# Experimental and Theoretical Study of One-Way Cyclic Lateral Responses of Piles in Sloping Ground
###### Abstract  
This study aims to investigate the one-way cyclic lateral responses of piles in sloping ground by means of experimental and theoretical analyses. For this purpose, a series of laboratory model experiments were performed for different cases of cycle number, load amplitude, and slope angle, and lateral static loading tests on both level ground and sloping ground were conducted for comparison. Based on these experimental observations, the effects of cycle number, load amplitude, and slope angle on the pile head deflection and the profiles of bending moment and subgrade reaction are discussed. The pile deflection profile is difficult to measure directly owing to the restriction of experimental conditions, and thus a supplementary finite beam element method (FBEM) is provided to compensate for this deficiency. The comparisons between experimental and theoretical results demonstrate that the FBEM can well predict the pile responses in sloping ground, either under one-way cyclic lateral loading or lateral static loading.  
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by developing degraded \(p\)-\(y\) curves [23] or adopting the strain superposition [24] during different loading cycles. In addition, the slope effect exacerbates the complexity of the problem.  
On the other hand, the slope effect is usually quantified by reducing subgrade reaction and lateral bearing capacity based on experimental investigations, numerical simulations, and theoretical analyses. Owing to the great persuasiveness and directness, the experiments have been commonly conducted to suggest a series of reduction coefficients for \(p\)-\(y\) curves under different slope angles, pile-slope distances, and material properties [25; 26; 27]. In addition, several recent model experiments were performed to directly investigate the slope effect by comparing the lateral bearing capacities of piles in sloping ground with those in level ground [28; 29]. Note that the full development of stress and strain in the experimental region is not easily obtained, and the experiments are commonly complicated, expensive, and time-consuming, and hence numerical simulation can be employed as an alternative method. For instance, the shear load transfer mechanism [30] and deformation mechanism [31] of piles in sloping ground were explained by the stress and strain developments from three-dimensional (3D) finite-difference and finite-element analyses; the slope-induced degraded \(p\)-\(y\) curves with analytical formulas were constructed for a wide range of cases based on large amounts of data from 3D finite-element analyses [32; 33]. Compared with the experimental and numerical investigations, the theoretical analyses may appear to be simpler and more convenient in the preliminary design of piles. A limit equilibrium-based theoretical model for the lateral bearing capacity of rigid piles in sloping ground indicated that the reduction of pile bearing capacity depends on the slope angle and material properties [34]. Subsequently, the design charts relating the lateral bearing capacity of piles to the slope angle were developed based on the analytical solutions for the undrained lateral bearing capacity of rigid piles [35]. The theoretical study of the slope effect on the subgrade reaction and lateral bearing capacity has continued [36; 37]; however, these studies are still within the scope of static loading.  
This study aims to investigate the one-way cyclic lateral responses of piles in sloping ground by means of experimental and theoretical analyses. The model experiments include static and dynamic loading cases, where the static cases in the level and sloping ground provide basic experimental parameters and serve as a benchmark, and the dynamic cases focus on the effects of cycle number, load amplitude, and slope angle on the pile responses. However, the pile deflection profiles are difficult to directly measure due to the restrictions of experimental conditions, and thus an alternative theoretical method, the finite beam element method (FBEM), is employed as a supplementary analysis.