A simplified equation of approximate interface profile in stratified coastal aquifers
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Hydraulic head
Closed-form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint-Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed-form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values.
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We developed a method to estimate aquifer transmissivity from the hydraulic-head data associated with the normal cyclic operation of a water supply well thus avoiding the need for interrupting the water supply associated with a traditional aquifer test. The method is based on an analytical solution that relates the aquifer's transmissivity to the standard deviation of the hydraulic-head fluctuations in one or more observation wells that are due to the periodic pumping of the production well. We analyzed the resulting analytical solution and demonstrated that when the observation wells are located near the pumping well, the solution has a simple, Dupuit like form. Numerical analysis demonstrates that the analytical solution can also be used for a quasi-periodic pumping of the supply well. Simulation of cyclic pumping in a statistically heterogeneous medium confirms that the method is suitable for analyzing the transmissivity of weakly or moderately heterogeneous aquifers. If only one observation well is available, and the shift in the phase of hydraulic-head oscillations between the pumping well and the observation well is not identifiable. Prior knowledge of aquifer's hydraulic diffusivity is required to obtain the value of the aquifer transmissivity.
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A practical new field method is proposed to evaluate hydraulic conductivity in partially saturated media near a water impoundment. The new method is an inverse procedure which utilizes a flow net constructed from the steady state total hydraulic head distribution around the water source. In the vicinity of constant head sources and downstream along any stream tube, wetness and conductivity generally decrease. Knowing the stream tube geometry and hydraulic gradient from the flow net, Darcy's law is used to determine unsaturated hydraulic conductivities within the stream tube relative to some segment of the stream tube where conductivity is known. This approach was used successfully to predict the unsaturated hydraulic conductivity which was input to two variably saturated numerical models, utilizing total hydraulic head fields generated by the models. This procedure is also applied to pressure head and water content data collected in the field surrounding a constant head borehole infiltration test originally designed to determine only saturated hydraulic conductivity above the water table. For practical purposes the new procedure compares very favorably with (1) results of a field experiment to obtain unsaturated hydraulic conductivity in situ using the instantaneous profile method and (2) values of unsaturated conductivity calculated from field and laboratory measurements of water content and pressure head.
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A novel direct-push (DP) probe was developed for in situ hydraulic conductivity measurements in unconfined sandy aquifers. It is a small-diameter tool with an intake screen and a built-in pressure transducer, and is directly pushed into the ground. Hydraulic conductivity k is estimated by pumping from an aquifer through the intake screen and, while doing so, measuring flow rate and water pressure. This paper describes first the DP system and then the procedures for estimating k values. The finite-element method was employed to obtain intake factors that correlate the measurements with the k values, and these intake factors were compared with those proposed for conventional borehole packer tests. Laboratory and field experiments were also performed to assess the usability of the DP equipment. The results showed that the k estimates obtained from the new probe agreed with those obtained by other methods. The results of this assessment indicate that the proposed DP technique is a promising tool for simple and rapid in situ measurements of hydraulic conductivity. Limitations to the technology are discussed, and further work is suggested.
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Cone of depression
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