A parsimonious approach for large-scale tracer test interpretation

Hydrogeology Journal - Dye tracing is an efficient method for spring watershed delineation, but is also used in surface waters to assess pollution migration over several kilometers. The aim of this...     

A practical approach for the interpretation of flowing well tests

Flowing well test is one of the tools employed to identify transmissivity and storage coefficient of a confined aquifer where the potentiometric surface is located above the ground surface, so that the groundwater flows naturally from the well without pumping. During a flowing well test, constant hydraulic head is preserved at the well while the discharge from the well decreases with time and the temporal variation of discharge provides significant information about aquifer characteristics. In this study, a simple and straightforward approach is presented as an alternative to a number of graphical or error minimization-based techniques available in the literature for analyzing data from flowing well tests. The proposed method employs a polynomial regression equation to establish a link between observed discharge and the theoretical dimensionless discharge that is introduced in the analytical solution, so as to retrieve the aquifer parameters. The method is tested with a vast number of synthetically generated data sets as well as a real data set reported in the literature. Besides its simplicity, the present method is seen to produce highly accurate and reliable estimations.     

A natural-gradient field tracer test for evaluation of pollutant-transport parameters in a porous-medium aquifer

This paper describes a natural-gradient field tracer test to characterise solute-transport properties in a sand and gravel aquifer in the Hebei Province, northern China. Some laboratory-scale column tests on aquifer material and a local-scale field borehole-dilution test have been conducted previously, but the field test reported herein represents the only large-scale tracer test in the aquifer, which is the sole water supply to the city of Shi Jiazhuang and which is threatened by urban pollution. The aim of the study was to quantify the transport behaviour of nonreactive pollutants in this aquifer. Little quantitative data are available concerning its solute-transport properties; thus, the results of the tracer test are significant and critical for understanding pollutant transport and fate. The in-situ tracer test was carried out in the aquifer using a slug injection of the geochemically conservative, radioactive iodine tracer ¹³¹I. The longitudinal (α _L ) and transverse (α _T ) hydrodynamic dispersivities for solute transport in the field are 1.72 and 0.0013 m, respectively. The ratio of longitudinal dispersivity α _L and the flow length at the field scale is 1:10. The ratio between α _L and α _T from the in-situ test (~1,300:1) demonstrates a dominant longitudinal dispersion in this fluvial sand and gravel aquifer. The tracer test further indicates a relatively short transit time for the aquifer (linear velocities ~13 m/d) under natural-gradient conditions. Electronic Publication     

Field tracer test for denitrification in a pyrite-bearing schist aquifer

A small-scale artificial tracer test performed on a schist aquifer in Brittany has helped clarify mechanisms and kinetics of in situ autotrophic denitrification. NO₃ was injected as a pulse simultaneously with a conservative tracer -Br⁻. During the test, which lasted 210 h, 73% of the injected Br⁻ was recovered, as against only 47% of the NO₃. The 26% difference in the recovery of the two injected species is interpreted as being the result of denitrification, in part due to the direct oxidation of pyrite present in the solid aquifer according to the reaction: 5FeS₂+14NO₃⁻+4H⁺→7N₂+10SO₄²⁻+5Fe²⁺+2H₂O, and in part due to subsequent iron oxidation according to the reaction: NO₃⁻+5Fe²⁺+6H⁺→1/2N₂+5Fe³⁺+3H₂O. Despite the potential increase in SO₄ and Fe resulting from denitrification through pyrite oxidation, the concentrations of these elements in the groundwater remain moderate due to the precipitation of minerals such as jarosite and/or natroalunite. Tracer transfer takes place in a heterogeneous medium which, according to the breakthrough curves, can be simplified to a dual-porosity aquifer comprising a high-permeability (fractures or large fissures) medium of low porosity from which only minor denitrification of circulating NO₃-bearing water was observed and a low-permeability (small fissures) medium of high porosity which induces a higher denitrification rate in the circulating NO₃-bearing water. The kinetics of the denitrification reaction are high compared with results obtained for other environments and can be described by a first-order model with a half life of 7.9 days for the low-porosity medium and only 2.1 days for the high-porosity medium.     

A geometric approach to two-dimensional finite strain compatibility: interpretation and review

The purpose of this paper is to collect, clarify, augment and modify the authors' previous work on the subject of finite strain compatibility. The derivations of the fundamental equations are reviewed so that the geometric meaning of each step can be explained. Besides providing a basis for the geological interpretations of the equations, these derivations also lead to a useful new form of the strain compatibility equations.We begin by showing that compatibility is a geometric property of continuous and smooth coordinate grids, and we derive and explain the coordinate grid compatibility equations. We then use the fact that every finite deformation may be described by two coordinate grids to derive finite strain compatibility equations in principal coordinates and Cartesian coordinates. The resulting strain compatibility equations are not easily solved for general strain fields in any coordinate system. Nonetheless, we show that many common geological strain patterns have simple geometries for which the compatibility equations can be interpreted. For example, if a deformation has constant strain in one direction, as most shear zones do, then compatibility provides an iterative method for determining the strain throughout the deformed region if the strain is initially known at any one point. Some of the other strain geometries to which we apply compatibility in this paper include simple shear, inhomogeneous pure shear, parallel and similar folding.     

Cone penetration test in sand: A numerical-analytical approach

Separation of the effects of initial horizontal stress and relative density on cone tip resistance in sandy soils has been a complicated issue for many years. In order to overcome this problem, a numerical modeling of CPT which has been verified by calibration chamber tests, has been used in this paper to achieve a reliable analytical solution. The analytical solution has resulted in two relationships for sleeve friction and cone tip resistance in terms of the initial conditions of sandy soil. Based on the presented solution, the initial horizontal stress and relative density can be determined according to CPT measurements.     

Correction to: A novel methodological approach for land subsidence prediction through data assimilation techniques

Computational Geosciences - A Correction to this paper has been published: https://doi.org/10.1007/s10596-021-10079-6     

A GIS-based approach for gully erosion susceptibility modelling: a test in Sicily, Italy

The aim of this study is to analyze the susceptibility conditions to gully erosion phenomena in the Magazzolo River basin and to test a method that allows for driving the factors selection. The study area is one of the largest (225 km²) watershed of southern Sicily and it is mostly characterized by gentle slopes carved into clayey and evaporitic sediments, except for the northern sector where carbonatic rocks give rise to steep slopes. In order to obtain a quantitative evaluation of gully erosion susceptibility, statistical relationships between the spatial distributions of gullies affecting the area and a set of twelve environmental variables were analyzed. Stereoscopic analysis of aerial photographs dated 2000, and field surveys carried out in 2006, allowed us to map about a thousand landforms produced by linear water erosion processes, classifiable as ephemeral and permanent gullies. The linear density of the gullies, computed on each of the factors classes, was assumed as the function expressing the susceptibility level of the latter. A 40-m digital elevation model (DEM) prepared from 1:10,000-scale topographic maps was used to compute the values of nine topographic attributes (primary: slope, aspect, plan curvature, profile curvature, general curvature, tangential curvature; secondary: stream power index; topographic wetness index; LS-USLE factor); from available thematic maps and field checks three other physical attributes (lithology, soil texture, land use) were derived. For each of these variables, a 40-m grid layer was generated, reclassifying the topographic variables according to their standard deviation values. In order to evaluate the controlling role of the selected predictive variables, one-variable susceptibility models, based on the spatial relationships between each single factor and gullies, were produced and submitted to a validation procedure. The latter was carried out by evaluating the predictive performance of models trained on one half of the landform archive and tested on the other. Large differences of accuracy were verified by computing geometric indexes of the validation curves (prediction and success rate curves; ROC curves) drawn for each one-variable model; in particular, soil texture, general curvature and aspect demonstrated a weak or a null influence on the spatial distribution of gullies within the studied area, while, on the contrary, tangential curvature, stream power index and plan curvature showed high predictive skills. Hence, predictive models were produced on a multi-variable basis, by variously combining the one-variable models. The validation of the multi-variables models, which generally indicated quite satisfactory results, were used as a sensitivity analysis tool to evaluate differences in the prediction results produced by changing the set of combined physical attributes. The sensitivity analysis pointed out that by increasing the number of combined environmental variables, an improvement of the susceptibility assessment is produced; this is true with the exception of adding to the multi-variables models a variable, as slope aspect, not correlated to the target variable. The addition of this attribute produces effects on the validation curves that are not distinguishable from noise and, as a consequence, the slope aspect was excluded from the final multi-variables model used to draw the gully erosion susceptibility map of the Magazzolo River basin. In conclusion, the research showed that the validation of one-variable models can be used as a tool for selecting factors to be combined to prepare the best performing multi-variables gully erosion susceptibility model.     

A parsimonious distributed model for simulating transient water flow in a high-relief karst aquifer

A mathematical model of a highly heterogeneous functioning karst aquifer is described. The aquifer is in a high-relief karst massif and, as is common for such locations, data are scarce and there are no borehole, piezometer or pumping-test data. The scarcity of data in this case required a parsimonious approach to ensure that the level of complexity of the model was commensurate with the amount, type and quality of the available data. Parsimony also requires the model to include the minimum essential components that account adequately for the data, which in this and similar cases are the functional dualities of the karst system: duality in recharge, flow and discharge. The model is three-dimensional (3D) in the sense that the aquifer is discretized into 3D voxels, although the flow is one-dimensional (1D) and vertical in the vadose zone, and horizontal and two-dimensional (2D) in the saturated zone. The parsimonious model was designed by coupling a 1D unsaturated gravity-driven flow along the vertical (along each column of voxels that discretize the aquifer) and a 2D unconfined Darcy flow in the saturated zone. In the context of this type of aquifer, preferential recharge through the network of karst conduits implies a rapid rise in the water table, the location and extension of which are model parameters. The karst springs are simulated by drains. The methodology, which is completely general, is illustrated by application to the karst aquifer in the Sierra de las Nieves mountains in southern Spain.     

Charcoal analysis for paleoenvironmental interpretation: A chemical assay

Pollen and charcoal analysis of radiocarbon-dated sediment cores from Duck Pond in the Cape Cod National Seashore provide a continuous 12,000-yr vegetation and climate history of outer Cape Cod. A Picea-Hudsonia parkland and then a Picea-Pinus banksiana-Alnus crispa boreal forest association grew near the site between 12,000 and 10,000 yr B.P. This vegetation was replaced by a northern conifer forest of Pinus strobus-P. banksiana, and, subsequently, by a more mesophytic forest (Pinus strobus, Tsuga, Quercus, Fagus, Acer, Ulmus, Fraxinus, Ostrya) as the climate became warmer and wetter by 9500 yr B.P. By 9000 yr B.P. a Pinus rigida-Quercus association dominated the landscape. High charcoal frequencies from this and subsequent levels suggest that the pine barrens association developed during a warmer and drier climate that lasted from 9000 to about 5000 yr B.P. Increased percentages of Pinus strobus pollen indicate a return to moister and cooler conditions by about 3500 yr B.P. A doubled sedimentation rate, increased charcoal, and increased herb pollen suggest land disturbance near the pond before European settlement. These results suggest a rapid warming in the northeast in the early Holocene and support a hypothesis of a rapid sea level rise at that time. Comparison of the pollen results from Duck Pond with those from Rogers Lake, Connecticut, illustrates the importance of edaphic factors in determining the disturbance frequency and vegetation history of an area.     

Comparison of two different models for pile thermal response test interpretation

Thermal response tests (TRTs) are regularly used to characterise the thermal resistance of borehole heat exchangers and to assess the thermal conductivity of the surrounding ground. It is becoming common to apply the same in situ testing technique to pile heat exchangers, despite international guidance suggesting that TRTs should be limited to hole diameters of 152 mm (6 in.). This size restriction arises from the increased thermal inertia of larger diameter heat exchangers, which invalidates the assumption of a steady state within the concrete needed to interpret the test data by traditional line source analysis techniques. However, new methods of analysis for pile heat exchangers have recently been developed that take account of the transient behaviour of the pile concrete. This paper applies these new methods to data from a multi-stage TRT conducted on a small diameter test pile. The thermal conductivity and thermal resistance determined using this method are then compared with those from traditional analytical approaches based on a line source analysis. Differences between the approaches are discussed, along with the observation that the thermal resistance may not be constant over the different test stages.     

Review: Geothermal heat as a tracer of large-scale groundwater flow and as a means to determine permeability fields

A review of coupled groundwater and heat transfer theory is followed by an introduction to geothermal measurement techniques. Thereafter, temperature-depth profiles (geotherms) and heat discharge at springs to infer hydraulic parameters and processes are discussed. Several studies included in this review state that minimum permeabilities of approximately 5?×?10^?17?<?k _min <10^?15?m² are required to observe advective heat transfer and resultant geotherm perturbations. Permeabilities below k _min tend to cause heat-conduction-dominated systems, precluding inversion of temperature fields for groundwater flow patterns and constraint of permeabilities other than being <k _min. Values of k _min depend on the flow-domain aspect-ratio, faults and other heterogeneities, anisotropy of hydraulic and thermal parameters, heat-flow rates, and the water-table shape. However, the k _min range is narrow and located toward the lower third of geologic materials, which exhibit permeabilities of 10^?21?<?k?<?10^?7?m². Therefore, a wide range of permeabilities can be investigated by analyzing subsurface temperatures or heat discharge at springs. Furthermore, temperature is easy and economical to measure and because thermal material properties vary far less than hydraulic properties, temperature measurements tend to provide better-constrained groundwater flow and permeability estimates. Aside from hydrogeologic insights, constraint of advective/conductive heat transfer can also provide information on magmatic intrusions, metamorphism, ore deposits, climate variability, and geothermal energy.     

Constraining performance assessment models with tracer test results: a comparison between two conceptual models

Tracer tests are conducted to ascertain solute transport parameters of a single rock feature over a 5-m transport pathway. Two different conceptualizations of double-porosity solute transport provide estimates of the tracer breakthrough curves. One of the conceptualizations (single-rate) employs a single effective diffusion coefficient in a matrix with infinite penetration depth. However, the tracer retention between different flow paths can vary as the ratio of flow-wetted surface to flow rate differs between the path lines. The other conceptualization (multirate) employs a continuous distribution of multiple diffusion rate coefficients in a matrix with variable, yet finite, capacity. Application of these two models with the parameters estimated on the tracer test breakthrough curves produces transport results that differ by orders of magnitude in peak concentration and time to peak concentration at the performance assessment (PA) time and length scales (100,000 years and 1,000 m). These differences are examined by calculating the time limits for the diffusive capacity to act as an infinite medium. These limits are compared across both conceptual models and also against characteristic times for diffusion at both the tracer test and PA scales. Additionally, the differences between the models are examined by re-estimating parameters for the multirate model from the traditional double-porosity model results at the PA scale. Results indicate that for each model the amount of the diffusive capacity that acts as an infinite medium over the specified time scale explains the differences between the model results and that tracer tests alone cannot provide reliable estimates of transport parameters for the PA scale. Results of Monte Carlo runs of the transport models with varying travel times and path lengths show consistent results between models and suggest that the variation in flow-wetted surface to flow rate along path lines is insignificant relative to variability in the amount of diffusive capacity that can be accessed along the transport pathway.

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Resumen Delimitando la eficacia de modelos de evaluación con resultados de pruebas de trazadores: una comparación entre dos modelos conceptuales.Se llevaron a cabo pruebas de trazadores para evaluar los parámetros de transporte de solutos en un rasgo rocoso a lo largo de una trayectoria de transporte de 5 m. Dos diferentes conceptualizaciones del transporte de solutos de porosidad doble aportan estimados de las curvas de avance de trazadores. Una de las conceptualizaciones (ritmo único) utiliza un coeficiente de difusión efectiva único en una matriz con profundidad de penetración infinita. Sin embargo, la retención del trazador entre diferentes trayectorias de flujo puede variar debido a que la relación entre la superficie mojada de flujo y el ritmo de flujo difiere entre las líneas de trayectoria. La otra conceptualización (multi-ritmo) utiliza una distribución continua de coeficientes de ritmos de difusión múltiple en una matriz con capacidad variable pero finita. La aplicación de los dos modelos con los parámetros estimados en base a las curvas de avance de trazadores producen resultados de transporte que difieren en varios órdenes de magnitud, tanto en concentración pico como en el tiempo en que se alcanza la concentración pico, en las escalas de evaluación de eficacia (PA) de tiempo y longitud (100,000 años y 1,000 m). Estas diferencias se examinan mediante el cálculo de límites de tiempo en que se considera que la capacidad difusiva actúa como un medio infinito. Estos límites se comparan en ambos modelos conceptuales y contra los tiempos característicos para difusión en escalas de PA y de prueba de trazador. Adicionalmente, se examinan las diferencias entre los modelos calculando de nuevo los parámetros para el modelo multi-ritmo a partir del modelo tradicional de doble porosidad a escala PA. Los resultados indican que para cada modelo la cantidad de la capacidad difusiva que actúa como un medio infinito sobre la escala de tiempo especificada explica las diferencias entre los resultados del modelo y que las pruebas de trazadores por sí solas no aportan cálculos confiables de los parámetros de transporte para la escala PA. Los resultados provenientes de corridas Monte Carlo de los modelos de transporte con distintos tiempos de viaje y diferentes longitudes de trayectorias muestran resultados consistentes entre modelos y sugieren que la variación en la relación de superficie de flujo mojada a ritmo de flujo a lo largo de las líneas de trayectoria es insignificante en relación con la variabilidad en la cantidad de capacidad difusiva que puede alcanzarse a lo largo de la trayectoria de transporte.

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Résumé Contraindre le bilan des performances des modèles avec les résultats de traçages: une comparaison entre deux modèles conceptuels.Des tests de traçage sont mis en oeuvre pour étudier les paramètres de transport de soluté dune roche sur une longueur de 5 m. Deux différents modèles de transport de soluté dans un milieu à double porosité fournissent des estimation des courbes de restitution. Lune des conceptualisations (unique taux de restitution) emploie un seul coefficient effectif de diffusion dans une matrice possédant une pénétration infinie en profondeur. Par ailleurs, la rétention du traceur entre les différentes lignes découlement peut varier comme le rapport des débits aux surfaces mouillées et comme le rapport de la différence de débits entres les lignes découlement. Lautre conceptualisation (taux multiple) emploie une distribution continue de coefficients de diffusion dans une matrice à capacité variable et finit. Lapplication de ces deux modèles avec les pa! ramètres estimés grâce aux courbes de restitution produit des résultats de transport qui différent de plusieurs ordres de grandeur dans la magnitude du pic, le temps du pic de concentration, au bilan des performances (PA) et aux échelles de distance (100,000 ans et 1,000 m). Ces différences sont éxaminées par lintermédiaire des temps limites pour que la capacité diffusive équivaille à un milieu infini. Ces limites sont comparées à travers les modèles conceptuels ainsi que les temps caractéristiques de diffusion à léchelle du test de traçage et à léchelle du PA. Par ailleurs, les différences entre les modèles sont éxaminées en réestimant les paramètres pour le modèle à taux multiple à partir des résultats du modèle à double porosité à léchelle du PA. Les résultats indiquent que pour chaque modèle la valeur de la capacité diffusive dans un milieu infini sur une période de temps spécifiée explique les différences entre les modèles et le ! fait que le test de traçage seul ne permet pas de déterminer les paramètres de transport à léchelle du PA. Les résultats des simulations Monte Carlo du modèle de transport avec des temps et des distances de transport variables montrent des résultats concordances entre les différents modèles et suggère que la variation que la variation entre surface mouillée et le rapport de la différence de débits entre les lignes découlement est insignifiante, en regard de la variabilité du montant de la capacité diffusive qui peut être accessible le long de la ligne de transport.

     

排弃物料力学性质大型三轴剪切试验研究

露天矿剥离堆积的排弃物料力学性质是矿山排土场设计与稳定性控制之关键科学问题。文章以西南某露天矿剥离排弃物料为研究对象,采用室内相似级配模拟试验制作了不同物质组成、级配、相对密度条件下的试样,采用剪后筛分试验研究了各试样在不同应力状态下的颗粒破碎机理及破碎率变化关系,采用大型三轴剪切试验测试了各试样的应力-应变关系及抗剪强度参数。试验结果表明:排弃物颗粒剪切破碎力学机制复杂,颗粒破碎率与物料组分、级配、相对密度及围压条件密切相关,与抗剪强度参数相关性强。应力-应变曲线无明显峰值强度,具有应变硬化特征,分析认为其与围压、相对密度水平较低有关。试验数据拟合曲线均表明:ε1/（σ1-σ3）与ε1为线性关系,-ε3与ε1为抛物线关系,相关系数均大于0.9。据此拟合曲线,求解出排弃物料的切线泊松比μt,修正了邓肯-张模型。对相同试验条件下对比试样（QG-B-3）应力-应变关系,采用邓肯-张模型（修正）进行了预测,预测结果与试验测试数据基本一致,验证了邓肯-张模型（修正）能够描述排弃物料力学特征。研究排弃物料剪切破碎机理与应力-应变特征,对露天矿排土场边坡变形控制具有重要的理论意义。     

An efficient knowledge-based approach for random variation interpretation in NDVI time series

Nowadays, detecting and interpreting random variation extracted from satellite image time series is a far-reaching real-world issue. A more adequate approach should be designed to deal with this challenge. In this paper, we propose an efficient knowledge-based approach for vegetation monitoring using normalized derivation vegetation index time series. First, a decomposition process is designed to separate seasonal, trend and remainder components. Then, a genetic based schema is proposed to generate association rules. The extracted knowledge is intended to interpret the remainder component extracted during the previous phase by discovering the hidden link between random variation and climate observations. For validation purpose, a database covering the regions in Northwestern Tunisia is used for a period starting from 2000 to 2012. The data have been derived from Moderate resolution Imaging Spectroradiometer and fused with ground climate data (temperature and precipitation) in the form of fuzzy association rules. The obtained results show the efficiency of the proposed approach by reducing the non-stationarity effect.     

Radon in groundwater as a tracer to assess flow velocities: two test cases from Israel

 Two test cases from Israel are presented herein employing the decay rate of radon along the flow path to assess groundwater flow velocities. Groundwater flow reaching the fault zone emerges in several places along the rift fault zone as thermal springs because of deep water confinement. The high water temperature of the surface is indicative of high vertical flow velocities, which maintains the original high temperatures. Knowing the Rn content at a source point and at a given down-gradient, and assuming no Rn addition from the water itself or along the flow path, one can calculate the flow velocity based on the Rn half-life time. The decay of Rn in western Galilee was found to be ∼570–150 pCi/l, and in the Dead Sea area from 5000–2000 pCi/l along a respective flow path of 1000 and 200 m, Based on the above, the calculated flow velocities were compared with those obtained from pumping tests in the study area. The method is applicable, because of the short Rn half-life, to cases of high Rn contents, short distances and high flow velocities. Received: 18 January 2000 · Accepted: 21 March 2000     

210Pb in the ocean: A pilot tracer for modeling particle reactive elements

We discuss the basic requirements for a successful modeling of²¹⁰Pb in the ocean as a test tracer for at least other lead isotopes, but also of other elements that behave similarly to lead. With the aid of realistic models of the oceanic circulation and the major biogeochemical cycles in it, the result is a dynamically consistent model of lead cycling that reproduces observed profiles within 10%.     

Trap-door problem with dry sand: A statical approach based upon model test kinematics

The trap-door problem with dry sand is treated in a statical analysis based upon model test kinematics. Integration of the equilibrium conditions along horizontal slices and introducing the mean value for the vertical stresses yields a differential equation for the trap-door force. Concerning the constitutive response of sand a statical model of a moving shear band is proposed as an internal boundary. Solutions for the trap-door force for the active and passive modes and for the ultimate and residual states are discussed.