Abstract In preloading ground improvement projects, vertical drains are frequently installed to accelerate the consolidation process of a soil stratum which is generally unsaturated and layered in natural. To address such issue, this study attempts to constitute a reliable two-dimensional (2D) plane strain consolidation system of layered unsaturated soil. A novel semi-analytical solution for this system is developed using the methods of Fourier expansion, Laplace transform and their inversions. In order to obtain the final solution, the proposed system is firstly converted into a set of ordinary differential systems using the methods of Fourier expansion and Laplace transform. By defining a set of new variable vectors, these ordinary differential systems are further changed into diagonal ones and solved. Then, the semi-analytical solutions for the pore-air and pore-water pressures and the soil settlement are formulated, and numerical inversion of Laplace transform is applied to obtain the final results in temporal domain. Through comparing against the existing solution and the finite difference solution, the validity and the accuracy of the proposed solutions are verified. Moreover, a worked example incorporating a step load is presented to illustrate the 2D plane strain consolidation behavior of layered unsaturated soil and the influence from the coefficient of horizontal permeability is investigated.

中文翻译：

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层状非饱和土二维平面应变固结的半解析解

摘要 在预压式地基改造工程中，为了加快自然层状土层的固结过程，经常会设置竖向排水管。为了解决这个问题，本研究试图构建一个可靠的二维（2D）层状非饱和土平面应变固结系统。使用傅立叶展开、拉普拉斯变换及其反演的方法为该系统开发了一种新的半解析解。为了得到最终解，首先使用傅里叶展开和拉普拉斯变换的方法将所提出的系统转换为一组普通的微分系统。通过定义一组新的变量向量，这些普通的微分系统进一步变为对角系统并求解。然后，制定了孔隙空气压力和孔隙水压力以及土壤沉降的半解析解，并应用拉普拉斯变换的数值反演得到时域的最终结果。通过与现有解和有限差分解的对比，验证了所提解的有效性和准确性。此外，还提出了一个包含阶跃荷载的工作实例来说明层状非饱和土的二维平面应变固结行为，并研究了水平渗透系数的影响。通过与现有解和有限差分解的对比，验证了所提解的有效性和准确性。此外，还提出了一个包含阶跃荷载的工作实例来说明层状非饱和土的二维平面应变固结行为，并研究了水平渗透系数的影响。通过与现有解和有限差分解的对比，验证了所提解的有效性和准确性。此外，还提出了一个包含阶跃荷载的工作实例来说明层状非饱和土的二维平面应变固结行为，并研究了水平渗透系数的影响。