Falling Head Conditions Research Articles

Geophysical and hydrological data assimilation to monitor water content dynamics in the rocky unsaturated zone

In recent years, geophysics is increasingly used to study the flow and transport processes in the vadose zone. Particularly, when the vadose zone is made up of rocks, it is difficult to install sensors in the subsurface to measure hydrological state variables directly. In these cases, the electrical resistivity tomography (ERT) represents a useful tool to monitor the hydrodynamics of the infiltration and to estimate hydraulic parameters and state variables, such as hydraulic conductivity and water content. We propose an integrated approach aimed at predicting water content dynamics in calcarenite, a sedimentary carbonatic porous rock. The uncoupled hydrogeophysical approach proposed consists in 4D ERT monitoring conducted during an infiltrometer test under falling head conditions. Capacitance probes were installed to measure water content at different depths to validate the estimations derived from ERT. A numerical procedure, based on a data assimilation technique, was accomplished by combining the model (i.e., Richards' equation) with the observations in order to provide reliable water content estimations. We have used a new data assimilation method that is easy to implement, based on the ensemble Kalman filter coupled with Brownian bridges. This approach is particularly suitable for strongly non-linear models, such as Richards' equation, in order to take into account both the model uncertainty and the observation errors. The proposed data assimilation approach was tested for the first time on field data. A reasonable agreement was found between observations and predictions confirming the ability of the integrated approach to predict water content dynamics in the rocky subsoil.

Analytical models of infiltration and redistribution for unsaturated flow in soils with vertically non-uniform saturated hydraulic conductivity

The Richards equation describes unsaturated water movement in soils. However, analytical solutions to the nonlinear Richards equation are possible only for simple and idealized conditions. In this paper, sharp front (SF) models are developed for vertically non-uniform soils, with the saturated hydraulic conductivity continuously decreasing with depth according to a power-law function. Analytical expressions for evolutions of water content profiles and fluxes past a control plane are developed for the three surface boundary conditions of constant saturation, applied surface flux, and redistribution that are applicable during and after rainfall events. Comparisons of model results with infiltrometer experimental data from Purdue University are provided for the special case of falling head conditions at the soil surface. Subsequently, model results are compared with numerical solutions of the Richards equation for different levels of vertical heterogeneity for rainfall events of finite duration so that all the three boundary conditions are employed. Results show that soil moisture fronts are steeper with increasing non-uniformity, making sharp front approximations more accurate for pre- and post-ponding conditions, but less so for redistribution. The developed model results are found to provide reasonable approximations to numerical solutions of the Richards equation for vertically non-uniform soils.

Methodology for Determining Laboratory and In Situ Hydraulic Conductivity of Asphalt Permeable Friction Course

The permeable friction course (PFC) is a layer of porous asphalt pavement overlain on conventional impervious hot-mix asphalt or portland cement concrete. The drainage properties of PFC are typically considered to be governed primarily by two hydraulic properties: hydraulic conductivity and porosity. Both of these hydraulic properties change over the life cycle of the PFC layer due to clogging of the pore space by sediment. Therefore, determination of the hydraulic conductivity and porosity of PFC can be problematic. Laboratory and particularly field tests are necessary for accurately determining the hydraulic conductivity of the PFC layer. Taking multiple measurements over the life of the pavement shows how these hydraulic characteristics change with time and the varying roadway conditions at which they are evaluated. Constant head laboratory testing has shown that PFC experiences a nonlinear flow relationship as described by the Forchheimer equation. In addition to the laboratory analysis of the hydraulic characteristics, a falling head field test is recommended to determine the in situ hydraulic conductivity. This incorporates the modeling techniques used in the laboratory testing and applies them to the falling head conditions used in the field. The result is a nondestructive test procedure for determining the in situ hydraulic conductivity which is necessary for estimating the extent to which the benefits associated with the drainage characteristics of the PFC layer will persist.

A method for automating data collection from a double-ring infiltrometer under falling head conditions

Estimating soil hydraulic properties, such as infiltration rate and hydraulic conductivity, is important for understanding hydrological processes such as rainfall and irrigation partitioning. Current infiltrometers can require considerable operator input to limit the number of readings that can be simultaneously performed. Therefore, the objective of this work was to develop a simple double-ring infiltrometer for automated data collection under falling head conditions. The design consisted of 15.2-cm tall inner- and outer-rings of 14.6 and 33.0 cm in diameter, respectively. The inner-ring was held in the centre of the outer-ring by a small pipe that also served as a handle. A small hole was drilled 3.8 cm from the bottom of each ring and a slightly larger hose passed through both holes. One hose end led into the inside of the inner-ring and the opposite end to the outside of the outer-ring. A pressure transducer was attached to the outside end of the hose. A datalogger was used to record the transducer output. This design was compared in-situ to a constant head method using a Mariotte bottle system on two distinct soils and tested on four different soil series ranging in textural class from a loamy sand to a clay. Soils had been fallow prior to this work for at least 2 years, except the loamy sand which had a 5-year-old Bahia grass (Paspalum notatum) stand. Although there were some differences between the two approaches, values estimated with the proposed method had less variability. This method allows a single user to collect multiple readings. Collected data can be used to estimate quasi-steady state and cumulative infiltration, and in situ hydraulic conductivity of saturated soil. The proposed procedure could be beneficial when multiple readings of soil hydraulic properties are required, such as when characterizing soil spatial variability.

Measuring Water Transmission Parameters in Vadose Zone Using Ponded Infiltration Techniques

The flow of soil water is characterized by water transmission parameters, field-saturated hydraulic conductivity, matric flux potential and sorptivity. Soil water flow is, in turn, the primary mechanism by which soil contaminants, such as excess plant nutrient, bacteria, viruses, salts, and industrial chemicals are transported. Consequently, knowledge of soil water transmission parameters is essential for understanding, preventing and remediating the contamination of soil water and ground water. This paper describes steady-state and transient methods for obtaining soil water transmission parameters from ponded infiltration under constant head and falling head conditions in surface rings and shallow auger holes. Also discussed are the conditions under which the various methods are most appropriate.

Analytical solutions of water table variation in a horizontal unconfined aquifer: Constant recharge and bounded by parallel streams

AbstractAnalysis of groundwater flow in an unconfined aquifer has received increasing attention by hydrogeologists for the design of drainage systems or the prediction of drawdown patterns of the water table in an aquifer neighbouring a pumping well. In this study, we attempt to analyse mathematically the variation of the water table in a horizontal unconfined aquifer receiving uniform recharge and bounded by parallel streams during a continuous cycle of rising and falling head conditions. The Boussinesq equation was taken to be the governing equation describing the transient changes in the water table. This problem was simplified to a one‐dimensional heat equation based on the assumption that the aquifer thickness is large enough compared to the water table changes and that the Dupuit–Forchheimer approximations are valid. We solved the heat equation using a method of variable separation in which the solution consists of both the steady‐state and nonsteady‐state solutions. With this method, the solutions could be obtained for various initial conditions such as different heads at the left and right boundaries and variable head distribution. In addition, simultaneous analysis of water table changes for both rising and falling head cases could be obtained. Comparison with other analytical solutions obtained for the linearized Boussinesq equation with Laplace transformation gives a nearly identical result, supporting the validity of the assumption and mathematical method used in this study. Advantages of the method over Laplace transformation can be found from the fact that our method renders the initial condition more flexible and simultaneous analysis of water table changes during rising and falling head cases can be done. Copyright © 2001 John Wiley & Sons, Ltd.

Analysis of Transient Data from Infiltrometer Tests in Fine‐Grained Soils

AbstractData collected during ring infiltrometer tests are often analyzed while assuming either that the effect of gravity is negligible (early‐time, transient data) or that it is dominant (late‐time, steady‐state data). In this paper, an equation is proposed for inter‐preting both early‐time and late‐time data measured during infiltration tests under falling head conditions. It is shown that the method used by previous authors for interpreting both early‐time data is a special case of the proposed equation. The equation is applied to data collected during tests performed in fine‐grained soils, and results are discussed. The analysis suggests that to assume a priori values of the soil sorptive number, as indicated in the literature for various soils, may in some cases lead to severely underes‐timated values of the saturated hydraulic conductivity. Conversely, in low permeability soils, to assume steady‐state gravity drainage may lead to order of magnitude overestimates of the saturated hydraulic conductivity. A dimensionless analysis provides characteristic times that correspond either to the duration of the log‐log half slope displayed by early‐time data or to the log‐log unit slope characteristic of late‐time data.

Estimating the hydraulic conductivity of slowly permeable and swelling materials from single‐ring experiments

The in situ determination of the field‐saturated hydraulic conductivity of low‐permeability porous materials is a major concern for both geotechnics and soil physics with regards to environmental protection or water resources management. Recent early‐time single‐ring infiltration experiments, involving sequential constant head and falling head conditions, allow its efficient estimation. Nevertheless, the theory on which the interpretation was based was still strictly valid to nondeformable soils and implicity relied on a particular form of the hydraulic conductivity‐soil water pressure head relationship. This theory is now extended to deformable materials, without any restrictive hypothesis. A new concept, bulk sorptivity, which characterizes the solid phase movement, is introduced. Field experiments, conducted on two liners of swelling and slowly permeable materials, revealed that neglecting the soil deformation induces an underestimation of the actual coefficient of permeability of the soil.

Analysis of Early‐Time and Steady State Single‐Ring Infiltration Under Falling Head Conditions

The prediction of infiltration of water into field soils requires measurements of the field‐saturated hydraulic conductivity (Kfs) and the matric flux potential corresponding to field saturation (ϕm). We develop analytical solutions for (1) early‐time, one‐dimensional infiltration into slowly permeable soils such as clay liners under the conditions of an initial constant head followed by a falling head phase and (2) steady state, three‐dimensional infiltration into permeable soils under the condition of steady state flow at a constant head followed by falling head conditions. Kfs and ϕm govern the shape of both solutions. The parameters are simultaneously identifiable, unique, and stable within the early‐time solution; however, there is a limited range in which the parameters of the steady state solution are unique. Laboratory and field experiments based on both solutions gave physically realistic best fit parameter values using the solutions in inversion procedures. Field measurements gave an excellent correlation between Kfs from steady state constant head and falling head techniques. The correlation between ϕm values was somewhat lower.