Computational Methods in Engineering

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In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it, is used to verify the developed code. Other scenarios, which are two-dimensional free surface tests on a laboratory rockfill, are used to verify the model. The model shows satisfactory performance in this regard. For example, on average, a mean absolute relative error of about 2.3%, in terms of pressure head was found to exist between modelling results and observed values. Further capabilities of the model are discussed by simulating overflow through self– spillway rockfill dams. Keywords: Finite element, Method, Fixed grid, Non-Darcy flow, Non-linear flow, Rock fill dam

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Biot equations that consider fluid and soil interaction at the same time are the most applicable relationships in the soil dynamic analysis. However, in dynamic analysis, due to the sudden increase in the excess pore pressure caused by seismic excitation and the occurrence of high hydraulic gradients, the assumption of the Darcy flow used in these equations is questionable. In the present study, in the u-p form of Biot equations, non-Darcy flow is considered. Also, the nonlinear behavior of soil is modeled by the Pastor-Zienkiewicz -Chan model. For validation, the VELACS No.1 experiment is modeled and the effect of the nonlinear fluid flow assumption on the results is examined. The results indicate that in the low permeability coefficients, the obtained results of the non-Darcy and Darcy flow are in agreement; however, in high permeability coefficients, these two methods differ by time and depth.