地面超载下摩擦单桩负摩阻力的连续介质力学解

Continuum mechanical solution for negative frictional resistance of single floating pile under ground overload

针对地面超载引起的摩擦单桩负摩阻力,提出了一种基于桩土相互作用和连续介质力学的竖向位移模型来模拟桩土系统位移,模型中包含了桩土轴线位移函数和沿径向的衰减函数;采用变分法得到了桩土系统的总势能,从而得到了位移模型中桩土位移和衰减函数的耦合控制方程;利用迭代法求解了这两个耦合函数,得到了桩身轴力、中性面、负摩阻力、下拉力和土弹簧等效刚度等关键参数的数学表达式;通过和原位试验及已有理论结果的对比,验证了所提方法的正确性。结果表明:桩土模量比对桩的负摩阻力和下拉力有显著影响,中性面位置与长细比密切相关,而与桩土模量比关系不大;随着桩土模量比增大和桩长细比减小,桩身同一位置处轴力增长明显,但增长速率变缓;地面超载作用下桩周土体位移最大沉降出现在地表处,且地表以下0.3倍桩长范围内为位移强烈影响区;桩长细比和桩土模量比的增加均会使桩周土体位移场影响范围增大。

A vertical displacement model based on pile-soil interaction and continuum mechanics was proposed to simulate the displacement of the pile-soil system in response to the negative friction force of a single pile caused by ground overload.The model included the displacement function of the pile-soil axis and the attenuation function along the radial direction.The total potential energy of the pile-soil system was obtained by using the variational calculus,and the coupled control equations for the pile-soil displacement and attenuation function in the displacement model were obtained.The iterative method was used to solve these two coupling functions,and mathematical expressions for key parameters such as pile axial force,neutral plane,negative frictional resistance,down-drag force,and equivalent stiffness of soil spring were obtained.The correctness of the proposed method were verified through comparison with in-situ experiments and existing theoretical results.The results show that the ratio of pile-soil modulus has a significant impact on the negative friction resistance and down-drag force of piles,and the position of the neutral plane is closely related to the slenderness ratio,while it is not closely related to the ratio of pile-soil modulus.As the pile-soil modulus ratio increases and the pile slenderness ratio decreases,the axial force at the same position of the pile increases significantly,but the growth rate slows down.The maximum settlement of soil displacement around piles under ground overload occurs at the surface,and the range of 0.3 times the pile length below the surface is a strongly affected area of displacement.The increase in pile slenderness ratio and pile-soil modulus ratio will both increase the range of influence on the displacement field of the soil around the pile.