Spatial Variability Of Hydraulic Parameters Research Articles

Reliability analysis of high core rockfill dam against seepage failure considering spatial variability of hydraulic parameters

Reliability analysis of high core rockfill dam against seepage failure considering spatial variability of hydraulic parameters

Seepage safety evaluation of high earth-rockfill dams considering spatial variability of hydraulic parameters via subset simulation

Seepage failure of high earth-rockfill dams have devastating consequences, and its safety analysis is of great importance in the design phase. However, the highest safety standards in high dams pose a challenge to the calculated efficiency of safety assessment. To address this problem, a random seepage safety assessment method which can consider the spatial variability of hydraulic parameters is proposed. Firstly, the spatial variability of the hydraulic parameters in the impervious materials is simulated using the covariance matrix decomposition under the framework of the non-intrusive finite element method. Then, according to the safety index of critical hydraulic gradient, the seepage stability formula is established to evaluate the safety state. Finally, considering that the highest safety standards in high dams make the probability of seepage hazard small (low failure probability event), it may require more than 10,000 deterministic calculations to complete the assessment process. Therefore, an efficient method based on subset simulation is proposed to optimize the computational efficiency. After the seepage safety evaluation of a 315 m high dam, the results show that the hydraulic conductivity of the core wall has the greatest influence on the seepage safety of the dam, and even under the influence of strong parameter spatial variability, its seepage failure probability is lower than 10-3. Compared with Monte Carlo simulation, the proposed method requires only 1/11 of the computation time at the 10-3 failure level. In addition, the results of grey relational analysis show that the coefficient of variation and correlation distance have obvious effects on seepage safety, and the autocorrelation distance has a greater effect.

Coupling non‐invasive imaging and reactive transport modeling to investigate water and oxygen dynamics in the root zone

AbstractOxygen (O2) availability in soils is vital for plant growth and productivity. The transport and consumption of O2 in the root zone is closely linked to soil moisture content, the spatial distribution of roots, as well as structure and heterogeneity of the surrounding soil. In this study, we measure three‐dimensional root system architecture and the spatiotemporal dynamics of soil moisture (θ) and O2 concentrations in the root zone of maize (Zea mays) via non‐invasive imaging, and then construct and parameterize a reactive transport model based on the experimental data. The combination of three non‐invasive imaging methods allowed for a direct comparison of simulation results with observations at high spatial and temporal resolution. In three different modeling scenarios, we investigated how the results obtained for different levels of conceptual complexity in the model were able to match measured θ and O2 concentration patterns. We found that the modeling scenario that considers heterogeneous soil structure and spatial variability of hydraulic parameters (permeability, porosity, and van Genuchten α and n), better reproduced the measured θ and O2 patterns relative to a simple model with a homogenous soil domain. The results from our combined imaging and modeling analysis reveal that experimental O2 and water dynamics can be reproduced quantitatively in a reactive transport model, and that O2 and water dynamics are best characterized when conditions unique to the specific system beyond the distribution of roots, such as soil structure and its effect on water saturation and macroscopic gas transport pathways, are considered.

Stochastic seepage analysis in embankment dams using different types of random fields

Random field theory has become a very popular approach for probabilistic analysis of earth dams. This study performs a stochastic analysis of seepage through an embankment dam to account for the spatial variability of hydraulic parameters. The originality of this study consists in using and comparing three types of Random Fields RFs for the seepage analysis: classical stationary RFs, conditional RFs (to consider the position of available measurements), and non-stationary RFs (to consider the mean variation with depth). The same sample of hydraulic conductivity values is considered to generate the three types of random fields. The hydraulic conductivity RFs are integrated into a Finite Element seepage analysis model to evaluate the flow velocity, hydraulic gradient, pore water pressure, and flow rate. The process is repeated by Monte Carlo simulations to characterize the spatial variability of the seepage results in terms of mean and standard deviation at each point of the studied dam and its foundation. The results show a higher dispersion for the stationary RF case and a lower dispersion for the conditional RF case. For the case study, the results also show that the use of different RFs for modelling the spatial variability of hydraulic conductivity induces differences that can be considered significant for flow velocity, moderate for hydraulic gradient and minor for pore pressure.

Probabilistic Risk Assessment of unsaturated Slope Failure Considering Spatial Variability of Hydraulic Parameters

Probabilistic risk assessment of slope failure evaluates the slope safety in a quantitative manner, which considers the failure probability and failure consequence simultaneously. However, risk assessment of unsaturated slope accounting for spatially variable soil-water characteristic curve (SWCC) model parameter and saturated hydraulic conductivity has been rarely reported. A probabilistic risk assessment approach is proposed in current study for rationally quantifying the unsaturated slope failure risk with the aid of Monte Carlo (MC) simulation. The SEEP/W and SLOPE/W modules contained in Geostudio software are applied to carry out deterministic analysis, where factor of safety (FS) of the unsaturated slope is calculated by Morgenstern–Price method. The spatially variable hydraulic parameters are characterized by their respective random fields that are transferred from the random void ratio field in this study, rather than generating them separately. The proposed approach is subsequently employed to an unsaturated slope example for exploring the influences of spatially variable void ratio. Results show that the unsaturated slope failure risk is considerably affected by the spatially variable void ratio, and the single exponential autocorrelation function (ACF) popularized in geotechnical engineering tends to underestimate the failure risk in the unsaturated slope risk assessment.

Reliability analysis of Unsaturated Slope Stability Considering Spatial Variability in Hydraulic Parameters

Reliability analysis of slope stability provides a rational framework for slope safety evaluation, which plays a key role in geotechnical decision making for landslide disaster prevention. However, previous studies mainly focused on the slope reliability analysis accounting for uncertainties in shear strength parameters. How to perform reliability analysis of unsaturated slope stability considering the spatial variability of hydraulic parameters remains an open question. This paper aims to systematically investigate the effects of spatial variability of hydraulic parameters on the unsaturated slope reliability. The random fields of hydraulic parameters are derived from the random void ratio field, instead of direct generation, for considering the spatial variability of hydraulic parameters in a rational manner. It is found that the coefficient of variation (COV) and scale of fluctuation (SOF) of void ratio affects the unsaturated slope failure probability significantly. Additionally, the failure probability is sensitive to the selection of auto-correlation function (ACF) in the unsaturated slope reliability analysis.

Impact of spatial variability in hydraulic parameters on plume migration within unsaturated surficial formations

Heterogeneities in textural properties of surficial formations at field scale result in spatial variations in hydraulic parameters governing unsaturated zone flow. This study aims at quantifying the influence of such variations on solute transport resulting from a localized source of radioactive contaminant at ground level.The study focuses on three hydraulic parameters related to the Mualem-van Genuchten formalism, namely the saturated hydraulic conductivity Ks, the parameter α inversely proportional to the air-entry value, and the parameter n related to the pore-size distribution. Sets of random fields accounting for spatial variability of these parameters are generated using lognormal distributions with different variances and correlation lengths. These random fields are used as inputs to an unsaturated flow and transport model to simulate radionuclide plume migration.Each simulated plume is characterized by its size (plume surface area), position (location of center of mass) and shape (elongation ratio) within the unsaturated zone. By comparison with the homogeneous medium, Ks-, α- and n-random fields generated with the mean variances computed through the analysis of a global soil database respectively result in average in (i) 25 (variable Ks), 20 (variable α) and 65% (variable n) increase in plume size; (ii) 0.8, 1 and 1.8 m horizontal offsets of the plume center; and (iii) 20, 30 and 50% decrease in plume circularity. In addition, changes in the variance values within one order of magnitude appear to have critical consequences only for the n parameter.The issue of spatial variability of hydraulic parameters is thus crucial for characterizing the evolution of pollutant plumes within an unsaturated zone and for developing better remediation strategies for industrial sites.

Seepage analysis of earth dams considering spatial variability of hydraulic parameters

To investigate the influence of spatial variability of hydraulic parameters on the flow in earth dams, saturated-unsaturated seepage is numerically simulated combining Monte Carlo simulation and random field theory. The van Genuchten model is adopted to represent soil-water characteristic curve (SWCC). The SWCC fitting parameters (a, n) and the saturated hydraulic conductivity parameter (ks) are considered as lognormal random fields. An approach of logarithmic translation is used for generating lognormal variables with lower limits greater than zero. The influence of the coefficient of variation (COV) and autocorrelation distance of hydraulic parameters on the flow rate is studied and compared. Sensitivity analysis indicates that the COVs of SWCC parameter n and saturated hydraulic conductivity ks have a larger effect on the flow rate than that of SWCC parameter a. A larger horizontal autocorrelation distance corresponds to a larger mean and COV of the flow rate. Neglecting the spatial variability of hydraulic parameters leads to overestimation of the mean and COV of the flow rate in earth dams, which could lead to conservative design of dams.

Assessing flow paths in a karst aquifer based on multiple dye tracing tests using stochastic simulation and the MODFLOW-CFP code

Karst systems show high spatial variability of hydraulic parameters over small distances and this makes their modeling a difficult task with several uncertainties. Interconnections of fractures have a major role on the transport of groundwater, but many of the stochastic methods in use do not have the capability to reproduce these complex structures. A methodology is presented for the quantification of tortuosity using the single normal equation simulation (SNESIM) algorithm and a groundwater flow model. A training image was produced based on the statistical parameters of fractures and then used in the simulation process. The SNESIM algorithm was used to generate 75 realizations of the four classes of fractures in a karst aquifer in Iran. The results from six dye tracing tests were used to assign hydraulic conductivity values to each class of fractures. In the next step, the MODFLOW-CFP and MODPATH codes were consecutively implemented to compute the groundwater flow paths. The 9,000 flow paths obtained from the MODPATH code were further analyzed to calculate the tortuosity factor. Finally, the hydraulic conductivity values calculated from the dye tracing experiments were refined using the actual flow paths of groundwater. The key outcomes of this research are: (1) a methodology for the quantification of tortuosity; (2) hydraulic conductivities, that are incorrectly estimated (biased low) with empirical equations that assume Darcian (laminar) flow with parallel rather than tortuous streamlines; and (3) an understanding of the scale-dependence and non-normal distributions of tortuosity.

Bulk velocity measurements by video analysis of dye tracer in a macro-rough channel

Steep mountain rivers have hydraulic and morphodynamic characteristics that hinder velocity measurements. The high spatial variability of hydraulic parameters, such as water depth (WD), river width and flow velocity, makes the choice of a representative cross-section to measure the velocity in detail challenging. Additionally, sediment transport and rapidly changing bed morphology exclude the utilization of standard and often intrusive velocity measurement techniques. The limited technical choices are further reduced in the presence of macro-roughness elements, such as large, relatively immobile boulders. Tracer tracking techniques are among the few reliable methods that can be used under these conditions to evaluate the mean flow velocity. However, most tracer tracking techniques calculate bulk flow velocities between two or more fixed cross-sections. In the presence of intense sediment transport resulting in an important temporal variability of the bed morphology, dead water zones may appear in the few selected measurement sections. Thus a technique based on the analysis of an entire channel reach is needed in this study. A dye tracer measurement technique in which a single camcorder visualizes a long flume reach is described and developed. This allows us to overcome the problem of the presence of dead water zones. To validate this video analysis technique, velocity measurements were carried out on a laboratory flume simulating a torrent, with a relatively gentle slope of 1.97% and without sediment transport, using several commonly used velocity measurement instruments. In the absence of boulders, salt injections, WD and ultrasonic velocity profiler measurements were carried out, along with dye injection technique. When boulders were present, dye tracer technique was validated only by comparison with salt tracer. Several video analysis techniques used to infer velocities were developed and compared, showing that dye tracking is a valid technique for bulk velocity measurements. RGB Euclidean distance was identified as being the best measure of the average flow velocity.

Investigating peat hydrological properties using field and laboratory methods: application to the Lanoraie peatland complex (southern Quebec, Canada)

AbstractFlow dynamics within a peatland are governed by hydraulic parameters such as hydraulic conductivity, dispersivity and specific yield, as well as by anisotropy and heterogeneity. The aim of this study is to investigate hydraulic parameters variability in peat through the use of different field and laboratory methods. An experimental site located in the Lanoraie peatland complex (southern Quebec, Canada) was used to test the different approaches. Slug and bail tests were performed in piezometer standpipes to investigate catotelm hydraulic conductivity. Combined Darcy tests and tracer experiments were conducted on cubic samples using the modified cube method (MCM) to assess catotelm hydraulic conductivity, anisotropy and dispersivity. A new laboratory method is proposed for assessing acrotelm hydraulic conductivity and gravity drainage using a laboratory experimental tank. Most of slug tests' recovery curves were characteristic of compressible media, and important variability was observed depending on the initial head difference. The Darcy experiments on cubic samples provided reproducible results, and anisotropy (Kh > Kv) was observed for most of samples. All tracer experiments displayed asymmetrical breakthrough curves, suggesting the presence of retardation and/or dual porosity. Hydraulic conductivity estimates performed using the experimental tank showed K variations over a factor of 44 within the upper 40 cm of the acrotelm. The results demonstrate that the intrinsic variability associated with the different field and laboratory methods is small compared with the spatial variability of hydraulic parameters. It is suggested that a comprehensive assessment of peat hydrological properties can be obtained through the combined use of complementary field and laboratory investigations. Copyright © 2007 John Wiley & Sons, Ltd.

Ergodicity of pumping tests

Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties with their constant counterparts averaged over the support volume of a test. Rigorous approaches for deriving representative (effective, apparent, upscaled, etc.) parameters employ either ensemble or spatial averaging. We derive a set of conditions under which these two paradigms yield identical results. We refer to them as conditions for the ergodicity of pumping tests. This allows one to use stochastic approaches to estimate the statistics of the spatial variability of hydraulic parameters on scales smaller than the support volume of a pumping test.

Modeling Two‐Dimensional Water Flow and Bromide Transport in a Heterogeneous Lignitic Mine Soil

Water and solute fluxes in lignitic mine soils and in many other soils are often highly heterogeneous. Here, heterogeneity reflects dumping‐induced inclined structures and embedded heterogeneous distributions of sediment mixtures and of lignitic fragments. Such two‐scale heterogeneity effects may be analyzed through the application of two‐dimensional models for calculating water and solute fluxes. The objective of this study was to gain more insight to what extent spatial heterogeneity of soil hydraulic parameters contributes to preferential flow at a lignitic mine soil. The simulations pertained to the “Bärenbrücker Höhe” site in Germany where previously water fluxes and applied tracers had been monitored with a cell lysimeter, and from where a soil block had been excavated for detailed two‐dimensional characterization of the hydraulic parameters using pedotransfer functions. Based on those previous studies, scenarios with different distributions of hydraulic parameters were simulated. The results show that spatial variability of hydraulic parameters alone can hardly explain the observed flow patterns. The measured bromide distributions both in the leachate and the residual concentrations in the soil could not be described at all. Consequently, the observed preferential flow at the site was probably caused by additional factors such as hydrophobicity, the presence of root channels, anisotropy in the hydraulic conductivity, and heterogeneous root distributions. To study the relative importance of these other factors by applying two‐dimensional flow models to such sites, the experimental database must be improved, especially with regard to the effects of hydrophobicity and the impacts of high‐root‐density zones. Single‐continuum model approaches may be insufficient for such sites.

Constant Rate Rainfall Infiltration in a Field of Variable α

Spatial variability of hydraulic parameters is an important factor in prediction of water flow and solute transport in unsaturated soils. An analytical solution for one‐dimensional constant rate rainfall infiltration in a homogeneous soil is incorporated into a model of a spatially variable field. The model is a composite of vertically homogeneous soil columns that differ in their hydraulic properties. In this study, horizontal variation in infiltration profiles is due to variation in the inverse macroscopic capillary length (α) of each column. The sill in travel time variance of wetting profiles with depth for the homogeneous column confirms the notion of a long‐time traveling wave of fixed shape. Variation in α slightly enhances the spread of wetting profiles and delays formation of the traveling wave. Identification of the mean α value is more critical than inclusion of variability in α for wetting profile simulations under the examined conditions.