Analytical solution of seismic analysis of piled-reinforced slopes

Stabilizing piles is a typical passive reinforcement measure that is widely used in slope and foundation excavation. In slope stability analysis, the force of a stabilizing pile is often taken as the fixed value. Obviously, this approach simplifies the impact of stabilized piles on the slope. Based on the passive effect of stabilizing piles, this study elaborates on the sliding mechanism of slopes under seismic conditions. To establish the relationship between the slope displacement and the force of the pile, a new method of equivalent displacement is proposed. The Newmark method and limit analysis are used to derive the formulas of slope displacement and safety factor. Through typical cases, different stabilizing pile models and the cumulative effect of multiple seismic loads are analyzed. In addition, the influence of various parameters on slope stability is discussed. The results show that (1) the stabilizing pile has an obvious passivity. The antisliding force is gradually released with the sliding and squeezing of the slope, showing the trend of increasing first and then stabilizing. (2) Under the condition of multiple seismic loads, the slope has a cumulative effect. If the passive effect of the pile is considered, the calculation result is more conservative. (3) The location of the pile and the length of the anchoring section have a more significant influence on the slope stability. Risk analysis based on displacement can be used in the design of reinforcement schemes.