It is imperative to the understanding of water movements and moisture conditions in unbound pavement layers and subgrades for different types of road constructions in various climatic conditions for improving the performance of roads. Especially, soil suction fluctuates significantly in unsaturated zone during drainage and imbibition process due to seasonal variation. Moreover, changing in volumetric moisture content and soil suction might be accelerated for the varying density of materials because of cyclic traffic loading. To address these issues, soil water retention curves (SWRC) of road base materials compacted at moulding moisture content and placement density similar to that expected in real life scenario are reported in this study. Simultaneous and continuous soil moisture and suction measurements are performed with a setup comprising of tensiometers and programmed bench scales. Tensiometer is inserted in the compacted soil mass, and the top surface boundary condition is set to evaporation. Soil suction is measured from tensiometer reading, while moisture content and outflow are obtained by weighing the soil column. In this study, we discuss following four aspects pertaining to the road base material: (i) variation of soil suctions with time; (ii) the SWRC of road base material in drying process; (iii) the estimation of unknown parameters of the existing models; (iv) the suitability of SWRC with existing prediction models. This research is expected to contribute to a better understanding and prediction of moisture migration and solute transport in road structures.
The coal seam gas industry has raised public concerns about the potential risk of groundwater contamination, where gases leaked from coal seams are thought to pollute groundwater. However, the basic principles and controlling parameters for gas seepage from deep ground formations to the ground surface have not been fully understood. As a possible mechanism for gas transport in the subsurface environment, discrete bubble flow was previously investigated using laboratory experiments by Ma et al. (Water Resour. Res, 2015, 51 (6), 4359–4373). This study developed a multiphase computational fluid dynamic (CFD) model to simulate discrete bubbly flow in a two-dimensional granular porous media at the pore scale. Following the experimental setup from Ma et al. (Water Resour. Res, 2015, 51 (6), 4359–4373), a “point source” with preset bubble fluxes was specified in a simulating domain representing the flume size in the earlier experiments. There were around 7,000 granular particles within this domain to model the porous media. This numerical model was validated by conserving the gas mass in the simulating domain. The simulation results provide more physical insights into complex bubble transport behaviour in porous media through specific plume parameters. The breakthrough time of the bubble plume and the cross-sectional averaged velocity of ambient pore water flow were manifested to be proportional to the gas release rates in the logarithmic scales. Also, the bubble plume width was also observed to be proportional to the gas release rates. Moreover, the gas distribution on the top boundary could be observed. The outcomes were further tested against the scaling solutions proposed by Ma et al. (Water Resour. Res, 2015, 51 (6), 4359–4373) with disagreements. The limitations of this multiphase computational fluid dynamic model were finally discussed.
This study investigates the intrinsic permeability of two water-based transparent soil surrogates (Aquabeads and hydrogel beads) in various aqueous environments. To maximise the efficiency of seepage tests for different solutes (salt and a surfactant) at different concentrations, a rapid approach was established to estimate the intrinsic permeabilities of these water-based granular polymers. Due to the geometric similarity of the pore structures formed by the packing of granular polymer beads of different sizes, the Kozeny–Carman permeability estimation can be directly applied to study the permeability (K), which primarily varies with the effective diameter (d e ). A systematic sieving analysis of these polymers was conducted to determine the values of both d e and K. The experimental results showed that both parameters monotonically decrease with increasing solute concentration. The critical shrinkage concentrations for salt and the surfactant were identified as 5–7 ppt and 0·02% (mass/volume), respectively. This study represents the first contribution to providing a sound understanding of the intrinsic permeabilities of these surrogate soils when saturated with various solutions. This study contributes to the physical modelling in geotechnics when using those materials.
In slurry shield tunnelling, the penetration of the supporting bentonite suspension must be reduced to a critical value to ensure safety and cost-efficiency during construction. Aiming to measure bentonite suspension penetration, this study adopted the spatial time domain reflectometry (spatial TDR) technique. Although traditional TDR can detect point-wise changes in bentonite suspension concentration of pore fluid, this technique has rarely been extended to spatial profile detection. Spatioscale tests with a flat ribbon cable TDR sensor demonstrated the potential of TDR waveform analysis for determining penetration depth. Relationships between penetration depth and waveform characteristics were established. The travel time specified by the dual tangents method decreased with increasing slurry penetration, and the determined travel time agrees well with that calculated by a newly proposed mixture equation. This novel approach enables the determination of penetration depth without visual observation, providing a powerful measuring solution for laboratory studies and slurry shield tunnelling.
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
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.
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.
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.
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.
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...
This work reviews the transient two-phase flow in porous media with engineering applications in Geotechnics. It initially overviews constitutive relationships, conventional theories, and experiments. Then, corresponding limitations are discussed according to conflicting observations and multiphase interfacial dynamics. Based on those findings, the dynamic nonequilibrium effects were so defined, which could also be abbreviated as dynamic/transient effects. Four advanced theories have already been developed to resolve these effects. This review collects them and discusses their pros and cons. In addition, this work further reviews the state-of-art in terms of experimental methods, influential factors in dynamic/transient effects, and modelling performance, as well as micromodel and numerical methods at pore-scale. Last, the corresponding geotechnical applications are reviewed, discussing their applicability in effective stress, shear strength, and deformation. Finally, the entire review is briefed to identify research gaps in Geotechnics.
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.
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.
