考虑真空加载过程的钉形搅拌复合地基固结解析解

考虑真空负压力随时间变化，推导出真空预压下钉形水泥土搅拌桩复合地基的固结控制方程和求解条件。将固结方程和求解条件进行函数变换，基于双层地基一维固结理论求解出桩间土和复合地基加固区中的平均超静孔隙水压力，然后获得了钉形搅拌桩复合地基的整体平均固结度。通过与数值模拟结果的比较，验证了固结解析解的合理性。利用提出的固结解析解，分析了桩置换率、扩大头尺寸、桩间土刚度及真空加载参数等因素对复合地基固结的影响。研究结果表明：真空下钉形搅拌桩复合地基的固结速率随桩置换率、扩大头高度和其下桩间土压缩模量的增加而增大，固结前期固结速率随扩大头半径的增加而增大，固结后期则影响很小。真空加载过程对复合地基的固结过程几乎没有影响。

Analytical solution for consolidation of composite ground with T-shaped deep cement mixing columns considering vacuum loading process

Considering change in negative vacuum pressure with time, the governing equations and the corresponding solution conditions for consolidation of the composite ground with T-shaped deep cement mixing (TDM) columns under vacuum preloading were derived. Based on one dimensional consolidation theory of a double-layer soil ground, the average excess pore water pressures within the improved zones and the surrounding soil were obtained by the functional transformation of the consolidation equations and solution conditions. The overall average consolidation degree of the composite ground with TDM columns was presented. Then, the rationality of the proposed solutions was verified by comparison with the numerical simulation results. Finally, the influence of the replacement ratio of the column, the column cap size, the stiffness of the surrounding soil and the vacuum loading parameter on the consolidation rate of the composite ground was investigated using the proposed solution.The results indicate that the consolidation rate of the composite ground increases with increasing the replacement ratio of the column , the height of its cap and the constrained modulus of the soil under the column cap. The consolidation is accelerated with increasing the radius of column cap in the early stage of consolidation, but it has insignificant influence in the later stage of consolidation process. The vacuum loading process has little effect on the consolidation of the composite ground.