等参元在饱和-非饱和路基水分场数值计算中的应用
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摘要
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.
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.
引文
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[12]肖超,金福喜,刘海鸿,等.开挖与降雨作用下边坡失稳机理及模拟分析[J].工程地质学报,2012,20(1):37-43.
[13] FREDLUND D G,RAHARDJO H.非饱和土力学[M].陈仲颐,译.北京:中国建筑工业出版社,1997:530.
[2]李东庆,周家作,张坤,等.季节性冻土的水-热-力建模与数值分析[J].中国公路学报,2012,25(1):1-7.
[3]毛雪松,李宁,王秉纲,等.多年冻土路基水-热-力耦合理论模型及数值模拟[J].长安大学学报(自然科学版),2006,26(4):16-19.
[4]付宏渊,曾铃,蒋中明,等.降雨条件下公路边坡暂态饱和区发展规律[J].中国公路学报,2012,25(3):59-64.
[5]王铁行.非饱和黄土路基水分场的数值分析[J].岩土工程学报,2008,30(1):41-45.
[6]李毅,伍嘉,李坤.基于FLAC3D的饱和-非饱和渗流分析[J].岩土力学,2012,33(2):617-622.
[7]陈盼,韦昌富,王吉利,等.近饱和条件下非饱和多孔介质渗流过程的数值分析[J].岩土力学,2012,33(1):295-300.
[8]韦立德,杨春和.考虑饱和-非饱和渗流、温度和应力耦合的三维有限元程序研制[J].岩土力学,2005,26(6):1000-1004.
[9] LAM L,FREDLUND D G. Transient Seepage Model for Saturated-Unsaturated Soil Systems:A Geotechnical Engineering Approach[J]. Canadian Geotechnical Journal,1987,24(4):565-580.
[10]李萍,李同录,王阿丹,等.黄土中水分迁移规律现场试验研究[J].岩土力学,2013,34(5):1331-1339.
[11] OLONADE K A,AGBEDE O A. A Study of Seepage Through Oba Dam Using Finite Element Method[J]. Civil and Environmental Research,2013,3(3):53-60.
[12]肖超,金福喜,刘海鸿,等.开挖与降雨作用下边坡失稳机理及模拟分析[J].工程地质学报,2012,20(1):37-43.
[13] FREDLUND D G,RAHARDJO H.非饱和土力学[M].陈仲颐,译.北京:中国建筑工业出版社,1997:530.