壁板桩群桩竖直荷载沉降关系的变分法分析

Variational analysis of load-settlement relationship of vertically loaded barrette groups

将壁板桩桩身竖向位移用有限级数函数表示,地基土体的荷载位移关系用Mindlin点对点的位移解表示,同时考虑壁板桩桩身剪应力沿其周边以及桩底法向应力沿桩底面分布的不均匀性,采用双重高斯数值积分法将基于变分原理建立的壁板桩群桩体系的总势能展开为简单的矩阵形式方程,并根据最小势能原理得到壁板桩群桩竖直荷载沉降关系的显式解答。与近似三维分析方法计算结果的对比验证了所提出解答的合理性,也展示了其计算速度更快,计算存储量要求更低的优点。

Based on the variational principle, the total potential energy of a general group of vertically loaded barrettes is established. By using the double Gauss numerical integration method, it is expanded to a simple equation of matrix form, in which a finite series is used to denote the vertical displacement of barrette shaft, Mindlin＇s point-to-point displacement solution is applied to describe the force-displacement relationship of ground soils, and allowance is made for the non-uniform distributions of both the side shear stresses along the perimeter of the barrette shaft and the normal stresses at the barrette base. In light of the principle of minimum potential energy, an explicit solution is obtained for the load-settlement relationship of barrette groups. The proposed solution is verified from the comparisons of the calculated results made with an approximate three-dimensional method. Its merits in higher computational velocity and greatly reduced computer storage memory are also illustrated.