Yechezkel Mualem

A new model for predicting the hydraulic conductivity of unsaturated porous media

A simple analytic model is proposed which predicts the unsaturated hydraulic conductivity curves by using the moisture content-capillary head curve and the measured value of the hydraulic conductivity at saturation. It is similar to the Childs and Collis-George (1950) model but uses a modified assumption concerning the hydraulic conductivity of the pore sequence in order to take into account the effect of the larger pore section. A computational method is derived for the determination of the residual water content and for the extrapolation of the water content-capillary head curve as measured in a limited range. The proposed model is compared with the existing practical models of Averjanov (1950), Wyllie and Gardner (1958), and Millington and Quirk (1961) on the basis of the measured data of 45 soils. It seems that the new model is in better agreement with observations.

Theoretical Prediction of Electrical Conductivity in Saturated and Unsaturated Soil

A conceptual model is proposed for the prediction of the electrical conductivity of bulk soil in saturated and in unsaturated states. The model is based on the hypothesis that the tortuosity factor affecting the bulk soil electrical conductivity is identical to that defined for prediction of the soil hydraulic conductivity. Simple mathematical functions are derived to forecast the soil electrical conductivity as a function of the water content. Experimental results of seven previous studies carried out on 26 soils were used for validation tests. The models efficiency as a predictive tool, in cases where limited experimental data are available, is found to be generally good.

A Modified Dependent-domain Theory Of Hysteresis

The dependent-domain theory of hysteresis developed here accounts for the effect of the pore-water blockage against air entry, while using the similarity hypothesis of the universal model (Mualem 1977). The resulting model is simpler and requires fewer data for calibration than previous dependent-domain models. Marked improvement is attained compared with the performance of the universal model. Three porous media—glass beads, sand, and sandy loam for which detailed data are available—were used to test the model. Computed primary and secondary scanning curves derived by the new model are compared with corresponding experimental curves, as well as computed curves based on Model II of Mualem (1974) or Model III of Mualem and Dagan (1975). The new model seems to agree with observations much better that Model II, which uses the same amount of data for calibration. The accuracy of the computed results is comparable to that found for the dependent-domain model of Mualem and Dagan (1975), which requires more experimental data.

Modeling the dynamics of seal formation and its effect on infiltration as related to soil and rainfall characteristics

The main physical aspects of soil surface seal formation caused by rainfall are modeled. The proposed model relates the surface sealing to the specific hydraulic and mechanical properties of the initially undisturbed soil as well as the physical characteristics of the rainfall applied, under given initial and boundary conditions defining the flow system. The soil disturbance resulting from the raindrop impacts is expressed in terms of an increase of the initial soil bulk density. The dynamics of seal formation at the soil surface are found to be related to the following variables: the rainfall intensity, the second moment of the drop-size density distribution, the maximal drop diameter, the compaction limit of the given soil, and its initial shear strength, which depends upon the initial soil bulk density and water content. Following Mualem and Assouline [1989], a nonuniform seal is considered, represented by an exponentially decreasing function of the bulk density with depth. The seal thickness is assumed to be dependent upon the rainfall rate. Its steady state value is assumed to be reached shortly after the beginning of rainfall so that it might be considered as constant during the stage of formation. A calibration procedure is presented on the basis of measured infiltration under sealing conditions. The results show that the proposed model addresses the main factors affecting soil sealing formation and is able to simulate the process of infiltration through sealing soils under saturated as well as unsaturated flow conditions.

Effect of rainfall‐induced soil seals on soil water regime: Wetting processes

The effects of a rainfall-induced soil seal on wetting processes are studied in the cases of two different soils: Hamra (sandy loam) and loess (loam). The soil seal is identified as the disturbed upper layer where the average hydraulic properties have been changed during rainfall from the initial properties that were identical to those of the undisturbed soil bed. These properties are derived by applying the seal model of Mualem and Assouline (1989), calibrated for the two soils. Determination of the seal thickness, bulk density, retention curve, and hydraulic conductivity function made it possible to solve systematically the flow equation for different boundary conditions, allowing the simulation of the wetting processes within the seal layer as well as the undisturbed profile underneath. The infiltration curves and the water content profiles during and after rainfall are derived for three rainfall intensities. The water content and the capillary head profiles, as well as the variation of these variables with time, at different depths under the soil surface, were also calculated. Smaller amounts of the rainfall infiltrate as the rainfall intensity increases. The infiltration rate diminishes faster as the rainfall intensity increases. The idea of a single infiltration curve as a function of the cumulative rainfall seems to be invalid. Each rainfall intensity yields a different infiltration curve. A rough validation test of the model yielded predicted infiltration curves closely bounded by the experimental results. The final infiltration rate after 50 mm of rainfall also seems to be a function of the rainfall intensity, with the higher rate obtained for the higher rainfall intensity as experimentally observed in other studies. Unlike the explanations found in literature, this study suggests that a shallower saturated zone within the seal layer is the reason for this phenomenon. This study points out that the disturbed layer which forms the surface seal is not saturated from the very beginning of rainfall. It has a significant water-holding capacity and, thus, takes time to reach saturation. Furthermore, under rainfall of high intensity, the seal layer reaches saturation only at its upper zone close to the soil surface. The lower part may remain unsaturated even after 50 mm rainfall and is larger for the soil of coarser texture.

Prediction of the soil boundary wetting curve

A previously developed model of hysteresis is formulated on a nondimensional scale using the effective saturation rather than the capillary head as the independent variable. The theoretical equations of the various hysteretic curves suggest that a universal hysteresis of unsaturated porous media prevails on the dimensionless scale. This study also proves that the common use of a primary loop instead of the main loop of hysteresis for calibrating the model is actually compatible with theory. Data of 10 soil-water hysteresis studies were used to examine the applicability of the theory. Based on the findings, this study suggests a method for predicting the soil boundary wetting curve from the measured primary loop. The computed and the measured parts of the boundary loop can be used concomitantly to calibrate Model II of Mualem (1974) in the complete domain of hysteresis. The proposed method was illustrated using the data of a sand sample.

Effect of rainfall-induced soil seals on the soil water regime: Drying interval and subsequent wetting

The effects of rainfall-induced soil seals on drying processes and on infiltration following drying intervals are simulated for two different soils, a loam and a sandy loam. The simulated drying processes include water content redistribution without evaporation and under a constant evaporation rate of 5 mm day−1. During evaporation, the water content at the seal surface decreases rapidly. A high water content gradient develops within the seal, which increases along the drying interval. It indicates that, at least during the first hours of drying, the seal layer fulfilled all the evaporation demand and therefore dries faster that an unsealed soil where the evaporation is supplied by a much deeper zone of the soil profile. This phenomenon is more accentuated in the loam than in the sandy loam soil. Considering the subsequent infiltration curves during rainfall following different drying intervals, the ponding time and the post-ponding infiltration rates increase when the antecedent drying period is longer, but no significant effect on the final infiltration is found following drying intervals of few days. Also, the water content at the sealed soil surface before rainfall seems to play a major role on infiltration. Very close infiltration curves were obtained after different drying intervals that ended with similar surface water content.

Soil sealing, infiltration and runoff

Arid zones are characterized by vast areas of bare soils, low annual precipitation, but high rainfall intensities with high kinetic energy. Desertification of less arid regions may also be a result of overgrazing and exploitation of vegetation beyond the land’s productive potential. Bare soils exposed to rainfall are subjected to physical and chemical processes which change the properties at the vicinity of the soil surface. When dried, a hard layer is formed in the soil surface which is viewed as a “crust”. This phenomenon, when disregarded, may be harmful to agriculture. It decreases the infiltration rate, reduces the available water at the root zone, increases runoff and soil erosion and affects seedlings and plant growth. Duley (1939) reported that raindrop impacts on the bare soil surface are the cause of such a low permeability crust. Hoogmoed and Stroosnijder (1984) studied the semi-arid region of the Sahel in Central Africa and concluded that it was very sensitive to crust formation and that, on average, 25% of the rain is lost by runoff. They also noted that on untilled soils, the presence of a crust is a permanent feature. The crust formation, which limits the cumulative infiltration of valuable water to the root zone, induces in fact a vicious cycle since it affects vegetation cover, thus leaving the soil surface bare and exposed to rainfall.

Soil seal formation and its effect on infiltration: Uniform versus nonuniform seal approximation

Two different approaches to the solution of the problem of flow through the dynamic stage of seal formation as well as through soil with a fully developed seal are studied. The first approach considers the disturbed seal layer and the undisturbed soil underneath as a continuous nonuniform soil profile. The second replaces the nonuniform seal by a uniform equivalent layer, thereby generating a homogeneous two-layer flow system. The depth-dependent properties of the nonuniform seal are expressed in terms of the exponential model of Mualem and Assouline [1989]. The dynamics of seal formation are modeled according to Assouline and Mualem [1997]. During the first rainfall on an undisturbed soil profile, when the seal layer is formed, the application of the first or the second approach has only a minor effect on the calculated infiltration curves. However, there is a significant difference between the two solutions regarding the dynamic changes of the water content in the soil surface and, consequently, within the seal layer. During subsequent rainfalls on a sealed soil profile, when the seal layer is completely developed, the differences between the two ways of accounting for the seal layer become evident, and their effects on the infiltration curve are much more significant. Representing the seal as an equivalent uniform layer increases the ponding time and the infiltration rates at the early stage of the process. The amplitude of these effects is increased when the rainfall rate is higher and the seal layer is thicker. An important result is that the relationship between infiltration rate and cumulative infiltration is unique in the case of a completely developed seal and when the seal is considered as a nonuniform layer. However, this relationship is not unique during seal formation, independent of the approach applied to represent the seal layer.

Research Note: Mobility of Herbicide Microcapsules in Saturated Granular Media

The mobility of the microcapsules in saturated granular media was estimated on the basis of conventional breakthrough experiments in vertical columns packed with sands for various physical and chemical conditions. Four types of microcapsules have been tested, all of them were found to have reasonable mobility in clean quartz sand, but not in sandy soil. The immobility in the sandy soil was attributed to some production deficiencies in terms of shape, size and quality of the coating surface. The size of the microcapsules should be considerably smaller than those produced with an order of magnitude of a few micrometers. They should also be more spherical and with a smoother surface. The addition of a proper dispersant had stabilized the microcapsules suspension, and facilitated their transport in the sand. A major flow factor affecting microcapsules mobility is the water flux. The microcapsules should be applied at a high irrigation rate, which also implies a high water content in the soil profile. Considering solely the mobility aspect, it seems that the prospect for successful application of the new method for weed control is limited to granular soils with a high hydraulic conductivity at/or near saturation. However, for the time being the most limiting problem is the production of quality microcapsules with good physical and chemical properties.