Abstract
The determination of overflow boundary is a prerequisite for the accurate solution of the seepage field by the finite element method. In this paper, a method for solving overflow boundary according to the maximum value of horizontal energy loss rate is proposed, which based on the analysis of the physical meaning of functional and the water head distribution of seepage field under different overflow boundaries. This method considers that the overflow boundary that makes the horizontal energy loss rate reach the maximum value is the real boundary overflow. Compared with the previous iterative computation method of overflow point and free surface, the method of solving overflow boundary based on the maximum horizontal energy loss rate does not need iteration, so the problem of non-convergence does not exist. The relative error of the overflow points is only 1.54% and 0.98% by calculating the two-dimensional model of the glycerol test and the three-dimensional model of the electric stimulation test, respectively. Compared with the overflow boundary calculated by the node virtual flow method, improved cut-off negative pressure method, initial flow method, and improved discarding element method, this method has a higher accuracy.
Highlights
The finite element method is widely used in the calculation of seepage fields because it can be applied to complex boundaries and complex soil layers
The overflow boundary of the seepage field is usually unknown, so it is impossible to define the boundary before finite element calculation
In the equivalent permeability coefficient method, Xie and Zhang (2005) iterated the overflow point with the free surface according to the difference between the water head and elevation until the absolute value of the difference between the water head and elevation is less than the convergence value
Summary
Seepage is an influencing factor that must be considered in civil engineering, such as the instability of banks and dams caused by seepage (Fox et al, 2006; Chu-Agor et al, 2008; Midgley et al, 2013); the anti-seepage of dams, channels, and buried sites (Mishra and Singh, 2005; Charles et al, 2010; John and Michael Duncan, 2010; Xu et al, 2013); and the problems related to seepage encountered in specific engineering (Kobayashi and de los Santos, 2007; Lu and Chiew, 2007; Hung et al, 2009; Batool and Brandon, 2013). By analyzing the water head distribution trend of the seepage field under different overflow boundary conditions, this method identified the boundary that minimizes the global total potential energy as the real overflow boundary. To sum up, based on the principle of global total potential energy minimization, through the analysis of the water head distribution of seepage field under different overflow boundaries, this paper puts forward a method to solve the overflow boundary based on the maximum of horizontal energy loss rate. Taking the seepage field under the real overflow boundary as the initial state, the horizontal hydraulic gradient that makes the water head decrease in the positive direction along the x-axis is defined as positive. The total potential energy selected by this method is a scalar index, and the water flow on the overflow boundary has the directionality pointing out of the domain. To verify the correctness of this method, two models with experimental solutions are calculated
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
