In unsaturated soil mechanics, the liquid bridge force is a significant source of soil cohesion and tensile strength. However, the classical Young-Laplace equation, which neglects the stratified nature of water at the nanoscale, fails to accurately capture the physical and mechanical behaviour of nanoscale liquid bridges. This study utilizes molecular dynamics simulations to investigate the wetting behaviour and mechanical mechanisms of liquid bridges between particles at the nanoscale. The study proposes dividing the liquid bridge force into three components: surface tension, matric suction, and adsorption force, to explain the mechanics of nanoscale liquid bridges more comprehensively. The results demonstrate that water layers within liquid bridges exhibit discrete stratified structures at the nanoscale. Moreover, the mechanical behaviour of liquid bridges is highly dependent on pore water volume and pore spacing. Specifically, the contact angle is positively correlated with the pore spacing, while the liquid bridge force increases with the pore water volume and is inversely proportional to the pore spacing. As the separation distance increases, the liquid bridge force gradually diminishes until rupture occurs. This research expands the applicability of the classical Young-Laplace equation and offers new insights into the mechanical properties of unsaturated soils, particularly clays.

Predictive modeling of dielectric heating in porous foods is challenging due to their nature as multiphase materials. To explore the relationship between the topological structure of multiphase foods and the accuracy of dielectric mixture models, the degree of anisotropy of two cooked rice samples with 26 and 32 % porosity was determined, and their dielectric properties were estimated using the Lichtenecker (LK), Landau-LifshitzLooyenga (LLL), and Complex Refractive Index Mixture (CRIM) equations. These properties were used in a predictive finite-element model for reheating an apparent homogeneous rice sample on a flatbed microwave (MW) for 120 s. The results were compared with experimental data and a validated two-element model. Unlike LK and LLL equations, the CRIM equation predicted heat accumulation towards the edges of the container at the two values of porosity ratio evaluated, in accordance with the experimental results and the isotropic nature of the sample. The simulated temperature distributions suggest that the three evaluated equations could predict the MW heating behavior of rice to some extent, but that in order to obtain more accurate results, it could be useful to obtain an empirical topology-related parameter specific for this sample. These results can provide insight on the relationship between the topology of the porous structure in the sample and the adequacy of different dielectric mixture models.

The occurrence of settlements induced by soil liquefaction will exert a substantial influence on buildings situated in earthquake-prone regions. Previous studies integrated the viscous-damping force into the governing equation to characterize building settlements and considered the apparent viscosity as an important parameter. The existing equation can be utilized to predict the settlement magnitude in the final stage as well as its evolution. However, due to the insufficient description of apparent viscosity, it is commonly regarded as a constant during the process of evaluating settlement. When adopting this mechanism, the evolution of building settlement often proves inadequate in fully capturing actual conditions. The aim of this study is to propose a prediction model for estimating liquefaction-induced settlement of shallow-founded buildings, which is formulated by an analytically differential equation. The proposed model incorporates the time-dependent viscosity of liquefied soil and introduces the concept of a soil column submerged in liquefied soil during seismic shaking. The evolution of settlement and the final settlement magnitude induced by soil liquefaction is evaluated through the analytical estimation, and these findings are subsequently compared with the results obtained from centrifuge experiments and numerical simulations. Furthermore, the proposed model is employed to investigate the correlation between building settlement and the geometric characteristics of shallow foundations. The proposed methodology shows considerable promise as an intermediate tool for assessing building settlement, offering practical simplicity in real scenarios.

The unified effective stress equation based on suction stress, a widely accepted method for calculating effective stress in unsaturated soils, provides a closed-form solution that enables the characterization of soils in both saturated and unsaturated states. The effect of desaturation on the water content of natural and treated soils was studied with respect to unconfined compressive strength (UCS) and indirect tensile strength (ITS). The soil's moisture-dependent behavior was characterized by the van Genuchten (Soil Sci Soc Am J 44:892-898, 1980. https://doi.org/10.2136/sssaj1980.03615995004400050002x) and Lu et al. (Water Resour Res, 2010. https://doi.org/10.1029/2009wr008646) models and implemented using the equation. Suction tests were conducted using the dew point and filter paper methods, alongside UCS and ITS tests, on silty clay soil and microsilica-treated soil with microsilica contents of 5%, 10%, and 15%. The equation was validated by comparing mean total stress (p) and mean effective stress (p ') to deviatoric stress (q) and analyzing the friction angle at different suction levels. It proved applicable to both natural and treated soils, with valid moisture content ranges of 4-17.5% and 6-20%, respectively. This study experimentally confirms the equation's effectiveness in characterizing the hydro-mechanical behavior of soils under varying moisture conditions.

In alpine tundra regions, snowmelt plays a crucial role in creating spatial heterogeneity in soil moisture and nutrients across various terrains, influencing vegetation distribution. With climate warming, snowmelt has advanced, lengthening the growing season while also increasing the risk of frost damage to evergreen dwarf shrubs like Rhododendron aureum in alpine tundra regions. To understand these long-term effects, we used remote sensing imagery to analyze nearly four decades (1985-2022) of snowmelt date and the distribution change of R. aureum in Changbai Mountain, East China's only alpine tundra. Results show that snowmelt advanced by 1-3 days/10 years, with faster rates at higher elevations and shady slopes (0.4-0.6 days/10 years more than sunny slopes), while R. aureum increased more on shady slopes under such conditions. Our study demonstrates that these shifts in snowmelt date vary significantly across topographies and reveals how topography and snowmelt changes interact to shape the distribution of evergreen shrubs under climate warming.

In complex physical systems, conventional differential equations fall short in capturing non-local and memory effects. Fractional differential equations (FDEs) effectively model long-range interactions with fewer parameters. However, deriving FDEs from physical principles remains a significant challenge. This study introduces a stepwise data-driven framework to discover explicit expressions of FDEs directly from data. The proposed framework combines deep neural networks for data reconstruction and automatic differentiation with Gauss-Jacobi quadrature for fractional derivative approximation, effectively handling singularities while achieving fast, high-precision computations across large temporal/spatial scales. To optimize both linear coefficients and the nonlinear fractional orders, we employ an alternating optimization approach that combines sparse regression with global optimization techniques. We validate the framework on various datasets, including synthetic anomalous diffusion data, experimental data on the creep behavior of frozen soils, and single-particle trajectories modeled by L & eacute;vy motion. Results demonstrate the framework's robustness in identifying FDE structures across diverse noise levels and its ability to capture integer-order dynamics, offering a flexible approach for modeling memory effects in complex systems.

This study investigated the hydraulic and mechanical behaviors of unsaturated coarse-grained railway embankment fill materials (CREFMs) using a novel unsaturated large-scale triaxial apparatus equipped with the axis translation technique (ATT). Comprehensive soil-water retention and constant-suction triaxial compression tests were conducted to evaluate the effects of initial void ratio, matric suction, and confining pressure on the properties of CREFMs. Key findings reveal a primary suction range of 0-100 kPa characterized by hysteresis, which intensifies with decreasing density. Notably, the air entry value and residual suction are influenced by void ratio, with higher void ratios leading to decreased air entry values and residual suctions, underscoring the critical role of void ratio in hydraulic behavior. Additionally, the critical state line (CSL) in the bi-logarithmic space of void ratio and mean effective stress shifts towards higher void ratios with increasing matric suction, significantly affecting dilatancy and critical states. Furthermore, the study demonstrated that the mobilized friction angle and modulus properties depend on confining pressure and matric suction. A novel modified dilatancy equation was proposed, which enhances the predictability of CREFMs' responses under variable loading, particularly at high stress ratios defined by the deviatoric stress over the mean effective stress. This research advances the understanding of CREFMs' performance, especially under fluctuating environmental conditions that alter suction levels. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Soil erosion has both on-farm and off-farm effects. On-farm, reduced soil depth can decrease land productivity, while off-farm, sediment transfer can damage streams, lakes, and estuaries. Therefore, optimal soil erosion modeling is a crucial first step in soil erosion research. One of the most important aspects of this modeling is the accuracy and applicability of the soil erosion factors used. Various methods for calculating these factors are discussed in the literature, but no single method is universally accurate. After an extensive review of the literature, we propose using the existing revised universal soil loss equation (RUSLE) factors for global application. Additionally, we conducted a grassroots-level experiment to demonstrate the effectiveness of the proposed methods. RUSLE is identified as the most suitable model for global-scale soil erosion modeling. We evaluated the potential impacts of climate and land use and land cover (LULC) by utilizing shared socio-economic pathways (SSPs) alongside projected LULC scenarios. A suitable general circulation model (GCM) was selected after comparing it with recorded data from a base period. This model was validated with experimental observations, confirming its effectiveness. This review article outlines the future direction of soil erosion modeling and provides recommendations.Graphical AbstractThe graphical abstract visually summarizes the comprehensive methodology and key findings associated with optimal soil erosion modeling and management. It highlights a structured approach, beginning with identifying optimal methods for assessing soil erosion factors: Rainfall and Runoff Erosivity (R), Soil Erodibility (K), Slope Length and Steepness (LS), Cover and Management (C), and Support Practice (P) integral components of the Revised Universal Soil Loss Equation (RUSLE). It illustrates the detailed methodological framework, emphasizing selecting suitable climate models for projecting future R factors, combined with projected land use and land cover (LULC) scenarios derived from Shared Socio-economic Pathways (SSPs). The scenarios shown range from lower emissions (SSP 126) to higher emissions (SSP 585), indicating progressive increases in future erosion risk. Moreover, it explicitly ties the research findings to policy recommendations, underscoring a holistic approach aligning soil conservation with Sustainable Development Goals (SDGs): specifically, Climate Action (SDG 13), Life on Land (SDG 15), and Zero Hunger (SDG 2). Suggested measures include integrating soil erosion control into broader policy frameworks, promoting sustainable land management practices such as agroforestry and contour plowing, and fostering policy integration and collaboration to enhance conservation effectiveness. Overall, the graphical abstract succinctly depicts how climate change, socio-economic dynamics, and LULC variations amplify future soil erosion risks, reinforcing the need for targeted, sustainable, and integrated soil conservation strategies globally.

Waterfront and submarine retaining structures are normally exposed to catastrophic seepage conditions under the effect of tidal and occasionally heavy rainfall effect, resulting in a decreased passive earth thrust and thus the higher risk of instability of retaining structures. To examine the effect of seepage flow on the magnitude and distribution of passive earth thrust, this paper assumes a composite curved-planar failure surface and presents a modified method of passive earth pressure considering the seepage flow effect. The flow field and pore pressure are firstly solved by the two-dimensional (2D) Laplace equation using the Fourier series expansion. The effective reaction force acting on the composite failure surface is then obtained using a modified K & ouml;tter equation. Compared to conventional methods based on limit equilibrium, the present method facilitates a straightforward assessment of both the magnitude and distribution of passive earth thrust without the prior assumption of the application point. The outcomes highlight that the passive earth thrust decreases with the ratios of permeability coefficients. The greater effective friction angle and a smaller ratio of permeability coefficients result in the lower application point of the passive earth thrust.

The plastic strain of calcareous sand is related to its stress path and particle breakage, rendering the hardening process complex. An expression for the stress-path-dependence factor was developed by analyzing the variations in plastic strain across different initial void ratios. A stress-path-independent hardening parameter was derived from the modified plastic work and was subsequently validated. Constant-proportion loading tests on calcareous sands confirmed the applicability of this hardening model. The results indicated that under isotropic compression, the plastic volumetric strain increased with increasing average effective stress, albeit at a decreasing growth rate. A positive linear relationship was observed between the volumetric strain modulus and relative breakage index. The proposed hardening parameter effectively captured the particle breakage and stress path effects in calcareous sand and was validated through theoretical calculations and laboratory tests, offering valuable insights into the mechanical behavior of fragile granular soils.