Determining Soil Hydraulic Properties from One‐step Outflow Experiments by Parameter Estimation: I. Theory and Numerical Studies

Abstract

The numerical feasibility of determining water retention and hydraulic conductivity functions simultaneously from one-step pressure outflow experiments on soil cores by a parameter estimation method is evaluated. Soil hydraulic properties are assumed to be represented by van Genuchten's closed-form expressions involving three unknown parameters: residual moisture content 6, and coefficients a and n. These parameters are evaluated by nonlinear least-squares fitting of predicted to observed cumulative outflow with time. Numerical experiments were performed for two hypothetical soils to evaluate limitations of the method imposed by constraints of uniqueness and sensitivity to error. Results indicate that an accurate solution of the parameter identification problem may be obtained when (i) input data include cumulative outflow volumes with time corresponding to at least half of the final outflow and additionally the final outflow volume; (ii) final cumulative outflow corresponds to a sufficiently large fraction (e.g., >0.5) of the total water between saturated and residual water contents; (iii) experimental error in outflow measurements is low; and (iv) initial parameter estimates are reasonably close to their true values.

Centrifuge modeling of one-step outflow tests for unsaturated parameter estimations

“…In addition, the inCorrespondence to: H. Nakajima (nakajima.hideo@aist.go.jp) verse method allows the simultaneous estimation of both the soil water retention and the unsaturated hydraulic conductivity function from a single transient experiment (Hopmans et al, 2002). Kool et al (1985) provided a detailed description of the framework for inverse methods and estimated three parameters in the van Genuchten model (van Genuchten, 1980) based on numerical and experimental data of one-step outflow tests. Their results indicated that an accurate solution of the parameter identification problem can be obtained when (i) the input data include the cumulative outflow volumes with time corresponding to at least half of the final outflow, and the final outflow volume, (ii) the final cumulative outflow corresponds to a sufficiently large fraction (e.g., >0.5) of the total water between saturated and residual water contents, (iii) experimental error in the outflow measurements is low, and (iv) initial parameter estimates are reasonably close to their true values.…”

“…Since it is impractical to conduct one-step gravity driven tests that fulfill the aforementioned first two conditions suggested by Kool et al (1985) (for example, several days of observation of drainage from a 2 to 3 m tall soil column may be required even for sand), pneumatic pressure or suction is usually applied at the top or bottom of small soil samples. However, such test configurations may result in non-uniform flow conditions.…”

Describing the soil physical characteristics of soil samples with cubical splines

“…When f describes the system under consideration correctly, the parameter vector p can sometimes be derived from simple input-output measurements, (e.g. the One-step outflow method (Kool et al 1985) or the Multi-step method (Van Dam et al 1990) in case of soil physical parameters). In these cases the input to the system is fully controlled and the output is measured.…”

Estimation of hydraulic conductivities of Yucca Mountain tuffs from sorptivity and water retention measurements

“…Inversion of the experimental data could also be accomplished by fitting the data to numerical solutions of the governing equation. This approach has occasionally been pursued (Zachmann et al, 1981;Kool et al, 1985;Finsterle and Pruess, 1995), but involves extensive computations. Furthermore, as the sorptivity can be measured without having to determine the details of the saturation or pressure profile, it would seem that inversion methods could be devised that do not require repeated numerical solutions of the full governing differential equation.…”