Abstract

One of the main causes of the appearance of dangerous geophysical slope phenomena is water saturation of slopes and the negative hydrodynamic impact of a stream of underground waters on them. In this work, an exact semi-inverse hydromechanical solution for a family of geophysical problems of a draining slope is obtained based on the theory of functions of a complex variable. Using the method of consecutive conformal mappings, an analytical interrelation between areas of complex potential and N.E. Zhukovskii’s complex is established. The interrelation allows one to determine all the necessary parameters of the filtration area. An example of calculation with the determination of aquifuge lines, seepage area, depression surface, and lines of flow and equipotential lines with construction of an orthogonal and quadratic hydrodynamic grid of the filtration flow seeping the draining slope is presented. A short estimate of the filtration effect on the suffusion and landslide stability of the soil body of the draining slope is given.

中文翻译：

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排水坡地球物理问题族的精确半反解

摘要

出现危险的地球物理斜坡现象的主要原因之一是斜坡的水饱和度以及地下水流对其产生的负面流体动力影响。在这项工作中，基于复变函数的理论，获得了一系列排水边坡地球物理问题的精确半逆流体力学解决方案。使用连续保形映射的方法，建立了复杂势能区域和NE Zhukovskii复杂物之间的分析相互关系。该相互关系允许确定过滤区域的所有必要参数。确定水层线，渗流面积，凹陷表面，给出了流线和等势线，该流线和等势线具有正交的和二次方的流体动力学网格，构成了渗漏斜率的渗流。给出了对排水坡土体的注水和滑坡稳定性的过滤效果的简短估计。