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

Well-aquifer configuraiton for Gringarten and Witherspoon (1972) solution for a pumping test in a fractured aquifer with vertical plane fracture

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.


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


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

  • variable pumping rates
  • multiple pumping wells
  • multiple observation wells


AQTESOLV benchmark for Gringarten and Witherspoon (1972) solution for a uniform-flux vertical plane fracture
Comparison of AQTESOLV (blue line) and published uniform-flux vertical plane fracture well function values (symbols) at the wellbore (Gringarten and Witherspoon 1972).


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.