This paper presents analytical solutions for nonlinear radial consolidation of soft soil with vertical drains under various cyclic loadings. By considering the nonlinear variations of compressibility and permeability expressed by the logarithm relations ( and ), the governing equation for nonlinear radial consolidation of the soil under equal strain and time-dependent loading is established. The analytical solutions are derived for nonlinear radial consolidation under haversine cyclic loading, trapezoidal cyclic loading, rectangular cyclic loading, and triangular cyclic loading. The presented solution is verified through the degeneration into the existing solutions for nonlinear radial consolidation under constant and ramp loadings, which shows the solution proposed in this paper is more general for nonlinear radial consolidation under time-dependent loading. The nonlinear radial consolidation behavior of the soil with vertical drains subjected to various cyclic loadings is investigated using the solutions developed. The proposed solutions can be effectively utilized in the analysis of nonlinear radial consolidation under various cyclic loadings.

中文翻译：

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循环荷载下垂直排水软土的非线性径向固结分析

本文提出了在不同循环荷载下垂直排水的软土非线性径向固结的解析解。通过考虑由对数关系（和）表示的可压缩性和渗透性的非线性变化，建立了等应变和时变荷载作用下土体的非线性径向固结控制方程。导出了在正弦周期荷载，梯形周期荷载，矩形周期荷载和三角形周期荷载下的非线性径向固结的解析解。通过退化为在恒定载荷和斜坡载荷下的非线性径向固结的现有解决方案，验证了所提出的解决方案，这表明本文提出的解决方案对于在时间依赖性载荷下的非线性径向固结更为通用。使用开发的解决方案，研究了承受各种循环载荷的垂直排水土的非线性径向固结行为。