A semi-analytical solution for saltwater intrusion with a very narrow transition zone

The Henry saltwater intrusion problem provides a semi-analytical solution that is largely used for benchmarking density-dependent groundwater flow models. The major drawback of this problem arises from the high dispersion value used by Henry (represented by the dimensionless parameter b?=?0.1). Finding a stable semi-analytical solution for small values of b is challenging due to the low convergence of the corresponding nonlinear system. In this work, an accurate semi-analytical solution is developed in the case of a very narrow transition zone corresponding to b?=?0.005. About 6,330 terms are used in the Fourier series to accurately represent the solution. The resolution of the corresponding highly nonlinear system is made possible by the modified Powell hybrid algorithm due to the analytical evaluation of the Jacobian, which drastically reduces the computational time. The new test problem is also investigated numerically using different numerical methods and different mesh sizes to show its high worthiness, compared to the standard Henry problem, for benchmarking density driven flow codes.     

Characterization of locally available soil as a liner material for solid waste landfills in Sri Lanka

This study aimed to develop a low-cost and effective clay liner material for solid waste landfills in Sri Lanka. A locally available clayey soil and its admixtures with 5 and 10% bentonite were examined for this purpose. Laboratory experiments to determine soil plasticity and swell index were carried out on the tested samples. Hydraulic conductivity (k) tests were carried out in the laboratory using water and an aqueous solution of CaCl₂ on unconsolidated samples prepared by either dry or slurry packing and pre-consolidated samples with five different consolidation pressures (p) from 10 to 200 kPa. Measured liquid limits for tested admixtures increased with increasing bentonite contents and correlated well with measured values of the swell index. The difference in permeant solutions had little effect on measured k values for both unconsolidated and pre-consolidated samples. The hydraulic conductivities were highly affected by changing p, i.e., the k values decreased on two orders of magnitude as p increased from 10 to 200 kPa. The Kozeny–Carman equation, a theoretical permeability model that expresses the k-porosity relationship, was applied to measured data including reported values. Results showed the Kozeny–Carman equation captured well the porosity-dependent k values for tested soils and their admixtures with bentonite under a wide range of void ratios, suggesting that the Kozeny–Carman equation is a useful tool to estimate the magnitude of k values for differently compacted soil and its bentonite admixtures.     

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solution of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The spatiotemporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases (k _p h > 0.8, where k _p is the peak wavenumber, and h is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths k _p h ≥ 1.2. The lifetimes of rogue events may reach up to 30–60 wave periods depending on the water depth. The maximum observed wave has a height of about three significant wave heights. A few randomly chosen in situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.     

Magnetic-resonance imaging and simplified Kozeny-Carman-model analysis of glass-bead packs as a frame of reference to study permeability of reservoir rocks

Permeability variation in reservoir rocks results from the combined effects of various factors, and makes porosity–permeability (?–k) relationships more complex, or, in some cases, non-existent. In this work, the ?–k relationship of macroscopically homogeneous glass-bead packs is deduced based on magnetic resonance imaging (MRI) measurement and Kozeny-Carman (K-C) model analysis; these are used as a frame of reference to study permeability of reservoir rocks. The results indicate: (1) most of the commonly used simplified K-C models (e.g. the simplified traditional (omitting specific surface area), high-order, threshold, and fractal models) are suitable for estimating permeability of glass-bead packs. The simplified traditional model does not present obvious dependence on rock samples. Whether for the glass-bead packs or clean natural sandstones, the sample coefficients almost remain invariant. Comparably, the high-order, the fractal, and the threshold models are strongly sample-specific and cannot be extrapolated from the glass-bead packs to natural sandstones; (2) the ?–k relationships of quartz sands and silty sandstones resemble those of the glass-bead packs, but they significantly deviate from the K-C models at low porosities due to small pore entry radius; (3) a small amount of intergranular cements (<10%v) does not affect the general variation trend of permeability with porosity but can potentially increase predictive errors of the K-C models, whereas in the case of more cements, the ?–k relationships of sandstones become uncertain and cannot be described by any of these K-C models.     

Steady infiltration from buried point source into heterogeneous cross‐anisotropic unsaturated soil

The paper presents the analytical solution for the steady‐state infiltration from a buried point source into two types of heterogeneous cross‐anisotropic unsaturated half‐spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half‐space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross‐anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd.     

Permeability of granular soil employing flexible wall permeameter

Understanding the changes in permeability of soil, when soil is subjected to high confining pressure and flow pressure, which may alter the textural and geomechanical characteristics of soil, is of great importance to many geo-engineering activities such as, construction of high-rise buildings near the coast or the water bodies, earthen dams, pavement subgrades, reservoir, and shallow repositories. It is now possible to evaluate the changes in permeability of soil samples under varying conditions of confining pressure and flow pressure using flexible wall permeameter (FWP). In the present study, investigation was carried out on a cylindrical sample of granular soil employing FWP under varied conditions of confining pressure (σ₃)—50–300 kPa, which can simulate the stress conditions equivalent to depth of about 20 m under the earth’s crust, and a flow pressure (f_p)—20–120 kPa, which is mainly present near the small earthen embankment dams, landfill liners, and slurry walls near the soft granular soil with high groundwater table. The obtained results indicate a linear relationship between hydraulic conductivity (k) with effective confining pressure (σ_eff.), k, decreasing linearly with an incremental change in σ_eff.. Further, k increases significantly with an increase in f_p corresponding to each σ_eff., and q increases significantly with increase in the f_p corresponding to each (σ₃). It was also observed that corresponding to the low f_p of 20 kPa, the reduction in k is nonlinear with σ_3. The percentage reduction in k is observed to be 9, 13, and 27% corresponding to σ₃ of 50–100, 100–200, and 200-300 kPa, respectively.     

Three-dimensional numerical and analytical study of horizontal group of square anchor plates in sand

In this paper, numerical and analytical methods are used to evaluate the ultimate pullout capacity of a group of square anchor plates in row or square configurations, installed horizontally in dense sand. The elasto-plastic numerical study of square anchor plates is carried out using three-dimensional finite element analysis. The soil is modeled by an elasto-plastic model with a Mohr–Coulomb yield criterion. An analytical method based on a simplified three-dimensional failure mechanism is developed in this study. The interference effect is evaluated by group efficiency η, defined as the ratio of the ultimate pullout capacity of group of N anchor plates to that of a single isolated plate multiplied by number of plates. The variation of the group efficiency η was computed with respect to change in the spacing between plates. Results of the analyses show that the spacing between the plates, the internal friction angle of soil and the installation depth are the most important parameters influencing the group efficiency. New equations are developed in this study to evaluate the group efficiency of square anchor plates embedded horizontally in sand at shallow depth (H = 4B). The results obtained by numerical and analytical solutions are in excellent agreement.     

Toward reliable calibration of aquifer hydrodynamic parameters: characterizing and optimization of arid groundwater system using swarm intelligence optimization algorithm

Despite advanced development in computational techniques, the issue of how to adequately calibrate and minimize misfit between system properties and corresponding measurements remains a challenging task in groundwater modeling. Two important features of the groundwater regime, hydraulic conductivity (k) and specific yield (S _y), that control aquifer dynamic vary spatially within an aquifer system due to geologic heterogeneity. This paper provides the first attempt in using an advanced swarm-intelligence-based optimization algorithm (cuckoo optimization algorithm, COA) coupled with a distributed hydrogeology model (i.e., MODFLOW) to calibrate aquifer hydrodynamic parameters (S _y and k) over an arid groundwater system in east Iran. Our optimization approach was posed in a single-objective manner by the trade-off between sum of absolute error and the adherent swarm optimization approach. The COA optimization algorithm further yielded both hydraulic conductivity and specific yield parameters with high performance and the least error. Estimation of depth to water table revealed skillful prediction for a set of cells located at the middle of the aquifer system whereas showed unskillful prediction at the headwater due to frequent water storage changes at the inflow boundary. Groundwater depth reduced from east toward west and southwest parts of the aquifer because of extensive pumping activities that caused a smoothening influence on the shape of the simulated head curve. The results demonstrated a clear need to optimize arid aquifer parameters and to compute groundwater response across an arid region.     

Model reduction and discretization using hybrid finite volumes for flow in porous media containing faults

In this paper, we study two different model reduction strategies for solving problems involving single phase flow in a porous medium containing faults or fractures whose location and properties are known. These faults are represented as interfaces of dimension N ? 1 immersed in an N dimensional domain. Both approaches can handle various configurations of position and permeability of the faults, and one can handle different fracture permeabilities on the two inner sides of the fracture. For the numerical discretization, we use the hybrid finite volume scheme as it is known to be well suited to simulating subsurface flow. Some results, which may be of use in the implementation of the proposed methods in industrial codes, are demonstrated.     

Buckling of layered elastic media: A cosserat-continuum approach and its validation

In this paper the stability of layered, anisotropic, hypoelastic media under initial stress is investigated. The bifurcation problem is formulated and solved numerically by use of a semi-analytical transfer matrix method. An alternative analytical approach in dealing with inhomogeneous media is developed by representing a periodically layered medium as a homogeneous Cosserat continuum. The Cosserat-continuum approach is validated against the numerical transfer matrix solution.     

Nonlinear consolidation in randomly heterogeneous highly compressible aquitards

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. The effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards is investigated by means of one-dimensional Monte Carlo numerical simulations where the lower boundary represents the effect of an instant drop in hydraulic head due to groundwater pumping. Two thousand realizations are generated for each of the following parameters: hydraulic conductivity (K), compression index (C _c), void ratio (e) and m (an empirical parameter relating hydraulic conductivity and void ratio). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system when compared to a nonlinear consolidation model with deterministic initial parameters. The deterministic solution underestimates the ensemble average of total settlement when initial K is random. In addition, random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady-state conditions.     

Modelling the effects of porous media deformation on the propagation of water-table waves in a sandy unconfined aquifer

This paper examines the influence of porous media deformation on water-table wave dispersion in an unconfined aquifer using a numerical model which couples Richards’ equation to the poro-elastic model. The study was motivated by the findings of Shoushtari et al. (J Hydrol 533:412–440, 2016) who were unable to reproduce the observed wave dispersion in their sand flume data with either numerical Richards’ equation models (assuming rigid porous media) or existing analytic solutions. The water-table wave dispersion is quantified via the complex wave number extracted from the predicted amplitude and phase profiles. A sensitivity analysis was performed to establish the influence of the main parameters in the poro-elastic model, namely Young’s modulus (E) and Poisson’s ratio (ν). For a short oscillation period (T?=?16.4 s), the phase lag increase rate (k _i) is sensitive to the chosen values of E and ν, demonstrating an inverse relationship with both parameters. Changes in the amplitude decay rate (k _r), however, were negligible. For a longer oscillation period (T?=?908.6 s), variations in the values of E and ν resulted in only small changes in both k _r and k _i. In both the short and long period cases, the poro-elastic model is unable to reproduce the observed wave dispersion in the existing laboratory data. Hence porous media deformation cannot explain the additional energy dissipation in the laboratory data. Shoushtari SMH, Cartwright N, Perrochet P, Nielsen P (2016) The effects of oscillation period on groundwater wave dispersion in a sandy unconfined aquifer: sand flume experiments and modelling. J Hydrol 533:412–440.     

双层饱和软土地基一维大应变固结研究

研究了双层软土地基一维非线性大应变固结问题,同时考虑了土体受沉积作用影响的自重分布以及渗透性在固结过程中的变化等因素。对此复杂问题,利用半解析法进行了求解。通过与已有的大应变固结解析解对比,检验了半解析法在大应变固结分析中的有效性。最后较为详细地分析了双层软土地基一维大应变固结性状,并与相应条件下的小应变固结作了比较。     

Large eddy simulation of extreme hydrodynamic forces on structures with mitigation walls using OpenFOAM

The objective of this study is to evaluate the performance of a large eddy simulation (LES) numerical model to assess the influence of mitigation walls with various cross sections on the tsunami-induced loading exerted on a freestanding structure. The validation of the model was performed using laboratory experiment results previously conducted by the second author. The employed experiments simulated a tsunami-like bore at two different impoundment depths, including 55 and 85 cm. The results showed that the one-equation subgrid-scale energy transport LES approach performs better than RANS models such as k-ε, k-ω and LRR and can accurately reproduce experimental data obtained for a wide range of experimental conditions.     

New models for heater wells in subsurface simulations, with application to the in situ upgrading of oil shale

Downhole electrical heating can be used to achieve the high temperatures required for in situ upgrading of oil shale or oil sands. Heater-well models are needed if this process is to be simulated accurately. The traditional Peaceman approach used for fluid injection and production wells may not be applicable because it does not capture transient effects, which can be important in downhole heater models. Standard models also neglect the effects of heterogeneity and temperature dependence in the rock properties. Here, we develop two new models for representing heater wells in reservoir simulators. The first model is applicable for homogeneous systems with properties that are not temperature dependent. For such cases, we develop a semi-analytical procedure based on Green’s functions to construct time-dependent heater-well indexes and heater-block thermal transmissibilities. For the general case, which can include both fine-scale heterogeneity and nonlinearity due to the temperature dependence of rock properties, we present a numerical procedure for constructing the heater-well model. This technique is essentially a near-well upscaling method and requires a local fine-scale solution in the near-well region. The boundary conditions are determined using a local-global treatment. The accuracy of the new heater-well models is demonstrated through comparison to reference solutions for example problems. The approach is then applied for the coarse-scale modeling of the in situ upgrading of oil shale, which entails a thermal-compositional simulation with chemical reactions. The model is shown to provide an accurate and efficient solution for this challenging problem.     

A novel fuzzy <Emphasis Type="Italic">K</Emphasis>-nearest neighbor inference model with differential evolution for spatial prediction of rainfall-induced shallow landslides in a tropical hilly area using GIS

This research represents a novel soft computing approach that combines the fuzzy k-nearest neighbor algorithm (fuzzy k-NN) and the differential evolution (DE) optimization for spatial prediction of rainfall-induced shallow landslides at a tropical hilly area of Quy Hop, Vietnam. According to current literature, the fuzzy k-NN and the DE optimization are current state-of-the-art techniques in data mining that have not been used for prediction of landslide. First, a spatial database was constructed, including 129 landslide locations and 12 influencing factors, i.e., slope, slope length, aspect, curvature, valley depth, stream power index (SPI), sediment transport index (STI), topographic ruggedness index (TRI), topographic wetness index (TWI), Normalized Difference Vegetation Index (NDVI), lithology, and soil type. Second, 70 % landslide locations were randomly generated for building the landslide model whereas the remaining 30 % landslide locations was for validating the model. Third, to construct the landslide model, the DE optimization was used to search the optimal values for fuzzy strength (fs) and number of nearest neighbors (k) that are the two required parameters for the fuzzy k-NN. Then, the training process was performed to obtain the fuzzy k-NN model. Value of membership degree of the landslide class for each pixel was extracted to be used as landslide susceptibility index. Finally, the performance and prediction capability of the landslide model were assessed using classification accuracy, the area under the ROC curve (AUC), kappa statistics, and other evaluation metrics. The result shows that the fuzzy k-NN model has high performance in the training dataset (AUC?=?0.944) and validation dataset (AUC?=?0.841). The result was compared with those obtained from benchmark methods, support vector machines and J48 decision trees. Overall, the fuzzy k-NN model performs better than the support vector machines and the J48 decision trees models. Therefore, we conclude that the fuzzy k-NN model is a promising prediction tool that should be used for susceptibility mapping in landslide-prone areas.     

寒区隧道围岩最大冻结深度计算的半解析方法

寒区隧道围岩的最大冻结深度是隧道抗冻胀结构设计、防排水与保温隔热层设计的重要基础参数。基于准稳态假定,采用积分法推导了能够考虑衬砌、保温层及冻结围岩中未冻水含量的寒区隧道围岩最大冻结深度的解析计算公式;利用围岩温度场数值模拟结果反演得出了解析计算公式中的参数影响半径与冻结半径比 的取值,从而得到了围岩最大冻结深度的半解析解。将所得解的计算结果与现场实测数据及数值模拟结果进行了对比,验证了所得解的合理性。利用得到的半解析解分析了工程冻土段围岩冻结深度的影响因素,结果表明：初始地温、年平均气温对冻结深度的影响最为明显,岩体骨架导热系数、岩体孔隙率的影响次之。     

Heave Studies on Fly Ash-Stabilised Expansive Clay Liners

Clay liners or compacted earthen barriers are important barrier materials used for preventing contaminant transport through soils. A low hydraulic conductivity (k) is a significant parameter that governs the design and construction of clay liners. Compacted expansive clays, which are montmorillonite clays, also have a very low hydraulic conductivity (k). When expansive clays are blended with fly ash, an industrial waste, the hydraulic conductivity (k) further reduces as the ash-clay blends result in increased dry densities at increased fly ash contents. Hence, fly ash-stabilised expansive clay can also be proposed as a unique clay liner material. As expansive clays undergo heave when they come into contact with water, it is necessary to study the heave behaviour of fly ash-stabilised expansive clay liners. This paper presents heave studies on fly ash-stabilised expansive clay liners. Fly ash in different contents by dry weight of the expansive clay was added to the clay, and the ash-clay blend was compacted as a liner overlying a natural field soil layer. Compacted lateritic clay was used for simulating the natural field soil into which contaminants migrate. Calcium chloride (CaCl₂) solution of varying concentration (5, 10, 20, 50, 100 and 500 mM) was used as the permeating fluid in the heave studies. The rate of heave and the amount of heave of the fly ash-stabilised expansive clay liners were monitored. Deionised water (DIW) was also used as inundating fluid for comparative study. Heave (mm) decreased with increase in solute concentration for all fly ash contents. For a given solute concentration, heave decreased up to a fly ash content of 20 % and thereafter it increased when the fly ash content was increased to 30 %. Heave of the fly ash-stabilised expansive clay liners was correlated with their permeability, liquid limit (LL) and free swell index (FSI) pertaining to the respective fly ash content and CaCl₂ concentration.     

Permeability Heterogeneity in a Fractured Sandstone–Mudstone Rock Mass in Xiaolangdi Dam Site, Central China

Abstract: Heterogeneity of permeability in fractured media is a hot research topic in hydrogeology. Numerous approaches have been proposed to characterize heterogeneity in the last several decades. However, little attention has been paid to correlate permeability heterogeneity with geological information. In the present study, several causes of permeability heterogeneity, that is, lithology, tectonism, and depth, are identified. The unit absorption values (denoted as ω), which are results obtained from the packer test, are employed to represent permeability. The variability of permeability in sandstone–mudstone is so significant that the value of unit absorptions span 3–4 orders of magnitude at any depth with several test sections. By declustering, it has been found that under a similar tectonic history, the means of permeability differ greatly at different formations as a result of different mudrock contents. It has also been found that in the same formation, permeability can be significantly increased as a result of faulting. The well-known phenomenon, the decrease in permeability with depth, is found to be caused by the fractures in the rock mass, and the relationship between permeability and depth can be established in the form of logω–logd. After subtracting the trend of ω with absolute depth, the mean of the residual value at each relative depth can be well correlated with the distribution of mudstone. The methods proposed in this paper can be utilized to research in similar study areas.     

Hydraulic Conductivity of Fly Ash-Amended Mine Tailings

The objective of this study was to evaluate the effect of fly ash addition on hydraulic conductivity (k) of mine tailings. Mine tailings used in this study were categorized as synthetic tailings and natural tailings; two synthetic tailings were developed via blending commercially-available soils and natural tailings were collected from a garnet mine located in the U.S. Two fly ashes were used that had sufficient calcium oxide (CaO) content (17 and 18.9 %) to generate pozzolanic activity. Hydraulic conductivity was measured on pure tailings and fly ash-amended tailings in flexible-wall permeameters. Fly ash was added to mine tailings to constitute 10 % dry mass of the mixture, and specimens were cured for 7 and 28 days. The influence of fly ash-amendment on k of mine tailings was attributed to (1) molding water content and (2) plasticity of the mine tailings. Tailings that classified as low-plasticity silts with clay contents less than 15 % exhibited a decrease in k when amended with fly ash and prepared wet of optimum water content (w _opt ). Tailings that classified as low-plasticity clay exhibited a one-order magnitude increase in k with addition of fly ash for materials prepared dry or near w _opt . The decrease in k for silty tailings was attributed to formation of cementitious bonds that obstructed flow paths, whereas the increase in k for clayey tailings was attributed to agglomeration of clay particles and an overall increase in average pore size. The results also indicated that the effect of curing time on k is more pronounced during the early stages of curing (≤7 days), as there was negligible difference between k for 7 and 28-days cured specimens.