非均匀地基与均匀地基解答之间的相似关系

Analogous relationship between solutions of nonhomogeneous and homogeneous foundations

考虑材料特性沿厚度按幂律梯度变化的非均匀地基,研究了在竖向和水平线荷载作用下,非均匀弹性地基与均匀弹性地基解答之间的转换关系。基于应变分量之间的变形协调条件,获得了非均匀弹性半空间在线荷载作用下的应力分量和应变分量的解析表达式,通过比较非均匀地基和均匀地基的解答,发现了它们之间的线性相关性,可将非均匀弹性地基在均布线荷载作用下的解答用相同条件下的均匀地基解答线性表示,得到了解答之间的相似转换系数的表达式,该系数集中反映了地基物理力学特性的非均匀程度。因此,借助于均匀地基的经典解答,可将非均匀地基问题的求解转化为对相似转换系数的计算,从而使得问题得以简化。为了方便应用,采用曲线图的形式给出了不同非均匀指数情形下的相似转换系数。

The problem of half-space nonhomogeneous foundation subjected to vertical and horizontal linear loads is studied. The linear transformative relation between the solutions of the nonhomogeneous foundation and the corresponding homogeneous foundation is analyzed. Based on deformation compatibility condition, the analytical expressions of stress and strain component are obtained. Through comparing solutions of nonhomogeneous foundation and the corresponding homogenous foundation, linearly correlation relation between the both is found. The solution of the nonhomogeneous foundation can be linearly expressed by that of homogenous foundation with the same conditions. The transformation factors between the solutions of two kinds of soil are derived in analytic forms, witch reflect the nonhomogeneous properties of the foundation. Therefore, solutions of the non-homogenous foundation can be reduced to that of a homogenous one and the calculation of the transition parameters, which simplifies the solution procedure. For the convenience of engineering application, analogous transformation coefficient is given by graphic form with different nonhomogeneous indices.