Abstract:

Due to the limitation of setting the upper boundary at the free surface located at the water table, the Theis well model in unconfined aquifers has some problems such as unsound theoretical basis and unreasonable physical meaning of parameters. To overcome these issues, firstly, the well model is revised by moving the free surface from the water table to the air entry plane, and takes the Boussinesq equation located at the air entry plane as the governing equation, and derives the analytical solution of the model; Then, a parameter inversion model is constructed to calibrate the model parameters. By comparing the revised model drawdown and the theoretical drawdown of the classical model with the measured drawdown, it verifies the rationality of the well revised model proposed in this paper. Then, the variation characteristics of the air entry plane elevation under the modified well model are discussed by using parameter sensitivity analysis. Finally, the computational method and variation characteristics of seepage velocity in the vertical direction of the air entry plane are discussed. It is found that the drawdown curve obtained by the revised model coincides with the measured drawdown curve; The air entry plane elevation increases with increasing distance from the center of the well and the specific yield and decreases with increasing pumping flow rate. In the early stage of pumping, the air entry plane elevation decreases with increasing hydraulic conductivity, but the opposite is true in the late stage of pumping. The calculation results of the analytical expressions of the seepage velocity in the vertical direction based on the water balance relation at the air entry plane (based on the linearized or non-linearized equation, using complete solutionor approximate solution) and based on continuity equation of seepage flow at the air entry plane (based on the linearized equation, using complete solution) under five conditions are basically consisent, and the trends of the curve are consistent with each other, showing a nonlinear increase with the prolongation of pumping time.

Key words: air entry plane, well model, fully penetrating well, Boussinesq equation, analytical solution, parameter inversion model