非稳定渗流问题的变分不等式方法及工程应用

A variational inequality approach for non-steady seepage problems and its application in engineering practices

Signorini型变法不等式方法是求解有自由面渗流问题的一种新方法,该方法理论基础严密,并克服了渗流溢出点的奇异性。通过给出一种含有Signorini型互补条件的抛物变分不等式(PVI)方法,将Signorini型变法不等式方法从稳定渗流分析拓展到非稳定渗流分析,并给出了其有限元数值计算格式和数值模拟流程。在此基础上,针对已有的砂槽模型试验数据,通过对比研究基于PVI方法的非稳定渗流分析成果和饱和-非饱和渗流分析结果,论证了该方法的有效性,并讨论了该方法的适用条件。最后,应用上述方法对含有复杂渗控措施的水布垭工程开展了非稳定渗流分析,通过与大坝坝体、趾板、灌浆廊道围岩、地下厂房围岩等部位实测渗压数据和坝后量水堰实测流量数据的对比分析,表明计算结果很好地反映了水布垭工程厂、坝区岩土体在蓄水及运行过程中渗流场的变化规律,系统揭示了混凝土面板、防渗帷幕、排水孔幕及排水廊道等工程渗控措施的渗流控制效应。研究成果对于含有复杂渗控措施、并具有稳定补给源的岩土工程非稳定渗流分析具有指导意义。

The variational inequality（VI） method of Signorini＇s type is a novel method for solving unconfined seepage problems.This method possesses a rigorous mathematical background,and theoretically overcomes the singularity of seepage-points.By presenting a parabolic variational inequality（PVI） formulation of Signorini＇s condition,the VI method of Signorini＇s type is extended from steady-state seepage analysis to non-steady seepage analysis.The finite element discretization of the PVI formulation is presented,together with a flowchart for numerical modeling.By using the data of an existing laboratory seepage test,the effectiveness and applicability of the proposed method were illustrated by comparing the non-steady seepage analysis results of the PVI method with the predictions of a saturated-unsaturated model.This method was further applied to capture the non-steady seepage flow behaviors of Shuibuya concrete faced rockfill dam（CFRD） and the surrounding rocks of the underground powerhouse,in which a complex seepage control system consisting of concrete face slabs,grouting curtain,drainage holes and drainage tunnels was deployed.Comparisons of the model results with the in-situ monitoring data（including pore water pressure,piezometric head and seepage flow rate instrumented in various locations） show that the calculation results well illustrate the non-steady seepage flow process and the seepage control effects during impounding and operation of the reservoir.