Steady-state Unsaturated Flow Research Articles

Three-dimensional tunnel face stability considering the steady-state seepage in saturated and unsaturated regions with changing water levels

For tunnels excavated in the unsaturated soils with changing water levels, there may be steady-state unsaturated flow above the water table and saturated flow below the water table toward the tunnel face due to the excavation. Changing water levels affect the adverse effect of the underwater saturated flow and the contribution of the unsaturated flow to the shear strength. To figure out the regularity concerning the region and magnitude of unsaturated and saturated flow effects, an analytical framework is developed within the kinematic approach of limit analysis combined with the numerical simulation. A suction stress-based equation is employed to express the contribution of unsaturated flow to shear strength. The development of the saturated flow below the water table is numerically simulated, and the resulting pore pressure distribution is extracted and interpolated on a 3D discrete rotational failure mechanism. The work rate balance equation incorporating the apparent cohesion due to unsaturated flow and the pore pressure affected by the saturated flow is established to optimize the critical face pressure. The proposed analytical framework is verified by comparisons with previous literature and numerical simulations of hydromechanical analysis. A parametric analysis is conducted to investigate the effect of groundwater levels, flow types, unsaturated properties, and hydraulic hysteresis on the tunnel face stability. The results show that it is only necessary to consider the effect of unsaturated flow and the differences caused by various unsaturated characteristics when the unsaturated zone is large enough. This work can provide a good reference for the design of face supports in the initial stage for tunnels excavated in unsaturated soils with changing groundwater levels.

Comparative performance of multiple linear regression and artificial neural network models in estimating solute-transport parameters

Indirect estimate of solute-transport parameters through pedo-transfer functions (PTFs) is becoming important due to expensive and time-consuming direct measurement of the parameters for a large number of soils and solutes. This study evaluated the relative performance of PTFs of multiple linear regression (MLR) and Artificial Neural Network (ANN) models in predicting velocity (<em>V</em>), dispersion coefficient (<em>D</em>) and retardation factor (<em>R</em>) of CaCl<sub>2</sub>, NaAsO<sub>2</sub>, Cd(NO<sub>3</sub>)<sub>2</sub>, Pb(NO<sub>3</sub>)<sub>2</sub> and C<sub>9</sub>H<sub>9</sub>N<sub>3</sub>O<sub>2</sub> (carbendazim) in five agricultural soils. <em>V</em>, <em>D</em> and <em>R</em> of the solutes were determined in repacked soil columns under steady-state unsaturated water flow conditions. Textural class, particle size distribution, bulk density, organic carbon, relative pH, clay%, grain size, and uniformity coefficient of the soils were determined. MLR and ANN models were calibrated with the measured data of four soils and verified for another soil. Root-Mean Square Error (RMSE) is significantly smaller (0.015) and modelling efficiency (EF) is significantly larger (0.999) for ANN model than those (0.096 and 0.954, respectively) for MLR model. Negative Mean Absolute Error (MAE) (-0.0002) of MLR model indicates overestimation, while positive MAE (0.00003) of ANN model indicates minimal underestimation. The ANN model is less biased than the MLR model during prediction. Thus, the ANN model can significantly enhance pollution transport prediction through soils with good accuracy.

Failure potential of a circular tunnel face under steady-state unsaturated flow condition

In natural geotechnical structures, especially for those in the vicinity of water bodies or subjected to rainfalls, the soil properties are more likely governed by the unsaturated soil constitutive model rather than the fully saturated or dry one. In this contribution, the theory of unsaturated soil mechanics is introduced to tackle the stability problem of a circular tunnel face under steady-state unsaturated flow condition. By making reference to the existing findings, a generalized analytical solution for the vertical suction stress profile is discussed which permits to deal with unsaturated soil problems with the classical limit analysis method. An extended Mohr-Coulomb yield criterion is presented to characterize the tunnel face failure in unsaturated soil where the effect of suction stress on tunnel face stability is interpreted as the apparent cohesion. The increase in shear strength of unsaturated soil due to the existing of apparent cohesion is considered as a combined effect of n, α, ks and q, which respectively correspond to the pore size parameter, the inverse of air entry value (AEV), the saturated hydraulic conductivity and the flow rate. Within the framework of limit analysis, an advanced three-dimensional (3D) failure mechanism is used to include the unsaturated shear strength parameters into the work rate equation which eventually yields the critical retaining pressure for tunnel face stability. Parametric analysis is performed to show the influence of different unsaturated soil parameters on tunnel face stability. Four representative soil types are investigated to give some suggestions for tunnel excavations and designs in unsaturated soil.

Colloid Transport in Aggregated Porous Media with Intra- and Interaggregate Porosities

Column tracer and colloid transport experiments were performed under both saturated and unsaturated steady state flow conditions in an aggregated porous medium with a bimodal pore size distribution (PSD): intra-aggregate porosity with a pore radius between 10–2 and 10–1 μm and interaggregate porosity ranged between 101 and 103 μm (interporosity). All experiments were carried out under unfavorable conditions for physicochemical attachment to solid–water interfaces, using negatively charged porous media and latex microspheres (1 μm). Both porous media and colloids used in this work were hydrophobic. The results obtained through experimental observations and numerical simulations in the aggregated medium were confronted with those obtained for a sandy medium, characterized by a narrow unimodal PSD with a pore radius which ranged between 101 and 102 μm (interporosity), to explore the relative importance of the PSD on water flow, colloid transport, and deposition. Physicochemical interactions between colloids ...

The role of interfacial tension in colloid retention and remobilization during two-phase flow in a polydimethylsiloxane micro-model

The work presented here consisted of steady-state and transient two-phase flow experiments on the role of interfacial tension in colloid transport. Experiments were performed in a polydimethylsiloxane (PDMS) micro-model containing a network of pores with a mean pore size of 30µm. The flow network covered an area of 1mm×10mm. Water and Fluorinert FC43 were used as the two immiscible liquids. Since PDMS is a hydrophobic material, Fluorinert was the wetting phase, and water was the non-wetting phase in this micro-model. The interfacial tension was changed by adding a Fluorinert-soluble surfactant into Fluorinert FC43 to change the interfacial tension from 55mN/m to 30mN/m. The colloids were fluorescent carboxylate-modified polystyrene microspheres and 300nm in diameter. We directly observed colloid movement using confocal microscopy. We also obtained colloid concentration breakthrough curves by measuring the fluorescent intensities in the outlet of the micro-model.The breakthrough curves showed that during steady-state unsaturated flow, fewer colloids were retained in the system when interfacial tension was lower. During transient flow, more colloids were remobilized by the moving Fluorinert-water interfaces (FWIs) and Fluorinert-water-solid contact lines (FWSCs) under high interfacial tension. Visualization results showed that, at low interfacial tension, the fluid-fluid interfaces were almost flat; thus, less interfacial area was available for colloid attachment.Generally, confocal images and measured breakthrough curves clearly demonstrate the effect of interfacial tension on colloid retention and remobilization.

Using Analytic Solution Methods on Unsaturated Seepage Flow Computations

This paper describes a change of variables applied to Richards’ equation for steady-state unsaturated seepage flow that makes the numerical representation of the new version of this highly nonlinear partial differential equation (PDE) much easier to solve, and the solution is significantly more accurate. The method is applied to two-dimensional unsaturated steady-state flow in a block of soil that is initially very dry until water is applied at the top. Both a quasi-linear version of relative hydraulic conductivity for which an analytic solution exists and a van Genuchten version of relative hydraulic conductivity are numerically solved using the original and new versions of the governing PDE. Finally, results of this research will be presented in this paper. It was found that for the test problem, the change-of-variables version of the governing PDE was significantly easier to solve and resulted in more accurate solutions than the original version of the PDE.

Estimating hysteresis in the soil water retention curve from monolith experiments

Water movement in unsaturated soils is commonly affected by hysteresis, a phenomenon often ignored as to keep the mathematical description of water flow and solute transport simple. In this study, the importance of hysteresis was quantified at lysimeter scale on two Belgian soils, a loamy and a sandy loam soil. Undisturbed soil monoliths (79cm diameter by 105cm height) were collected in each soil and the flow studied for various boundary conditions. Each monolith was equipped with different measuring devices to monitor online soil water content, pressure head, and outlet water fluxes. Four unsaturated steady state flow experiments were conducted on each monolith. Hydraulic properties were obtained by inverting the governing flow equation of Richards, using a global multilevel coordinate search inversion algorithm. Measured soil water contents, pressure heads, and outlet water fluxes were used in the objective function. First soil hydraulic parameters in the retention and hydraulic conductivity functions were estimated neglecting hysteresis and compared with the functions obtained using approaches considering hysteresis in their analysis. Hysteresis was incorporated in the retention curve using the simple empirical model proposed by Scott et al. (1983) and using the universal conceptual model of Mualem (1977). Hysteresis in both soils was characterized by a relative large difference between the main drying and wetting soil water retention curves. However, results showed that the effect of hysteresis was different on various components of water flow in the two studied soils. The Scott's model considerably improved pressure head estimates in the loamy soil and Mualem's model somewhat improved the soil water content estimates in the sandy loam soil. Outlet water fluxes in both soils were less sensitive to hysteresis. In general, the simple hysteretic model of Scott was more successful in studying hysteresis in both studied soils.

Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach

This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84].

Correction to “Explicit analytical solutions for one‐dimensional steady state flow in layered, heterogeneous unsaturated soils under random boundary conditions”

[1] In this study, we directly derive first-order analytical solutions to the pressure head moments (mean and variance) for one-dimensional steady state unsaturated flow in randomly heterogeneous layered soil columns under various random boundary conditions. We assume that the constitutive relation between the unsaturated hydraulic conductivity and the pressure head follows an exponential model, and treat the saturated hydraulic conductivity Ks as a random function and the pore size distribution parameter α as a random constant. Unlike the solution given in Lu and Zhang (2004) in which Kirchhoff transformation was used and the solution to pressure head variance was presented as a function of (cross-)covariances related to the intermediate, Kirchhoff-transformed variable, the solution to the pressure head variance presented in this paper is an explicit function of the input variabilities. In addition, we also give analytical solutions to the statistics of the unsaturated hydraulic conductivity and the effective water content. These first-order analytical solutions are compared with those from Monte Carlo simulations. We also investigated the effect of uncertain boundary conditions, the relative contribution of input variabilities to the head variance, and the possible errors introduced by treating the correlated α field as a random constant in the analytical solutions. The results indicate that the uncertain constant head at the bottom of a deep soil column may not have a significant effect on predicting flow statistics in the upper portion of the column. Furthermore, it is found that treating α as a random constant is justified when the correlation length of α is relatively large as compared to the layer thickness.

Potassium leaching in undisturbed soil cores following surface applications of gypsum

Displacement studies on leaching of potassium (K+) were conducted under unsaturated steady state flow conditions in nine undisturbed soil columns (15.5 cm in diameter and 25 cm long). Pulses of K+ applied to columns of undisturbed soil were leached with distilled water or calcium chloride (CaCl2) at a rate of 18 mm h−1. The movement of K+ in gypsum treated soil leached with distilled water was at a similar rate to that of the untreated soil leached with 15 mM CaCl2. The Ca2+ concentrations in the leachates were about 15 mM, the expected values for the dissolution of the gypsum. When applied K+ was displaced with the distilled water, K+ was retained in the top 10–12.5 cm depth of soil. In the undisturbed soil cores there is possibility of preferential flow and lack of K+ sorption. The application of gypsum and CaCl2 in the reclamation of sodic soils would be expected to leach K+ from soils. It can also be concluded that the use of sources of water for irrigation which have a high Ca2+ concentration can also lead to leaching of K+ from soil. Average effluent concentration of K+ during leaching period was 30.2 and 28.6 mg l−1 for the gypsum and CaCl2 treated soils, respectively. These concentrations are greater than the recommended guideline of the World Health Organisation (12 mg K+ l−1).

Virus Transport during Infiltration of a Wetting Front into Initially Unsaturated Sand Columns

We investigated the effect of different flow conditions on the transport of bacteriophage phiX174 in Memphis aquifer sand. Virus transport associated with a wetting front moving into an initially unsaturated horizontal sand column was experimentally compared with that observed under steady-state saturated vertical flow. Results obtained by sectioning the sand columns showthattotal (retained and free) resident virus concentrations decreased approximately exponentially with the travel distance. The rate of decline was similar under both transient unsaturated flow and steady-state saturated flow conditions. Total resident virus concentrations near the inlet were an order of magnitude greater than the virus concentration of the influent solution in both experiments, indicating continuous virus sorption during flow through this zone. Virus retardation was quantified using the ratio of the centroids of the relative saturation and virus concentration versus relative distance functions. The mean retardation factors were 6.43 (coefficient of variation, CV = 14.4%) and 8.22 (CV = 8.22%) for the transient unsaturated and steady-state saturated flow experiments, respectively. Attest indicated no significant difference between these values at P < 0.05. Air-water and air-water-solid interfaces are thought to enhance virus inactivation and sorption to solid particles. The similar retardation factors obtained may be attributable to the reduced presence of these interfaces in the two flow systems investigated as compared to steady-state unsaturated flow experiments in which these interfaces occur throughout the entire column.

Explicit analytical solutions for one‐dimensional steady state flow in layered, heterogeneous unsaturated soils under random boundary conditions

In this study, we directly derive first‐order analytical solutions to the pressure head moments (mean and variance) for one‐dimensional steady state unsaturated flow in randomly heterogeneous layered soil columns under various random boundary conditions. We assume that the constitutive relation between the unsaturated hydraulic conductivity and the pressure head follows an exponential model, and treat the saturated hydraulic conductivity Ks as a random function and the pore size distribution parameter α as a random constant. Unlike the solution given in Lu and Zhang (2004) in which Kirchhoff transformation was used and the solution to pressure head variance was presented as a function of (cross‐)covariances related to the intermediate, Kirchhoff‐transformed variable, the solution to the pressure head variance presented in this paper is an explicit function of the input variabilities. In addition, we also give analytical solutions to the statistics of the unsaturated hydraulic conductivity and the effective water content. These first‐order analytical solutions are compared with those from Monte Carlo simulations. We also investigated the effect of uncertain boundary conditions, the relative contribution of input variabilities to the head variance, and the possible errors introduced by treating the correlated α field as a random constant in the analytical solutions. The results indicate that the uncertain constant head at the bottom of a deep soil column may not have a significant effect on predicting flow statistics in the upper portion of the column. Furthermore, it is found that treating α as a random constant is justified when the correlation length of α is relatively large as compared to the layer thickness.

Impact of rainfall intensity on the transport of two herbicides in undisturbed grassed filter strip soil cores

Two series of displacement experiments with isoproturon and metribuzin herbicides were performed on two undisturbed grassed filter strip soil cores, under unsaturated steady-state flow conditions. Several rainfall intensities (0.070, 0.147, 0.161, 0.308 and 0.326 cm h − 1 ) were used. A water tracer (bromide) was simultaneously injected in each displacement experiment. A descriptive analysis of experimental breakthrough curves of bromide and herbicides combined with a modeling analysis showed an impact of rainfall intensity on the solute transport. Two contrasting physical non-equilibrium transport processes occurred. Multiple (three) porosity domains contributed to flow at the highest rainfall intensities, including preferential flow through macropore pathways. Macropores were not active any longer at intermediate and lowest velocities, and the observed preferential transport was described using dual-porosity-type models with a zero or low flow in the matrix domain. Chemical non-equilibrium transport of herbicides was found at all rainfall intensities. Significantly higher estimated values of degradation rate parameters as compared to batch data were correlated with the degree of non-equilibrium sorption. Experimental breakthrough curves were analyzed using different physical and chemical equilibrium and non-equilibrium transport models: convective–dispersive model (CDE), dual-porosity model (MIM), dual-permeability model (DP), triple-porosity, dual permeability model (DP-MIM); each combined with both chemical instantaneous and kinetic sorption.

Remobilization of Americium in calcareous soil columns under experimental rhizospheric conditions

The biogeochemical behaviour of americium in subsurface soils plays a dominant role on its potential migration, but is currently poorly known. This research investigates the relevant processes controlling americium biogeochemical speciation in the rhizosphere of an agricultural soil. Lixiviation tests were performed on columns packed with a calcareous soil contaminated with 241 Am, under steady-state unsaturated or saturated hydric flow conditions. The columns were percolated with various soil solutions, containing citrate and/or glucose to simulate root exudates. The bio-physico-chemical parameters of the outlet solutions were monitored continuously. The percolation of a solution in equilibrium with the soil or containing low exudate concentrations (10 -4 M) released less than 5 mBq/cm 3 of americium. Poor remobilisations were also observed when injecting 10 -2 M glucose solutions, despite effective glucose microbial degradation, production of secondary ligands, and important chemical changes. On the contrary, percolation of 10 -2 M citrate solution released 1000 times more americium, in accordance with previous studies. 10000 times greater releases were observed when glucose was added to citrate at 10 -2 M. The remobilisation of americium resulting from both dissolution of calcite and iron oxides, and complexation by citrate, as well as the applicability of simple parameterisation of partition coefficient are discussed.

Stochastic simulations of steady state unsaturated flow in a three-layer, heterogeneous, dual continuum model of fractured rock

Unsaturated flow through fractured rocks is a concern in the siting and performance of waste disposal facilities such as the proposed geological repository at Yucca Mountain, Nevada. We simulated a small two-dimensional cross-section of welded volcanic tuff, representative of Yucca Mountain stratigraphy, using spatially correlated, randomly heterogeneous fracture permeability fields and homogeneous matrix permeability continua representing various degrees of welding. Ten realizations each of fracture permeability fields for four different variances ( σ 2=0.5, 1.0, 1.5, and 2.0) were generated by the direct Fourier transform method (Robin, M.J.L., Gutjahr, A.L., Sudicky, E.A., Wilson, J.L., 1993. Cross-correlated random field generation with the direct Fourier transform method, Water Resour. Res. 29(7)2385–2398) independently for the welded Tiva Canyon Tuff (TCw), the non-welded Paintbrush Tuff (PTn), and the welded Topopah Spring Tuff (TSw), the latter being the proposed primary repository horizon. Numerical simulations were run for steady state flow at three different uniform water flux boundary conditions. Boundary conditions along the sides were impermeable and the base was open to gas and liquid flow. Numerical simulations were performed using the dual-continuum, two-phase flow simulator METRA, which represents matrix and fractures as dual overlapping continua, where liquid flux between continua can be restricted by a uniform factor. Fracture–matrix interaction was modeled as being less restricted in the PTn as compared to the TCw/TSw. Heterogeneous fracture permeability fields generated strong preferential flow in the TCw/TSw fracture continuum and significant preferential flow in the uniformly permeable, PTn matrix continuum. Flow focusing led to a local increase in saturation, which in turn increased relative permeability to water along the preferential pathways, causing water to flow faster. The development of the preferential pathways reduced the wetted surface area for fracture–matrix interaction leaving a large volume of the rock isolated from the preferential flow pathways. Statistical analysis of water flux values in the three units showed that the magnitude of the ensemble variance, indicating preferential flow pathways, increased with both the variance of fracture permeability and the water flux boundary condition, reaching a plateau in the TCw/TSw fracture continuum units after flowing approximately 10 correlation scales of the vertical fracture permeability. Ensemble covariance of water flux normal to the layering revealed long range correlations in all units, which is longer than the correlation length of the fracture permeability fields. This suggests that the water flux boundary condition influences preferential flow in unsaturated dual continua media. These results suggest that careful analysis of information on fracture permeability variability obtained from pneumatic and hydraulic tests is an important component in understanding deep percolation processes.

Quantitative indices to characterize the extent of preferential flow in soils

Mathematical calculations or physical measurements to evaluate the extent of preferential solute transport or quantitatively distinguish the contribution of different transport processes are lacking in literature. Displacement studies on leaching of bromide and two pesticides were conducted under unsaturated steady state flow conditions in 24 undisturbed soil columns collected each from the two sites differing in soil structure and organic carbon content. The breakthrough curves (BTCs), developed using the leachate data of all individual columns, exhibited different shapes including some with early breakthrough and increased tailing which qualitatively indicates the presence of preferential flow. Transport parameters of bromide BTCs fitted to the convection-dispersion equation and a non-equilibrium two-region model were determined using the program CXTFIT and also by time moment method. Using these parameters and the time moments of BTCs of non-preferential and preferential flow columns (PFCs), the contribution of mechanisms other than hydrodynamic dispersion and two-region effect to the overall variance of PFCs was evaluated. The results indicated that the respective values of 0.5 and 1.0 for the first normalized moment ( μ 1′) and skewness (S) of bromide BTCs could be used as reference indices to denote the extent of preferential flow. An integrated parameter, PFSP, defined as the ratio of variance due to preferential flow vis-a-vis variance caused by hydrodynamic dispersion and two region effect, has been proposed to ascertain or compare the risk of preferential flow in soils. Though the transport parameters, temporal moments and PFSP were significantly correlated for all types of columns, these were not notably related with any soil property.

Analytic Element Modeling of Cylindrical Drains and Cylindrical Inhomogeneities in Steady Two-Dimensional Unsaturated Flow

The analytic element method, first developed for modeling flow in saturated porous media, is adapted to the solution of the governing equation for steady flow in unsaturated porous media. The governing equation for steady-state unsaturated flow is made amenable to analytic element solution through transformation with the Kirchhoff integral, representation of the hydraulic conductivity by an exponential function of the pressure head, and use of a coordinate transformation. A number of analytic elements are available for the resulting modified Helmholtz equation; analytic element equations are presented for uniform flow, cylindrical drains, and cylindrical inhomogeneities. The analytic element solution allows for the analytic evaluation of the pressure head, saturation, and Darcy flux at any point in the vadose zone. The applicability of the analytic element method to simulate unsaturated flow is demonstrated by solving for several cases of steady flow in a region containing arbitrarily located cylindrical inhomogeneities, and for flow in a region containing one cylindrical inhomogeneity and two cylindrical drains.

Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation

In this study, we derive analytical solutions of the first two moments (mean and variance) of pressure head for one-dimensional steady state unsaturated flow in a randomly heterogeneous layered soil column under random boundary conditions. We first linearize the steady state unsaturated flow equations by Kirchhoff transformation and solve the moments of the transformed variable up to second order in terms of σ Y and σ β , the standard deviations of log hydraulic conductivity Y=ln( K s) and of the log pore size distribution parameter β=ln( α). In addition, we also give solutions for the mean and variance of the unsaturated hydraulic conductivity. The analytical solutions of moment equations are validated via Monte Carlo simulations.

Suction Profiles and Scale Factors for Unsaturated Flow Under Increased Gravitational Field

Scale factors for centrifuge modelling have been traditionally defined using dimensional analysis concepts. This is the case, for example, of centrifuge modelling of unsaturated water flow. However, scale factors governing suction, discharge velocity, and time obtained using dimensional analysis have often differed from those obtained from methodologies not based on dimensionless groups. In this paper, a consistent framework is developed for analytic determination of suction profiles for steady-state unsaturated flow under both natural and increased gravitational fields. This framework allows deduction of the scale factors, which emerge from direct comparison of the analytic solutions for model and prototype without the need to use dimensionless groups. For centrifuge conditions leading to an approximately uniform acceleration field, the suction profile in the prototype is found to be the same as that in the model, while the discharge velocity is found to be properly scaled by 1/ N and time by N 2 , where N is the average acceleration ratio between model and prototype. If acceleration field is not uniform, the scale factors should be defined as a function of the centrifuge radius and model length. In addition, evaluation of the effect of different test conditions allows identification of the suction profiles and test setup best suited for hydraulic conductivity determination using centrifuge techniques.

Flow Focusing in Unsaturated Fracture Networks: A Numerical Investigation

A numerical modeling study is presented to investigate flow–focusing phenomena in a large‐scale fracture network, constructed using field data collected from the unsaturated zone of Yucca Mountain, Nevada, the proposed repository site for high‐level nuclear waste. The two‐dimensional fracture network for an area of 100 by 150 m contains more than 20000 fractures. Steady state unsaturated flow in the fracture network is investigated for different boundary conditions and rock properties. Simulation results indicate that flow paths are generally vertical, and that horizontal fractures mainly provide pathways between neighboring vertical paths. In addition to fracture properties, flow–focusing phenomena are also affected by rock–matrix permeability, with lower matrix permeability leading to a high degree of flow focusing. The simulation results further indicate that the average spacing between flow paths in a layered system tends to increase and flow tends to become more focused, with depth.