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Keywords = unsaturated soil condition

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35 pages, 7550 KB  
Article
Stability Analysis of Tunnel Face in Nonhomogeneous Soil with Upper Hard and Lower Soft Strata Under Unsaturated Transient Seepage
by Wenjun Shao, De Zhou, Long Xia, Guihua Long and Jian Wang
Mathematics 2026, 14(3), 537; https://doi.org/10.3390/math14030537 - 2 Feb 2026
Abstract
To enhance the assessment accuracy of tunnel face instability risks of active collapse during shield tunneling, this study establishes a novel unified analytical framework that couples the effects of unsaturated transient seepage induced by excavation drainage with soil stratification and heterogeneity. Grounded in [...] Read more.
To enhance the assessment accuracy of tunnel face instability risks of active collapse during shield tunneling, this study establishes a novel unified analytical framework that couples the effects of unsaturated transient seepage induced by excavation drainage with soil stratification and heterogeneity. Grounded in unsaturated effective stress theory, the framework explicitly incorporates matric suction into the Mohr–Coulomb failure criterion via suction stress and apparent cohesion. By employing a horizontal two-layer nonhomogeneous soil model and solving the one-dimensional vertical Richards’ equation, an analytical solution for the face drainage boundary is derived to quantify the spatiotemporal evolution of suction stress and apparent cohesion. Subsequently, the critical support pressure is evaluated using the upper bound theorem of limit analysis, incorporating a horizontal layer-discretized rotational failure mechanism and the power balance equation. The validity of the proposed framework is confirmed through comparative analyses. Parametric studies reveal that in the upper hard and lower soft strata, the critical support pressure decreases and converges over time, indicating that unsaturated transient seepage exerts a significant influence in the short term that stabilizes over the long term. Additionally, sand–silt stratum exhibits lower overall stability and higher sensitivity to groundwater levels and temporal factors compared to silt–clay stratum. Conversely, silt–clay stratum displays a non-monotonic evolution with increasing cover-to-diameter ratios (C/D), reaching a minimum critical support pressure at approximately C/D = 1.1. Regarding heterogeneity, the internal friction angle of the lower layer exerts dominant control over the critical support pressure compared to seepage velocity, while the influence of other strength parameters remains secondary. These findings provide a theoretical basis for the time-dependent design of tunnel face support pressure under excavation drainage conditions. Full article
(This article belongs to the Special Issue Mathematical Modeling and Analysis in Mining Engineering)
17 pages, 3128 KB  
Article
Semi-Analytical Solutions for Consolidation in Multi-Layered Unsaturated Silt with Depth-Dependent Initial Condition
by Junhao Chen, Bote Luo, Xun Wu, Shi Shu and Juan Qiang
Appl. Sci. 2026, 16(3), 1168; https://doi.org/10.3390/app16031168 - 23 Jan 2026
Viewed by 105
Abstract
This paper presents an analytical model for one-dimensional consolidation analysis of multi-layered unsaturated soils under depth-dependent initial conditions. The general solutions are derived explicitly using the Laplace transform. By combining these general solutions with interfacial continuity conditions between layers and the boundary conditions, [...] Read more.
This paper presents an analytical model for one-dimensional consolidation analysis of multi-layered unsaturated soils under depth-dependent initial conditions. The general solutions are derived explicitly using the Laplace transform. By combining these general solutions with interfacial continuity conditions between layers and the boundary conditions, the reduced-order system is solved via the Euler method to obtain analytical solutions in the Laplace domain. Numerical inversion of the Laplace transform is then performed using Crump’s method to yield the final analytical solutions in the time domain. The model incorporates initial conditions that account for both uniform and linear distributions of initial excess pore pressure within the soil stratum. The proposed solution is verified by reducing it to degenerated cases (e.g., uniform initial pressure) and comparing it with existing analytical solutions, showing excellent agreement. This confirms the model’s correctness and demonstrates its generalization to multi-layered systems with depth-dependent initial conditions. Focusing on a double-layered unsaturated soil system, the one-dimensional consolidation characteristics under depth-dependent initial conditions are investigated by varying the physical parameters of individual layers. The proposed solution can serve as a theoretical reference for the consolidation analysis of multi-layered unsaturated soils with depth-dependent initial conditions. Full article
(This article belongs to the Section Civil Engineering)
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20 pages, 8261 KB  
Article
Effect of Matric Suction and Drying-Wetting Cycles on the Strength of Granite Residual Soil in Fujian Pumped Storage Power Station Slopes, China
by Xiudong Xie, Zhidong Xie, Chenyang Wang and Yan Su
Sustainability 2026, 18(2), 748; https://doi.org/10.3390/su18020748 - 12 Jan 2026
Viewed by 173
Abstract
The stability of bank slopes in pumped storage power stations is crucial, particularly in regions where frequent water level fluctuations occur. This study aims to investigate the degradation mechanism of bank slope under such fluctuating conditions, focusing on granite residual soil from the [...] Read more.
The stability of bank slopes in pumped storage power stations is crucial, particularly in regions where frequent water level fluctuations occur. This study aims to investigate the degradation mechanism of bank slope under such fluctuating conditions, focusing on granite residual soil from the pumped storage power stations in Fujian, China. To explore the effects of drying-wetting cycles and matric suction on soil shear strength, drying and wetting cycles were conducted with unsaturated triaxial shear tests. The results revealed that the shear parameter strengthening effect occurs when the matric suction increases from 50 kPa to 200 kPa. Moreover, during the first five drying-wetting cycles, soil shear strength decreased sharply, with cohesion and internal friction angle decreasing by approximately 15.4% and 11.2%, respectively. This degradation trend stabilized in the later cycles. Scanning Electron Microscopy (SEM) analysis of the soil microstructure showed an evolution from a dense structure to a penetrating cavity during the cycles. This change reflects that the strength degradation characteristics of granite residual soils are controlled by the synergistic effects of structural and frictional mechanisms, manifesting as initial degradation followed by stabilization. Additionally, by fitting the nonlinear characteristics of the experimental data, shear strength evolution functions for matric suction and drying-wetting cycles were established, revealing the effect of these factors on strength degradation. These findings provide a theoretical basis for the stability analysis of bank slopes in pumped storage power stations, offering insights into soil behavior under fluctuating water levels. Full article
(This article belongs to the Special Issue Sustainable Environmental Analysis of Soil and Water)
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23 pages, 8301 KB  
Article
Seepage Heat Transfer Characteristics and Leakage Detection Index of Embankments Under Seepage Failure Conditions
by Jiangyin Yang, Zhenzhong Shen, Zhongming Jiang, Xiangyi Huang, Junhui Liao, Zhangxin Huang and Zekai Ma
Water 2026, 18(2), 163; https://doi.org/10.3390/w18020163 - 8 Jan 2026
Viewed by 288
Abstract
In recent years, infrared detection technology for embankment leakages has become a popular research topic. The seepage and heat transfer characteristics of embankments under seepage failure conditions form the theoretical basis of infrared detection technology for leakage hazards. Nevertheless, a majority of prior [...] Read more.
In recent years, infrared detection technology for embankment leakages has become a popular research topic. The seepage and heat transfer characteristics of embankments under seepage failure conditions form the theoretical basis of infrared detection technology for leakage hazards. Nevertheless, a majority of prior research has relied on predetermined seepage pathways, which fail to accurately simulate the actual scenarios encountered in engineering practice. Accordingly, taking a typical soil embankment in the Dongting Lake area as the research object, a seepage damage test of the embankment body and surface soil of the embankment foundation was conducted. The mechanical and seepage damage of the embankment soil was established. FLAC3D6.0 software was used to develop a coupled numerical model of the unsaturated seepage, temperature, and stress of the embankment based on the damage model. The distribution laws of the seepage and temperature fields in the embankment body and foundation were calculated and analyzed. The results of this study show that there is a strong correlation between seepage, temperature, and structure during local seepage failure and even the overall structural failure of the embankment. Moreover, the evolution of the downstream embankment toe and surface temperature shows a phased change. By capturing this feature, it is possible to quickly screen the seepage location of an embankment to thereby provide a basis for determining the infrared detection indicators of the embankment. Full article
(This article belongs to the Section Soil and Water)
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23 pages, 7328 KB  
Article
Assessing the Influence Zone and Drainage Efficiency of Geotextiles with Enhanced Lateral Drainage Abilities in Unsaturated Soil Systems
by Shakeel Abid Mohammed and Jorge G. Zornberg
Geosciences 2026, 16(1), 22; https://doi.org/10.3390/geosciences16010022 - 1 Jan 2026
Viewed by 310
Abstract
The hydraulic performance of woven geotextiles is frequently overlooked in roadway design, despite their extensive use for reinforcement applications. Woven geotextiles are typically manufactured from hydrophobic polymers such as polypropylene or polyester and can act as capillary barriers under unsaturated conditions. This results [...] Read more.
The hydraulic performance of woven geotextiles is frequently overlooked in roadway design, despite their extensive use for reinforcement applications. Woven geotextiles are typically manufactured from hydrophobic polymers such as polypropylene or polyester and can act as capillary barriers under unsaturated conditions. This results in moisture accumulation at the soil–geotextile interface, adversely impacting long-term pavement performance. Such problems can be effectively mitigated using geotextiles with enhanced lateral drainage (ELD) capabilities, which are engineered with hydrophilic fibers to facilitate capillary-driven lateral water movement under unsaturated conditions. This functionality facilitates the redistribution of moisture away from the interface, mitigating moisture retention and enhancing drainage performance. The hydraulic performance of geotextiles with enhanced lateral drainage capabilities under unsaturated conditions remains insufficiently understood, particularly in terms of their influence zone and drainage efficiency. For this reason, the present study evaluates the lateral drainage behavior of an ELD geotextile using a soil column test, compared against a control setup without a geotextile and with a non-woven geotextile. Two moisture migration scenarios, namely capillary rise and vertical infiltration, were simulated, with the water table varied at multiple depths. Moisture sensors were embedded along the column depth to monitor real-time water content variations. Results show that the ELD geotextile facilitated efficient lateral drainage, with a consistent influence zone extending up to 2 inches below the fabric. Under infiltration, the ELD geotextile reduced moisture accumulation by 30% around the geotextile, highlighting its superior drainage behavior. These findings encourage practicing engineers to adopt rational, performance-based designs that leverage ELD geotextiles to enhance subgrade drainage and moisture control in pavement and geotechnical applications. Full article
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21 pages, 4646 KB  
Article
A Non-Linear Suction-Dependent Model for Predicting Unsaturated Shear Strength
by Kalani Rajamanthri and Claudia E. Zapata
Geosciences 2026, 16(1), 12; https://doi.org/10.3390/geosciences16010012 - 23 Dec 2025
Viewed by 349
Abstract
Accurate evaluation of unsaturated shear strength remains a significant challenge in geotechnical engineering because of the nonlinear interaction between matric suction and shear strength. Existing models often assume a linear contribution of suction and are generally restricted to low suction ranges, limiting their [...] Read more.
Accurate evaluation of unsaturated shear strength remains a significant challenge in geotechnical engineering because of the nonlinear interaction between matric suction and shear strength. Existing models often assume a linear contribution of suction and are generally restricted to low suction ranges, limiting their predictive capability under highly unsaturated conditions. This study investigated the nonlinear response of unsaturated shear strength through single-stage direct shear tests conducted under constant water content. Two soil types: a high-plasticity clay and a low-plasticity silty clay were examined across a wide suction range extending beyond the air-entry value (AEV). The results revealed a nonlinear behavior expressed as a distinct bi-linear trend, with shear strength increasing with suction up to the optimal moisture condition and then exhibiting a clearly altered rate of increase at higher suction levels. To capture this nonlinear behavior of unsaturated shear strength with suction, an exponential shear strength equation was proposed and validated using eight additional published datasets encompassing different soil classifications and suction magnitudes. The proposed formulation demonstrates that accounting for non-linearity is essential for accurately estimating the unsaturated shear strength of the soil. Moreover, the proposed exponential model outperforms both the well-established linear model of Fredlund and the nonlinear power law model of Abramento and Carvalho, thereby providing a unified framework for capturing the nonlinear interaction of matric suction on unsaturated shear strength. Full article
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14 pages, 1300 KB  
Article
A Theoretical Model for Pipe Roof Support in Shallow Buried Tunnels Considering Changes in Water Content
by Jingsong Chen, Mu He, Yan Wang, Jianbo Wu, Yujing Wei and Hongwei Yang
Water 2025, 17(24), 3521; https://doi.org/10.3390/w17243521 - 12 Dec 2025
Viewed by 322
Abstract
Environmental conditions at shallow-buried tunnel portals often cause stratum moisture content variations, where pipe roof support is commonly used for pre-reinforcement. While studies show water content significantly affects soil strength, its impact on pipe roof behavior remains largely unexplored. This study develops a [...] Read more.
Environmental conditions at shallow-buried tunnel portals often cause stratum moisture content variations, where pipe roof support is commonly used for pre-reinforcement. While studies show water content significantly affects soil strength, its impact on pipe roof behavior remains largely unexplored. This study develops a theoretical model for pipe roof longitudinal internal forces and deformations using Pasternak two-parameter foundation theory, incorporating subgrade reaction and shear moduli expressions that vary with saturation. Validation against field measurements shows good agreement with peak values, confirming model reliability. Parametric analysis reveals that increasing water content markedly amplifies pipe roof deformation: in unsaturated ground, deflection and rotation increase significantly with water content, while peak bending moment and shear force near the tunnel face slightly decrease. Under saturated conditions, the increases in deflection and rotation become substantially greater. The model quantitatively evaluates water content’s influence on pipe roof mechanical behavior, providing a theoretical basis for optimizing support systems in water-rich strata. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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21 pages, 5733 KB  
Article
Salinity Distribution as a Hydrogeological Limit in a Karstic Watershed in Yucatan
by Iris Neri-Flores, Ojilve Ramón Medrano-Pérez, Flor Arcega-Cabrera, Ismael Mariño-Tapia, César Canul-Macario and Pedro Agustín Robledo-Ardila
J. Mar. Sci. Eng. 2025, 13(12), 2317; https://doi.org/10.3390/jmse13122317 - 6 Dec 2025
Viewed by 581
Abstract
In coastal regions, the interaction between freshwater and seawater creates a dynamic system in which the spatial distribution of salinity critically constrains the use of freshwater for human consumption. Although saline intrusion is a globally widespread phenomenon, its inland extent varies significantly with [...] Read more.
In coastal regions, the interaction between freshwater and seawater creates a dynamic system in which the spatial distribution of salinity critically constrains the use of freshwater for human consumption. Although saline intrusion is a globally widespread phenomenon, its inland extent varies significantly with hydrological conditions, posing a persistent threat to groundwater quality and sustainability. This study aimed to characterize salinity distribution using an integrated karst-watershed approach, thereby enabling the identification of both lateral and vertical salinity gradients. The study area is in the northwestern Yucatan Peninsula. Available hydrogeological data were analyzed to determine aquifer type, soil texture, evidence of saline intrusion, seawater fraction, vadose zone thickness, and field measurements. These included sampling from 42 groundwater sites (open sinkholes and dug wells), which indicated a fringe zone approximately 5 km in size influenced by seawater interaction, in mangrove areas and in three key zones of salinity patterns: west of Mérida (Celestun and Chunchumil), and northern Yucatan (Sierra Papacal, Motul, San Felipe). Vertical Electrical Sounding (VES) and conductivity profiling in two piezometers indicated an apparent seawater influence. The interface was detected at a depth of 28 m in Celestun and 18 m in Chunchumil. These depths may serve as hydrogeological thresholds for freshwater abstraction. Results indicate that saltwater can extend several kilometers inland, a factor to consider when evaluating freshwater availability. This issue is particularly critical within the first 20 km from the coastline, where increasing tourism exerts substantial pressure on groundwater reserves. A coastal-to-inland salinity was identified, and an empirical equation was proposed to estimate the seawater fraction (fsea%) as a function of distance from the shoreline in the Cenote Ring trajectory. Vertically, a four-layer model was identified in this study through VES in the western watershed: an unsaturated zone approximately 2.6 m thick, a confined layer in the coastal Celestun profile about 9 m thick, a freshwater lens floating above a brackish layer between 8 and 25 m, and a saline interface at 37 m depth. The novelty of this study, in analyzing all karstic water surfaces together as a system, including the vadose zone and the aquifer, and considering the interactions with the surface, is highlighted by the strength of this approach. This analysis provides a better understanding and more precise insight into the integrated system than analyzing each component separately. These findings have significant implications for water resource management in karst regions such as Yucatan, underscoring the urgent need for sustainable groundwater management practices to address seawater intrusion. Full article
(This article belongs to the Special Issue Marine Karst Systems: Hydrogeology and Marine Environmental Dynamics)
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19 pages, 2515 KB  
Article
Failure Mode of Rectangular Shallow Tunnel in Unsaturated Fine-Grained Soil Under Temperature Influence
by Wenjun Shao, Hong Liao and De Zhou
Mathematics 2025, 13(22), 3671; https://doi.org/10.3390/math13223671 - 16 Nov 2025
Viewed by 278
Abstract
Failure analysis has always been among the key research focuses in underground tunneling, particularly in forecasting the collapse risk of tunnel crowns, which bears great engineering and practical significance for tunnel safety assessment. In practical engineering, the soil surrounding shallow tunnels and other [...] Read more.
Failure analysis has always been among the key research focuses in underground tunneling, particularly in forecasting the collapse risk of tunnel crowns, which bears great engineering and practical significance for tunnel safety assessment. In practical engineering, the soil surrounding shallow tunnels and other underground chambers is typically unsaturated. With the advancement of tunneling technology, shallow tunnels affected by ground temperatures are increasingly common, making it essential to incorporate temperature effects into the stability analysis of unsaturated shallow tunnels. This paper proposes a novel framework for analyzing the stability of shallow rectangular tunnel crowns under temperature influence. By adopting a temperature-dependent effective stress model for unsaturated soils combined with the soil–water characteristic curve, temperature influence is integrated into the calculation of apparent cohesion in unsaturated soils. The upper bound theorem and a multi-rigid-block failure mechanism are adopted to assess crown stability, with the geometry of the failure mechanism determined through a compatible velocity field. New analytical expressions are derived. Through calculating the internal energy dissipation rate, considering temperature effects and external work rate, the critical support pressure at the tunnel crown is obtained using the Sequential Quadratic Programming (SQP). Discussions of temperature and other unsaturated soil parameters are carried out to explore their effects on the stability of shallow tunnels. Results demonstrate that temperature significantly influences the tunnel’s critical support pressure, with the extent of this impact primarily dependent on the unsaturated soil type and seepage conditions. Furthermore, the theoretical framework developed in this study provides a more accurate description for unsaturated fine-grained soils. This study introduces a novel integration of thermal influences into the upper bound theorem, applying this enhanced methodology to the stability assessment of shallow rectangular tunnel crowns. The resulting failure model and analytical framework establish a rigorous upper bound solution for crown stability, thereby furnishing a more accurate theoretical foundation for subsequent tunnel face support strategies. Full article
(This article belongs to the Special Issue Multiscale Modeling in Engineering and Mechanics, 2nd Edition)
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17 pages, 5736 KB  
Article
Investigation of Water-Stability Behaviors in Coastal Mud Multiply Modified by Cement and Coarse-Particle Spoil
by Zipeng Qin, Yan Tian, Xianding Guo, Jiongzhang Chen, Huang Huang, Zongkai Ye, Dongxue Wang, Erjin Xu, Hanwei Huang and Xinxin Chen
J. Mar. Sci. Eng. 2025, 13(11), 2105; https://doi.org/10.3390/jmse13112105 - 5 Nov 2025
Viewed by 567
Abstract
This study investigates the water-stability performance and stabilization mechanism of a hybrid-modified dredged muck sampled from the protection channel of the southern seawall, Cangnan County, China, and explores the feasibility of reusing the modified soil as backfill or non-structural fill behind the dike [...] Read more.
This study investigates the water-stability performance and stabilization mechanism of a hybrid-modified dredged muck sampled from the protection channel of the southern seawall, Cangnan County, China, and explores the feasibility of reusing the modified soil as backfill or non-structural fill behind the dike body. The muck was amended with two industrial by-products: (i) coarse-grained spoil excavated from an adjacent power-plant project, serving as a particle-size modifier, and (ii) ordinary Portland cement, acting as the chemical stabilizer. Unconfined compressive strength (UCS) tests were conducted on specimens cured for 7 d and 28 d under both saturated and unsaturated conditions, complemented by scanning electron microscopy (SEM) to elucidate microstructural evolution. An optimal mix proportion that satisfies the prescribed water-stability criterion while maintaining cost-effectiveness was thereby identified. Experimental results demonstrate that cement content, coarse-spoil fraction and curing age govern the water-stability behavior, with cement dosage exerting the most pronounced influence. A 28 d cured blend containing only 5% cement yielded a low water-stability coefficient (31.8%) and negligible post-immersion strength. Conversely, a ternary mixture comprising 40% muck, 60% coarse spoil and 15% cement achieved the highest water stability, recording UCS values of 1582 kPa (saturated) and 2025 kPa (unsaturated), corresponding to 78.1%. These findings provide a theoretical basis and practical guidance for the valorization of waste soils in coastal engineering and for the design/construction of seawalls. These findings not only provide a theoretical basis and practical guidance for the valorization of waste soils in coastal engineering and for the design/construction of seawalls, but also substantially expand the available material source, drive down construction costs, and markedly mitigate the environmental impacts associated with the off-site disposal of excavated waste. Full article
(This article belongs to the Section Coastal Engineering)
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18 pages, 3181 KB  
Article
Effect of Matrix Properties and Pipe Characteristics on Internal Erosion in Unsaturated Clayey Sand Slope
by Olaniyi Afolayan, Anna Lancaster and Jack Montgomery
Geosciences 2025, 15(10), 405; https://doi.org/10.3390/geosciences15100405 - 17 Oct 2025
Viewed by 584
Abstract
Soil piping is the process by which subsurface water creates and enlarges channels, or “pipes,” within soil, enabling rapid and preferential flow beneath the surface. The collapse of these eroded pipes can lead to land degradation, gully formation, and potential damage to overlying [...] Read more.
Soil piping is the process by which subsurface water creates and enlarges channels, or “pipes,” within soil, enabling rapid and preferential flow beneath the surface. The collapse of these eroded pipes can lead to land degradation, gully formation, and potential damage to overlying infrastructure. While the structural consequences of pipe collapse are well recognized, there is limited understanding of the factors controlling pipe collapse and how water within the pipe influences moisture levels within a slope. This study used physical models of unsaturated slopes to examine how compaction conditions, pipe characteristics, and hydraulic conditions affect the progression of internal erosion. Models were created with different initial pipe sizes, moisture contents, densities at compaction and levels of pipe connectivity. Volumetric water content (VWC) sensors and cameras were used to monitor the slope response to subsurface flow, and measurements of pipe geometry were collected after the tests. Results showed that lower initial soil water content was more susceptible to pipe collapse, while higher water content showed improved pipe stability and sustained preferential flow. Fully connected pipes grew through erosion due to the pipe flow, while disconnected pipes grew mainly through local pipe collapse. Hydraulic equilibrium and soil erodibility affected the final pipe morphology more than the initial pipe size. These experimental results demonstrate that soil fabric and hydraulic connectivity of the pipe control the progression of piping, likelihood of collapse, and movement of water within the soil matrix. Full article
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21 pages, 8864 KB  
Article
Numerical Analysis of Seepage Damage and Saturation Variation in Surrounding Soil Induced by Municipal Pipeline Leakage
by Shuangshuang Wang, Fengyin Liu, Ke Wang, Jingyu Cui and Xuguang Zhao
Appl. Sci. 2025, 15(20), 11088; https://doi.org/10.3390/app152011088 - 16 Oct 2025
Cited by 1 | Viewed by 629
Abstract
Surface subsidence and seepage damage in surrounding soils induced by leakage from municipal water supply pipelines pose significant risks to urban infrastructure. To clarify how leakage water diffuses in unsaturated soils and to assess seepage damage potential, this study established a numerical model [...] Read more.
Surface subsidence and seepage damage in surrounding soils induced by leakage from municipal water supply pipelines pose significant risks to urban infrastructure. To clarify how leakage water diffuses in unsaturated soils and to assess seepage damage potential, this study established a numerical model based on the Richards equation combined with the van Genuchten (VG) model. The model was validated against physical model tests using remolded Q3 loess, ensuring consistency in soil parameters and leakage conditions. Simulation results reveal that soil saturation evolution follows three stages—initial, rising, and stable—with preferential flow paths forming above the leakage point before gradually evolving into radial diffusion controlled by both pressure and gravity. The extent of the saturated zone increases with pipeline pressure, but the enhancement effect diminishes as pressure rises, reflecting the nonlinear water-retention characteristics of loess. Seepage damage risk was evaluated using the Terzaghi critical hydraulic gradient criterion. The results show that higher pressures enlarge the critical zone more rapidly, yet its ultimate radius stabilizes within approximately 2.3 m around the leakage point. Moreover, this study proposes that potential seepage damage may occur once effective saturation reaches about 85%, corresponding to the air-entry value of loess, thus providing a more conservative criterion for engineering risk assessment. Overall, the validated Richards-based numerical model reproduces the key features of leakage-induced unsaturated diffusion and offers practical guidance for identifying seepage-prone zones and mitigating subsidence hazards in municipal water supply systems. Full article
(This article belongs to the Special Issue Tunnel Construction and Underground Engineering)
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21 pages, 4657 KB  
Article
Study on Influence of Initial Compaction Degree and Water Content on Water-Holding and Permeability Characteristics of Loess
by Yunliang Ma, Jiasheng Shen, Jinlong Wang, Yasheng Luo, Meng Li, Yanxiang Tian, Kaihao Zheng, Zimin Yin, Pandeng Wang and Xintian Pu
Appl. Sci. 2025, 15(20), 11039; https://doi.org/10.3390/app152011039 - 15 Oct 2025
Cited by 1 | Viewed by 680
Abstract
The water retention and permeability characteristics of loess are core factors governing geological disaster prevention and engineering stability in the loess regions of northwest China. This study focuses on Yangling loess, systematically conducting soil water characteristic curve (SWCC) measurements and saturated permeability tests [...] Read more.
The water retention and permeability characteristics of loess are core factors governing geological disaster prevention and engineering stability in the loess regions of northwest China. This study focuses on Yangling loess, systematically conducting soil water characteristic curve (SWCC) measurements and saturated permeability tests under different initial compaction degrees and water contents using a pressure plate apparatus and a TST-55 permeameter. By combining fitting analyses of the Gardner, Fredlund–Xing, and Van Genuchten SWCC models, the study reveals the influence mechanism of initial conditions on the water retention properties of Yangling loess. Furthermore, the unsaturated hydraulic conductivity of loess was predicted using the Van Genuchten–Mualem model. Finally, a quantitative relationship model between hydraulic conductivity and multiple factors (initial compaction degree, water content, and matric suction) was constructed using the response surface methodology. The results indicate the following: (1) A higher initial compaction degree and water content lead to a higher air entry value of loess, resulting in stronger water retention capacity. Among the three models, the Van Genuchten model exhibits the optimal fitting effect for the SWCC of Yangling loess. Its parameter a (related to the air entry value) decreases significantly with increasing compaction degree, while parameter n (pore size distribution index) increases linearly. The SWCC model, considering compaction degree, established based on these findings, can accurately predict the water retention characteristics in the high suction range (0~1200 kPa). This model’s precision in the high-suction segment is particularly valuable, as it addresses a critical range for engineering applications where soil behavior transitions from near-saturated to highly unsaturated states. (2) When loess transitions from a saturated to an unsaturated state, the hydraulic conductivity decreases up to 104 times. Both increased initial compaction degree and water content lead to a significant reduction in hydraulic conductivity. This drastic reduction highlights the sensitivity of loess permeability to saturation changes, which is attributed to the rapid reduction in interconnected pore channels as soil suction increases and pore spaces are filled or compressed under higher compaction. (3) The response surface prediction model quantitatively reveals the influence weights of various factors on hydraulic conductivity in the order of matric suction > initial compaction degree > initial water content. The model exhibits a high coefficient of determination (R2 = 0.9861), enabling rapid and accurate prediction of the hydraulic conductivity of Yangling loess. This high precision confirms that the model effectively captures the complex interactions between the factors, providing a reliable tool for practical engineering calculations. This study provides a new model and experimental basis for the accurate prediction of unsaturated loess hydraulic properties. The proposed SWCC model, considering compaction degree and the response surface model for hydraulic conductivity, offers practical tools for engineers and researchers, facilitating more precise design and risk assessment in collapsible loess areas. Full article
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26 pages, 18752 KB  
Article
Rate-Dependent Residual Strength of Unsaturated Slip-Zone Soil Under Suction-Controlled Conditions
by Jin Yuan, Rui Zhu, Yanpian Mao, Lanlan Xu, Jianfan Zhao, Chao Zhang and Shu Zhang
Geosciences 2025, 15(10), 397; https://doi.org/10.3390/geosciences15100397 - 14 Oct 2025
Cited by 1 | Viewed by 651
Abstract
Reservoir landslides undergo saturated–unsaturated transitions under hydrological variations. Matric suction significantly influences slip-zone soil strength. Existing studies lack analysis of suction–rate–strength coupling, while Amontons’ model fails for cohesive soils. This study investigated Huangtupo landslide slip-zone soil in the upper reaches of the Yangtze [...] Read more.
Reservoir landslides undergo saturated–unsaturated transitions under hydrological variations. Matric suction significantly influences slip-zone soil strength. Existing studies lack analysis of suction–rate–strength coupling, while Amontons’ model fails for cohesive soils. This study investigated Huangtupo landslide slip-zone soil in the upper reaches of the Yangtze River using pressure plate and saturated salt solution methods to determine the soil–water characteristic curve. Suction-controlled ring shear tests were conducted under three matric suction levels (Ψ = 0, 200, and 700 kPa) across net normal stresses (σnet = 100–800 kPa) and shear rates (γ˙ = 0.05–200 mm/min). Key findings revealed the following: (1) significant suction–rate coupling effects were shown, with 700 kPa suction yielding 30% higher residual strength than saturated conditions, validating matric suction’s role in enhancing effective stress and particle contact strength; (2) residual cohesion showed strong logarithmic correlation with shear rate, with the fastest growth below 10 mm/min, while the residual friction angle varied minimally (0.68°), contributing little to overall strength; (3) a bivariate model relating residual cohesion to γ˙ and Ψ was established, overcoming traditional single-factor limitations. The study demonstrates that dual-parameter Coulomb modeling effectively captures multi-field coupling mechanisms in unsaturated slip-zone soils, providing theoretical foundations for landslide deformation prediction and engineering design under dynamic hydrological conditions. Full article
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39 pages, 19794 KB  
Article
Cylindrical Coordinate Analytical Solution for Axisymmetric Consolidation of Unsaturated Soils: Dual Bessel–Trigonometric Orthogonal Expansion Approach to Radial–Vertical Composite Seepage Systems
by Yiru Hu and Lei Ouyang
Symmetry 2025, 17(10), 1714; https://doi.org/10.3390/sym17101714 - 13 Oct 2025
Viewed by 568
Abstract
This study develops a novel analytical solution for three-dimensional axisymmetric consolidation of unsaturated soils incorporating radial–vertical composite seepage mechanisms and anisotropic permeability characteristics. A groundbreaking dual orthogonal expansion framework is established, utilizing innovative Bessel–trigonometric function coupling to solve the inherently complex spatiotemporal coupled [...] Read more.
This study develops a novel analytical solution for three-dimensional axisymmetric consolidation of unsaturated soils incorporating radial–vertical composite seepage mechanisms and anisotropic permeability characteristics. A groundbreaking dual orthogonal expansion framework is established, utilizing innovative Bessel–trigonometric function coupling to solve the inherently complex spatiotemporal coupled partial differential equations in cylindrical coordinate systems. The mathematical approach synergistically combines modal expansion theory with Laplace transform methodology, achieving simultaneous spatial expansion of gas–liquid two-phase pressure fields through orthogonal function series, thereby transforming the three-dimensional problem into solvable ordinary differential equations. Rigorous validation demonstrates exceptional accuracy with coefficient of determination R2 exceeding 0.999 and relative errors below 2% compared to numerical simulations, confirming theoretical correctness and practical applicability. The analytical solutions reveal four critical findings with quantitative engineering implications: (1) dual-directional drainage achieves 28% higher pressure dissipation efficiency than unidirectional drainage, providing design optimization criteria for vertical drainage systems; (2) normalized matric suction variation exhibits characteristic three-stage evolution featuring rapid decline, plateau stabilization, and slow recovery phases, while water phase follows bidirectional inverted S-curve patterns, enabling accurate consolidation behavior prediction under varying saturation conditions; (3) gas-water permeability ratio ka/kw spanning 0.1 to 1000 produces two orders of magnitude time compression effect from 10−2 s to 10−4 s, offering parametric design methods for construction sequence control; (4) initial pressure gradient parameters λa and λw demonstrate opposite regulatory mechanisms, where increasing λa retards consolidation while λw promotes the process, providing differentiated treatment strategies for various geological conditions. The unified framework accommodates both uniform and gradient initial pore pressure distributions, delivering theoretical support for refined embankment engineering design and construction control. Full article
(This article belongs to the Section Engineering and Materials)
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