基于修正侧阻抗力矩的刚性单桩水平承载力解析解

Analytical solution of lateral bearing capacity of rigid single piles based on modified shaft resisting moment

为了更准确地考虑竖向摩擦效应对刚性单桩水平承载力的影响,假定被动侧桩周径向土压力呈余弦函数分布,建立被动侧桩周最大径向土压力与总土抗力的关系。对径向土压力和竖向摩阻力模拟结果进行反演得到修正的桩–土界面竖向摩擦因数,推导侧阻抗力矩解析表达式。然后,假定极限土抗力、水平地基反力模量随深度线性增加,水平地基反力模量随地面处水平位移非线性减小,导得了桩侧土均未屈服、旋转点以上部分土体屈服、旋转点上下均有土体屈服三阶段下的水平力和力矩平衡方程。鉴于数值迭代程序的复杂性,采用位移加载方式,计算时将地面处水平位移y0视为已知量,旋转点深度a视为变量,通过变形得到水平承载力解析解。通过与有限元分析、模型试验和现场试验的结果进行比较,验证了该方法的正确性。最后,利用该方法分析桩径、内摩擦角以及水平力作用点高度对刚性单桩水平承载力、最大弯矩和旋转点深度的影响。结果表明:采用余弦函数可以很好地表征被动侧桩周径向土压力分布,根据修正的桩-土界面竖向摩擦因数计算的侧阻抗力矩更符合实际;忽略侧阻抗力矩作用会明显低估刚性单桩的水平承载力,低估程度随着桩径、内摩擦角以及水平力作用点高度的增大而增大。

For considering the effect of the vertical friction on the lateral bearing capacity of rigid single piles more accurately,the relationship between the maximum compressive soil pressure around the passive side and the total soil resistance was established by presuming that the compressive soil pressure around passive side presents a cosine function distribution. The modified vertical friction coefficient of the pile-soil interface was obtained by inverse derivation of the simulations of compressive soil pressure and vertical friction resistance. On this basis,the analytical expression of the shaft resisting moment was derived. Assuming that both the ultimate soil resistance and the modulus of horizontal subgrade reaction increase linearly with depth and the modulus of the horizontal subgrade reaction decreases nonlinearly with the displacement at ground surface,the equilibrium equations of the horizontal force and the moment were derived under three stages:soil resistance without yielding,soil resistance with yielding only in a region above the rotation point,and soil resistance with yielding in regions both above and below the rotation point. For avoiding the complexity of the numerical iteration program,the analytical solution of the lateral bearing capacity was obtained by regarding the horizontal displacement(y0) at the ground surface as a known quantity and the depth of the rotation point(a) as a variable with consideration of displacement loading method. Compared with the results of finite element analysis,model test and field test,the correctness of the proposed method was verified. Based on the verified analytical solution,a parametric analysis was carried out to explore the influential factors(e.g. pile diameter,internal friction angle and height of lateral force) of the lateral bearing capacity,maximum bending moment and rotation point depth of rigid single pile. The results show that the cosine function can satisfactorily characterize the distribution of compressive soil pressure around the passive side,and the calculated shaft resisting moment from the modified vertical friction coefficient of the pile-soil interface is more realistic.Ignoring the effect of the shaft resisting moment will significantly underestimate the lateral bearing capacity of rigid single pile,and the degree of underestimation increases with the increase of pile diameter,internal friction angle and the height of lateral force.