To facilitate understanding and calculation, hydrogeologists have introduced the influence radius. This parameter is now widely used, not only in the theoretical calculation and reasoning of well flow mechanics, but also in guiding production practice, and it has become an essential parameter in hydrogeology. However, the reasonableness of this parameter has always been disputed. This paper discusses the nature of the influence radius and the problems of its practical application based on mathematical reasoning and analogy starting from the Dupuit formula and Thiem formula. It is found that the influence radius is essentially the distance in the time–distance problem in physics; therefore, it is a function of time and velocity and is influenced by hydrogeological conditions and pumping conditions. Additionally, the influence radius is a variable and is essentially different from the hydrogeological parameters reflecting the natural properties of aquifers such as the porosity, specific yield, and hydraulic conductivity. Furthermore, the parameterized influence radius violates the continuity principle of fluids. In reality, there are no infinite horizontal aquifers, and most aquifers are replenished from external sources, which is very different from theory. The stable or seemingly stable groundwater level observed in practice is simply a coincidence that occurs under the influence of various practical factors, which cannot be considered to explain the rationality of applying this parameter in production calculations. Therefore, the influence radius cannot be used to evaluate the sustainable water supply capacity of aquifers, nor can it be used to guide the design of groundwater pollution remediation projects, the division of water source protection areas, and the scheme of riverbank filtration wells. Various ecological and environmental problems caused by groundwater exploitation are related to misleading information from the influence radius theory. Generally, the influence radius does not have scientific or practical significance, but it can easily be misleading, particularly for non-professionals. The influence radius should not be used in the sustainable development and protection of groundwater resources, let alone in theoretical models. From the perspective of regional overall planning, the calculation and evaluation of sustainable development and the utilization of groundwater resources should be investigated in a systematic manner.
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