Green-Ampt One-Dimensional Infiltration from a Ponded Surface into a Heterogeneous Soil

Saturated hydraulic conductivity and wetting front pressure head (as soil properties) on an abrupt Green-Ampt front are assumed to increase and decrease with depth of a porous heterogeneous soil subject to a constant ponding or infiltration-evaporation depleted ponding on the surface. The corresponding Cauchy problem for a nonlinear ordinary differential equation describing the wetting front propagation in the soil profile is solved by computer algebra routines. Sensitivity of the cumulative infiltration to variation of hydraulic conductivity and capillarity is studied. A concave-convex infiltration graph is obtained for some values of parameters of the assumed exponential growth/decay of conductivity/capillarity. Texture of soil samples collected from a pedon is used for calculation of conductivity from a pedotransfer function. Synthesis of heterogeneity resulting in a specified front dynamics is discussed.     

Sensitivity Analysis of Soil Hydraulic Properties on Subsurface Water Flow in Furrows

Knowledge of the sensitivity of various soil hydraulic properties is beneficial for model development and application purposes. It can lead to better estimated values, better understanding, and thus reduced uncertainty. In the present study, an extensive sensitivity analysis was performed to investigate the effects that various soil hydraulic properties have on subsurface water flow below furrows during two successive irrigation events to see which irrigation event was more sensitive and to analyze the effect of spatial variations in the initial soil water contents within the soil profile. Testing the sensitivity of the various soil hydraulic parameters in the van Genuchten-Mualem expression was carried out using the HYDRUS-2D model for two irrigation events 10?days apart. Results showed that the first irrigation event was clearly more sensitive than the second one. The latter event was mainly associated with the nonuniformity of the initial soil water contents within the soil profile. Pressure heads in the soil profile were more sensitive than cumulative outlet fluxes and soil water contents. Sensitivity analysis results for pressure heads, cumulative fluxes, and water contents indicated that in every case the most sensitive parameter was the hydraulic property shape factor (n) followed by the saturated water content (θs), the saturated hydraulic conductivity (Ks), the residual water content (θr), and the shape factor in the soil water retention curve (α), with the pore-connectivity parameter (l) the least sensitive parameter during both irrigation events. Pressure head sensitivity analysis for all parameters studied showed that the least sensitivity was linked with the wetting front as it gradually moved deeper with time, and the highest sensitivity was observed in those regions where the initial soil water contents were lower. Similarly, for water contents, higher sensitivity occurred in the drier regions during the first irrigation event and near the moisture front in the second irrigation event. Both pressure heads and water contents showed some sensitivity near the soil surface during both irrigation events, suggesting the importance of evaporation from the soil surface.     

Effect of Wet-Dry Cycling on Swelling and Hydraulic Conductivity of GCLs

Atterberg limits, free swell, and hydraulic conductivity tests were conducted to assess how wet-dry cycling affects the plasticity and swell of bentonite, and the hydraulic conductivity of geosynthetic clay liners (GCLs) hydrated with deionized (DI) water (pH 6.5), tap water (pH 6.8), and 0.0125-M CaCl2 solution (pH 6.2). The plasticity of bentonite hydrated with DI water increased during each wetting cycle, whereas the plasticity of bentonite hydrated with tap water and CaCl2 decreased during each wetting cycle. Wet-dry cycling in DI water and tap water had little effect on swelling of the bentonite, even after seven wet-dry cycles. However, swelling decreased dramatically after two wetting cycles with CaCl2 solution. Hydraulic conductivity of GCL specimens remained low during the first four wetting cycles (～1 × 10?9 cm∕s). However, within five to eight cycles, the hydraulic conductivity of all specimens permeated with the 0.0125-M CaCl2 solution increased dramatically, to as high as 7.6 × 10?6 cm∕s. The hydraulic conductivity increased because cracks, formed during desiccation, did not fully heal when the bentonite rehydrated. In contrast, a specimen continuously permeated for 10 months with the 0.0125-M CaCl2 solution had low hydraulic conductivity (～1 × 10?9 cm∕s), even after eight pore volumes of flow.     

离子型稀土一维垂直入渗规律及最大粒径的影响试验研究

为了研究不同最大粒径离子型稀土土样对入渗规律的影响,利用自制的试验装置进行离子型稀土垂直入渗试验.水头高度恒定为 6 cm,土样最大粒径分别为 2.36 mm、1.18 mm、0.6 mm 和 0.3 mm. 在试验结果的基础上,利用改进的 Green-Ampt 模型分析离子型稀土入渗的饱和导水率和基质吸力. 结果表明,随着入渗时间的递增,累积入渗深度和湿润锋运移速率分别呈 “快速增加-缓慢发展 ”和 “快速减小-缓慢发展”的趋势.湿润锋运移速率与入渗时间之间满足幂函数关系,土样最大粒径对幂函数参数有较大影响.入渗率与湿润锋倒数之间具有良好的线性相关性.随着土样最大粒径的增加,饱和导水率和基质吸力也逐渐增加,二者与最大粒径之间呈指数函数关系.      

Experimental Validation and Applications of a Fluid Infiltration Model

Horizontal infiltration experiments were performed to validate a plug flow model that minimizes the number of parameters that must be measured. Water and silicone oil at three different viscosities were infiltrated into glass beads, desert alluvium, and silica powder. Experiments were also performed with negative inlet heads on air-dried silica powder, and with water and oil infiltrating into initially water moist silica powder. Comparisons between the data and model were favorable in most cases, with predictions usually within 40% of the measured data. The model is extended to a line source and small areal source at the ground surface to analytically predict the shape of two-dimensional wetting fronts. Furthermore, a plug flow model for constant flux infiltration agrees well with field data and suggests that the proposed model for a constant-head boundary condition can be effectively used to predict wetting front movement at heterogeneous field sites if averaged parameter values are used.     

Simulation of the St. Francis Dam-Break Flood

A two-dimensional (2D) simulation of flooding from the 1928 failure of St. Francis Dam in southern California is presented. The simulation algorithm solves shallow-water equations using a robust unstructured grid Godunov-type scheme designed for wetting and drying and achieves good results. Flood extent and flood travel time are predicted within 4 and 10% of observations, respectively. Representation of terrain by the mesh is identified as the dominant factor affecting accuracy, and an iterative process of mesh refinement and convergence checks is implemented to minimize errors. The most accurate predictions are achieved with a uniformly distributed Manning n = 0.02. A 50% increase in n increases travel time errors to 25% but has little effect on flood extent predictions. This highlights the challenge of a priori travel time prediction but robustness in flood extent prediction when topography is well resolved. Predictions show a combination of subcritical and supercritical flow regimes. The leading edge of the flood was supercritical in San Francisquito Canyon, but due to channel tortuosity, the wetting front reflected off canyon walls causing a transition to subcritical flow, considerably larger depths, and a standing wave in one particular reach that accounts for a 30% fluctuation in discharge. Elsewhere, oblique shocks locally increased flood depths. The 2D dam-break model is validated by its stability and accuracy, conservation properties, ability to calibrate with a physically realistic and simple resistance parametrization, and modest computational cost. Further, this study highlights the importance of a dynamic momentum balance for dam-break flood simulation.     

Effects of Electroosmosis on Natural Soil: Field Test

A unique configuration of horizontal sheet-like electrodes was used in the field at a site in Ohio that was underlain by silty clay glacial drift to induce electroosmotic flow and to characterize the effects of electroosmosis on soil properties (e.g., electrical conductivity and pH). The lower electrode was created at a depth of 2.2 m by filling a flat-lying hydraulic fracture with granular graphite, and the upper one was a metallic mesh placed at a depth of 0.4 m and covered with sand. The electrodes were attached to a DC power supply, creating an electrical gradient of 20–31 V∕m and a current of 42–57 A within approximately 20 m3 of soil. Total energy applied was 5,500 kW?h during approximate 4 months of operation. Electroosmotic flow rates of 0.6–0.8 L∕h were observed during tests lasting several weeks, although total flow rate (electroosmotic plus hydraulic) was strongly influenced by fluctuations of the ground-water table. The ratio of applied current to voltage decreased from 0.9 to 0.6 A∕V and was mainly due to a decrease in electrical conductivity of the soil. A low pH front developed at the anode and migrated toward the cathode. The velocity of the pH front per unit voltage gradient was 0.014 (cm∕day)/(V∕m). This was 40 times slower than what has been reported from laboratory experiments using kaolinite as a medium. These results confirm the feasibility of using horizontal electrodes at shallow depths, but they also underscore some important differences between the geochemical effects observed during field tests in natural soils and those seen in laboratory tests using ideal materials.     

Electrical impedance tomography of complex conductivity distributions with noncircular boundary

Electrical impedance tomography (EIT) uses low-frequency current and voltage measurements made on the boundary of a body to compute the conductivity distribution within the body. Since the permittivity distribution inside the body also contributes significantly to the measured voltages, the present reconstruction algorithm images complex conductivity distributions. A finite element model (FEM) is used to solve the forward problem, using a 6017-node mesh for a piecewise-linear potential distribution. The finite element solution using this mesh is compared with the analytical solution for a homogeneous field and a maximum error of 0.05% is observed in the voltage distribution. The boundary element method (BEM) is also used to generate the voltage data for inhomogeneous conductivity distributions inside regions with noncircular boundaries. An iterative reconstruction algorithm is described for approximating both the conductivity and permittivity distributions from this data. The results for an off-centered inhomogeneity showed a 35% improvement in contrast from that seen with only one iteration, for both the conductivity and the permittivity values. It is also shown that a significant improvement in images results from accurately modeling a noncircular boundary. Both static and difference images are distorted by assuming a circular boundary and the amount of distortion increases significantly as the boundary shape becomes more elliptical. For a homogeneous field in an elliptical body with axis ratio of 0.73, an image reconstructed assuming the boundary to be circular has an artifact at the center of the image with an error of 20%. This error increased to 37% when the axis ratio was 0.64. A reconstruction algorithm which used a mesh with the same axis ratio as the elliptical boundary reduced the error in the conductivity values to within 0.5% of the actual values.     

Comparison of Soil Hydraulic Property Measurement Methods

Unsaturated and saturated soil hydraulic properties were determined and compared for three sandy soils at adjacent field sites. Drying soil–water retention curves were measured on soil specimens using a pressure plate apparatus. Saturated hydraulic conductivities (Ks) were measured with a Guelph permeameter and falling head tests. Parameter optimization was used to simultaneously estimate the drying and wetting soil–water retention and hydraulic conductivity curves from cone permeameter and multistep inflow/outflow data. Ks values from all test methods were within an order of magnitude of each other at each site and, as expected, trended with bulk density. The Guelph permeameter generally yielded the highest Ks values. The soil–water retention curves were similar in shape, except for the cone permeameter curves, which had steeper slopes due to rapid flow of water into the soil. Relative hydraulic conductivity curves were similar in character to the soil–water retention curves. Each method provided important information about the soil hydraulic properties. No one method provided the entire range of information provided by all of the tests combined, and no one method was found to be superior to the others.     

Evaluation of Hopscotch Method for Transient Ground-Water Flow

The hopscotch finite-difference technique is shown to be a fast and accurate way to simulate transient, saturated, ground-water flow in relatively typical but heterogeneous 2D and 3D domains. The odd-even hopscotch (OEH) and line hopscotch methods are reviewed, and their implementation for saturated ground-water flow is presented. The OEH scheme, which is a second-order accurate explicit process, is efficient, requiring only six floating point operations per mesh node and time step, and is unconditionally stable (for saturated ground-water flow). Numerical experiments on typical 2D meshes (2,500 nodes) with synthetic, randomly heterogeneous hydraulic conductivity, suggest that the OEH process is approximately 1.5 times faster than the alternating direction implicit method and 3–4 times faster than the Crank-Nicolson implicit method using preconditioned conjugate gradient iteration. Similar experiments on medium-sized 3D meshes (87,500 nodes) suggest that the OEH process is between 7 and 10 times faster than the Crank-Nicolson preconditioned conjugate gradient method. Although the numerical results presented illustrate only typical test problem performance, they nevertheless clearly indicate promise for using OEH to simulate transient ground-water flow in 2D and, especially, 3D heterogeneous domains requiring fine spatial meshes.     

Formation of Secondary Containment Systems Using Permeation of Colloidal Silica

U.S. Environmental Protection Agency (USEPA) regulations require the capture of spills from liquid tanks containing hazardous chemicals by using a secondary containment system. Compacted clay or geomembrane liners are commonly used in secondary containment systems, but they are cumbersome when used in conjunction with existing liquid tanks because of pipeline networks surrounding the tanks. This study evaluates the formation of hydraulic barriers for secondary containment through the permeation of colloidal silica grout. A simplified infiltration model is presented to predict the downward movement of the colloidal silica grout into a soil layer, considering the time-dependent increase in dynamic viscosity of the colloidal silica for different concentrations of an electrolyte accelerator. Because the simplified infiltration model cannot predict the soil-grout interaction or the permeation of the colloidal silica by fingering, its results were calibrated by using the observations from a large-scale column test involving the permeation of colloidal silica into sand. The predicted position of the wetting front was found to match that of the experiment when the parameter governing the change in viscosity of the colloidal silica was increased by a factor of 30. The infiltration model calibrated with observations from column infiltration experiments provides a simple approach to the design of the secondary containment systems using permeation of colloidal silica.     

Unsaturated Soil Seepage Analysis Using a Rational Transformation Method with Under-Relaxation

The finite-element method provides a convenient and effective means for solving problems of seepage in unsaturated soils. However, convergence difficulties exist in numerical simulations of unsaturated flow analyses because of the high nonlinearity of the soil hydraulic properties. This technical note presents a combination approach consisting of a rational function transformation method and a common under-relaxation technique to solve the h-based form of Richards equation. Numerical studies show that this combined method can use a larger time step and corresponding oscillation-free mesh size to produce acceptable results and also converge to a stable solution quickly in each time step.     

Effect of Desiccation on Compacted Natural Clays

Specimens prepared from eight natural clayey soils used for clay liners and covers were subjected to cycles of wetting and drying. Volumetric shrinkage strains were recorded during drying. Specimens in which cracks formed during drying were subjected to hydraulic conductivity testing. Results of the study indicate that volumetric shrinkage strains are influenced by soil properties and compaction conditions. Volumetric shrinkage strain increased with increasing plasticity index and clay content, and as the compaction water content increased or decreased relative to optimum water content. Volumetric shrinkage strain decreased with increasing compactive effort. Specimens with the largest volumetric shrinkage strains typically contained the largest number of cracks. Hydraulic conductivity testing indicated that cracking of the specimens resulted in an increase in hydraulic conductivity, sometimes as large as three orders of magnitude.     

南方离子型稀土一维水平入渗规律试验研究

离子型稀土原地浸矿工艺中浸矿液入渗直接影响稀土资源的高效开采与利用.基于自制试验装置进行离子型稀土一维水平入渗试验,溶浸液选取3 %硫酸铵溶液,研究了4种不同粒径稀土的累积入渗长度、湿润锋运移速率、入渗率等变化规律.结果表明:随着入渗时间的递增,累计入渗长度呈先快速增加、后缓慢发展的趋势;湿润锋运移速率和入渗率先达到最大值、后快速减小再趋于稳定,湿润锋运移速率与时间之间的关系符合幂函数关系v=λ·t-0.5;土样饱和渗透系数为0.001 3~0.002 5 cm/min,其数值随着最大粒径增大而递增,研究结果有利于实现原地浸矿的科学化.      

Numerical Model for Analyzing Slug Tests in Vertical Cutoff Walls

Analysis of a slug test estimating the hydraulic conductivity of a vertical cutoff wall is complicated by the high compressibility of backfill materials and by the proximity of a well to the edge of the cutoff wall. An implicit finite-difference program, named Slug_3, was developed to analyze results of slug tests in the vertical cutoff wall. The program uses block-centered mesh formulation, considers variable hydraulic conductivity and specific storage, and has automatic time-step control and mesh generation. The geometry and flux-boundary condition in the well-intake section is fully considered, and the interface between a cutoff wall and natural soil formation is modeled as a constant head-boundary condition. Also, a filter cake can be simulated in Slug_3. Slug_3 is verified by comparing results with an analytical solution for a partially penetrating well in aquifers and another numerical code, MODFLOW-96, for a vertical cutoff wall. The program provides a new analytic tool for analyzing slug-test results from vertical cutoff walls and is unique in the ability to simulate variable hydraulic properties, which can be particularly important for highly compressible materials such as soil–bentonite backfill in a cutoff wall.     

Finite-Element Modeling of Floodplain Flow

A new methodology for a robust solution of the diffusive shallow water equations is proposed. The methodology splits the unknowns of the momentum and continuity equations into one kinematic and one parabolic component. The kinematic component is solved using the slope of the water level surface computed in the previous time-step and a zero-order approximation of the water head inside the mass-balance area around each node of the mesh. The parabolic component is found by applying a standard finite-element Galerkin procedure, where the source terms can be computed from the solution of the previous kinematic problem. A simple 1D case, with a known analytical solution, is used to test the accuracy of the model. A second test is performed by comparing, in a more complex case, the flow rates computed by the model with the flow rates directly estimated from the computed water heads. An application to a real 2D case of flood flow on a river floodplain shows the practical advantages of the methodology.     

Mathematical Formulation and Validation of a Mixed Finite Element–Finite Difference Model for Simulating Phreatic Surfaces

The phreatic surface in an unconfined aquifer exists as a movable interface between the saturated and unsaturated zones. The movement of the phreatic surface depends on recharge, hydraulic conductivity, porosity, and horizontal and vertical flows. The location of the phreatic surface helps define the variably saturated flow domain in the subsurface. The variably saturated flow process in the subsurface is described by a parabolic partial differential equation. In this equation, the hydraulic conductivity and soil moisture capacity are used as the subsurface characteristics. The location of the phreatic surface is governed by a first-order partial differential equation. The governing parabolic partial differential equation is solved using a variational finite element formulation. The first order phreatic surface equation is then solved by loosely coupling with the governing parabolic partial differential equation describing the variably saturated flow. In the present study, a two-dimensional space is used to investigate the movement of the phreatic surface in a variably saturated unconfined flow domain. Based on the time-varying solutions of hydraulic heads, the location of the phreatic surface is simulated in a finite two-dimensional space.     

Cartesian Cut Cell Two-Fluid Solver for Hydraulic Flow Problems

A two-fluid solver which can be applied to a variety of hydraulic flow problems has been developed. The scheme is based on the solution of the incompressible Euler equations for a variable density fluid system using the artificial compressibility method. The computational domain encompasses both water and air regions and the interface between the two fluids is treated as a contact discontinuity in the density field which is captured automatically as part of the solution using a high resolution Godunov-type scheme. A time-accurate solution has been achieved by using an implicit dual-time iteration technique. The complex geometry of the solid boundary arising in the real flow problems is represented using a novel Cartesian cut cell technique, which provides a boundary fitted mesh without the need for traditional mesh generation techniques. A number of test cases including the classical low amplitude sloshing tank and dam-break problems, as well as a collapsing water column hitting a downstream obstacle have been calculated using the present approach and the results compare very well with other theoretical and experimental results. Finally, a test case involving regular waves interacting with a sloping beach is also calculated to demonstrate the applicability of the method to real hydraulic problems.     

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.