Calculation Of Seepage Spill Point Position Based On The Total Potential Energy In The Real Domain

The study of the free surface problem of seepage flow has become an important research topic in the direction of Geotechnical engineering.The main task of the seepage calculation is to calculate the seepage flow,water head,hydraulic slope and other seepage factors,so as to provide the basis for the seepage stability analysis and the selection of reasonable seepage control design scheme.The determination of the free surface of the seepage is the key to solve the seepage field,and the position of the seepage spill point is the prerequisite for the accurate calculation of the free surface of the seepage.Based on the finite element method,a method to determine the position of the spill point and calculate the free surface of seepage flow in the two-dimensional stable seepage field is proposed.The research results include:(1)The global total potential energy method has high accuracy and no iterations when the seepage spill point is calculated by previous finite element method.However,the global total potential energy contains the region above the free surface(virtual domain),and induces some deviation in calculation results.Based on the global total potential energy,a concept of total potential energy in real domain is proposed in this paper.The virtual potential energy is deducted from global total potential energy,which eliminates the deviations caused by virtual domain potential energy and improves the calculation accuracy of the spill point.The calculation results of engineering examples show that the method based on the total potential energy of real domain has higher accuracy and stability.(2)Based on the theory of total potential energy in the real domain,the virtual domain elements above the free surface are treated differently: the infiltration coefficient of the virtual domain unit is adjusted or the virtual domain unit is discarded in the finite element calculation.As well as the difference of the minimum potential in the real domain,variable permeability coefficient adjustment point method,variable permeability coefficient curve fitting method,throwing element adjustment point method and throwing element curve fitting method are put forward.Respectively,using four methods to calculate the engineeringexample,throwing element adjustment point method has a higher calculation accuracy.(3)The virtual element method is often used to solve the problem of free surface.But this method needs to adjust the element passing through the free surface continuously,which makes the iteration efficiency slow and causes the element deformity.A curve fitting method is proposed in this paper to obtain a high-accurate free surface without re-adjusting the elements.Practical engineering examples show that the method is efficient,stable and accurate.