等参元在饱和-非饱和路基水分场数值计算中的应用

APPLICATION OF ISOPARAMETRIC ELEMENT IN ANALYSIS OF SATURATED-UNSATURATED TRANSIENT SEEPAGE OF SUBGRADE

采用四边形等参元研究建立饱和-非饱和路基水分场的有限元算法。以往的研究只给出了应用三角形单元时的路基水分场有限元计算方法,而三角形单元精度较低。从能量守恒的原理出发,采用Galerkin加权余量法推导得到四边形等参元来分析渗流问题的有限元格式。进一步基于Jacobi矩阵转换及Gauss数值积分,确定了该方法中刚度矩阵的元素计算式,并给出了容量矩阵及其元素表达式。该方法考虑了土体各向异性以及渗透系数与坐标轴不重合等情况,是非饱和土瞬态渗流分析的一般形式。进而通过算例说明四边形单元在分析具有对称性的问题时精度优于三角形单元。最后通过对路基水分场的计算得到了在连续降雨条件下路基饱和区扩展规律,验证了该方法的适用性。

A FEM for unsaturated transient seepage was established by using quadrilateral isoparametric element. It created a function by using element’s node hydraulic head and shape function instead of the real head in the Richard seepage control equation. With the help of Galerkin weighted residual method,a FEM equation was given for analyzing 2-dimensional transient seepage problem. Further more,based on the Jacobi matrix and Gauss numerical integral,it determined the elements of stiffness and capacity matrix. This method considered not only the soil anisotropy but also the inconsistercy between the permeability coefficient and the coordinate axis which was a general form of transient seepage analysis for unsaturated soils. It is a common form for transient seepage. In the end,two examples illustrated the node accuracy of quadrilateral element and the correctness of this FEM equation.Finally,the law of subgrade saturation area under the condition of rainfall was obtained by calculating the subgrade moisture field and the applicability of this method is verified.