A concise representation of hysteretic soil hydraulic properties is given based on a combination of M. T. van Genuchten's (1980) parametric K-O-h model and P.S. Scott et al.'s (1983) empirical hysteresis model modified to account for air entrapment. The resulting model yields compact closed-form expressions for the hysteretic water retention curve O(h) and soil water capacity C(h), as well as for the hydraulic conductivity function K(h). Depending on the degree of simplification involved, the model entails a total of 6-9 parameters which can be calibrated from direct measurements of O(h) and saturated conductivity or by an inverse solution approach from transient flow experiments. Comparison of modelpredicted and measured K-O-h relations for eight soils revealed one case in which model predictions were very poor. Model accuracy was judged to be acceptably good in the other cases. Mualem's modified (Y. Mualem, 1984) dependent domain model was found to be more accurate for soils with very narrow pore size distributions. Use of a simplified version of the proposed model with two parameters eliminated provided overall accuracy very similar to that of the more complex model. Numerical simulations of flow during transient infiltration and drainage using the proposed model and a variant of Y. Mualem's (1984) modified dependent domain model did not differ greatly and agreed reasonably well with experimental water content distributions, even when scanning curves were not described very accurately. By contrast, simulations without consideration of hysteresis produced highly unacceptable results. It is concluded that the proposed model provides a convenient and simple means of incorporating hysteretic effects into numerical flow models to provide significant improvement in prediction accuracy with little additional effort and with minimal data requirements. though these models may not be the easiest to use. Recently, Scott et al. [1983] introduced a simple empirical hysteresis model and showed that this model predicts scanning curves and hysteretic flow processes for different soils quite well. daynes [1984] evaluated four different hysteresis models and found that the different models gave generally equivalent results. In the event of approximately equivalent accuracy, ease of incorporating the hysteresis model into a numerical flow analysis will be a primary consideration. Although models with demonstrated effectiveness in modeling hysteretic flow are available and the importance of hysteresis has been shown many times in laboratory studies, hysteresis is usually ignored in studie•' of field-scale flow and transport problems. As Royer and Vachaud [1975] noted, one rationale for disregarding hysteresis is that spatial variability of hydraulic properties may overwhelm local hysteretic effects. While this is a feasible argument, certain evidence to the contrary has been observed. Stauffer and Dracos [1984] argue that the observed fast response of groundwater to infiltration in watersheds can be explained by hysteresis in the...

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.

The inverse problem of determining unsaturated soil hydraulic properties from one‐dimensional, transient infiltration and redistribution events is analyzed. Hydraulic properties are assumed to be described by an extension of van Genuchten's (1980) model which allows for hysteresis in the retention function and air entrapment. Unknown parameters in the model are estimated from observed water contents and heads during transient flow by numerical inversion of the unsaturated flow equation. The inverse problem is formulated as a weighted least squares problem and solved using an efficient Levenberg‐Marquardt algorithm. The flow event consists of ponded infiltration followed by gravity drainage with evaporation at the soil surface. Sensitivity analyses indicate that observations during ponded infiltration should be made near the position of the wetting front. The location of observation points during the drying stage is less critical than during the infiltration stage, but for the relatively high imposed evaporative flux sensitivity of pressure head is highest near the soil surface. Large differences in sensitivity are observed among the various model parameters. Unknown evaporative fluxes are approximated in the inverse solution as an equivalent first‐type boundary condition requiring only periodic measurements of surface water content during the drying stage. Little error is incurred provided accurate measurements are possible. Corruption of input data with random error is shown to have a larger effect on the predicted conductivity function than on the retention function and more effect on the wetting branch of the hysteretic retention function than on the drying. When measurements are subject to error and the assumed parametric model for water retention and conductivity relations is not exact, it may no longer be possible to detect hysteresis in the retention function.

Unsaturated hydraulic properties of four soils of varying particle size distributions were evaluated by determining values of the five parameters in van Genuchten's (1980) hydraulic model. Saturated conductivities (Ks) and saturated water contents (θs) were directly measured and values of residual water content (θr) and the parameters α and n were evaluated by a nonlinear inversion method to minimize various objective functions. Method I uses an objective function involving sums of squared deviations between measured cumulative outflow with time Q(t) for one‐step pressure desorption and numerically simulated outflow from saturation to a final pressure head h = − 10 m. Method II supplements Q(t) data with the measured equilibrium water content θ at h = − 150 m, while Method III employs equilibrium θ(h) data only. Method I yields the most accurate description of Q(t) and the independently determined hydraulic diffusivity D(θ). A fair description of θ(h) is obtained within the range of the one‐step experiment but at lower θ predictions are less reliable especially for finer‐textured soil. Method II extends the range of validity of the predicted θ(h) to lower θ with generally small effects on predicted D(θ) and Q(t). Method III gives the best description of θ(h) but at the expense of accuracy in Q(t) and D(θ). Implications for routine evaluation of soil hydraulic properties are discussed.

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A procedure is presented for estimating cation exchange capacity (CEC) and exchange selectivity coefficients from miscible displacement experiments on undisturbed soil columns. The procedure provides an alternative to batch experiments and is applicable to scenarios involving either binary homovalent exchange or binary monodivalent exchange. Gapon's exchange equation is used in the latter case. Parameters are determined by nonlinear, least‐squares inversion of column effluent concentration histories. The procedure requires that hydraulic flux and total solution normality be kept constant. It is also assumed that ion exchange takes place instantaneously. When this assumption is violated, it is still possible to obtain a good description of the observed data, but the parameter estimates may be meaningless. The feasibility of estimating the dispersion coefficient in the advection‐dispersion equation along with the ion exchange parameters is evaluated. Results indicate that this is generally not possible for continuous injection experiments, but much better results are obtained for pulse injection experiments.

This document describes two modeling studies conducted by HydroGeoLogic, Inc. for the U.S. NRC under contract no. NRC-04-89-O90, entitled, "Validation and Testing of the VAM2D Computer Code." VAM2D is a two-dimensional, variably saturated flow and transport code, with applications for performance assessment of nuclear waste disposal. The computer code itself is documented in a separate NUREG document (NUREG/CR-5352, 1989). The studies prsented in this report involve application of the VAM2D code to two diverse subsurface modeling problems. The first one involves modeling of infiltration and redistribution of water and solutes in an initially dry, heterogeneous field soil. This application involves detailed modeling over a relatively short, 9-month time period. The second problem pertains to the application of VAM2D to the modeling of a waste disposal facility in a fractured clay, over much larger space and time scales and with particular emphasis on the applicability and reliability of using the equivalent porous medium approach for simulating flow and transport in fractured geologic media. Reflecting the separate and distinct nature of the two problems studied, this report is organized in two separate parts. iii TABLE OF COINTENTS Section