Narrow Results

We establish a new model for seepage of a liquid to a chink in the cracked deformable layer, an initial value problem of nonlinear fractional differential equation with variable coefficients, then design a numerical scheme of order 2 to solve this initial value problem. This new model theoretically explains the operating thickness H of a layer depending on the values of pressure gradient on the whole chink rather than on one point, which is practiced by a large amount of data. Compared with the Dontsov equation, our fractional model considers more aspects of the whole process. The earlier rejected results can also be considered in the display lines of the fractional model.

According to mathematical model of rock and soil, it calculated seepage field of tailing water channel under different conditions. The results showed that under condition of no.1, the seepage discharge from outside to inside of channel is 0.394 m3/h and the discharge under plastic concrete cut-off is 0.358m3/h, and that under condition of no.2, the seepage discharge from outside to inside of channel is 0.249 m3/h and the discharge under plastic concrete cut-off is 0.236m3/h. Under condition of no.1, the outflow of saturation line is at elevation of 411.0m which is under sand and gravel filling layer and near boundary of drift gravel sand layer. Under condition of no.2, the outflow of saturation line is at elevation of 403.0m which is under drift gravel sand layer and near rock foundation. The results showed that numerical simulation can be used to do with seepage problems of tailing water channel.