Simplified analysis method of singular point source in three-dimensional finite element calculation
Relief wells are an important means of seepage control,and the infiltration at the bottom of shallow relief wells cannot be ignored.When utilizing the finite element method for seepage field analysis in relation to wells,a significant disparity exists between the aquifer's dimensions and the well's radius.Achieving reasonable accuracy necessitates limiting the mesh size around the well to centimeters or less,albeit at the cost of reduced efficiency.To enhance efficiency,the well bottom is commonly approximated as a point source in analytical models.The head gradient near the point source is extremely large,which is a singular point.In the finite element method,equivalent treatment is usually required to ensure the global accuracy.This paper presents a method for simulating point sources with zero-volume point elements which is based on the correction well water level method,the method uses the point source analytical solution and the tetrahedral seepage element to deduce the explicit solution of the point source element.By using this point source element to simulate the bottom of well,the point source can be simulated by using a large grid without losing the global accuracy,which greatly improves the efficiency of simulating the point source by using the three-dimensional finite element.The paper thoroughly outlines the derivation process for the explicit solution of the point element,verifies its calculation accuracy,and investigates the applicability range of simplified calculation methods.Lastly,the practical application of this method in drainage decompression and anti-floating engineering is presented.
seepagefinite element methodwell pointsingular point element
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