Power Series Calculation Method of Pile(Wall) Deflection Deformation with Trapezoidal Distributed Subgrade Reaction Coefficients

For ground with trapezoidal distributed subgrade reaction coefficients caused by natural sedimentation, a calculation model for pile(wall) deflection deformation under lateral loads was established. Based on the theory of power series solution of differential equations, a power series solution for pile(wall) deflection deformation that considers the trapezoidal distribution of lateral loads and subgrade reaction coefficients was proposed. The power series solution can be degraded into the traditional K-method and m-method formulas for calculating pile(wall) deflection deformation. The results show that when the number of calculation terms of the power series solution is taken as 20, the maximum relative truncation error of the horizontal displacement is 0.19%, and the calculation accuracy can meet the requirements of theoretical analysis and engineering calculation. For long pile(wall) with a converted depth $\overline{h}$ greater than 5 m, it is suggested to calculate at 5 m. The analysis of engineering examples demonstrates the validity. The proposed power series calculation method solves the problem of pile(wall) deflection deformation with trapezoidal distributed subgrade reaction coefficients under lateral loads, which the traditional K-method and m-method cannot solve. Compared with the finite element method, the computational efficiency of the deterministic method is improved. Therefore, the proposed method can support the establishment of calculation methods for complex problems such as pile(wall) deflection deformation in multi-layered ground and anti-slide piles under local lateral loads.