International Journal for Numerical and Analytical Methods in Geomechanics最新文献_第2页

Integrating Grain to Ground Motion Data for Critical Rock Bridge and Slope Failure Analysis 临界岩桥与边坡破坏分析的颗粒与地震动数据集成

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-26 DOI: 10.1002/nag.70421

Antoinette Tordesillas, Shuo Zhou, Leonnardo Probst, Pat Bellett, Michal Nitka, Jacek Tejchman

{"title":"Integrating Grain to Ground Motion Data for Critical Rock Bridge and Slope Failure Analysis","authors":"Antoinette Tordesillas, Shuo Zhou, Leonnardo Probst, Pat Bellett, Michal Nitka, Jacek Tejchman","doi":"10.1002/nag.70421","DOIUrl":"https://doi.org/10.1002/nag.70421","url":null,"abstract":"Rock masses can fail catastrophically with little warning, yet their stability depends on hidden internal connections that channel forces and localise damage. Among these, rock bridges–a “known unknown” in slope mechanics–lock fractured rock and control how failure unfolds, but their concealed geometry and uncertain strength obscure where and how damage initiates. We present a data‐driven framework that treats rock masses as force–motion flow networks, with three key innovations: the critical rock bridge path is conceptualised as a recurrent bottleneck within the prefailure force‐transmission network of a rock mass, damage evolution cast as a network attack process, and internal connections interpreted as kinematic constraints resisting relative motion. By linking grain‐scale micromechanics with radar‐derived surface displacements on active slopes, we track the evolution of kinematic constraints and quantify prefailure damage. This physics‐informed, data‐driven approach integrates laboratory and field scales, providing a framework for identifying and characterising damage propagation along critical rock bridges in the prefailure regime across scales, on Earth and beyond.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"1 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148836264","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}

引用次数: 0

Large‐Strain Consolidation and Settlement of Stratified Saturated Clay Deposits: A One‐Dimensional Semi‐Analytical Framework 层状饱和粘土沉积物的大应变固结和沉降：一维半解析框架

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-26 DOI: 10.1002/nag.70425

Yifan Xu, Yunpeng Zhang, Chuanxun Li, Wenbing Wu

{"title":"Large‐Strain Consolidation and Settlement of Stratified Saturated Clay Deposits: A One‐Dimensional Semi‐Analytical Framework","authors":"Yifan Xu, Yunpeng Zhang, Chuanxun Li, Wenbing Wu","doi":"10.1002/nag.70425","DOIUrl":"https://doi.org/10.1002/nag.70425","url":null,"abstract":"Large‐strain consolidation of stratified saturated clays is difficult to model analytically or even semi‐analytically within existing frameworks. This paper proposes a layer‐wise modal solution for one‐dimensional large‐strain consolidation of stratified saturated clay foundations. The formulation is developed in the Lagrangian coordinate system and considers the nonlinear evolution of compressibility and permeability. By using an exponential transformation, the nonlinear governing equation in each layer is converted into a linear diffusion equation. Unlike conventional approaches that determine undetermined coefficients from boundary and interface conditions, the proposed method introduces time‐dependent interface pore‐pressure functions and solves them through nonlinear flux‐continuity closure equations. The solution is verified against analytical solutions, COMSOL simulations, and field measurements from the Teven Road trial embankment. Results demonstrate its accuracy in predicting pore‐pressure dissipation and settlement evolution in stratified soft clay foundations.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"15 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148836260","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}

引用次数: 0

An Anisotropic Constitutive Model for Crushable Geomaterials Based on Non‐Stationary Critical State Line Concept 基于非平稳临界状态线概念的可破碎岩土材料各向异性本构模型

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-26 DOI: 10.1002/nag.70424

Hesam Dejaloud, Hamed Taghavizade, Mohammad Rezania

{"title":"An Anisotropic Constitutive Model for Crushable Geomaterials Based on Non‐Stationary Critical State Line Concept","authors":"Hesam Dejaloud, Hamed Taghavizade, Mohammad Rezania","doi":"10.1002/nag.70424","DOIUrl":"https://doi.org/10.1002/nag.70424","url":null,"abstract":"In this paper, the dependencies of granular soil behaviour on particle crushing and fabric anisotropy are formulated within a novel model based on bounding surface plasticity theory enriched by the non‐stationary critical state line (NCSL) concept. By introducing a flexible decay function, the variation in the position and slope of the CSL with the magnitude of particle crushing is regulated. The originality of the model extends beyond its ability to capture the pre‐ and post‐failure behaviour of crushable geomaterials, as the elastic moduli are also modified to depend on both the stress state and the extent of particle breakage. The capabilities of the model are demonstrated against published data from triaxial compression tests on the widely studied Cambria sand and a compacted coal wash reject material from Australia. It is shown that the proposed model consistently captures the behaviour of crushable geomaterials across a wide range of void ratios, stress levels and particle breakage states, using a unified set of parameter values. The formulation of this anisotropic model has been kept sufficiently simple to facilitate its straightforward future implementation into a continuum‐based numerical framework for boundary value problem simulations.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"31 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148836259","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}

引用次数: 0

Analytical Methodology to Determine Thermally Induced Soil Deformation From Laboratory Data 从实验室数据确定热致土壤变形的分析方法

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-21 DOI: 10.1002/nag.70407

Jibril B. Coulibaly, Alessandro F. Rotta Loria

{"title":"Analytical Methodology to Determine Thermally Induced Soil Deformation From Laboratory Data","authors":"Jibril B. Coulibaly, Alessandro F. Rotta Loria","doi":"10.1002/nag.70407","DOIUrl":"https://doi.org/10.1002/nag.70407","url":null,"abstract":"Experimental laboratory investigations underlie most of the knowledge about the mechanics of soils under non‐isothermal conditions and their thermally induced deformation. Despite advances, the understanding of thermally induced deformation of soils remains inconsistent, hindering the development of a coherent framework that can advance science and engineering. Considering this challenge, this paper presents an analysis of the established methodology to determine thermally induced soil deformations from laboratory experiments. Established equations are re‐derived, verified, and compared, and the resulting predictions are analyzed. Data support that the quantification of thermally induced soil deformations can be affected by volume corrections and calibrations, the integration of conservation equations under non‐isothermal conditions, the misuse of thermal expansion coefficients, and the lack of repeatability tests and uncertainty quantification. Quantitative analyses support the conclusion that these aspects contribute to the contradictions in the state‐of‐the‐art. Therefore, this work proposes an updated methodology to experimentally quantify the thermally induced deformation of soils, whose widespread adoption is supported by the provision of an open‐source toolbox that implements the proposed changes to the state‐of‐the‐art: The Thermally Induced Deformation Analysis Library, TIDAL.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"25 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148768444","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}

引用次数: 0

Micro‐Parameter Sensitivity Analysis and Validation of the Mechanical Behaviour of Soft–Hard Composite Rock Based on 2D‐DEM 基于2D - DEM的软-硬复合岩石力学行为微参数敏感性分析与验证

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-20 DOI: 10.1002/nag.70415

Jin‐Hua Li, Yan‐Long Li, En‐Long Liu, Pan Wang, Wen‐Xiang Liu, Yang Yang

{"title":"Micro‐Parameter Sensitivity Analysis and Validation of the Mechanical Behaviour of Soft–Hard Composite Rock Based on 2D‐DEM","authors":"Jin‐Hua Li, Yan‐Long Li, En‐Long Liu, Pan Wang, Wen‐Xiang Liu, Yang Yang","doi":"10.1002/nag.70415","DOIUrl":"https://doi.org/10.1002/nag.70415","url":null,"abstract":"Calibration of microparameters in numerical simulations is a critical factor affecting model accuracy. To determine the relationship between macro‐ and microparameters in composite rock masses and the influence of soft rock layer proportions on mechanical properties, this study employed PFC2D software to construct numerical models of composite rock masses with varying soft‐to‐hard layer thickness ratios. A systematic analysis was conducted to investigate the influence of microparameters on macro‐mechanical properties. For composite rock bodies with varying soft rock layer thicknesses, as the soft rock proportion increases, the failure mode gradually shifts from shear failure dominated by hard rock to foliated failure dominated by soft rock. Cracks propagate along bedding planes and are constrained by hard rock layers. When the soft rock layer thickness increases from 10% to 90%, the total number of cracks increases by approximately twofold, while the proportion of shear cracks decreases from 75% to 40%. The crack counting rate exhibits exponential growth with stress and synchronizes with stress amplitude, peaking at 180–200 times/s − 1 . Laboratory test results align with numerical simulations, demonstrating that the PFC model accurately predicts composite rock mass strength (error ≤3.7%) and elastic modulus (error ≤4.6%). This study provides theoretical support for correlating macro‐ and micro‐mechanical properties in composite rock masses of varying hardness, offering significant reference value for stability assessment and reinforcement design in underground engineering.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"19 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148768445","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}

引用次数: 0

Research on the Macro‐Micro Energy Evolution Law and Segmented Damage Constitutive Model of Sandstone Under Dry‐Wet Cycles 干湿循环作用下砂岩宏观-微观能量演化规律及损伤本构模型研究

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-20 DOI: 10.1002/nag.70399

Senlin Gao, Qingyang Ren, Bin Chen, Songqiang Xiao, Hang Song, Yanping Jia

{"title":"Research on the Macro‐Micro Energy Evolution Law and Segmented Damage Constitutive Model of Sandstone Under Dry‐Wet Cycles","authors":"Senlin Gao, Qingyang Ren, Bin Chen, Songqiang Xiao, Hang Song, Yanping Jia","doi":"10.1002/nag.70399","DOIUrl":"https://doi.org/10.1002/nag.70399","url":null,"abstract":"The periodic fluctuation of reservoir water levels induces dry‐wet cycles, deteriorating sandy rock slope stability and potentially triggering collapses. This study investigates the degradation mechanism of Three Gorges Reservoir fine sandstone through uniaxial compression tests and PFC2D simulations under varying dry‐wet cycles. Key findings include: (1) Increasing cycles reduce uniaxial compressive strength and elastic modulus (showing “V‐shaped” and “N‐shaped” degradation trends), while permeability and porosity rise, and P‐wave velocity declines. (2) Crack growth is nonlinear, dominated by shear cracks and high‐angle microcracks, with force chains aligning with the loading direction. (3) Dissipation energy rate follows a “W‐shaped” trend, while elastic energy rate exhibits an “M‐shaped” pattern; both energies at crack initiation, damage, and peak stress correlate exponentially with cycle count ( K sd being more sensitive). (4) Dry‐wet cycles weaken intergranular bonds, reduce elastic energy storage ( U e ), increase dissipated energy ( U d ), lower M ‐value stability, and shift failure from brittle to ductile. (5) A Weibull‐based segmented damage model effectively simulates sandstone behavior under cyclic conditions. These insights enhance understanding of reservoir slope stability under hydrological fluctuations.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"380 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148768446","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}

引用次数: 0

Study on Key Parameters of Automatic Roadway Formation Without Pillar by Roof Cutting Based on Floor Failure 基于底板破坏的无顶板自动成巷关键参数研究

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-19 DOI: 10.1002/nag.70414

Xingxing Zhang, Yubing Gao, Huacheng Sun, Qingli Liu, Chuanjiu Zhang, Qiukai Gai

{"title":"Study on Key Parameters of Automatic Roadway Formation Without Pillar by Roof Cutting Based on Floor Failure","authors":"Xingxing Zhang, Yubing Gao, Huacheng Sun, Qingli Liu, Chuanjiu Zhang, Qiukai Gai","doi":"10.1002/nag.70414","DOIUrl":"https://doi.org/10.1002/nag.70414","url":null,"abstract":"Floor water inrush threatens the safe mining of the mine. The automatic roadway formation without pillar by roof cutting (ARFPRC) method can reduce the floor water inrush risk. However, the key parameters for mining above confined aquifers are difficult to determine. In response, this study proposes a design method for determining the key parameters of ARFPRC based on floor failure. First, the unique advantages of ARFPRC in reducing floor water inrush risk is elucidated. Then, numerical simulation studies are conducted to analyze the characteristics of floor damage under different roof cutting parameters, leading to the determination of the optimal parameters. It is also clarified that grouting reinforcement to improve rock properties is beneficial for preventing water inrush. Subsequently, a field test of floor grouting reinforcement was conducted on site. After its effectiveness was confirmed through geophysical detection, the ARFPRC industrial test was carried out. Finally, based on the measured depth of floor failure, it was demonstrated that the designed parameters effectively controlled floor damage. The research findings provide a theoretical foundation and engineering guidance for the application of ARFPRC technology in mining areas with the risk of floor water inrush.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"116 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148768447","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}

引用次数: 0

Clay and Sand Model Extended to Unsaturated Conditions: Implementation and Validation Within a Symbolic Algebra–Based Framework 粘土和砂模型扩展到非饱和条件：在基于符号代数的框架内的实现和验证

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-17 DOI: 10.1002/nag.70401

Arianna Pucci, Ignacio Giomi, Giulia Guida, Vicente Navarro, Francesca Casini

{"title":"Clay and Sand Model Extended to Unsaturated Conditions: Implementation and Validation Within a Symbolic Algebra–Based Framework","authors":"Arianna Pucci, Ignacio Giomi, Giulia Guida, Vicente Navarro, Francesca Casini","doi":"10.1002/nag.70401","DOIUrl":"https://doi.org/10.1002/nag.70401","url":null,"abstract":"This study presents a fully coupled hydro‐mechanical implementation of the Clay and Sand Model (CASM) extended to partially saturated conditions (U‐CASM) within the COMSOL Multiphysics environment. The formulation adopts Bishop's effective stress and suction as stress variables and incorporates alternative loading–collapse surfaces, dilatancy laws, and a porosity‐dependent water retention curve. The main contribution lies in a fully customised implementation strategy based on symbolic algebra, which enables user‐defined constitutive modelling, simplifies equation integration, and reduces programming effort within a multiphysics framework. The model is verified against benchmark simulations for clays and sands under drained and undrained conditions in both saturated and unsaturated states. Validation against triaxial and oedometer data confirms the ability of the model to reproduce soil behaviour over a wide range of stress paths and suction levels, while highlighting the influence of alternative constitutive assumptions. A field‐scale application further demonstrates the capability of the framework to capture key hydro‐mechanical features of partially saturated soils, including collapse upon wetting.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"341 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754633","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}

引用次数: 0

Analytical Method for Longitudinal Response of Shield Tunnels Under Arbitrary Loading Based on the Kerr Foundation Model 基于Kerr基础模型的任意荷载作用下盾构隧道纵向响应分析方法

IF 4 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-17 DOI: 10.1002/nag.70413

Yukai Zhou, Weiming Huang, Jinchang Wang, Xiaojia Ji, Guobo Wang, Jinpin Chen

{"title":"Analytical Method for Longitudinal Response of Shield Tunnels Under Arbitrary Loading Based on the Kerr Foundation Model","authors":"Yukai Zhou, Weiming Huang, Jinchang Wang, Xiaojia Ji, Guobo Wang, Jinpin Chen","doi":"10.1002/nag.70413","DOIUrl":"https://doi.org/10.1002/nag.70413","url":null,"abstract":"The operational safety of existing shield tunnels is increasingly threatened by construction activities in the proximity domain. Accurate prediction of their longitudinal response is thus of great importance. Previous research usually adopted the Winkler or Vlasov foundation models coupled with Euler‐Bernoulli beams to establish analytical solutions. However, the solutions were tailored solely to and available for a specific disturbance scenario, which required an extension when encountering diverse ones. In addition, they are insufficient to capture the behavior of the soil continuum. To address these issues, this paper presents a comprehensive model by integrating the more advanced three‐parameter Kerr foundation model with Timoshenko beam theory. By introducing the state‐space method, a unified solution procedure is developed for predicting the tunnel response. The method's validity and versatility are demonstrated through comparisons with field measurements and existing solutions under three distinct scenarios: new tunnel undercrossing, adjacent pit excavation, and surface surcharge. Finally, a sensitivity analysis for the excavation case examines the influences of soil elastic modulus, pit‐tunnel angle, and burial depth. The proposed framework offers a unified and efficient approach applicable to various disturbances, providing an efficient tool for the prediction of shield tunnel deformation.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"22 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754634","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}

引用次数: 0

A Geometrically Regularized Gradient-Damage Model With Orthogonality-Based Energy Split for Dynamic Anisotropic Compression-Shear Fracture 基于正交能量分裂的各向异性动态压剪断裂几何正则化梯度损伤模型

IF 3.6 2区工程技术

International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2026-08-11 Epub Date: 2026-06-25 DOI: 10.1002/nag.70377

Hui Li, Shanyong Wang

{"title":"A Geometrically Regularized Gradient-Damage Model With Orthogonality-Based Energy Split for Dynamic Anisotropic Compression-Shear Fracture","authors":"Hui Li, Shanyong Wang","doi":"10.1002/nag.70377","DOIUrl":"https://doi.org/10.1002/nag.70377","url":null,"abstract":"<p>This study proposes a novel geometrically regularized gradient-damage model for simulating dynamic mixed-mode fracture in orthotropic materials with tension–compression asymmetry. In this model, a thermodynamic framework is formulated by incorporating damage dissipation into internal energy evolution, from which the constitutive relation and the damage energy release rate are derived. The geometry of sharp cracks is regularized using a functional of crack surface density, resulting in a volumetric expression for the Griffith-type crack dissipation energy. By enforcing energetic equivalence between the crack dissipation energy and the damage dissipation energy, a gradient damage evolution law is obtained. An orthotropic Helmholtz free energy decomposed by an orthogonality-based volumetric–deviatoric–spectral split operator is introduced to consider the material anisotropy and tension-compression asymmetry. A hybrid driving force for unified modelling of mixed-mode fracture, is then proposed by combining the decomposed free energy with the Mohr–Coulomb criterion and three mode-dependent fracture energies. The resultant governing equations are discretized within the finite element framework and solved via an alternate minimization Newton–Raphson algorithm. Its accuracy and robustness are verified through three benchmark problems of 2D and 3D dynamic fracture. The results demonstrate the proposed method is powerful in modelling complex dynamic anisotropic mixed-mode fracture.</p>","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"50 13","pages":"5185-5212"},"PeriodicalIF":3.6,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/nag.70377","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0