中文摘要：

在隧洞涌水量预测分析中，由于地质条件等不确定性带来岩体介质渗透性的空间变异性，所以渗流场不可避免地具有随机性。于是将岩体介质渗透张量视为三维各向异性空间随机场，并利用三维可分离向量随机场的局部平均法对随机场进行离散，从而得到一系列随机变量来近似描述随机场。然后基于一阶摄动法随机变分原理，推导出了三维非稳定渗流场随机有限元列式，通过对随机有限元列式的求解，得到非稳定渗流的随机渗流场，结合一阶Taylor级数展开随机有限元法，推导出渗流场中流量的均值和方差的计算公式，并编制相应的程序。最后，以一隧洞开挖为算例，进行涌水量的随机预测，并验证所提方法和程序的正确性和可行性。

英文摘要：

In prediction of water inflow in tunnel, the water inflow is generally random because of the spatial variability of permeability in rock mass, so the random analysis of prediction of water inflow is necessary. Thus, the spatial variability of permeability in rock mass is described by regarding permeability tensor as three- dimensional anisotropic random field, and vector separable local average method is adopted for discretion of random field. Then the stochastic finite element governing equations of three-dimensional unsteady seepage are deduced based on random variational principle in first order perturbation method. Furthermore, the three- dimensional unsteady random seepage field can be derived and the formulas of mean and standard deviations of flow rate are deduced combining with the first order Taylor series stochastic finite element method. Finally, some programs are developed for proposed method; and an example for stochastic prediction of water inflow is given. The results indicate that the proposed method is feasible.