Analytical, Numerical and Experimental Studies on Steady-State Seepage Through 3D Rockfill Trapezoidal Dikes

Seepage through dikes under steady-state conditions is a classical problem in geotechnics. Several analytical solutions exist for estimating seepage through 2D dikes. In practice, many dikes have a limited length in the third dimension. This is particularly true for water flow through a waste rock barricade to hold backfill slurry in underground stopes. Three-dimensional solutions are necessary to evaluate seepage through 3D trapezoidal dikes. In this study, existing 2D solutions developed for estimating seepage through 2D dikes under steady-state conditions are presented and generalized for 3D dikes. The validity of these 3D generalized solutions is tested by numerical modeling with FLAC3D. Results show that the 3D solution based on a generalization of the Dupuit solution predicts seepage variation as a function of upstream hydraulic head well, but fails to describe seepage variation as a function of downstream hydraulic head. Further analyses reveal that the Dupuit model involves assumptions by which the flow path can be underestimated and the mean flow cross-section from the bottom to the top surface of the downstream water tends to be overestimated. The 3D generalized Dupuit solution was therefore modified by adding two calibration coefficients, one for the flow path length and another for the mean flow cross-section. The two calibration coefficients were then obtained by calibration against a few 3D numerical results. The validity of the proposed and calibrated analytical solution was then tested against additional numerical results. Finally, both the numerical model and the proposed calibrated analytical solutions were validated by laboratory test results.