渗流有限元数值计算及其在基坑工程中的应用

发布时间：2018-01-24 02:04

本文关键词： 渗流溢出点降水影响半径能量损失率基坑涌水量　出处：《烟台大学》2017年硕士论文　论文类型：学位论文

【摘要】：基坑涌水量计算是合理设计降水方案的关键,而确定降水影响半径是计算基坑涌水量的关键。在现行规范中,降水影响半径根据经验公式计算,有时计算结果误差较大。在水文地质条件已知的情况下,基坑渗流场可以简化为Laplace方程的定解问题。理论上有限元法可以准确计算基坑渗流场,然而由于溢出边界未知,无法在计算前对其定义,影响了计算精度。因此,求解溢出边界是准确计算基坑渗流场降水半径等参数的前提。论文对降水影响半径等问题进行了研究,主要成果如下:(1)从能量角度出发,提出基于能量损失率极大值确定渗流溢出点的一种方法,将使渗流场水平方向能量损失率达到极大值的溢出点认定为真实溢出点。与虚单元法、等效渗透系数法、单元矩阵调整法等方法中溢出点的确定方法相比,本文方法有物理意义明确、不需迭代、容易收敛的优点。(2)编制了能量损失率极大法计算稳定渗流问题的有限元计算Fortran程序。利用该程序计算了有试验解和解析解的二维、三维模型,所求溢出点与真实位置的相对误差仅为1.29%、1.67%、0.98%;与节点虚流量法、初流量法、改进初流量法、改进截至负压法、改进丢单元法计算的溢出点位置对比,本文算法的相对误差较小,具有很高的精度。(3)通过对基坑涌水量计算模型的分析,降水影响半径与渗流溢出点属于渗流场模型的两个相关变量,即在地下水位确定时,已知两者中的一个就可以求解另一个。将基于能量损失率极大值确定渗流溢出点方法应用于基坑降水影响半径的计算,对两个基坑工程实例进行有限元数值计算,算得其降水影响半径分别为37.23m、10.16m,以规范经验公式计算的降水影响半径为44.72m、32.17m,相对误差分别为16.72%、68.42%。对影响稳定渗流场中降水影响半径的因素进行分析,探讨了误差产生的原因,提出以本文算法作为工程涌水量计算中降水影响半径的计算方法。
[Abstract]:The calculation of foundation pit water discharge is the key to reasonable design of dewatering scheme, and the determination of the influence radius of precipitation is the key to calculate the water inflow of foundation pit. In the current code, the influence radius of dewatering is calculated according to empirical formula. When hydrogeological conditions are known, the seepage field of foundation pit can be simplified to a definite solution of Laplace equation. Theoretically, the finite element method can accurately calculate the seepage field of foundation pit. However, because the overflow boundary is unknown, it can not be defined before calculation, which affects the accuracy of calculation. The solution of overflow boundary is the premise of accurately calculating the parameters such as the radius of seepage field of foundation pit. The main results are as follows: 1) from the point of view of energy, the influence radius of precipitation is studied in this paper. A method of determining seepage overflow point based on the maximum value of energy loss rate is proposed. The overflow point which makes the energy loss rate of horizontal direction reach the maximum value is regarded as the true overflow point. Compared with the methods such as equivalent permeability coefficient method, element matrix adjustment method and so on, the method in this paper has clear physical meaning and does not need iteration. The advantage of easy convergence is to compile the Fortran program for the finite element calculation of the steady seepage problem by the maximum energy loss rate method. The program is used to calculate the two dimensional solutions with both experimental and analytical solutions. In 3D model, the relative error between the overflow point and the real position is only 1.29 and 1.670.98; Compared with node virtual flow method, initial flow method, improved initial flow method, improved end negative pressure method and improved unit loss method, the relative error of this algorithm is small. Through the analysis of the calculation model of foundation pit water inflow, the influence radius of precipitation and seepage overflow point belong to two related variables of seepage field model, that is, when the groundwater level is determined. One of the two is known to solve the other. The method of determining seepage overflow point based on the maximum of energy loss rate is applied to the calculation of the influence radius of foundation pit dewatering. The finite element numerical calculation of two foundation pit engineering examples shows that the influence radius of precipitation is 37.23 m / 10. 16 m, respectively, and the influence radius of precipitation is 44.72 m calculated by the standard empirical formula. 32.17m, the relative error is 16.72and 68.42.The factors influencing the influence radius of precipitation in the steady seepage field are analyzed, and the causes of the errors are discussed. This paper presents a method for calculating the influence radius of precipitation in the calculation of engineering water inflow.
【学位授予单位】：烟台大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU753

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