D from the crest or farther. These values can be implemented into p-y curves software, such as LPILE, to determine the straining actions required for design of a laterally loaded pile near sloping ground.