Improvement of Dupuit model：with infiltration recharge

The model proposed by Dupuit (1863) is a “steady well flow model of Round Island aquifer”. The Dupuit model only considers lateral boundary conditions， and the upper boundary precipitation infiltration recharge condition is not considered. Therefore，Dupuit model can only be used in the dry season to obtain the parameters of aquifer system by groundwater well flow test，but can't be used to predict groundwater dynamic. In this paper，the Dupuit model of groundwater well flow is developed to consider the effect of uniform and steady infiltration recharge (evaporation and discharge shows negative value). Based on the principle of mass balance，assuming that the groundwater flow obeys Darcy's law and satisfies Dupuit's assumption，the differential equation of groundwater flow in polar coordinates is established， and then the corresponding discharge equation and water level equation are established according to the boundary conditions. These equations can be used to calculate hydrogeological parameters by well flow test under the condition of precipitation infiltration recharge，and to predict the effect of groundwater pumping under the corresponding conditions. It is discussed that the introduction of Dupuit hypothesis can bring benefits to the analytical study of this problem, which can reduce the dimension (omitting z variables). At the same time, it may deviate from the Dupuit assumption near the groundwater ridge and the pumping well. It is suggested that these areas should be avoided in the arrangement of observation holes when the aquifer parameters are obtained by pumping test.