Most semi-circular bend (SCB) tests on concrete have been conducted with a pre-crack with a straight-through tip, thereby undermining the determination of the tensile fracture toughness (KIc). Therefore, the present study involved mixed-mode (tensile–shearing) fracture propagation in concrete semi-circular chevron-notched disks (i.e., with a sharp notch tip) using SCB tests and the FRANC2D numerical simulation software. The inclined notch angle (β) was varied from 0° to 70° while the other settings remained fixed, and the crack mouth opening displacement (CMOD) of the notch was measured constantly. The stress distribution was analyzed using finite-element simulations, and the experimental results showed that this testing method was robust. The maximum failure load and the fracture propagation angle increased with β, and wing fracture was observed. With FRANC2D simulating these SCB tests successfully, it was found that the tensile stress concentration around the notch tip moved toward the upper face of the notch, and the compressive stress concentration formed on the notch tip. The tensile mode was generated as the CMOD kept increasing for β = 0–30°, whereas the mixed mode became more evident as the CMOD kept decreasing for β = 45–70°. The fracture process zone was found for β = 0–30° but not for β = 45–70°. This mixed-mode fracture is predicted better by the criterion of extended maximum tangential strain than by other criteria, and there is a linear relationship between CMOD and KIc, as examined previously for pavement and concrete materials.
The coal seam gas and underground coal gasification industry has caused concerns with the risk of potential groundwater contamination. Gases leaked from coal seams are thought to be a source of groundwater pollution. However, the basic principles and controlling parameters for gases seepage from deep ground formations to the surface are not fully understood. Microbubble transport, as a possible mechanism for gases transport in the subsurface, is investigated here through a laboratory-scale experiment. Microbubbles were generated from a bubble diffuser and released into a 2D artificial transparent porous medium. The point source of bubble injection was used to simulate the release of gases from geological faults/fractures. The medium's transparency enabled a clear visualization of the bubble pathways. Images captured by cameras were used to facilitate analyses on the bubble transport behavior affected by advection and dispersion.
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.
Although many unsaturated soil experiments have successfully delivered positive outcomes, most studies just concisely illustrated sensor techniques, because their main objectives focused on bridging research gaps. Inexperienced research fellows might rarely follow up those techniques, so they could encounter very trivial and skill-demanding difficulties, undermining the quality of experimental outcomes. With a motivation to avoid those, this work introduces technical challenges in applying three sensor techniques: high precision tensiometer, spatial time-domain reflectometry (spatial TDR) and digital bench scales, which were utilized to measure three fundamental variables: soil suction, moisture content and accumulative outflow. The technical challenges are comprehensively elaborated from five aspects: the functional mechanism, assembling/manufacturing approaches, installation procedure, simultaneous data-logging configurations and post data/signal processing. The conclusions drawn in this work provide sufficient technical details of three sensors in terms of the aforementioned five aspects. This work aims to facilitate any new research fellows who carry out laboratory-scale soil column tests using the three sensors mentioned above. It is also expected that this work will salvage any experimenters having troubleshooting issues with those sensors and help researchers bypass those issues to focus more on their primary research interests.
The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.
In transient multiphase seepage, soil water retention behaviour deviates from equilibrium, leading to dynamic nonequilibrium effects in which suction and water content change asynchronously. This yields flow-rate-dependent soil water retention curves that critically affect predictions of fluid and solute transport in vadose zone and undermine the safety assessment of unsaturated soil slope stability. This brief review synthesises advances and challenges in understanding this behaviour through examining microscale multiphase physical mechanisms and macroscale influences of soil type and hydraulic history. Key experimental techniques, from instrumented soil columns to advanced electromagnetic and imaging methods, are evaluated alongside their limitations. There is also an analysis of continuum- and pore-scale numerical models, including those incorporating dynamic capillary coefficients, pore network models, and multiphase computational fluid dynamics. Despite progress, major challenges persist, including the empirical nature and scale-dependence of model parameters, path-dependent hysteresis, and the lack of a unified theoretical framework that couples dynamic capillarity with soil deformation. Future interdisciplinary efforts integrating advanced experimentation, multiscale numerical modelling, and multiphase physics-based constitutive theories are essential to develop predictive tools for more accurate vadose-zone hydrology and related engineering applications. Document Type: Invited review Cited as: Yan, G., Liu, B., Bore, T., Torres, S. A. G., Li, L., Scheuermann, A. Advances in dynamic soil water retention behaviour and implications for vadose zone hydrology. Capillarity, 2026, 19(1): 26-38. https://doi.org/10.46690/capi.2026.04.03
A transparent water-based polymer named Aquabeads has been recently applied to model natural soil because its high transparency facilitates studies of the geotechnical problems using the visual technique. Before physically modelling flow in the hydrated Aquabeads, it is necessary to determine its hydraulic properties. According to many previous studies, the noncrushed Aquabeads were gravel-size particles but had the hydraulic conductivity (k) of clean medium sand under unconsolidated conditions. For investigating this inconsistency, the constant head tests are conducted using a rigid wall permeameter in this study. The preliminary results show that the k calculated using Darcy’s law highly agree with prior studies. However, the nonlinearity between the hydraulic gradients and Reynolds numbers (Re > 1) indicates the non-Darcy flow regime. Also, an initial hydraulic gradient was observed, thus raising concerns about local heterogeneity. With multiple manometer readings, the analysis for each layer shows that the k decreases from top to bottom with flow regimes transition. After each test, a layer of crushed samples was found on the porous plate when unloading the specimen. In conclusion, Darcy’s law is only robust to calculate the k of partially crushed Aquabeads for Re < 1. Instead, Forchheimer flow should be considered in future physical modelling work for Re > 1. The inconsistency is due to inevitably sample crushing.
Flash delay (non-equilibrium phenomenon) occurred in refrigerant flow in a capillary affects apparently the prediction accuracy of refrigerant flow rate in a capillary. “Combined nucleation” theory that accounts for both “homogeneous nucleation” and “wall nucleation” was developed, based on which, a flash flow model was established. Underpressure, an important parameter reflecting non-equilibrium phenomenon in a capillary, was obtained with this flash flow model. The simulation results agree well with the experimental data. The results show that underpressure increases with increase of the mass flow rate of refrigerant and also increases with decrease of inlet temperature.
Different land utilization types have unignorable impacts on adjacent aquifers, so studying the effects of varying land utilization types on groundwater balance and groundwater table in arid and semi-arid areas is crucial to facilitate the rational development of territorial space and groundwater resource management. This study investigated the relationship between land utilization type variations and groundwater dynamics from spatial and temporal scales in Huocheng plain, Xinjiang, China, via taking advantage of different land utilization maps provided by remote sensing techniques in 1990, 2000, and 2015. Based on the analysis of results, the findings can be summarized as follows. First, the cultivated and construction land has expanded significantly in the past 25 years. The migration of the regional center of cultivated land was insignificant, as it is still located almost in the center of the entire study area. However, the transfer span of the location center of construction land was more prominent, and its moving direction was mainly from south to northeast, directly affecting the groundwater balance state and groundwater table. Second, the total amount of groundwater storage exhibited a remarkable reduction, from a recharge in 1990 to a continuous discharge in 2000–2015, during which the total recharge and discharge had both continuously declined. Meanwhile, recharging and discharging elements were also changed profoundly as less groundwater recharges from ambient aqueous environments and more groundwater extraction. Thus, human activities were the fundamental driving terms causing the changes in groundwater sources. Third, the groundwater table gradually and continuously dropped from south to northeast in the study area over time. The drawdown of spatially averaged groundwater tables was positively correlated with construction and cultivated area extension. In addition, compared to the former literature, this study offers an alternative approach for groundwater protection and optimization of territorial space development and utilization in arid and semi-arid areas.
Granular Flow through Porous Media: Implications for GeologicalFluid Dynamics
The soil water retention curve (SWRC) is usually measured by the axis translation technique (ATT), assuming a specimen thickness of a few centimetres. Usually, this assumption is unquestionable to ensure the representative elementary volume (REV). However, such an assumption cannot always be conserved with coarser soil regarding the local heterogeneities generated by larger pore sizes. In addition, the authentic SWRC is supposed to be the soil moisture profile above the phreatic surface. Those issues, therefore, raise concerns about the scale effects in SWRC. With an aim to investigate them, this work compared the primary drainage SWRCs of coarse, medium and fine sand measured by the standard hanging column and full-scale soil column (150 cm). The soil moisture profile at the final drainage stage was detected using the spatial time domain reflectometry (spatial TDR) technique with a presentation of sensor calibrations and validations. The observations showed discrepancies between SWRCs given by two methods in terms of air entry value (AEV) and slope of SWRC but agreements on residual moisture content. Moreover, such differences could be alleviated with the soil becoming finer and better graded. Finally, the physical reasons are discussed, referring to local heterogeneity and pressure gradient changes on the top boundary. In conclusion, the full-scale soil column test can be utilised to avoid scale effects, despite demanding high costs and massive labour efforts. Also, a shorter soil column incorporating point-wise suction and moisture sensors in prior studies could be an alternative solution.
The behaviour of footings on geosynthetic-reinforced soils has been investigated by many researchers through experimental and numerical modelling under stress-controlled or strain-controlled conditions. A new experimental set-up was designed under a stress-controlled condition, with the application of the particle image velocimetry (PIV) technique. A series of model footing tests was carried out using this equipment to investigate the behaviour of the geosynthetic-reinforced soil below a strip footing. The deformation inside the soil mass below the strip footing was determined using the PIV technique. The reinforcing performances of single-layer and multi-layer geotextile and single-layer geogrid embedded at different depths were compared and discussed by analysing the load–settlement curves. It is found that there is a stepwise increase phenomenon in settlement under the stress-controlled condition. The ultimate bearing capacities were determined from the obtained stepwise load–settlement curves using three approaches: the tangent intersection method, the tail linear method and the allowable settlement method. The three approaches were coded in a Python program in order easily to determine and compare the results. In addition, the experimental model footing tests were simulated using the finite-element method under the same stress condition with good agreement for a settlement range within 0·1B.
Soil water retention curve (SWRC) as the constitutive relationship of hydro-mechanical coupling bridge of unsaturated soil has been experimentally investigated decades regarding impacts from dynamic effects in sandy soil and deformation in soft soil. However, due to...
Liquid slip flow with a Knudsen number Kn = 0.001-0.1 plays a dominant role in confined flow channels. Its physical origin can be attributed to the intermolecular fluid-solid (F-S) interaction force. To this end, we propose herein continuous force functions (decaying either exponentially or by a power law) between fluid particles and two confined flat walls in the framework of the mesoscopic lattice Boltzmann model (LBM). The analytical solutions for density profile, velocity profile, slip length, and permeability ratio are derived and related to the mesoscale F-S interaction parameters and the size of the gap of the flow channel. Through nondimensionalization of the analytical solutions, we obtain the dimensionless numbers that indicate the key feature of slip-flow systems for each of the proposed force functions. The analytical solutions are strictly consistent with the LBM solutions. We suggest reasonable ranges for the F-S interaction parameters based on the observed range of density ratio (film fluid to bulk fluid) and the increasing permeability ratios with narrowing gap size. Within the given range of interaction parameters, simple relationships between permeability ratios and dimensionless numbers are provided by fitting. The curves for continuous F-S interaction force with two free parameters are calibrated for a hydrophobic surface by using LBM simulations, which were validated a priori by comparison with the slip velocity profile measured in a benchmark flow experiment. The mesoscopic LBM model based on the proposed F-S interaction force functions provides a robust framework to elucidate the physical process of liquid slip flow.
Flash delay (non-equilibrium phenomenon) occurred in refrigerant flow in a capillary affects apparently the prediction accuracy of refrigerant flow rate in a capillary. “Combined nucleation” theory that accounts for both “homogeneous nucleation” and “wall nucleation” was developed, based on which, a flash flow model was established. Underpressure, an important parameter reflecting non-equilibrium phenomenon in a capillary, was obtained with this flash flow model. The simulation results agree well with the experimental data. The results show that underpressure increases with increase of the mass flow rate of refrigerant and also increases with decrease of inlet temperature.
