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A fundamental assumption in numerous studies of heat transfer in porous media is local thermal equilibrium (LTE), which assumes that the temperature of the porous media at the fluid and solid interface is in instantaneous equilibrium. Although significant efforts have been made to quantify the occurrence and consequences of local thermal nonequilibrium (LTNE), where the temperatures of the fluid and adjacent solid phases differ, there is no simple expression for quantifying the occurrence and effects of local thermal disequilibrium. Using a numerical model combining LTE and LTNE models, we develop here two simple general criteria based on Darcian velocities (q) and particle sizes (dp) of porous media for determining when LTNE effects occur (denoted as g(dp, q)) and when they become significant (denoted as f(dp, q)). Results show that using an LTE model can result in an underestimation of effective thermal diffusivity and the unaffected Darcian velocities when g(dp, q) > 0. It is possible that using the LTE model can result in an underestimation of the effective thermal diffusivity by more than 200 times within Darcian velocities ranging from 0 to 60 m/d. In the case of g(dp, q) < 0, the use of the LTE model can result in an overestimation of effective thermal diffusivity and Darcian velocities. The performances of the newly developed general criteria are demonstrated using three typical data sets and corresponding numerical models. These data sets include new heat tracer tests conducted in the laboratory and the field, as well as temperature‐time series collected in streambed sediments from a previous study by Shanafield et al. (2012, https://doi.org/10.5194/hessd‐9‐4305‐2012). The potential LTNE effects should be considered when using heat as a tracer to characterize flow and heat transport in porous media in the presence of Darcian velocities less than 2 m/d and particle sizes larger than 10 mm. Plain Language Summary This study explores heat transport in saturated porous media and in particularly potential temperature differences between water and solid phases, a phenomenon called local thermal nonequilibrium (LTNE). While typically neglected, we demonstrate that under some hydraulic conditions LTNE effects should be addressed in more accurate modeling of heat transport in natural porous media. We presented two new criteria on the occurrence and becoming significant of LTNE effects and validated them using three case studies, including both laboratory and field experiments. These findings provide new insights into flow and heat transport processes controlling a range of applications, such as hydrogeological investigations, and subsurface energy storage and extraction. Key Points New general criteria are developed for determining when LTNE effects occur and when they become significant Three case studies involving different particle sizes and Darcian velocities are used to verify the reliability of the proposed criteria Local thermal nonequilibrium effects can result in an increase in effective thermal diffusivity by more than 200 times at Darcian velocities ranging from 0 to 60 m/d

Natural rock often suffers from cyclic wetting–drying involving different water types, and the resulting deterioration may differ from laboratory tests using distilled water or salt solutions. An inappropriate estimation of this deterioration effect may lead to fatal geological hazards and engineering failures. A multiscale study is conducted to investigate the physical and mechanical features of sandstone in Three Gorges Reservoir region (TGR sandstone) subjected to cyclic wetting–drying of Yangtze River water. During this study, three types of water, i.e., Yangtze River water, ionized water having similar ion compositions as the Yangtze River water, and distilled water, are used for comparison. The results show that the multiscale physical properties including mineral compositions (especially calcite and albite), micro-pore parameters, computed tomography values, and macro-mechanical parameters (i.e., Young’s modulus, uniaxial compression strength and tensile strength) are remarkably altered during the cyclic wetting–drying process. Significant correlations are found between these numerous multiscale properties. The results indicate that changes of mineral compositions and microstructure are the primary reasons for the deterioration of sandstone strength. The deterioration effect of distilled water on TGR sandstone is the least, while the effect of ionized water is the greatest, and that of river water being intermediate. These differences are ascribed to different chemical interactions, together with possible microorganism effects for river water, as microorganisms in river water potentially weaken the deterioration of cyclic wetting–drying of river water. In situ water is recommended for studying how rock properties are affected by water–rock interactions in real settings.

Understanding the fluid flow and solute transport in karst conduits is significant for preventing pollutants (treated as solutes) in karst areas. This study evaluates the evolution of eddies in semi‐circular rough conduits under different hydrodynamic conditions and their effects on solute transport. As inlet flow velocity increases, the non‐Fickian coefficient (a parameter used for qualifying the tailing of BTCs) increases first then decreases afterward. A critical equilibrium concentration is found when the concentration of the main flow stream and the concentration of the eddy zone reaches the same value, signaling the moment at which the mass transfer (due to diffusion) between the main flow stream and the eddy zone drops to zero. Such a critical equilibrium concentration and its corresponding moment of occurrence are found to follow two distinctive logarithmic functions of the inlet flow velocity. These findings provide crucial technical support for groundwater pollution control in karst areas. Plain Language Summary Eddies are commonly seen when groundwater moves through highly permeable porous media, fractures, or conduit media, and understanding their effects on pollutants (treated as solutes) transport is crucial. In this study, we designed a semicircular rough conduit to reveal the mechanism of solute transport under different hydrodynamic conditions using a combined experimental and numerical simulation approach. The occurrence of the eddy zone and its influence on solute transport are revealed in great detail by analyzing the breakthrough curves (BTCs). This study provides a scientific basis for groundwater pollution control, especially in karst areas, demonstrating the relevance and applicability of our research to the field of geophysical fluid dynamics. Key Points The non‐Fickian effect increases first and then decreases gradually with the increase of inlet flow velocity The transformation mechanism process of advection and hydrodynamic diffusion is revealed The relationship between the equilibrium concentration, corresponding time and flow velocity at different stages is quantified

Accurate estimation of slope stability based on numerous candidate estimation methods is difficult as different results may be yielded. It becomes even more challenging when only limited data of geotechnical parameters (e.g., shear strength parameters) are available to evaluate slope reliability. Based on the Bayesian sequential updating technology, a hybrid framework for slope reliability was proposed in this study, through which prior knowledge, multiple estimation methods, and corresponding model uncertainties could be integrated to estimate slope reliability using a small amount of geotechnical data. Three slope examples with various stratigraphic configurations and soil properties were used to illustrate the accuracy and efficiency of the proposed framework, during which the Bishop’s simplified method, the upper bound limit analysis method, and the finite element method were adopted. The results showed that with results of direct Monte Carlo simulation based on each method as the benchmark, a compromised mean of the factor of safety (μFS), and conservative standard deviation of the factor of safety (σFS) and failure probability (Pf) were yielded through the proposed framework. When the sample size of geotechnical parameters was greater than a threshold, the estimated μFS was stable, while the σFS and Pf synchronously varied within a small range with the increase in sample size. Demonstrations of the three examples indicated that the proposed hybrid framework can provide reliable and accurate estimations of slope reliability. The proposed framework may serve as a promising vehicle for slope/landslide engineering including failure and preventative mechanisms, movement prediction, and back analysis of geotechnical parameters in a probabilistic context, and big data analysis of geological and geotechnical problems as well.

Hydrologically mediated hot moments (HM‐HMs) of transient anomalous diffusion (TAD) denote abrupt shifts in hydraulic conditions that can profoundly influence the dynamics of anomalous diffusion for pollutants within heterogeneous aquifers. How to efficiently model these complex dynamics remains a significant challenge. To bridge this knowledge gap, we propose an innovative model termed “the impulsive, tempered fractional advection‐dispersion equation” (IT‐fADE) to simulate HM‐HMs of TAD. The model is approximated using an L1‐based finite difference solver with unconditional stability and an efficient convergence rate. Application results demonstrate that the IT‐fADE model and its solver successfully capture TAD induced by hydrologically trigged hot phenomena (including hot moments and hot spots) across three distinct aquifers: (a) transient sub‐diffusion arising from sudden shifts in hydraulic gradient within a regional‐scale alluvial aquifer, (b) transient sub‐ or super‐diffusion due to convergent or push‐pull tracer experiments within a local‐scale fractured aquifer, and (c) transient sub‐diffusion likely attributed to multiple‐conduit flow within an intermediate‐scale karst aquifer. The impulsive terms and fractional differential operator integrated into the IT‐fADE aptly capture the ephemeral nature and evolving memory of HM‐HMs of TAD by incorporating multiple stress periods into the model. The sequential HM‐HM model also characterizes breakthrough curves of pollutants as they encounter hydrologically mediated, parallel hot spots. Furthermore, we delve into discussions concerning model parameters, extensions, and comparisons, as well as impulse signals and the propagation of memory within the context of employing IT‐fADE to capture hot phenomena of TAD in aquatic systems. Plain Language Summary Hydrologically mediated hot moments (HM‐HMs) encompass sudden shifts in water flow conditions in aquifers, exerting substantial influence on the migration of pollutants. To enhance our comprehension and modeling of these occurrences, we propose a mathematical model termed the Impulsive, Tempered Fractional Advection‐Dispersion Equation (IT‐fADE). This model employs specialized mathematical operators to effectively capture the rapid changes caused by HM‐HMs and to efficiently solve the associated equations. Our assessment of the IT‐fADE model across three distinct aquifers demonstrates its aptitude in faithfully depicting the transient anomalous diffusion of pollutants resulting from HM‐HMs. The IT‐fADE model incorporates specific terms and operators that represent the dynamic nature of HM‐HMs and their impact on pollutant mobility. In summary, the IT‐fADE model furnishes a tool for comprehending and modeling the repercussions of hydrologically triggered hot events on pollutant migration in aquifers. This framework may help researchers and scientists better quantify how pollutants will behave in these environments whose conditions can change abruptly. Key Points An impulsive, tempered fractional model captured transient anomalous diffusion (TAD) due to hydrologically mediated hot moments (HM‐HMs) The impulsive term and fractional differential operator in the new model describe the ephemeral and dynamic nature of HM‐HMs of TAD The sequential HM‐HM model fitted the pollutant breakthrough curves affected by parallel hydrologically mediated hot spots

To remove contaminants from a layered heterogeneous porous system where the flow direction is parallel to the horizontal layering, the flushing front may advance faster in one layer than the other, resulting in a significant vertical concentration gradient across the layer interface. This gradient leads to mass exchange between the layers due to the vertical dispersive transport. Such a mass exchange phenomenon can greatly alter the mass (and heat if the temperature is a concern) distribution in a multi-layer porous media system but has never been investigated before in a quantitative manner. In this study, high-resolution finite-element numerical models have been employed to investigate how transport properties affect contaminant transport during flushing, using a two-layer system as an example. The results showed that the porosity and retardation factor play similar roles in affecting mass flux across the interface. Increasing the porosity (or retardation factor) of one layer with a faster flushing velocity would decrease the total mass flux across the interface of the layers, while increasing the porosity (or retardation factor) of the layer with a slower flushing velocity played an adverse influence. Furthermore, increasing the transverse dispersivity of any layer increased the mass flux across the interface of the two layers. However, changes in the transverse dispersivity did not affect the spatial range (or gap along the flow direction) in which significant vertical mass flux occurs. This study has important implications for managing contaminant remediation in layered aquifers.

Zigui Basin is a major landslide-prone region in the Three Gorges Reservoir region of China, and the stabilizing pile is an effective and widely employed countermeasure to reinforce landslides in this region. However, stabilizing piles are mostly designed using deterministic and stability-oriented methods, which generally ignore the system performance and cost-effectiveness. Using the Majiagou landslide reinforced with stabilizing piles as a case study, a probabilistic multi-objective optimization framework for the design of stabilizing piles is proposed and illustrated. Specifically, performance objectives related to failure probability, system robustness and life-cycle cost of the landslide-stabilizing pile system with feasible designs are evaluated, then the best compromised design is obtained by means of Pareto optimality. Expert knowledge and professional judgment are required to set necessary restrictions and finally determine the optimal design. The results show that there is a better design of stabilizing piles than the existing one, with which acceptable reinforcement effectiveness, compromised life-cycle cost and robust system performance can be realized. The optimal design will also vary with the concerned performance objectives and knowledge-based judgment. Further relationships and interpretations between design parameters and system responses are discussed through parametric analyses.

Geometry of a single fracture has significant influence on the fluid flow in fractured rocks. However, quantification of geometry–flow relationship in a rock fracture is still far from being completed. The primary goal of this study was to identify a few key geometric parameters for quantifying its impact on fluid flow in a single rock fracture and then to evaluate its hydraulic conductivity. The concept of a threshold aperture is first introduced to estimate the effective area involved in the flow process in a single rock fracture. It is assumed that only those zones with greater apertures than a threshold value are involved in the flow process. The effect of variable aperture distributions on flow in a single rock fracture is quantified based on the cumulative distribution of individual apertures of sampling points. The surface roughness is decomposed into primary roughness (i.e. the large-scale waviness of the fracture morphology) and secondary roughness (i.e. the small-scale unevenness) with a wavelet analysis. The influence of surface roughness on the fluid flow in a single rock fracture is quantified with the normalized area of primary roughness and the standard deviation of secondary roughness. By combining the variable aperture distributions and the surface roughness on flow, an empirical equation to estimate the intrinsic hydraulic aperture and hydraulic conductivity of a single rock fracture is proposed. In addition, a series of high-precision hydraulic tests are conducted on 60 artificial tensile fractures to verify the proposed equation. The results show that the proposed equation predicts the intrinsic hydraulic aperture and hydraulic conductivity of a single rock fracture very well.

Nitrogen and phosphorus are commonly recognized as causing eutrophication in aquatic systems, and their transport in subsurface environments has also aroused great public attention. This research presented four natural clay minerals (NCMs) evaluated for their effectiveness of NH4+ and PO43- adsorption from wastewater. All the NCMs were fully characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), BET analysis, and adsorption kinetics and isotherms to better understand the adsorption mechanism-property relationship. The results show that the adsorption efficiency of the four NCMs for phosphate was better than that for ammonia nitrogen. The removal rate of phosphate was higher than 65%, generally in the range of 80%-90%, while the removal rate of ammonia nitrogen was less than 50%. The adsorption kinetic behavior followed the pseudo-second-order kinetic model. The ammonia nitrogen adsorption isotherm was in good agreement with the Freundlich isotherm equilibrium model, and the phosphate adsorption isotherm matched the Langmuir model. Among all the NCMs studied, bentonite (7.13 mg/g) and kaolinite (5.37 mg/g) showed higher adsorption capacities for ammonia nitrogen, while zeolite (0.21 mg/g) and attapulgite (0.17 mg/g) showed higher adsorption capacities for phosphate. This study provides crucial baseline knowledge for the adsorption of nitrogen and phosphate by different kinds of NCMs.

China's so-called Three North Shelterbelt Program (3NSP) has produced a vast area of lined forest reconstruction in the semi-arid regions. This study uses the lined rain-fed Pinus sylvestris var. mongolica (PSM) sand-fixing forest in the eastern part of Mu Us Sandy Land in Northwestern China as an example to investigate the ecohydrological process in this region. Rain gauges, newly designed lysimeters and soil moisture sensors are used to monitor precipitation, deep soil recharge (DSR) and soil water content, where DSR specifically refers to recharge that can reach a depth more than 200 cm and eventually replenish the underneath groundwater reservoir. This study shows that there are two obvious moisture recharge processes in an annual base for the PSM forest soil: a snowmelt-related recharge process in the spring and a precipitation-related recharge process in the summer. The recharge depth of the first process can reach 180 cm without DSR occurring (in 2018). The second process results in noticeable DSR in 2018. Specifically, the DSR values over 2016-2018 are 1, 0.2, and 1.2 mm, respectively. To reach the recharge depths of 20, 40, 80, 120, 160, and 200 cm, the required precipitation intensities have to be 2.6, 3.2, 3.4, 8.2, 8.2, and 13.2 mm/d, respectively. The annual evapotranspiration in the PSM forest is 466.94 mm in 2016, 324.60 mm in 2017, and 183.85 mm in 2018. This study concludes that under the current precipitation conditions (including both dry- and wet-years such as 2016-2018), water consumption of PSM somewhat equals to the precipitation amount, and PSM has evolved over years to regulate its evapotranspiration in response to annual precipitation fluctuations in Mu Us Sandy Land of China.