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In groundwater hydrology, aquitard heterogeneity is often less considered compared to aquifers, despite its significant impact on groundwater hydraulics and groundwater resources evaluation. A semi‐analytical solution is derived for pumping‐induced well hydraulics and groundwater budget with consideration of vertical heterogeneity in aquitard hydraulic conductivity (K) and specific storage (Ss). The proposed new solution is innovative in its partitioning of the aquitard into multiple homogeneous sub‐layers to enable consideration of various forms of vertically heterogeneous K or Ss. Two scenarios of analytical investigations are explored: one is the presence of aquitard interlayers with distinct K or Ss values, a common field‐scale occurrence; another is an exponentially depth‐decaying aquitard Ss, a regional‐scale phenomenon supported by statistical analysis. Analytical investigations reveal that a low‐K interlayer can significantly increase aquifer drawdown and enhance aquifer/aquitard depletion; a high‐Ss interlayer can noticeably reduce aquifer drawdown and increase aquitard depletion. Locations of low‐K or high‐Ss interlayers also significantly impact well hydraulics and groundwater budget. In the context of an exponentially depth‐decaying aquitard Ss, a larger decay exponent can enhance aquifer drawdown. When using current models with a vertically homogeneous aquitard, half the sum of the geometric and harmonic means of exponentially depth‐decaying aquitard Ss should be used to calculate aquitard depletion and unconfined aquifer leakage. [ABSTRACT FROM AUTHOR]

Clay is widely encountered in nature and directly influences seepage behaviors, exerting a crucial impact on engineering applications. Under low hydraulic gradients, seepage behaviors have been observed to deviate from Darcy's law, displaying a non-linear trend. However, the impacts of clay content on non-linear seepage behavior and its pore-scale mechanisms to date remain unclear. In this study, constant-head seepage experiments were conducted in sand–clay porous media under various hydraulic gradients. Low-field nuclear magnetic resonance (LF-NMR) technology was utilized to monitor the bound-water and free-water contents of sand–clay porous media under different seepage states. The results show a threshold hydraulic gradient (i0) below which there is no flow, and a critical hydraulic gradient (icr) below which the relationship between the hydraulic gradient (i) and seepage velocity (v) is non-linear. Both hydraulic gradients increased with clay content. Moreover, the transformation between bound water and free water was observed during the seepage-state evolution (no flow to pre-Darcy or pre-Darcy to Darcy). As the hydraulic gradient reached the i0, the pore water pressure gradually overcame the adsorption force of the bound-water film, reducing the thickness of the bound-water film, and causing non-linear seepage behavior. When i0 < i < icr, the enlarging hydraulic gradient triggers the thinning of bound water and enhances the fluidity of pore water. Moreover, the increasing clay content augments the bound-water content required for the seepage state's change. [ABSTRACT FROM AUTHOR]

Hydraulic conductivity generally decreases with depth in the Earth's crust. The hydraulic conductivity–depth relationship has been assessed through mathematical models, enabling predictions of hydraulic conductivity in depths beyond the reach of direct measurements. However, it is observed that beyond a certain depth, hydraulic conductivity tends to stabilize; this phenomenon cannot be effectively characterized by the previous models. Thus, these models may make inaccurate predictions at deeper depths. In this work, we introduce an innovative exponential model to effectively assess the conductivity–depth relationship, particularly addressing the stabilization at greater depths. This model, in comparison with an earlier power-like model, has been applied to a globally sourced dataset encompassing a range of lithologies and geological structures. Results reveal that the proposed exponential model outperforms the power-like model in correctly representing the stabilized conductivity, and it well captures the fast stabilization effect of multiple datasets. Further, the proposed model has been utilized to analyze three distinct groups of datasets, revealing how lithology, geological stabilization, and faults impact the conductivity–depth relationship. The hydraulic conductivity decays to the residual hydraulic conductivity in the order (fast to slow): metamorphic rocks, sandstones, igneous rock, mudstones. The mean hydraulic conductivity in stable regions is roughly an order of magnitude lower than unstable regions. The faults showcase a dual role in both promoting and inhibiting hydraulic conductivity. The new exponential model has been successfully applied to a dataset from a specific engineering site to make predictions, demonstrating its practical usage. In the future, this model may serve as a potential tool for groundwater management, geothermal energy collection, pollutant transport, and other engineering projects. [ABSTRACT FROM AUTHOR]

Aquifer hydraulic parameters play a critical role in investigating various groundwater hydrology problems (e.g., groundwater depletion and groundwater transport), and the Theis formula for constant-rate pumping tests is commonly used to estimate them. However, the pumping rate in the field usually varies with time due to some factors, making the classical constant-rate model unsuitable for accurate parameter estimation. To address this issue, we developed a novel dimensionless-form analytical solution for variable-rate pumping tests involving piecewise-constant approximations for variable pumping rates. Analysis of the time–drawdown curves revealed that the first-step type curve was consistent with the Theis curve. However, the curves of subsequent steps deviated from the Theis curve and were associated with the first dimensionless inflection time (t1,D), which depended on the hydraulic conductivity (K) and specific storage (Ss) of the confined aquifers. On this basis, a new type curve method for estimating the aquifer K and Ss was proposed by matching the observed drawdown data with a series of type curves dependent on t1,D. Furthermore, this method can handle recovery drawdown data. We applied this method to a field site in Wuxi City, Jiangsu Province, China, by analyzing the drawdown data from four pumping tests. The hydraulic parameters estimated using this method were in close agreement with those calibrated via PEST. The calibrated K values were further validated by comparing them with lithology-based results. In summary, the geometric means of K and Ss were 6.62 m/d and 3.16 × 10−5 m−1 for the first confined aquifer and 0.92 m/d and 2.34 × 10−4 m−1 for the second confined aquifer. [ABSTRACT FROM AUTHOR]

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Aquifer hydraulic parameters are commonly inferred from constant‐rate pumping tests, while variable pumping rates are frequently encountered in actual field conditions. In this study, we propose a generally applicable dimensionless form of the analytical solution for variable‐rate pumping tests in confined aquifers. In particular, we adopt a piecewise‐linear fitting of variable pumping rates and propose a new type‐curve method for estimating the hydraulic conductivity (K) and specific storage (Ss) of the investigated confined aquifer. For each test, a series of type curves, which depend on the variable pumping rates, the location of observation wells and the introduced first dimensionless inflection time, need to be provided for matching the observed drawdown data on a log‐log graph. We first demonstrate the applicability and robustness of this method through a synthetic pumping test. Subsequently, we apply this method to analyze drawdown data from four pumping tests conducted within a multilayered aquifer/aquitard system in Wuxi city, Jiangsu Province, China. The parameter estimates are then compared with those reported by PEST. The K and Ss values estimated by the new type‐curve method are found to be quite close to PEST‐based estimates. Parameter estimation results demonstrate the difference in K and Ss values between observation wells. The difference could be attributed to the spatial heterogeneity in K and Ss. A future research topic may focus on the characterization of K and Ss heterogeneity with the currently available drawdown data from variable‐rate pumping tests. Article impact statement: Enriching the methods for the characterization of aquifer hydraulic parameters. [ABSTRACT FROM AUTHOR]

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (Ss) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and Ss of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test. [ABSTRACT FROM AUTHOR]

• Transience of a variable is treated as 1D spatial heterogeneity for optimization. • Transience of streambed K can be identified via geostatistical inverse modeling. • The new methodology is validated through synthetic and field data investigations. Quantitative investigation of the interaction between surface water and groundwater relies on the determination of transience of streambed hydraulic conductivity (K sb). The commonly used successive inversion approach (i.e., the inversion is repeated over successive time steps) of interpreting aquifer hydraulic response data belongs to different optimization windows consists of a sizable number of inversion sub-processes and tends to lose sharp changes in K sb. This study treats the transience of a parameter in the time domain as the heterogeneity in 1D space domain and uses geostatistical inverse modeling to characterize such transience. The methodology is first tested through a group of ten synthetic cases with independently generated random transient patterns of K sb. Results of these synthetic cases reveal the capability of geostatistical inverse modeling to effectively characterize the general varying pattern as well as sharp changes in K sb. Subsequently, the methodology is applied to interpret the aquifer hydraulic response data measured at the Rhône River site, Town of Fully, Switzerland. A significant improvement in model calibration is observed when the methodology is compared to the successive inversion approach. The field investigation reveals that the transience of in-situ K sb is closely related to stream stage variations. Particularly, multiple occurrences of sharp increases and decreases in K sb appear when the stream stage lowers below and rises above the aquifer head. The driving mechanism for these sharp variation events is that fine-grained sediments within the streambed can be partly washed away when the aquifer water flows toward the river, and vice versa. The geostatistical approach has the potential to help investigate other physical or chemical processes in groundwater hydrology associated with transient changes in K sb. [ABSTRACT FROM AUTHOR]

• An analytical model is developed to handle horizontal aquifer/aquitard heterogeneity. • A high- K aquitard window tends to dampen tide-induced aquifer head fluctuations. • Aquifer head fluctuations may be dampened by a large-size high- S s aquitard window. • Sandbox experiments validated the effects of a high- K aquitard window. Low-permeability aquitards are important sedimentary units that protect the underlying confined aquifers from contamination by seawater and anthropogenic sources in coastal leaky aquifer systems. Therefore, the integrity of the aquitard is of crucial importance. However, the aquitard integrity may be vulnerable to horizontal heterogeneities in the form of aquitard windows. In this study, an innovative analytical model was developed to describe groundwater flow in a coastal leaky aquifer system with horizontal heterogeneities in hydraulic properties of either the aquitard or the confined aquifer. Consequently, the effects of aquitard windows, which manifest as horizontally local heterogeneities in hydraulic conductivity and/or specific storage, on the tidal wave propagation can be considered in the analysis. Analytical solutions were derived for tidal-head or constant-flux inland boundary conditions. The derivation process avoided previous methodologies that involved the assembly of large-size matrices. The newly developed analytical model can cover multiple existing analytical models that are associated with the assumptions of homogeneity in hydraulic properties of the aquifer and the aquitard, infinite horizontal extent of the coastal leaky aquifer system, impermeability of the aquitard, or ignorance of aquitard storativity. Analytical investigations revealed that high-permeability aquitard windows acting as preferential-flow conduits tended to dampen the tide-induced head propagation within the underlying confined aquifer. Moreover, an aquitard with a higher storativity (but the same permeability) and of considerable size can result in an apparent propagation bias. The newly developed analytical model in this study was further corroborated through sandbox experiments. Both piezometer measurements and parameter estimates indicated the non-negligible effects of high-permeability aquitard windows on the tidal wave propagation. The sandbox investigation also highlighted the importance of geostatistical inverse modeling in characterizing local heterogeneities within the confined aquifer and in detecting the location and size of aquitard windows, when measurement data of tide-induced aquifer head fluctuations were provided. [ABSTRACT FROM AUTHOR]

The design and optimization of the dewatering scheme for deep foundation pits in a highly permeable heterogeneous layer are critical to protect water resources, control subsidence and mitigate environmental impacts. Numerical simulation is an important and sometimes the only tool in the design of dewatering schemes, especially when the dewatering projects are planned under complex hydrogeological conditions with limited data. The open excavation method was chosen for a project to drain a deep foundation pit (35–44 m) in an upland river valley landscape. Quaternary alluvial deposits (129.0 m thick) are generally distributed in the riverbed and the overburden consists mainly of alluvial-diluvial sandy gravel cobbles, clayey soils, sandy clay, and silty fine sand, making the study area very heterogeneous. There may be water inrush from foundation pit, uneven subsidence and deformation due to the uneven structure of the sand and slope stability. MODFLOW-USG (Unstructured Grid) and Subsidence and Aquifer-System Compaction (SUB) Package were used to create a coupled 3-D groundwater flow-subsidence numerical model for foundation pit dewatering. MODFLOW-USG provides greater flexibility in the design of the grid to achieve a high degree of accuracy in numerical simulation, while effectively reduces computational costs. A combination of waterproof curtain and a partial penetrating well was proposed for lowering the groundwater table. The optimized dewatering scheme with a curtain depth of 60 m and a hydraulic conductivity of 0.00518 m/d, and four rows of dewatering wells with an equal row spacing of 40 m, well depth of 50 m, and well spacing of 12.5 m in each row can meet the dewatering requirements with minimum groundwater discharge in the scenarios. The numerical simulation of this study provides a powerful and useful tool for dewatering and subsidence control of deep foundation pit under complex hydrogeological conditions. • Optimized schemes for deep foundation pit dewatering under complicated hydrogeological conditions is determined. • 3-D Coupled groundwater flow-subsidence numerical model is established considering construction of dewatering well and curtain. • MODFLOW-USG provides greater flexibility in grid design to achieve a high degree of accuracy in dewatering schemes simulation. [ABSTRACT FROM AUTHOR]

A hydrogeological unit with a considerable thickness usually demonstrates depth-decaying hydraulic conductivity (K) at the regional scale. In this study, we investigated transient well hydraulics (i.e., aquifer and aquitard drawdown) and groundwater budget (i.e., fractions of groundwater withdrawal including aquifer depletion, aquitard depletion and leakage from the unconfined aquifer) within a leaky aquifer system considering an exponentially decaying K of the aquitard, parameterized with a dimensionless decay coefficient (A d). Relevant semi-analytical solutions were derived using the Laplace transform and Hankel transform techniques, while drawdown and groundwater budget characteristics and their sensitivities to A d were theoretically analyzed. Theoretical analysis results suggested that a larger A d consistently leads to a larger aquifer drawdown, a smaller aquitard drawdown, a larger fraction of aquifer depletion and a smaller fraction of leakage from the unconfined aquifer. Sensitivity analysis results also indicated critical effects of A d on well hydraulics and groundwater budget. Comparative analysis revealed that none of the three typical mean values of depth-decaying aquitard K can perfectly characterize the well hydraulics and groundwater budget from early to intermediate times. However, the harmonic and geometric mean values can be feasibly used to calculate the final fractions of aquifer depletion and aquitard depletion at late times, respectively. Limitations of the newly developed analytical model have also been discussed. Practical investigations of vertical aquitard heterogeneity and further applications of this new model are recommended. [ABSTRACT FROM AUTHOR]

• Analytical solution for periodic aquitard deformation based on Euler's formula. • To analyse effects of phase difference between periodic hydraulic head variations. • A new method proposed to estimate aquitard hydraulic parameters. • Field application case to confirm the importance of phase difference. Extensometers provide long-term records of deformation over a depth interval of interest. An overconsolidated aquitard usually undergoes elastic deformation if the hydraulic head within adjacent aquifers remains higher than the preconsolidation head within the aquitard. The vertical hydraulic conductivity K v and elastic skeletal specific storage S ske are two critical parameters that control the deformation behavior of an overconsolidated aquitard, and they could be interpreted from valuable extensometer data. An analytical solution for the elastic aquitard deformation caused by periodic hydraulic head variations (PHHV) within adjacent aquifers is derived using the separation of variables method based on Euler's formula. The phase difference in PHHV between adjacent aquifers is found to reduce the amplitude of periodic aquitard deformation. Meanwhile, the phase difference is found to cause no influence on the growth pattern of the phase shift, which is between the periodic aquitard deformation and PHHV, versus the period. A new parameter estimation method is further proposed to interpret aquitard K v and S ske from periodic aquitard deformation data. This new method yields robust K v and S ske estimates of a moderately thick aquitard, whose deformation history has been recorded by an extensometer, located in Shanghai, China. The field study confirms that the phase difference in PHHV between the aquifers adjacent to the overconsolidated aquitard of interest cannot be ignored. [ABSTRACT FROM AUTHOR]