Insufficient bearing capacity of foundations is hazardous for construction engineering, and improper construction scheme can also lead to unexpected problems. Vertical drains are always installed in the soil foundations to accelerate the consolidation process and thus improve the bearing capacity. According to the consolidation theory proposed by Fredlund, the consolidation of unsaturated vertical drain foundation is investigated with analytical solutions, in which smear effect, drain resistance, and depth-dependent initial excess pore pressures (i.e., excess pore-air and pore-water pressures) are considered. In the derivative process, the decoupling method and Fourier series expansion method are applied. The reliability of the current solutions is verified by comparing the degenerate ones with existing solutions. Sensitivity analysis is conducted to assess the consolidation characteristics of the proposed model against modeling sizes, smear coefficients, drain resistance factors, and distribution coefficients. The analytical model has the advantages of simplicity and easy to implement in practical engineering.

中文翻译：

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深度依赖初始条件下非饱和垂直排水地基固结的解析解

地基承载力不足对建筑工程来说是危险的，施工方案不当也会导致意想不到的问题。垂直排水管始终安装在土基中，以加速固结过程，从而提高承载能力。根据 Fredlund 提出的固结理论，采用解析解研究非饱和垂直排水地基的固结，其中涂抹效应、排水阻力和与深度相关的初始超孔隙水压力（即超孔隙空气压力和孔隙水压力） ） 被考虑。在导数过程中，应用了解耦法和傅里叶级数展开法。通过将退化的解决方案与现有解决方案进行比较来验证当前解决方案的可靠性。进行敏感性分析以根据建模尺寸、涂抹系数、排水阻力系数和分布系数评估所提出模型的固结特性。该解析模型具有简单、易于在实际工程中实施的优点。