This paper presents a new approximate solution to study the settlement of rigid footings resting on a soft soil improved with groups of encased stone columns. The solution development is fully analytical, but finite element analyses are used to verify the validity of some assumptions, such as a simplified geometric model, load distribution with depth and boundary conditions. Groups of encased stone columns are converted to equivalent single encased columns with the same cross-sectional area and the same ratio of encasement stiffness to column diameter. In this way, the problem becomes axially symmetric. Soft soil is assumed as linear elastic but plastic strains are considered in the column using the Mohr-Coulomb yield criterion and a non-associated flow rule with a constant dilatancy angle. Soil profile is divided into independent horizontal slices and equilibrium of stresses and compatibility of deformations are imposed in the vertical and horizontal directions. The solution is presented in a closed form and may be easily implemented in a spreadsheet. Comparisons of the proposed solution with numerical analyses show a good agreement for the whole range of common values, which confirms the validity of the solution and its hypotheses.

中文翻译：

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刚性基础下封闭石柱沉降的解析解

本文提出了一种新的近似解决方案，用于研究软土上刚性基础的沉降，并通过成组的包裹石柱进行改良。解决方案的开发是完全分析的，但有限元分析用于验证一些假设的有效性，例如简化的几何模型、随深度和边界条件的载荷分布。围护石柱组转换为具有相同横截面积和相同围护刚度与柱直径之比的等效单围护柱。这样，问题就变成轴对称的了。软土被假定为线弹性，但使用莫尔-库仑屈服准则和具有恒定剪胀角的非关联流动规则来考虑柱中的塑性应变。土体剖面被分成独立的水平切片，并在垂直和水平方向上施加应力平衡和变形相容。该解决方案以封闭形式呈现，并且可以在电子表格中轻松实现。所提出的解决方案与数值分析的比较表明，整个共同值范围具有良好的一致性，这证实了解决方案及其假设的有效性。