Hydraulic Boundary Research Articles

Groundwater flow system of the Abijata-Langano-Ziway lakes basin, Ethiopia

The Abijata-Langano-Ziway Lakes Basin (ALZLB) is situated in the Central part of the Main Ethiopian Rift. The availability and dynamics of groundwater in the Abijata-Langano-Ziway Lakes Basin (ALZLB) are primarily controlled by its geological and hydrogeological characteristics, shaped by volcanic-tectonic and sedimentary processes. The basin faces significant challenges, including drastic change in land use pattern, rapid population growth sustained by subsistence farming, over-extraction of water resources, and vulnerability to climate change and fragile ecosystems. These issues emphasize the urgent need for effective water resource management.To understand this complex system, a numerical groundwater flow model was employed to characterize the groundwater flow system within the ALZLB and examine its interaction with surface water bodies. The MODFLOW model translates the conceptual understanding of the basin's hydrogeology into a mathematical representation, allowing for numerical analysis. The model incorporates input parameters such as hydraulic conductivity and boundary conditions representing groundwater inflow and outflow. Steady-state numerical calculation was used to characterize the qualitative hydrogeological conceptual model into numerical representation and thereby describe the groundwater system.The calibrated model exhibited excellent agreement between simulated and observed groundwater levels. Statistical measures indicated a strong correlation (R2 = 0.98) and high efficiency (NSE = 0.97) in replicating the observed data. Additionally, the Mean Error (ME) of −8.3 m suggests minimal bias in the simulations. Further analysis of the histogram residuals revealed that a significant portion of the simulated values (65 % and 82 %) fell within ±20 m and ±30 m of the observed groundwater levels, respectively. This revealed the model's accuracy in capturing the groundwater system's behavior.The model identified groundwater recharge and constant head boundaries as the primary sources of groundwater inflow, contributing 445 million cubic meters per year (MCM/year) and 90 MCM/year, respectively. Conversely, constant head boundaries represented the most significant outflow pathway, with a simulated discharge of 519 MCM/year. The calibrated balance between inflow and outflow (discrepancy of −0.75 %) confirms that the model effectively simulates steady-state groundwater flow conditions. The calibrated model demonstrates the model's capability to accurately represent the basin's groundwater system.

A physics knowledge-based surrogate model framework for time-dependent slope deformation: Considering water effect and sliding states

The surrogate model serves as an efficient simulation tool during the slope parameter inversion process. However, the creep constitutive model integrated with dynamic damage evolution poses challenges in development of the required surrogate model. In this study, a novel physics knowledge-based surrogate model framework is proposed. In this framework, a Transformer module is employed to capture strain-driven softening-hardening physical mechanisms. Positional encoding and self-attention are utilized to transform the constitutive parameters associated with shear strain, which are not directly time-related, into intermediate latent features for physical loss calculation. Next, a multi-layer stacked GRU (gated recurrent unit) network is built to provide input interfaces for time-dependent intermediate latent features, hydraulic boundary conditions, and water-rock interaction degradation equations, with static parameters introduced via external fully-connected layers. Finally, a combined loss function is constructed to facilitate the collaborative training of physical and data loss, introducing time-dependent weight adjustments to focus the surrogate model on accurate deformation predictions during critical phases. Based on the deformation of a reservoir bank landslide triggered by impoundment and subsequent restabilization, an elasto-viscoplastic constitutive model that considers water effect and sliding state dependencies is developed to validate the proposed surrogate model framework. The results indicate that the framework exhibits good performance in capturing physical mechanisms and predicting creep behavior, reducing errors by about 30 times compared to baseline models such as GRU and LSTM (long short-term memory), meeting the precision requirements for parameter inversion. Ablation experiments also confirmed the effectiveness of the framework. This framework can also serve as a reference for constructing other creep surrogate models that involve non-time-related across dimensions.

The John Mitchell Lecture 2022: thinking conceptually about groundwater problems

Many excavations and tunnels experience problems and instability caused by uncontrolled groundwater inflows or groundwater pressures that influence stability and soil behaviour. A range of groundwater control measures can be used to overcome these problems and create stable and workably dry conditions below groundwater level. A key challenge for designers is that the performance of the various different techniques is strongly influenced by the hydrogeological conditions at a site. Furthermore, the available ground investigation data may have data gaps or considerable uncertainty regarding key parameters such as hydraulic conductivity or hydraulic boundary conditions. This means that, when working with real-world data sets, there are some groundwater problems where analysis involves so many assumptions and uncertainties that the design outcomes are of little practical value. This paper will discuss how thinking conceptually about groundwater problems can be of great benefit when developing of groundwater control schemes, and that a robust conceptual model helps reduce the risk of designs being developed using inappropriate techniques. Historic examples from the 19 th Century and early 20 th century (before sophisticated methods of groundwater analysis were available) are described, where developing a conceptual understanding of groundwater conditions was vital in developing practical engineering solutions.

Susceptibility of hydraulic structures to internal erosion: modeling of suffusion process

Internal erosion is a primary cause of hydraulic structure failure, manifesting as two key phenomena: piping erosion and suffusion. These processes differ in their geometrical and hydraulic boundary conditions, resulting in varying levels of failure risk. Piping erosion is the more hazardous and rapid process, often leading to immediate failure if not promptly addressed. In contrast, suffusion gradually alters the permeability of the medium, potentially culminating in failure after a prolonged period of development. In this study, we propose a model for suffusion based on Darcy’s law, Papamichos' erosion law, and Einstein's viscosity evolution relation. The model describes the temporal evolution of the average porosity in the porous medium, the concentration of eroded particles in the fluid, and the mass of particles eroded, while highlighting the impact of hydraulic and mechanical parameters, such as the erosion coefficient and maximum porosity, on this evolution. The numerical solution is obtained using the finite difference method, with the sample discretized into elementary layers. For discretization, an explicit off-centered scheme was adopted. The simulation results reveal that suffusion is strongly influenced by soil hydraulic and mechanical parameters, particularly the erosion coefficient (λ) and final porosity (Ømax).

Analytical solution for one-dimensional chemo-hydro-mechanical coupled consolidation under time-dependent loading in buffer clay layer

An analytical method is developed for solving the coupled chemo-hydro-mechanical consolidation in a clay buffer layer under time-dependent loading. The coupled governing equations for the chemo-hydro-mechanical process are established in the time and spatial domain first. Then the governing equations are decoupled into two partial differential equations by introducing two variables. The analytical solutions corresponding to ramp and exponential loadings are finally derived based on the initial and boundary conditions. The developed analytical solutions are verified via comparing with the numerical results simulated by COMSOL Multiphysics. Based on the developed solutions, selected parametric study is carried out to investigate the influence of major parameters and hydraulic boundary conditions on the contaminants transport and pore water pressure dissipation in buffer clay layer. The results show that the major parameters have effects on the generation and dissipation of pore pressure, while only effective coefficient of diffusion, coefficient of ultrafiltration and relative change of total density of pore liquid significantly affect the contaminant migration process. Compared with a single drainage boundary, the pore pressure dissipation and contaminant migration in a double drainage soil layer are much faster. The longer the loading time of mechanical loading, the more significant the negative pore pressure caused by the concentration gradient.

Deep Learning-Based Calculation Method for the Dry Beach Length in Tailing Ponds Using Satellite Images

The dry beach length determines the hydraulic boundary of tailings impoundments and significantly impacts the infiltration line, which is crucial for the tailings dam. A deep learning method utilizing satellite images is presented to recognize the dry beach area and accurately measure the length of dry beaches in tailing ponds. Firstly, satellite images of various tailing ponds were gathered and the collection was enlarged to create a dataset of satellite images of tailing ponds. Then, a deep learning method was created using YOLOv5-seg to identify the dry beach area of tailing ponds from satellite images. The mask of the dry beach region was segmented and contour extraction was then carried out. Finally, the beach crest line was fitted based on the extracted contour. The pixel distance between the beach crest line and the dry beach boundary was measured and then translated into real distance by ground resolution. This paper’s case study compared the calculated length of dry beach with the real length obtained by field monitoring. The results of the case study showed that the minimum error of the method was 2.10%, the maximum error was 3.46%, and the average error was 2.70%, indicating high precision for calculating dry beach length in tailing ponds.

Experimental Study on Heat Conduction and Water Migration of Composite Bentonite Samples.

The joints of buffer material composite blocks as potential weak parts in the engineering barrier system of a high-level radioactive waste (HLW) repository must be studied in depth. Therefore, a laboratory experiment device suitable for unsaturated composite bentonite samples was developed. The evolution of temperature and volumetric water content at different locations of Gaomiaozi (GMZ) composite bentonite samples with time before and after simulated water inflow was measured by the experiment device. According to the experimental results, the thermal conductivity and hydraulic conductivity of the joint location after healing of the composite bentonite samples were obtained. The experimental results show that the change in the internal temperature of the composite bentonite samples is mainly affected by the temperature boundary and that the change in the internal water has little effect on it. In a short period of time, the loading of hydraulic boundary conditions only makes the volumetric water content of the soil near the hydraulic boundary increase significantly but has little effect on other locations. And, affected by the temperature boundary, the volumetric water content of the soil near the temperature boundary gradually decreases with time. The process of hydration swelling of the composite bentonite sample is accompanied by the adjustment of stress. The composite bentonite samples are continuously squeezed to the joint area after hydration swelling, the whole composite samples are generally homogenized, and the joints between the composite bentonite samples tend to heal. The thermal conductivity and permeability of the joint location after healing can meet the requirements of the engineering barrier of the HLW repository.

Galerkin Kantorovich Method for Solving the Terzaghi’s One-Dimensional Soil Consolidation Equation

This paper presents the Galerkin-Kantorovich variational method for solving the Terzaghi’s one-dimensional consolidation equation for two-way drainage conditions. The solution was considered as an infinite series of known coordinate (shape) functions and unknown function of time which we sought such that the resulting functional is minimized. The shape functions satisfied the hydraulic boundary conditions at the boundary of the consolidating soil. Galerkin-Kantorovich variational integral equation was thus formulated for the initial boundary value problem using residual minimization principles. The solution resulted in a system of first order ordinary differential equations in which was solved for Orthogonalization principles were used to obtain the integration constants in terms of initial pore water pressure, thus yielding the general solution. Solutions for constant initial excess pore water pressure were obtained and found to be the closed-form solution. The solutions were presented in terms of global (average) degrees of consolidation and tabulated. The results obtained were exact and identical with results previously found using separation of variables techniques.

Comparative study of two-phase flow approaches for modeling conjugate heat transfer in a three-dimensional wavy microchannel-heat sink with CuO-water nanofluid

This study aims to numerically investigate the conjugate heat transfer (CHT) and the changes in the hydraulic and thermal terms of laminar flow (300 ≤ Re ≤ 800) in a 3-D wavy microchannel heat sink (MCHS). The obtained results from different nanofluid flow simulated models will be compared. The numerical simulation approaches used include single-phase, mixture, Eulerian, DPM, and DDPM. The effect of adding 1%, 3%, and 6% concentration of CuO nanoparticles (100 nm) in deionized water as the base fluid is examined on various parameters such as local and axial temperature, heat transfer convective coefficient, friction factor, Nusselt number (Nu), velocity distribution, and thermal and hydraulic boundary layer parameters. The substrate surface, due to its larger area surface and the amplitude of the sinusoidal wave, has a greater impact on the nanofluid flow as a channel bottom conjugate surface compared to others. The results obtained from the different models show close agreement with each other for various cases. For example, at Re = 304, the average Nu and friction factor for pure water are approximately 10.43 and 0.0260, respectively. For water with 0.01 concentration of CuO nanoparticles, Nu is found to be in the range of 10.43–10.78, and the friction factor ranges from 0.260 to 0.290, depending on the approach used for simulation. This shows a 2% increase in Nusselt number compared to a 0.05% increase in the friction factor. Moreover, these values increase by approximately 5.7% and 11.3% on average with an increase in CuO nanoparticle concentration to 0.06. Additionally, the DPM and DDPM models show a 15% difference in the scattering of CuO nanoparticles compared to the Eulerian-Eulerian models. The single-phase model presented in this study yields similar results to the multiphase approaches. Furthermore, the PEC parameter increases by about 1.9% with the addition of CuO nanoparticles at a concentration of 0.06.

A flow through coaxial cell to investigate high frequency broadband complex permittivity: Design, calibration and validation

This paper presents a new apparatus: a large flow through coaxial cell designed for broadband dielectric characterization of material under controlled hydraulic and chemical boundaries. The cell is calibrated with a single measurement made on a perfectly known dielectric liquid (deionized water) together with an optimization procedure. Then, two methods are proposed to compute the dielectric characteristics: an iterative solver and an optimization method. These two methods are systematically investigated for two reference liquids: a low loss dielectric material (ethylene glycol) and high loss dielectric liquid (saline solutions with different concentration). Tabulated data were used to perform a quantitative error analysis in terms of estimated complex permittivity. The results have shown high performance in terms of real part and good performance in terms of real part. The measurements on saline solution also highlight the impact of electrode polarization with dramatic effect in the lower part of the frequency range.

Stability analysis of a hydropower plant containing pipe and channel flows

Abstract This work studies the operational stability of the tailrace network containing mixed types of flows in a hydropower station with the complex frequency-domain networked transfer matrix method. First, the networked transfer matrix of the system plant is built based on the dynamic equations of the pipes, channels and hydraulic boundaries in the system. Then, the model is applied to analyze the stable state of the water conveyance network of a hydropower plant located in southwest China. The values of hydraulic state variables at the critical stable point under the multi-machine operating condition are obtained via eigenvalue analysis. The proposed overall transfer matrix model is proved to achieve satisfactory performance by the comparison of the statistic indexes obtained from modeling computation and those from the measured data.

Effects of dynamic capillarity on the shear strength of sandy soils during transient two‐phase flow: Insights from non‐equilibrium triaxial simulations

AbstractModeling two‐phase flow in unsaturated porous media is not only important to vadose zone hydrology but also of great value in diverse disciplines. Common approaches use a simplified relationship between fluid pressure difference and saturation, neglecting the influence of saturation change rates. However, many studies have suggested that the applicability of this approach is limited to situations where the rate of change in saturation is insignificant. Despite several studies highlighting the importance of non‐equilibrium capillarity effects in unsaturated flow modeling, its significance in the mechanical response of the porous medium remains unclear. This study thus aims to address this gap by comparing the simulation results of the traditional static approach and an advanced approach that incorporates dynamic capillarity effects. The comparison is conducted under various flow boundary conditions to assess the magnitude of the differences between the two approaches. The results indicate that as the hydraulic boundary conditions’ absolute values increase, the contrast between the mechanical response of the two simulation scenarios (dynamic and static) becomes more significant. For instance, the dynamic model can predict shear strengths up to 50% higher than the static model. This highlights the importance of considering non‐equilibrium effects while modeling the mechanical behavior of an unsaturated porous medium. Finally, the parametric study of the effect of dynamic coefficient, air entry value, and saturated conductivity reveals the more pronounced effect of the dynamic coefficient on the mechanical response.

A U-Net architecture as a surrogate model combined with a geostatistical spectral algorithm for transient groundwater flow inverse problems

Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems, and inverse techniques play a fundamental role in modeling hydrogeological parameters and assessing their uncertainties. Nonetheless, the use of a forward model in these methods can be highly time-consuming, especially with an increasing number of model parameters. To address this issue, we propose a surrogate model based on a U-Net architecture that replaces the transient groundwater flow model, reducing runtime and enabling a fast quantification of uncertainties related to key parameters, including heterogeneous hydraulic conductivity, boundary conditions, specific storage, and pumping rate. The surrogate is trained using limited evaluations of the forward model to learn the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. The physical principles of the studied problem, including boundary conditions, specific storage, and source terms, are also mapped and introduced as inputs to the model to enhance its understanding of the governing equation of transient groundwater flow. To speed up learning using image–image regression, the previously predicted transient hydraulic heads also serve as an input to predict the transient heads at the current time step. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem, a pumping test of 12 h, using the surrogate model in place of the forward model. Our study demonstrates that the trained U-Net accurately reproduces the state variables corresponding to a specific parameter field, and in terms of computational demand, using U-Net as a surrogate model reduces the required computational time by approximately an order of magnitude for the defined problem. The proposed approach offers an efficient and accurate method for groundwater flow parameter characterization and uncertainty quantification in complex aquifer systems.

Consolidation effects on pipe-soil interaction due to tunneling

Existing studies on soil-pipe interaction due to tunneling mainly focus on short-term responses. However, in areas with high water tables and low permeability soil, long-term ground movement and associated pipe responses may occur due to dissipation of excess pore pressure generated during tunnel construction. In this paper, a Winkler solution with time-varying subgrade modulus and the corresponding greenfield soil displacement formula are developed to investigate the tunneling effects on existing pipelines. The pipe is considered as an infinite Euler beam of finite width resting on a poroelastic half-space, and adhesion and drainage effects between the pipe and soil are considered using bounding techniques. The greenfield consolidation settlement is evaluated using a modified Gaussian curve. The findings indicate that the subgrade modulus decreases while greenfield soil displacement increases during the consolidation process. The time-dependent behavior of the subgrade modulus is governed by the drainage condition at the pipe-soil interface, whereas the greenfield soil displacement is primarily influenced by the drainage condition at the tunnel-soil interface. The study reveals that the bonded contact condition, hydraulic boundary condition, and displacement constraint conditions all influence the bending moment of the pipe.

How borehole wall elasticity affects wellbore storage capacity in periodic hydraulic tests

Characterizing fluid transport and pore pressure diffusion is key for monitoring and understanding many natural (e.g., seismically active zones and volcanic systems) and engineered environments (e.g., enhanced geothermal reservoirs and CO2 underground storage). Borehole hydraulic testing allows for inferring relevant properties of the probed subsurface volume, such as, for example, its transmissivity and diffusivity, assessing the governing flow regime as well as detecting the presence of hydraulic boundaries. Periodic hydraulic tests (PHT) achieve these objectives using an oscillatory fluid injection procedure while measuring the fluid pressure response in monitoring boreholes. The relevant information on the pressure diffusion process occurring in a probed formation is retrieved from the phase shifts and amplitude ratios between the flow rate and the interval pressure. In general, the interpretation of PHT data relies on the assumption that the pressure diffusion process is largely unaffected by the deformation of the probed rock volume. To assess this assumption, we present a conceptual PHT model based on the theory of poroelasticity to investigate the role played by hydromechanical coupling (HMC) effects during PHT and to assess whether and to what extent additional mechanical information can be extracted from these tests. These effects include the influence of the borehole wall deformation on the wellbore storage coefficient Sw, which quantifies the difference between the injected flow rates and those actually entering the porous formation. We show that, in homogeneous formations, the commonly taken approach based on the uncoupled diffusion solution for radial flow reproduces the results of our HMC model. However, neglecting the deformation effect of the borehole wall on the storage capacity of the system during injection can lead to underestimations of both transmissivity and diffusivity, particularly at shorter oscillation periods. We present analytical expressions for the borehole wall deformation contribution to Sw, which depends on the shear modulus and does not change with the oscillatory period. We show that it is possible to obtain the effective Sw along with the transmissivity and diffusivity using observations at various oscillatory periods. In the presence of hydraulic boundaries, such as no-flow or constant-pressure boundaries, at a given distance from the injection borehole, Sw becomes period-dependent, introducing apparent variations in the inferred shear modulus of the formation if the associated HMC effects are not accounted for. Our results thus highlight the importance of accounting for HMC effects in PHT data interpretation, not only to reliably and accurately characterize and monitor hydraulic properties but also to fully exploit the potential of PHT to provide additional information on the mechanical behavior of the probed rock volume.

A physics-based model for fluvial valley width

Abstract. The width of fluvial valley floors is a key parameter to quantifying the morphology of mountain regions. Valley floor width is relevant to diverse fields including sedimentology, fluvial geomorphology, and archaeology. The width of valleys has been argued to depend on climatic and tectonic conditions, on the hydraulics and hydrology of the river channel that forms the valley, and on sediment supply from valley walls. Here, we derive a physically based model that can be used to predict valley width and test it against three different datasets. The model applies to valleys that are carved by a river migrating laterally across the valley floor. We conceptualize river migration as a Poisson process, in which the river changes its direction stochastically at a mean rate determined by hydraulic boundary conditions. This approach yields a characteristic timescale for the river to cross the valley floor from one wall to the other. The valley width can then be determined by integrating the speed of migration over this timescale. For a laterally unconfined river that is not uplifting, the model predicts that the channel-belt width scales with river flow depth. Channel-belt width corresponds to the maximum width of a fluvial valley. We expand the model to include the effects of uplift and lateral sediment supply from valley walls. Both of these effects lead to a decrease in valley width in comparison to the maximum width. We identify a dimensionless number, termed the mobility–uplift number, which is the ratio between the lateral mobility of the river channel and uplift rate. The model predicts two limits: at high values of the mobility–uplift number, the valley evolves to the channel-belt width, whereas it corresponds to the channel width at low values. Between these limits, valley width is linked to the mobility–uplift number by a logarithmic function. As a consequence of the model, valley width increases with increasing drainage area, with a scaling exponent that typically has a value between 0.4 and 0.5, but can also be lower or higher. We compare the model to three independent datasets of valleys in experimental and natural uplifting landscapes and show that it closely predicts the first-order relationship between valley width and the mobility–uplift number.

Analysis of seepage failure probability for high core rockfill dams during rapid drawdown of reservoir water level

Rapid drawdown (RDD) is an abnormal reservoir flood control operation that may cause seepage failure of high core rockfill dams. In this paper, a novel framework combining Bayesian inference and transient unsaturated seepage simulation is proposed to evaluate the seepage failure probability of the core during RDD. The dynamic hydraulic boundaries utilized in the simulation are first determined by the performance of water release structures. The extreme learning machine (ELM) is then employed as the surrogate model to establish the mapping relationship between material parameters with simulated seepage pressure and hydraulic gradient. The Bayesian inference method is applied to characterize the uncertainty of material parameters based on seepage monitoring data. Finally, the posterior distribution samples of random parameters are utilized to calculate the seepage failure probability of the core. The seepage safety of the core under different drawdown rates is studied with a real 186 m high core rockfill dam. The results reveal that a faster RDD rate can lead to an increased probability of seepage failure. The maximum failure probability is 35.56 % for the four release structures working together (about 0.316 m/h), higher than 23.16 % for the three release structures (about 0.165 m/h). It is also found that the peak of seepage failure probability often occurs in the middle stage of RDD. Therefore, to ensure the safety of the project, it is important to control the RDD rate and carefully monitor the seepage pressure. From the point of view of seepage failure, the proposed method for evaluating the safety of core rockfill dams under RDD is of high guiding significance to the risk assessment of similar projects under extreme conditions.

Influence of hydrogen blending on the operation of natural gas pipeline network considering the compressor power optimization

Blending hydrogen into the existing natural gas pipeline network is regarded as the most potential transportation mode on the utility-scale. However, the impact of hydrogen on the operation performance of the pipeline remained unclear. This paper analyzes the economic and environmental performance of natural gas pipeline under different hydrogen blending ratios and different hydraulic boundary conditions. In order to reduce the operation costs and carbon emissions in each condition, this paper establish a non-linear optimization model to get the new operation plan of the pipeline system. Further, in order to characterize different boundary conditions of the system, four scenarios, namely, the baseline scenario (BS), the setpoint of flow rate scenario (SF), the setpoint of pressure (SP), and the setpoint of heat flow rate (SH) are proposed in this paper. Two studied cases demonstrated that: (1) the original compressor for natural gas can adapt to a hydrogen blending without change the type of compressor. (2) The optimization model has significant potential in reducing the economic cost and carbon emissions of the system with an average decrease of 11.48%. (3) For every 1% of hydrogen added, the annual operating cost of the system is reduced by $0.73 million (3.29%) in SF, 0.017 million (0.08%) in SP, or increased by $1.67 million (7.50%) in SH. Moreover, the annual carbon emission is reduced by 0.38 kt (3.53%) in SF, 0.047 kt (0.44%) in SP, or increased by 0.76 kt (7.14%) in SH. However, when the hydrogen mixing ratio is more than 8%, the contrary trend may occur. (4) The maximum blending ratio at different points of the multi-source pipeline network are physically interdependent. The paper proposed an optimization model for the 2-E analysis of the pipeline and can provide theoretical guidance for the further application of this transportation mode.

Indentation over a transversely isotropic, poroelastic, and layered half-space

Poroelastic materials are common in nature and have applications in many engineering fields. In this paper, we derive a general solution of indentation over a multilayered half-space consisting of transversely isotropic and poroelastic materials. The rigid disc-shaped indenter is subjected to a vertical force of Heaviside time-variation. The solution is expressed in terms of the recently introduced powerful Fourier-Bessel series (FBS) system of vector functions combined with the unconditionally stable dual-variable and position method for dealing with layering. Since the problem is a mixed boundary-value one, the Green's functions due to a vertical ring-load are first derived which are then utilized in the integral least-square formulation to derive the solution. In terms of the FBS method, the expansion coefficients, which are further called Love numbers, are discrete, and therefore can be pre-calculated and used repeatedly for different field points on the surface. As such, the solution based on the new FBS method is more efficient and accurate than previous integral-transform methods. This new FBS method is particularly attractive when dealing with mixed boundary-value problems where time-variation is further involved. Numerical examples are conducted to validate the accuracy of the proposed solution and to demonstrate the effects of material layering, geometry, and hydraulic boundary conditions on the contact performance of the material system.

Characterizing uncertainty in process-based hydraulic modeling, exemplified in a semiarid Inner Mongolia steppe

Assessing root sources of three uncertainties – parameterization of soil hydraulic characteristics, boundary conditions, and estimation of source/sink terms – is a significant challenge in soil water transport modeling. This study aims to evaluate the uncertainty of three each widely-used parameter estimation methods affecting plot-scale water dynamics. The study employs HYDRUS, a process-based hydrologic model, to incorporate these uncertainties and compare model predictions to measured values in a semiarid Inner Mongolia steppe, China. Soil hydraulic parameters are determined using two direct methods (laboratory-derived approach and evaporation method) and one indirect method (neural network). While each hydraulic parameter method generally simulates soil moisture dynamics, the evaporation method performed better, especially under dry conditions. This suggests that measuring the intensity properties, such as unsaturated hydraulic conductivity, with the evaporation method is crucial for reasonable soil moisture simulation. The study also demonstrates the impact of different applied boundary conditions on simulated soil moisture, specifically the partitioning of reference FAO evapotranspiration via one direct method (soil fraction cover) and two indirect methods (leaf area index and crop height). The partitioning via soil fraction cover reflected a better simulation. Additionally, the study compares the uncertainties of root water uptake function with root growth parameters and constant root depth referenced to grass and pasture, and finds no significant difference among them. Comparing three sources of uncertainty in predicting soil moisture, the study concludes that the input soil hydraulic parameter is more sensitive than evapotranspiration partitioning or representation of root water uptake function. Our study highlights that measuring soil intensity properties can better reflect the effects of land use change, such as compaction, on field water transports.