考虑固结群桩竖向应力相互作用的积分方程分析方法

采用Biot 固结方程,分别以等长和不等长两桩为分析对象,将受竖向荷载作用的桩土体系分解成半空间饱和扩展土和虚拟桩,基于竖向应变协调关系建立桩土相互作用的第二类Fredholm 积分方程,求解出不同固结状态时的桩身轴力分布。在等长两桩中,由于邻近桩的存在,桩身附加轴力主要分布于桩身20%～80%深度处,其影响程度随着桩间距的增加而减弱。进一步将等长两桩分析扩展至群桩研究中,分析表明：群桩效应引起了桩顶荷载的不均匀分布；土体固结对桩身内力分布也有一定的影响,固结后角桩承担的荷载有所下降。桩长不等时,长短桩之间的相互作用效应并不一致,表现为两桩桩顶承受相同荷载时长桩沿桩身附加轴力增加较短桩明显。最后,将不等长桩相互作用系数应用于群桩的优化分析中,在保证总桩长和桩基沉降基本相当的情况下,通过调整不同位置的桩长使得各桩受力趋于合理。

Integral equation method for interaction effect of stress of vertically loaded pile groups considering consolidation

The interaction effect of stress is obtained for two vertically loaded piles which are of equal or different pile lengths embedded in the homogeneous poroelastic saturated soils governed by the Biot’s theory. The pile-soil system is decomposed into an extended soil and two fictitious piles, and the compatibility condition between the axial strain of the fictitious piles and the extended soil is established. This approach yields the governing Fredholm integral equations of the second kind, and the basic unknowns of the axial force and settlement along the pile shaft are calculated. For the piles with the same length, the additional force along the pile shaft can be observed at 20%~80% depth of pile length due to the adjacent pile and decreases with the pile spacing. Extending two-pile model into pile group analysis, pile group effect will lead to the differences in load at the pile heads. The consolidation effect can alter the distribution of axial stress along the pile shafts. The loadings acting on the corner piles decrease. For the piles with different dimensions, the interactions among long and short piles are different, and the additional axial force along the long pile is greater than that along the short one. The combination of long and short piles is applied to the optimization of pile groups. The results show that adjusting the pile length within a pile group can reduce the differential pile-head loadings without increasing the total pile length and pile-head settlement.