# Gringarten and Witherspoon Solution for Fractured Aquifers with a Single Vertical Plane Fracture

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Additional Topics

A mathematical solution by Gringarten and Witherspoon (1972) is useful for determining the hydraulic properties (hydraulic conductivity, specific storage, hydraulic conductivity anisotropy and fracture length) of **fractured** aquifers with a single vertical plane fracture intersecting the pumped well. Analysis involves matching the solution to drawdown data collected during a pumping test. The solution estimates hydraulic conductivity anisotropy in a horizontal (x-y) plane.

AQTESOLV provides visual and automatic methods for matching the Gringarten and Witherspoon solution to pumping test and recovery test data. This easy-to-use and intuitive software promotes rapid and accurate determination of aquifer properties.

## Assumptions

The following assumptions apply to the use of the Gringarten and Witherspoon solution for a vertical fracture:

- aquifer has infinite areal extent
- aquifer has uniform thickness
- aquifer potentiometric surface is initially horizontal
- fractured aquifer represented by anisotropic nonleaky confined system with a single plane vertical fracture that fully penetrates aquifer
- flow is unsteady
- water is released instantaneously from storage with decline of hydraulic head
- diameter of control well is very small so that storage in the well can be neglected

## Solution

Options

AQTESOLV provides the following options for the Gringarten and Ramey horizontal fracture solution:

- variable pumping rates
- multiple pumping wells
- multiple observation wells

## Benchmark

## References

Gringarten, A.C. and P.A. Witherspoon, 1972. A method of analyzing pump test data from fractured aquifers, Int. Soc. Rock Mechanics and Int. Assoc. Eng. Geol., Proc. Symp. Rock Mechanics, Stuttgart, vol. 3-B, pp. 1-9.