### Abstract

We consider steady state unsaturated flow in bounded randomly heterogeneous soils under the influence of random forcing terms. Our aim is to predict pressure heads and fluxes without resorting to Monte Carlo simulation, upscaling or linearization of the constitutive relationship between unsaturated hydraulic conductivity and pressure head. We represent this relationship through Gardner's exponential model, treating its exponent α as a random constant and saturated hydraulic conductivity, K(s), as a spatially correlated random field. This allows us to linearize the steady state unsaturated flow equations by means of the Kirchhoff transformation, integrate them in probability space, and obtain exact integro-differential equations for the conditional mean and variance-covariance of transformed pressure head and flux. We solve the latter for flow in the vertical plane, with a point source, by finite elements to second-order of approximation. Our solution compares favorably with conditional Monte Carlo simulations, even for soils that are strongly heterogeneous.

Original language | English (US) |
---|---|

Title of host publication | Computational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology |

Editors | L.R. Bentley, J.F. Sykes, C.A. Brebbia, W.G. Gray, G.F. Pinder, L.R. Bentley, J.F. Sykes, C.A. Brebbia, W.G. Gray, G.F. Pinder |

Publisher | A.A.Balkema |

Pages | 785-792 |

Number of pages | 8 |

ISBN (Print) | 9058091252 |

State | Published - 2000 |

Event | Computational Methods in Water Resources - Calgary, Canada Duration: Jun 25 2000 → Jun 29 2000 |

### Other

Other | Computational Methods in Water Resources |
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Country | Canada |

City | Calgary |

Period | 6/25/00 → 6/29/00 |

### Fingerprint

### ASJC Scopus subject areas

- Earth and Planetary Sciences(all)
- Engineering(all)
- Environmental Science(all)

### Cite this

*Computational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology*(pp. 785-792). A.A.Balkema.

**Direct solution of unsaturated flow in randomly heterogeneous soils.** / Lu, Z.; Neuman, Shlomo P; Guadagnini, A.; Tartakovsky, D. M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Computational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology.*A.A.Balkema, pp. 785-792, Computational Methods in Water Resources, Calgary, Canada, 6/25/00.

}

TY - GEN

T1 - Direct solution of unsaturated flow in randomly heterogeneous soils

AU - Lu, Z.

AU - Neuman, Shlomo P

AU - Guadagnini, A.

AU - Tartakovsky, D. M.

PY - 2000

Y1 - 2000

N2 - We consider steady state unsaturated flow in bounded randomly heterogeneous soils under the influence of random forcing terms. Our aim is to predict pressure heads and fluxes without resorting to Monte Carlo simulation, upscaling or linearization of the constitutive relationship between unsaturated hydraulic conductivity and pressure head. We represent this relationship through Gardner's exponential model, treating its exponent α as a random constant and saturated hydraulic conductivity, K(s), as a spatially correlated random field. This allows us to linearize the steady state unsaturated flow equations by means of the Kirchhoff transformation, integrate them in probability space, and obtain exact integro-differential equations for the conditional mean and variance-covariance of transformed pressure head and flux. We solve the latter for flow in the vertical plane, with a point source, by finite elements to second-order of approximation. Our solution compares favorably with conditional Monte Carlo simulations, even for soils that are strongly heterogeneous.

AB - We consider steady state unsaturated flow in bounded randomly heterogeneous soils under the influence of random forcing terms. Our aim is to predict pressure heads and fluxes without resorting to Monte Carlo simulation, upscaling or linearization of the constitutive relationship between unsaturated hydraulic conductivity and pressure head. We represent this relationship through Gardner's exponential model, treating its exponent α as a random constant and saturated hydraulic conductivity, K(s), as a spatially correlated random field. This allows us to linearize the steady state unsaturated flow equations by means of the Kirchhoff transformation, integrate them in probability space, and obtain exact integro-differential equations for the conditional mean and variance-covariance of transformed pressure head and flux. We solve the latter for flow in the vertical plane, with a point source, by finite elements to second-order of approximation. Our solution compares favorably with conditional Monte Carlo simulations, even for soils that are strongly heterogeneous.

UR - http://www.scopus.com/inward/record.url?scp=0033667808&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033667808&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0033667808

SN - 9058091252

SP - 785

EP - 792

BT - Computational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology

A2 - Bentley, L.R.

A2 - Sykes, J.F.

A2 - Brebbia, C.A.

A2 - Gray, W.G.

A2 - Pinder, G.F.

A2 - Bentley, L.R.

A2 - Sykes, J.F.

A2 - Brebbia, C.A.

A2 - Gray, W.G.

A2 - Pinder, G.F.

PB - A.A.Balkema

ER -