Direct solution of unsaturated flow in randomly heterogeneous soils

Z. Lu, Shlomo P Neuman, A. Guadagnini, D. M. Tartakovsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationComputational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology
EditorsL.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
PublisherA.A.Balkema
Pages785-792
Number of pages8
ISBN (Print)9058091252
StatePublished - 2000
EventComputational Methods in Water Resources - Calgary, Canada
Duration: Jun 25 2000Jun 29 2000

Other

OtherComputational Methods in Water Resources
CountryCanada
CityCalgary
Period6/25/006/29/00

Fingerprint

unsaturated flow
Hydraulic conductivity
Soils
hydraulic conductivity
Fluxes
Integrodifferential equations
soil
upscaling
Linearization
simulation
point source
Monte Carlo simulation

ASJC Scopus subject areas

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

Cite this

Lu, Z., Neuman, S. P., Guadagnini, A., & Tartakovsky, D. M. (2000). Direct solution of unsaturated flow in randomly heterogeneous soils. In 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 (Eds.), 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.

Computational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology. ed. / 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. A.A.Balkema, 2000. p. 785-792.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lu, Z, Neuman, SP, Guadagnini, A & Tartakovsky, DM 2000, Direct solution of unsaturated flow in randomly heterogeneous soils. in LR Bentley, JF Sykes, CA Brebbia, WG Gray, GF Pinder, LR Bentley, JF Sykes, CA Brebbia, WG Gray & GF Pinder (eds), 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.
Lu Z, Neuman SP, Guadagnini A, Tartakovsky DM. Direct solution of unsaturated flow in randomly heterogeneous soils. In Bentley LR, Sykes JF, Brebbia CA, Gray WG, Pinder GF, Bentley LR, Sykes JF, Brebbia CA, Gray WG, Pinder GF, editors, Computational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology. A.A.Balkema. 2000. p. 785-792
Lu, Z. ; Neuman, Shlomo P ; Guadagnini, A. ; Tartakovsky, D. M. / Direct solution of unsaturated flow in randomly heterogeneous soils. Computational methods in water resources - Volume 2 - Computational methods,surface water systems and hydrology. editor / 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. A.A.Balkema, 2000. pp. 785-792
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