半正弦循环荷载作用下的一维非线性固结
1D non-linear consolidation under haversine repeated loading

针对高速公路、机场、铁路等设施上的交通荷载易引发路基土的固结沉降问题，将交通荷载视为半正弦循环荷载，分析该类荷载作用下土体的固结过程以及荷载间歇期、荷载频率、初始超静孔隙水压力等参量对固结过程的影响。通过修正Davis假定，使一维非线性固结控制方程适用于模拟具有非零初始超静孔隙水压力条件的饱和土固结过程，采用分离变量法推导半正弦循环荷载作用下一维非线性固结方程通解，并给出初始超静孔隙水压力为常数、正三角形分布和倒三角形分布3种典型初始条件下的解析解。模拟了不同的荷载间歇期、荷载频率和初始超静孔隙水压力条件下均质饱和黏土的固结过程。结果表明：固结过程中超静孔隙水压力峰值随时间增大而减小，有效应力和平均固结度峰值随时间增大而增大；初始条件的差异对固结过程的早期具有明显的影响，当初始超静孔隙水压力为0时，有效应力和平均固结度峰值均最大，其他情况下从大到小依次为倒三角形分布、正三角形分布、矩形分布；间歇期或荷载频率的差异对整个固结过程均存在影响，随着间歇期的增大，达到稳定时的平均固结峰值减小，固结过程延缓，随着荷载频率的减小，平均固结度峰值增大，固结过程加快。
For the problems of consolidation settlement of subgrade soil caused by traffic loads, which were considered as haversine repeated loading, on expressways, airports, railways and other traffic facilities, the paper analyzed soil consolidation process and the influence of loading rest periods, loading frequency and soil initial excess pore water pressure. By modifying the Davis’s hypotheses, the 1D nonlinear consolidation governing equation could be applied to saturated soil consolidation process under the condition of non-zero initial excess pore water pressure. The general solutions of the governing equation were derived via the separation variable method under haversine repeated loading. The analytical solutions with three typical initial conditions, including initial excess pore water pressure as constant, regular triangular distribution and inverted triangular distribution were reported. Consolidation process of homogeneous saturated soil was simulated for different conditions, such as rest periods of loading, frequencies of loading and initial excess water pressure. The results show that the peak value of excess pore-water pressure decreases with time, but effective stress and average consolidation increase with time. The effects of the initial conditions on the consolidation process happens mainly during the early stages of consolidation. Under zero initial excess pore-water pressure condition, peaks of effective stress and average consolidation degree are the highest. Other cases from large to small in order are inverse triangular distribution condition, triangular distribution condition, and rectangle distribution condition. The differences of rest periods or loading frequencies have an impact on all stages of the consolidation process. With the increase of the rest period, the peak of the average consolidation degree decreases when reaching the static state and the consolidation process is delayed. With the decrease of loading frequency, the average consolidation peak increases, and the consolidation process is accelerated