### Abstract

This study develops a mathematical model for simulating the hydraulic head distribution in response to pumping in a sloping fault zone aquifer under a water table boundary condition. A two-dimensional equation with a sink term representing the pumping is used for describing the head distribution in the aquifer. In addition, a first-order free surface equation is adopted to represent the change in water table at the outcrop. The analytical solution of the model, derived by the Laplace and finite Fourier cosine transforms, is expressed in terms of a double series. A finite difference solution within a deformable grid framework is developed to assess the solution obtained by specifying the free surface equation at the outcrop. Based on the analytical solution, we have found that the model's prediction tends to overestimate drawdown in a late pumping period. The temporal head distribution is independent of the aquifer slope if the water table change is small, and exhibits a double-humped shape due to the effect of the free surface. The temporal drawdown predicted from the analytical solution is further compared with those measured from a pumping test conducted in northern Portugal. Key Points An analytical solution for head in a sloping unconfined aquifer is developed The effect of the aquifer slope on temporal and spatial head is addressed The simplified free surface equation specified at the outcrop is assessed

Original language | English |
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Pages (from-to) | 4079-4094 |

Number of pages | 16 |

Journal | Water Resources Research |

Volume | 50 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jan 2014 |

### Keywords

- analytical solution
- deformable grid
- finite difference solution
- finite Fourier cosine transform
- free surface equation
- Laplace transform

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## Cite this

*Water Resources Research*,

*50*(5), 4079-4094. https://doi.org/10.1002/2013WR014212