The combination of permeable and impermeable columns is commonly employed to enhance the stability of natural ground and expedite the consolidation process while effectively reducing foundation settlement. This study presents a comprehensive investigation of the consolidation characteristics of unsaturated composite foundations (USCF) using various methods. Firstly, a mathematical model is developed under the assumption of equal strain, considering depth-dependent initial stress. To obtain more generalized analytical solutions for excess pore pressures and foundation settlement, separation of variables, Laplace transformation, and inversion Laplace transformation are employed. Secondly, the accuracy of the proposed analytical solutions is validated by comparing them with two specific cases reported in the existing literature, achieved by reducing the compression modulus of columns. Lastly, a series of parameters are investigated to examine the consolidation characteristics of USCF considering depth-dependent initial stress. The results demonstrate that the final settlement of the foundation will be overestimated while the variation of vertical stress along the depth is neglected. Furthermore, adjusting the values of area replacement ratios proves to be more effective and straightforward than modifying the compression modulus of columns in the reinforcement treatment of USCF.

中文翻译：

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考虑深度相关初始应力的透水和不透水柱改进的非饱和复合地基固结解析解

通常采用透水柱和不透水柱的组合来增强自然地基的稳定性，加快固结过程，同时有效减少地基沉降。本研究采用各种方法对非饱和复合地基 (USCF) 的固结特性进行了全面研究。首先，在等应变假设下建立了一个数学模型，考虑了与深度相关的初始应力。为了获得超孔隙水压力和地基沉降的更广义的解析解，采用了变量分离、拉普拉斯变换和反演拉普拉斯变换。其次，通过与现有文献中报告的两个具体案例进行比较，验证了所提出的分析解决方案的准确性，这是通过降低柱的压缩模量来实现的。最后，研究了一系列参数，以检验考虑深度相关初始应力的 USCF 固结特性。结果表明，当忽略竖向应力沿深度的变化时，会高估地基的最终沉降。此外，在 USCF 加固处理中，调整面积替换率的值比修改柱的压缩模量更有效、更直接。