Saturated high plasticity clays show complex nonlinear, rate‐dependent, and hysteresis behaviors under non‐monotonic stress paths, requiring advanced mathematical constitutive equations for accurate description. Taking into account the inherent advantages of kinematic hardening mechanisms in simulating complex stress histories, this paper presents a novel fractional order kinematic hardening viscoplastic model for describing complex rate‐dependent features of saturated high plasticity clays: first, the modified isotach viscosity is extended into general loading conditions to consider both loading and unloading rate effects; second, a combined rate‐dependent isotropic‐rotational‐kinematic hardening law is built through current and conjugate stress points res the non‐intersection of two surfaces and smooth transition; third, a stress‐fractional operator is defined to represent the non‐orthogonal plastic flow direction in the proposed model; fourth, based on the consistency condition on the bubble surface, the increment form of stress‐strain‐strain rate relationship can be formulated and implemented into a finite element code. Parametric analyses are then adopted to demonstrate the model's capabilities under different loading paths. Finally, three different saturated clays, namely natural Boom clay, Hong Kong marine deposits, and an Earth dam core compacted clay, are employed to validate the model's effectiveness and performance via various rate‐dependent non‐monotonic element test results.
{"title":"Capturing Complex Rate‐Dependent Behaviors of Saturated Clays: A Fractional Consistency Kinematic Hardening Viscoplastic Approach","authors":"Wei Cheng, Zhen‐Yu Yin","doi":"10.1002/nag.70277","DOIUrl":"https://doi.org/10.1002/nag.70277","url":null,"abstract":"Saturated high plasticity clays show complex nonlinear, rate‐dependent, and hysteresis behaviors under non‐monotonic stress paths, requiring advanced mathematical constitutive equations for accurate description. Taking into account the inherent advantages of kinematic hardening mechanisms in simulating complex stress histories, this paper presents a novel fractional order kinematic hardening viscoplastic model for describing complex rate‐dependent features of saturated high plasticity clays: first, the modified isotach viscosity is extended into general loading conditions to consider both loading and unloading rate effects; second, a combined rate‐dependent isotropic‐rotational‐kinematic hardening law is built through current and conjugate stress points res the non‐intersection of two surfaces and smooth transition; third, a stress‐fractional operator is defined to represent the non‐orthogonal plastic flow direction in the proposed model; fourth, based on the consistency condition on the bubble surface, the increment form of stress‐strain‐strain rate relationship can be formulated and implemented into a finite element code. Parametric analyses are then adopted to demonstrate the model's capabilities under different loading paths. Finally, three different saturated clays, namely natural Boom clay, Hong Kong marine deposits, and an Earth dam core compacted clay, are employed to validate the model's effectiveness and performance via various rate‐dependent non‐monotonic element test results.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"5 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146215682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shan Tong, Kristin M. Sample‐Lord, Yu‐Chao Li, Guan‐Nian Chen
Diffusion and membrane behavior of clays and clay‐soil mixtures are important properties for predicting long‐term performance of engineered containment barriers. Concurrent measurement of effective diffusion coefficients ( D * ) and membrane efficiencies (ω) of unsaturated soil typically is performed with a modified through‐diffusion test apparatus where relatively thick high air entry (HAE) disks are required at the specimen boundaries to maintain a constant degree of saturation. The presence of the HAE disks between the circulated solutions and the specimen inhibits direct monitoring of the concentration gradient that develops across the specimen, which is critical to accurate calculation of D * and ω. In this study, an analytical model (TDM‐U) is proposed to depict solute distribution within a multilayer system composed of soil, HAE disks, and porous stones, and support evaluation of diffusive and membrane behavior properties of both saturated and unsaturated specimens. Based on the comparison with numerical simulation and other two existing models, the proposed model yielded a relatively high accuracy of less than 5% relative error in calculated D * over a wide range of flow rates spanning from 5 × 10 −11 m 3 /s to 7.5 × 10 −9 m 3 /s, with different inflow/outflow port locations, and for both saturated and unsaturated soil conditions. Ultimately, the proposed TDM‐U model exhibited a strong correlation with experimental data under different degrees of saturation and pore water concentration, and can potentially support more reliable predictions of contaminant transport processes in engineered barriers.
{"title":"Analytical Assessment of Solute Distribution for Evaluation of Diffusion and Membrane Behavior Properties of Saturated and Unsaturated Soils","authors":"Shan Tong, Kristin M. Sample‐Lord, Yu‐Chao Li, Guan‐Nian Chen","doi":"10.1002/nag.70268","DOIUrl":"https://doi.org/10.1002/nag.70268","url":null,"abstract":"Diffusion and membrane behavior of clays and clay‐soil mixtures are important properties for predicting long‐term performance of engineered containment barriers. Concurrent measurement of effective diffusion coefficients ( <jats:italic> D <jats:sup>*</jats:sup> </jats:italic> ) and membrane efficiencies (ω) of unsaturated soil typically is performed with a modified through‐diffusion test apparatus where relatively thick high air entry (HAE) disks are required at the specimen boundaries to maintain a constant degree of saturation. The presence of the HAE disks between the circulated solutions and the specimen inhibits direct monitoring of the concentration gradient that develops across the specimen, which is critical to accurate calculation of <jats:italic> D <jats:sup>*</jats:sup> </jats:italic> and ω. In this study, an analytical model (TDM‐U) is proposed to depict solute distribution within a multilayer system composed of soil, HAE disks, and porous stones, and support evaluation of diffusive and membrane behavior properties of both saturated and unsaturated specimens. Based on the comparison with numerical simulation and other two existing models, the proposed model yielded a relatively high accuracy of less than 5% relative error in calculated <jats:italic> D <jats:sup>*</jats:sup> </jats:italic> over a wide range of flow rates spanning from 5 × 10 <jats:sup>−11</jats:sup> m <jats:sup>3</jats:sup> /s to 7.5 × 10 <jats:sup>−9</jats:sup> m <jats:sup>3</jats:sup> /s, with different inflow/outflow port locations, and for both saturated and unsaturated soil conditions. Ultimately, the proposed TDM‐U model exhibited a strong correlation with experimental data under different degrees of saturation and pore water concentration, and can potentially support more reliable predictions of contaminant transport processes in engineered barriers.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"14 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The material point method (MPM) is widely employed to simulate granular flows. Although explicit time integration is favored in most current MPM implementations for its simplicity, it cannot rigorously incorporate the incompressible µ ( I )‐rheology, an efficient model ubiquitously adopted in other particle‐based numerical methods. While operator‐splitting‐based explicit‐implicit MPM can overcome this limitation for incompressible fluids, its extension to dense granular flows governed by µ ( I )‐rheology remains unexplored. To bridge this gap, this study proposes an explicit‐implicit MPM framework specifically for incompressible dense granular flows governed by the µ ( I ) rheology, augmented by a novel regularization technique that eliminates pathological viscosity divergence inherent to the original µ ( I ). The explicit‐implicit MPM framework comprises two steps: (i) an explicit predictor for velocity estimation, and (ii) an implicit corrector for solving the Pressure Poisson equation and updating velocity. In particular, a staggered grid is adopted for both steps to improve pressure stability and computational efficiency, and the Multigrid Preconditioned Conjugate Gradient method (MGPCG) is utilized for efficient pressure solution. The framework is further rigorously validated against a series of experimental benchmarks. Analysis of the regularization method is also conducted, revealing that: (i) decreasing the regularization parameter λ increases viscosity at low strain rates, reducing the runout; (ii) L1 regularization produces a longer runout than the higher‐order formulations (L2–L4), while L2–L4 generate similar deposition patterns, indicating negligible benefit from the added mathematical complexity, and (iii) Unlike PFEM, where decreasing λ severely increases computational cost, the explicit‐implicit MPM computes regularization explicitly in the predictor step, maintaining λ ‐invariant efficiency.
{"title":"Explicit‐Implicit Material Point Method for Dense Granular Flows With a Novel Regularized µ ( I ) Model","authors":"Hang Feng, Zhen‐Yu Yin","doi":"10.1002/nag.70273","DOIUrl":"https://doi.org/10.1002/nag.70273","url":null,"abstract":"The material point method (MPM) is widely employed to simulate granular flows. Although explicit time integration is favored in most current MPM implementations for its simplicity, it cannot rigorously incorporate the incompressible <jats:italic>µ</jats:italic> ( <jats:italic>I</jats:italic> )‐rheology, an efficient model ubiquitously adopted in other particle‐based numerical methods. While operator‐splitting‐based explicit‐implicit MPM can overcome this limitation for incompressible fluids, its extension to dense granular flows governed by <jats:italic>µ</jats:italic> ( <jats:italic>I</jats:italic> )‐rheology remains unexplored. To bridge this gap, this study proposes an explicit‐implicit MPM framework specifically for incompressible dense granular flows governed by the <jats:italic>µ</jats:italic> ( <jats:italic>I</jats:italic> ) rheology, augmented by a novel regularization technique that eliminates pathological viscosity divergence inherent to the original <jats:italic>µ</jats:italic> ( <jats:italic>I</jats:italic> ). The explicit‐implicit MPM framework comprises two steps: (i) an explicit predictor for velocity estimation, and (ii) an implicit corrector for solving the Pressure Poisson equation and updating velocity. In particular, a staggered grid is adopted for both steps to improve pressure stability and computational efficiency, and the Multigrid Preconditioned Conjugate Gradient method (MGPCG) is utilized for efficient pressure solution. The framework is further rigorously validated against a series of experimental benchmarks. Analysis of the regularization method is also conducted, revealing that: (i) decreasing the regularization parameter <jats:italic>λ</jats:italic> increases viscosity at low strain rates, reducing the runout; (ii) L1 regularization produces a longer runout than the higher‐order formulations (L2–L4), while L2–L4 generate similar deposition patterns, indicating negligible benefit from the added mathematical complexity, and (iii) Unlike PFEM, where decreasing <jats:italic>λ</jats:italic> severely increases computational cost, the explicit‐implicit MPM computes regularization explicitly in the predictor step, maintaining <jats:italic>λ</jats:italic> ‐invariant efficiency.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"48 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chunyi Cui, Benlong Wang, Zhimeng Liang, Hailong Liu, Gang Li, Linqi Niu, Liqiang Sun
Utilizing the dynamic theory of 3D continuous medium and 1D elastic rod, this paper obtains a new close‐formed solution for the torsional vibration of pipe piles, with regard to both the pipe pile defect and the surrounding soil radial heterogeneity effect. Firstly, combining Laplace transform and complex stiffess transfer method, the tangential stress on the pipe pile from the soils can be obtained. Secondly, the close‐formed solution for the torsional vibration characteristics (TVC) of pipe pile head is derived, via combining the continuity conditions of the soil‐pipe pile system and the transmissibility of impedance functions. Further, using the inverse Fourier transform (IFT) and the convolution theorem, a semi‐analytical solution for the time‐domain reflected signal function of pile head velocity is achieved. Finally, the accuracy of the reduced solutions derived in this paper is validated via a comparison analysis with existing theoretical solutions. Moreover, a parameterized analysis is implemented to discuss the impacts of different types of pile defects and radial heterogeneity effects on the TVC of pipe piles.
{"title":"A New Close‐Formed Solution for Torsional Vibration of a Defective Pipe Pile in Radially Heterogeneous Soils","authors":"Chunyi Cui, Benlong Wang, Zhimeng Liang, Hailong Liu, Gang Li, Linqi Niu, Liqiang Sun","doi":"10.1002/nag.70263","DOIUrl":"https://doi.org/10.1002/nag.70263","url":null,"abstract":"Utilizing the dynamic theory of 3D continuous medium and 1D elastic rod, this paper obtains a new close‐formed solution for the torsional vibration of pipe piles, with regard to both the pipe pile defect and the surrounding soil radial heterogeneity effect. Firstly, combining Laplace transform and complex stiffess transfer method, the tangential stress on the pipe pile from the soils can be obtained. Secondly, the close‐formed solution for the torsional vibration characteristics (TVC) of pipe pile head is derived, via combining the continuity conditions of the soil‐pipe pile system and the transmissibility of impedance functions. Further, using the inverse Fourier transform (IFT) and the convolution theorem, a semi‐analytical solution for the time‐domain reflected signal function of pile head velocity is achieved. Finally, the accuracy of the reduced solutions derived in this paper is validated via a comparison analysis with existing theoretical solutions. Moreover, a parameterized analysis is implemented to discuss the impacts of different types of pile defects and radial heterogeneity effects on the TVC of pipe piles.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"29 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhihai Zhang, Hong Xiao, Xuhao Cui, Yang Wang, Yihao Chi, Dan Liu, Mahantesh M. Nadakatti
Dynamic stabilization is a critical process for enhancing the service performance of the ballast bed. This improvement occurs specifically following tamping activities have been completed. To deepen our understanding of the operational mechanisms of dynamic stabilizing machines and to improve maintenance efficiency, this paper innovatively introduces the block assembly method and polyhedral units for the rapid construction of a 3‐D simulation model of the ballasted track post long‐section tamping. This method enables the high‐fidelity virtual reconstruction of the complete ballasted track tamping process. By considering the spatial coupling vibration effects between the stabilizing machine and the long track panel, we propose a flexible rail transition grid simulation method alongside an eight‐wheel non‐coplanar demodulation technique, culminating in the development of a virtual unit module. Utilizing multimedia coupling theory and equivalent replacement concepts, we establish a high‐fidelity coupling model of dual dynamic stabilizing machines and the ballasted track, with the model validated by extensive in‐situ testing. The findings indicate a non‐positive correlation between the effectiveness of the stabilizing operation and the excitation frequency. Specifically, a high stabilizing frequency does not optimize the ballast bed state, and frequencies exceeding 30 Hz pose a risk of collapse for the side slope ballast. Conversely, when the stabilizing frequency is maintained between 25 Hz and 30 Hz, the change plastic deformation rate of ballast bed is low, and the lowest is 18.5%, suggesting optimal elasticity and effective stabilizing operations. This research provides critical theoretical support for the simulation analysis and operational parameter selection in stabilizing operations.
{"title":"Dynamic Stabilizing in Ballasted Railway Maintenance: Novel Model and Parameter Optimization Based on DEM‐MFBD Coupling Method","authors":"Zhihai Zhang, Hong Xiao, Xuhao Cui, Yang Wang, Yihao Chi, Dan Liu, Mahantesh M. Nadakatti","doi":"10.1002/nag.70259","DOIUrl":"https://doi.org/10.1002/nag.70259","url":null,"abstract":"Dynamic stabilization is a critical process for enhancing the service performance of the ballast bed. This improvement occurs specifically following tamping activities have been completed. To deepen our understanding of the operational mechanisms of dynamic stabilizing machines and to improve maintenance efficiency, this paper innovatively introduces the block assembly method and polyhedral units for the rapid construction of a 3‐D simulation model of the ballasted track post long‐section tamping. This method enables the high‐fidelity virtual reconstruction of the complete ballasted track tamping process. By considering the spatial coupling vibration effects between the stabilizing machine and the long track panel, we propose a flexible rail transition grid simulation method alongside an eight‐wheel non‐coplanar demodulation technique, culminating in the development of a virtual unit module. Utilizing multimedia coupling theory and equivalent replacement concepts, we establish a high‐fidelity coupling model of dual dynamic stabilizing machines and the ballasted track, with the model validated by extensive in‐situ testing. The findings indicate a non‐positive correlation between the effectiveness of the stabilizing operation and the excitation frequency. Specifically, a high stabilizing frequency does not optimize the ballast bed state, and frequencies exceeding 30 Hz pose a risk of collapse for the side slope ballast. Conversely, when the stabilizing frequency is maintained between 25 Hz and 30 Hz, the change plastic deformation rate of ballast bed is low, and the lowest is 18.5%, suggesting optimal elasticity and effective stabilizing operations. This research provides critical theoretical support for the simulation analysis and operational parameter selection in stabilizing operations.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"300 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Phatharaphong Yensri, Asaad Faramarzi, Nicole Metje, David N. Chapman
Tunnelling in urban environments can significantly affect existing buried structures such as pile foundations. However, the current understanding of how tunnelling‐induced ground movements influence the stability and serviceability of piles remains limited. This knowledge gap presents potential risks that must be addressed during tunnel design and construction. This study investigates the impact of adjacent tunnelling on long piles supported superstructure through a series of three‐dimensional numerical analyses. The numerical model was validated using data from a well‐documented case study. The analysis considered four tunnel depths and four horizontal clearances, along with varying pile lengths and tunnel volume losses. Key responses of the pile, including induced axial force, bending moment, vertical displacement and safety factor were examined. From these results, a safety zone was proposed based on an integrated interpretation of the pile responses under different tunnelling scenarios. The findings indicate that for piles ranging from 40 to 50 m in length, the safety clearance can be classified into four relative depth zones based on tunnel depth. For piles exceeding 50 m, the influence zone can be grouped into two depth categories. These results offer valuable guidance for geotechnical engineers involved in tunnel alignment and risk mitigation when working near long pile foundations. Given the increasing utilisation of underground space in densely populated areas, the insights from this research contribute to more informed, effective and sustainable urban planning and infrastructure development strategies.
{"title":"Numerical Investigation of Bored Tunnelling Effects on Pile‐Supported Superstructures","authors":"Phatharaphong Yensri, Asaad Faramarzi, Nicole Metje, David N. Chapman","doi":"10.1002/nag.70275","DOIUrl":"https://doi.org/10.1002/nag.70275","url":null,"abstract":"Tunnelling in urban environments can significantly affect existing buried structures such as pile foundations. However, the current understanding of how tunnelling‐induced ground movements influence the stability and serviceability of piles remains limited. This knowledge gap presents potential risks that must be addressed during tunnel design and construction. This study investigates the impact of adjacent tunnelling on long piles supported superstructure through a series of three‐dimensional numerical analyses. The numerical model was validated using data from a well‐documented case study. The analysis considered four tunnel depths and four horizontal clearances, along with varying pile lengths and tunnel volume losses. Key responses of the pile, including induced axial force, bending moment, vertical displacement and safety factor were examined. From these results, a safety zone was proposed based on an integrated interpretation of the pile responses under different tunnelling scenarios. The findings indicate that for piles ranging from 40 to 50 m in length, the safety clearance can be classified into four relative depth zones based on tunnel depth. For piles exceeding 50 m, the influence zone can be grouped into two depth categories. These results offer valuable guidance for geotechnical engineers involved in tunnel alignment and risk mitigation when working near long pile foundations. Given the increasing utilisation of underground space in densely populated areas, the insights from this research contribute to more informed, effective and sustainable urban planning and infrastructure development strategies.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"24 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pengqiang Yu, Yang Liu, Kejia Wu, Xiaoxiao Wang, Dongsheng Li
The ostensibly uniform macroscopic deformation of granular materials belies intensive fluctuations of microscopic and mesoscopic kinematics. This study employs the discrete element method to analyze the spatial characteristics of local kinematic fluctuations under different shear conditions and quantifies the consistency between multi‐scale kinematics and macroscopic behavior. With shear progression, displacement fluctuation vortices evolve from uniform small vortices into dominant large structures containing numerous small vortices, heralding shear band formation, characterized by a sequence of coherently rotating and interconnected small vortices. Within these bands, while particle displacement fluctuations are subdued, profound rotational motions lead to pronounced inter‐particle relative displacements, designating the shear band as an optimal energy dissipation structure. The probability density distribution forms of microscopic and mesoscopic kinematic fluctuations and their evolutionary trends are independent of the loading path. At the microscale, both particle displacement and rotation fluctuations follow ‐Gaussian distributions. Notably, prior to shear band formation, the distribution of normalized displacement fluctuations maintains its form with increasing strain, whereas the distribution characterizing particle rotation sharpens, reflecting a more pronounced peak and heavier tails. At the mesoscale, Loop volumetric strain and rotation exhibit ‐Gaussian distributions, while Loop deviatoric strain follows a Gamma distribution. The average micro‐ and mesoscopic kinematics align with macroscopic behaviors throughout shearing, regardless of loading paths.
{"title":"Multiscale Analysis of Local Fluctuations in Granular Materials Subject to Quasi‐Static Shear","authors":"Pengqiang Yu, Yang Liu, Kejia Wu, Xiaoxiao Wang, Dongsheng Li","doi":"10.1002/nag.70272","DOIUrl":"https://doi.org/10.1002/nag.70272","url":null,"abstract":"The ostensibly uniform macroscopic deformation of granular materials belies intensive fluctuations of microscopic and mesoscopic kinematics. This study employs the discrete element method to analyze the spatial characteristics of local kinematic fluctuations under different shear conditions and quantifies the consistency between multi‐scale kinematics and macroscopic behavior. With shear progression, displacement fluctuation vortices evolve from uniform small vortices into dominant large structures containing numerous small vortices, heralding shear band formation, characterized by a sequence of coherently rotating and interconnected small vortices. Within these bands, while particle displacement fluctuations are subdued, profound rotational motions lead to pronounced inter‐particle relative displacements, designating the shear band as an optimal energy dissipation structure. The probability density distribution forms of microscopic and mesoscopic kinematic fluctuations and their evolutionary trends are independent of the loading path. At the microscale, both particle displacement and rotation fluctuations follow ‐Gaussian distributions. Notably, prior to shear band formation, the distribution of normalized displacement fluctuations maintains its form with increasing strain, whereas the distribution characterizing particle rotation sharpens, reflecting a more pronounced peak and heavier tails. At the mesoscale, Loop volumetric strain and rotation exhibit ‐Gaussian distributions, while Loop deviatoric strain follows a Gamma distribution. The average micro‐ and mesoscopic kinematics align with macroscopic behaviors throughout shearing, regardless of loading paths.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"19 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study proposes a theoretical framework for predicting active non‐limit earth pressure on retaining structures with narrow backfill, based on the stress characteristics method (SCM) integrated with a displacement‐dependent shear strength mobilization model. The method captures the progressive transition from at‐rest to active states while incorporating geometric constraints, soil cohesion, and interface behavior. Validation against reduced‐scale model tests shows strong agreement in pressure distributions, failure mechanisms, and total thrust evolution. Compared to existing analytical solutions, the proposed approach improves prediction accuracy without relying on predefined failure surfaces and extends applicability to cohesive soils. Both experimental and theoretical results demonstrate that the critical wall displacement required to fully mobilize active earth pressure is largely insensitive to the backfill aspect ratio, enabling simplified mobilization modeling for narrow backfill conditions. Parametric analyses further reveal that narrower backfills result in lower active earth pressure throughout the non‐limit process and shift the application point of the resultant force upward due to enhanced soil arching, while cohesive soils exhibit a downward shift associated with tensile crack development. These findings provide a robust and practical tool for designing retaining structures in spatially constrained environments, improving both prediction accuracy and design efficiency.
{"title":"Predicting Active Non‐Limit Earth Pressure on Retaining Structures With Narrow Backfill: A Stress Characteristics Approach","authors":"Hao‐Biao Chen, Guang‐Zai Chen, Ming‐Guang Li, Nian‐Wu Liu, Jin‐Jian Chen","doi":"10.1002/nag.70276","DOIUrl":"https://doi.org/10.1002/nag.70276","url":null,"abstract":"This study proposes a theoretical framework for predicting active non‐limit earth pressure on retaining structures with narrow backfill, based on the stress characteristics method (SCM) integrated with a displacement‐dependent shear strength mobilization model. The method captures the progressive transition from at‐rest to active states while incorporating geometric constraints, soil cohesion, and interface behavior. Validation against reduced‐scale model tests shows strong agreement in pressure distributions, failure mechanisms, and total thrust evolution. Compared to existing analytical solutions, the proposed approach improves prediction accuracy without relying on predefined failure surfaces and extends applicability to cohesive soils. Both experimental and theoretical results demonstrate that the critical wall displacement required to fully mobilize active earth pressure is largely insensitive to the backfill aspect ratio, enabling simplified mobilization modeling for narrow backfill conditions. Parametric analyses further reveal that narrower backfills result in lower active earth pressure throughout the non‐limit process and shift the application point of the resultant force upward due to enhanced soil arching, while cohesive soils exhibit a downward shift associated with tensile crack development. These findings provide a robust and practical tool for designing retaining structures in spatially constrained environments, improving both prediction accuracy and design efficiency.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"34 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a THM coupled field‐enriched finite element method is proposed to simulate water‐ice phase transition induced crack propagation in fractured rock masses. The governing equations of temperature, phase, fluid flow and deformation are based on the thermo‐poroelastic theory and Allen–Chan equation, in which the relationships among these physical fields are fully coupled. Two field variables are introduced to characterize the crack properties, and to describe water‐ice phase transition. The coupled multiphysics governing equations are solved by the staggered Newton‐Raphson iterative algorithm. The accuracy of the proposed method is carefully validated by homogeneous freezing of intact media, unidirectional freezing of cracking media, freezing and deformation of intact sandstone in the aspects of experimental results and previous numerical solutions. Additionally, the performance of the proposed method for simulating water‐ice phase transition induced crack propagation in fractured rock masses is validated and compared with the experimental results and FDEM results. Finally, the application of the proposed method in frost induced cracking of slope in shallow cold regions has been realized. The numerical results have shown that the proposed method is able to accurately simulate water‐ice phase transition induced crack propagation in rock masses, and to simulate evolution of the water‐ice phase transition interface.
{"title":"A Thermo‐Hydro‐Mechanical‐Phase Transition Coupled Field‐Enriched Finite Element Method for Simulating Water‐Ice Phase Transition Induced Crack Propagation in Rock Masses","authors":"Xiaoping Zhou, Kunlin Liu, Linyuan Han","doi":"10.1002/nag.70261","DOIUrl":"https://doi.org/10.1002/nag.70261","url":null,"abstract":"In this paper, a THM coupled field‐enriched finite element method is proposed to simulate water‐ice phase transition induced crack propagation in fractured rock masses. The governing equations of temperature, phase, fluid flow and deformation are based on the thermo‐poroelastic theory and Allen–Chan equation, in which the relationships among these physical fields are fully coupled. Two field variables are introduced to characterize the crack properties, and to describe water‐ice phase transition. The coupled multiphysics governing equations are solved by the staggered Newton‐Raphson iterative algorithm. The accuracy of the proposed method is carefully validated by homogeneous freezing of intact media, unidirectional freezing of cracking media, freezing and deformation of intact sandstone in the aspects of experimental results and previous numerical solutions. Additionally, the performance of the proposed method for simulating water‐ice phase transition induced crack propagation in fractured rock masses is validated and compared with the experimental results and FDEM results. Finally, the application of the proposed method in frost induced cracking of slope in shallow cold regions has been realized. The numerical results have shown that the proposed method is able to accurately simulate water‐ice phase transition induced crack propagation in rock masses, and to simulate evolution of the water‐ice phase transition interface.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"242 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xu Song, Ren‐Peng Chen, Zhen‐Hua Li, Chang‐Wei Miao, Jun‐Qing Wang, Lin Liu, Jin Tang, Fan‐Yan Meng
The development of the soil arching effect plays a crucial role in determining the overburden pressure of the shield tunnel. Stress level and associated soil mechanical behavior significantly affect the soil arching effect. Based on the experimental results of the deep‐buried shield tunneling, this paper proposes an analytical approach to predict the overburden pressure of the deep‐buried shield tunnel in sand, considering the soil dilatancy and the progressive development of the soil arching. Firstly, the relationship between the soil dilatancy and the development direction of the shear band is quantitatively described. Then, the formula for calculating the overburden pressure concerning the soil arching height is derived. Afterward, the relationship between the soil arching height and the ground loss ratio is established. Thus, the theoretical relationship between the overburden pressure and the ground loss ratio is promoted, and the predicted ground reaction curve (GRC) is obtained. The 1 g model tests and the centrifugal model test are selected to verify the accuracy of the proposed methodology. The results show that the predicted GRCs agree with the test results. Finally, the influence of tunnel cover‐to‐depth ratio ( C / D ), soil internal friction angle, and tunnel diameter on the development of the soil arching ratio with the increasing ground loss ratio is discussed. Compared with the theory for soil arching effect proposed by Terzaghi, this approach can quantitatively describe the evolution process of the soil arching effect and obtain continuous GRCs.
{"title":"Analytical Approach to Predict the Overburden Pressure of the Deep‐Buried Shield Tunnel","authors":"Xu Song, Ren‐Peng Chen, Zhen‐Hua Li, Chang‐Wei Miao, Jun‐Qing Wang, Lin Liu, Jin Tang, Fan‐Yan Meng","doi":"10.1002/nag.70274","DOIUrl":"https://doi.org/10.1002/nag.70274","url":null,"abstract":"The development of the soil arching effect plays a crucial role in determining the overburden pressure of the shield tunnel. Stress level and associated soil mechanical behavior significantly affect the soil arching effect. Based on the experimental results of the deep‐buried shield tunneling, this paper proposes an analytical approach to predict the overburden pressure of the deep‐buried shield tunnel in sand, considering the soil dilatancy and the progressive development of the soil arching. Firstly, the relationship between the soil dilatancy and the development direction of the shear band is quantitatively described. Then, the formula for calculating the overburden pressure concerning the soil arching height is derived. Afterward, the relationship between the soil arching height and the ground loss ratio is established. Thus, the theoretical relationship between the overburden pressure and the ground loss ratio is promoted, and the predicted ground reaction curve (GRC) is obtained. The 1 <jats:italic>g</jats:italic> model tests and the centrifugal model test are selected to verify the accuracy of the proposed methodology. The results show that the predicted GRCs agree with the test results. Finally, the influence of tunnel cover‐to‐depth ratio ( <jats:italic>C</jats:italic> / <jats:italic>D</jats:italic> ), soil internal friction angle, and tunnel diameter on the development of the soil arching ratio with the increasing ground loss ratio is discussed. Compared with the theory for soil arching effect proposed by Terzaghi, this approach can quantitatively describe the evolution process of the soil arching effect and obtain continuous GRCs.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"97 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146169378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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