Design optimization for automatically generating optimal design results is a promising technique for enhancing the efficiency of design processes and outcomes. However, its development for soil nail reinforced slopes is limited since the traditional slope stability analysis using the limit equilibrium method (LEM) becomes relatively time‐consuming when the LEM is repetitively employed during design optimization. In this article, an improved LEM for slip surfaces within reinforced slopes is developed, which eliminates the need for dense slice division by only aligning several sampling points using Gaussian quadrature. Unlike conventional design methods, wherein soil nails are represented by predetermined fixed point loads, the proposed improved LEM considers them through equivalent point loads adaptively updated according to the slip surface and nail positions to avoid overly conservative design results. Moreover, an adaptive slope stability analysis (ASSA) is proposed for reinforced slopes, offering an effective evaluation of stability without the need to step through all potential slip surfaces. The effectiveness of the proposed method is validated through several examples, demonstrating substantial computational cost savings of 98.5% compared to directly implementing traditional LEM‐based analysis methods in design optimization, as well as material savings of 30% relative to results from manually designing.
{"title":"Soil Nail Design Optimization Through Adaptive Slope Stability Analysis Using Improved Limit Equilibrium Method","authors":"Weihang Ouyang, Kai Liu, Si‐Wei Liu","doi":"10.1002/nag.70252","DOIUrl":"https://doi.org/10.1002/nag.70252","url":null,"abstract":"Design optimization for automatically generating optimal design results is a promising technique for enhancing the efficiency of design processes and outcomes. However, its development for soil nail reinforced slopes is limited since the traditional slope stability analysis using the limit equilibrium method (LEM) becomes relatively time‐consuming when the LEM is repetitively employed during design optimization. In this article, an improved LEM for slip surfaces within reinforced slopes is developed, which eliminates the need for dense slice division by only aligning several sampling points using Gaussian quadrature. Unlike conventional design methods, wherein soil nails are represented by predetermined fixed point loads, the proposed improved LEM considers them through equivalent point loads adaptively updated according to the slip surface and nail positions to avoid overly conservative design results. Moreover, an adaptive slope stability analysis (ASSA) is proposed for reinforced slopes, offering an effective evaluation of stability without the need to step through all potential slip surfaces. The effectiveness of the proposed method is validated through several examples, demonstrating substantial computational cost savings of 98.5% compared to directly implementing traditional LEM‐based analysis methods in design optimization, as well as material savings of 30% relative to results from manually designing.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"1 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122037","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}
Kaijun Zhang, Linzhong Li, Xiao Yang, Manlin Liu, Yi Tian
In practical geotechnical engineering, boundary conditions often exhibit partially pervious characteristics. Previous research on the consolidation behavior of saturated media within a finite domain has generally overlooked the effect of boundary perviousness on the consolidation behavior. This study develops a modified analytical model to examine the plane strain consolidation of saturated porous media with a partially pervious vertical boundary. By incorporating the existing generalized solution with the partially pervious vertical boundary condition, the analytical derivation is first carried out in the transformed domain. The corresponding exact solution in the physical domain is subsequently obtained through a Fourier series expansion combined with Crump's numerical Laplace inversion technique. The reliability of the developed analytical solution is verified by comparing the present results with those in the literature under conditions of full perviousness. Using the proposed solution, numerical calculations are then performed to investigate the effects of boundary perviousness parameters and loading width on the consolidation behavior. Furthermore, the evolution of excess pore water pressure, settlement, and horizontal displacement over space and time is analyzed. The results demonstrate the significant influence of partially pervious boundaries on excess pore water pressure dissipation and soil displacement evolution.
{"title":"Plane Strain Consolidation of Saturated Soils in a Finite Rectangular Domain With Partially Pervious Vertical Boundaries","authors":"Kaijun Zhang, Linzhong Li, Xiao Yang, Manlin Liu, Yi Tian","doi":"10.1002/nag.70253","DOIUrl":"https://doi.org/10.1002/nag.70253","url":null,"abstract":"In practical geotechnical engineering, boundary conditions often exhibit partially pervious characteristics. Previous research on the consolidation behavior of saturated media within a finite domain has generally overlooked the effect of boundary perviousness on the consolidation behavior. This study develops a modified analytical model to examine the plane strain consolidation of saturated porous media with a partially pervious vertical boundary. By incorporating the existing generalized solution with the partially pervious vertical boundary condition, the analytical derivation is first carried out in the transformed domain. The corresponding exact solution in the physical domain is subsequently obtained through a Fourier series expansion combined with Crump's numerical Laplace inversion technique. The reliability of the developed analytical solution is verified by comparing the present results with those in the literature under conditions of full perviousness. Using the proposed solution, numerical calculations are then performed to investigate the effects of boundary perviousness parameters and loading width on the consolidation behavior. Furthermore, the evolution of excess pore water pressure, settlement, and horizontal displacement over space and time is analyzed. The results demonstrate the significant influence of partially pervious boundaries on excess pore water pressure dissipation and soil displacement evolution.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"30 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122038","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}
Lei Zhang, Xin Jiang, Rong Sun, Canyang Cui, Jianbiao Du, Hanyan Gu, Yanjun Qiu
This study proposes a unified analytical framework for unsaturated active earth pressure to evaluate retaining wall stability under transient rainfall infiltration. The framework incorporates three critical wall displacement modes: translation (T), rotation about the top (RT), and rotation about the base (RB). Guided by finite element analyses that systematically characterize the evolution of principal stress trajectories and failure surface morphologies under each mode, an analytical solution is derived. This solution integrates an extended Mohr‐Coulomb strength criterion, a generalized wetting front infiltration model, and an inclined‐slice limit equilibrium approach featuring an interlayer shear coefficient to quantify inter‐slice shear forces. Experimental and numerical validations confirm the method's reliability. Parametric studies demonstrate that a deepening wetting front increases the lateral active earth pressure and the overturning moment on the retaining wall, thereby significantly reducing stability. The applicability of the resultant force acting at one‐third of the wall height is governed by the combined effects of wall displacement modes, soil matric suction, slope inclination, and wall‐soil interface friction angle. This methodology establishes a theoretically rigorous yet practical tool for stability assessment under extreme rainfall events, offering crucial insights for engineering design optimization.
{"title":"Active Earth Pressure From Unsaturated Soils With Displacement Modes of Rigid Retaining Wall Under Rainfall Conditions","authors":"Lei Zhang, Xin Jiang, Rong Sun, Canyang Cui, Jianbiao Du, Hanyan Gu, Yanjun Qiu","doi":"10.1002/nag.70256","DOIUrl":"https://doi.org/10.1002/nag.70256","url":null,"abstract":"This study proposes a unified analytical framework for unsaturated active earth pressure to evaluate retaining wall stability under transient rainfall infiltration. The framework incorporates three critical wall displacement modes: translation (T), rotation about the top (RT), and rotation about the base (RB). Guided by finite element analyses that systematically characterize the evolution of principal stress trajectories and failure surface morphologies under each mode, an analytical solution is derived. This solution integrates an extended Mohr‐Coulomb strength criterion, a generalized wetting front infiltration model, and an inclined‐slice limit equilibrium approach featuring an interlayer shear coefficient to quantify inter‐slice shear forces. Experimental and numerical validations confirm the method's reliability. Parametric studies demonstrate that a deepening wetting front increases the lateral active earth pressure and the overturning moment on the retaining wall, thereby significantly reducing stability. The applicability of the resultant force acting at one‐third of the wall height is governed by the combined effects of wall displacement modes, soil matric suction, slope inclination, and wall‐soil interface friction angle. This methodology establishes a theoretically rigorous yet practical tool for stability assessment under extreme rainfall events, offering crucial insights for engineering design optimization.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"11 13 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122039","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}
Stick‐slip dynamics of shear bands is vital to the evolution of geological hazards such as earthquakes and landslides. Extensive studies have been conducted to analyze the effect of the particle geometry on the stick‐slip dynamics. However, the impact of the initial positions of these particles has rarely been studied. With the aid of discrete element method modeling, the influence of particle size on the stick‐slip dynamics is revisited, with particular emphasis on initial particle positions. The initial particle positions in this study are sampled with Monte Carlo simulations. The results illustrate that a shear band with larger particles tends to exhibit fewer stick‐slip events, longer recurrence time, and more evident friction drop. The stick‐slip dynamics is strongly affected by initial particle positions, and the effects increase with the particle size. Parameteric analyses indicate that these effects could only be slightly influenced by the contact models of the particles, model parameters, boundary conditions, and model dimensions. These findings provide new insights into the stick‐slip dynamics and emphasize how the initial particle positions influence the stick‐slip dynamics of faults and earthquakes.
{"title":"Effect of Particle Size on Stick‐Slip Dynamics of Shear Bands Considering Randomness of Initial Particle Positions in Discrete Element Modeling","authors":"Wenping Gong, Wei Xiong, Shaoyan Zhang, Huiming Tang, Lei Wang, Ying Zhao","doi":"10.1002/nag.70249","DOIUrl":"https://doi.org/10.1002/nag.70249","url":null,"abstract":"Stick‐slip dynamics of shear bands is vital to the evolution of geological hazards such as earthquakes and landslides. Extensive studies have been conducted to analyze the effect of the particle geometry on the stick‐slip dynamics. However, the impact of the initial positions of these particles has rarely been studied. With the aid of discrete element method modeling, the influence of particle size on the stick‐slip dynamics is revisited, with particular emphasis on initial particle positions. The initial particle positions in this study are sampled with Monte Carlo simulations. The results illustrate that a shear band with larger particles tends to exhibit fewer stick‐slip events, longer recurrence time, and more evident friction drop. The stick‐slip dynamics is strongly affected by initial particle positions, and the effects increase with the particle size. Parameteric analyses indicate that these effects could only be slightly influenced by the contact models of the particles, model parameters, boundary conditions, and model dimensions. These findings provide new insights into the stick‐slip dynamics and emphasize how the initial particle positions influence the stick‐slip dynamics of faults and earthquakes.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"70 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122421","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}
Yifei Gong, Ming Huang, Chun Zhu, Yi Tan, Murat Karakus, Zhigang Tao, Wei Sun
As coal mining in China advances to greater depths, deep and steeply inclined layered roadways are increasingly subjected to high‐stress environments, leading to pronounced nonuniform deformation and instability. These failure behaviors pose significant challenges to roadwatability control and engineering safety. To address this problem, this study investigates the −1000 meters (m) steeply inclined roadway of the Qishan Mine in Xuzhou and aims to clarify the deformation evolution mechanism under deep high‐stress conditions and to evaluate the applicability of second‐generation negative Poisson's ratio (2G‐NPR) bolts for large‐deformation control. Building on previously conducted physical model tests, a 3DEC numerical model was established to reproduce the full deformation–failure process of the surrounding rock. A key contribution of this work is the calibration and numerical implementation of the mechanical characteristics of 2G‐NPR bolts, including their high ductility and constant‐resistance plateau behavior, enabling realistic representation of NPR reinforcement in discrete‐element simulations. The calibrated model was then applied to assess the reinforcing effects of NPR bolts in deep layered rock masses. The results reveal a distinct asymmetric deformation pattern, with the roadway roof and right side identified as critical instability zones. Deformation and failure are dominated by slip and separation along the layered structural planes under high stress. Owing to their constant resistance and large elongation capacity, 2G‐NPR bolts substantially suppress large deformations, reducing roadway sidewall displacement by more than 20% compared with traditional bolt support. This study provides new insights into the deformation mechanisms of deep, steeply inclined layered roadways and demonstrates the engineering advantages of 2G‐NPR bolts, offering an effective reinforcement strategy for controlling large deformations in deep mining environments.
{"title":"Numerical Calibration and Stabilization Performance of Second‐Generation Negative Poisson's Ratio Bolts in Deep Steeply Inclined Roadways","authors":"Yifei Gong, Ming Huang, Chun Zhu, Yi Tan, Murat Karakus, Zhigang Tao, Wei Sun","doi":"10.1002/nag.70229","DOIUrl":"https://doi.org/10.1002/nag.70229","url":null,"abstract":"As coal mining in China advances to greater depths, deep and steeply inclined layered roadways are increasingly subjected to high‐stress environments, leading to pronounced nonuniform deformation and instability. These failure behaviors pose significant challenges to roadwatability control and engineering safety. To address this problem, this study investigates the −1000 meters (m) steeply inclined roadway of the Qishan Mine in Xuzhou and aims to clarify the deformation evolution mechanism under deep high‐stress conditions and to evaluate the applicability of second‐generation negative Poisson's ratio (2G‐NPR) bolts for large‐deformation control. Building on previously conducted physical model tests, a 3DEC numerical model was established to reproduce the full deformation–failure process of the surrounding rock. A key contribution of this work is the calibration and numerical implementation of the mechanical characteristics of 2G‐NPR bolts, including their high ductility and constant‐resistance plateau behavior, enabling realistic representation of NPR reinforcement in discrete‐element simulations. The calibrated model was then applied to assess the reinforcing effects of NPR bolts in deep layered rock masses. The results reveal a distinct asymmetric deformation pattern, with the roadway roof and right side identified as critical instability zones. Deformation and failure are dominated by slip and separation along the layered structural planes under high stress. Owing to their constant resistance and large elongation capacity, 2G‐NPR bolts substantially suppress large deformations, reducing roadway sidewall displacement by more than 20% compared with traditional bolt support. This study provides new insights into the deformation mechanisms of deep, steeply inclined layered roadways and demonstrates the engineering advantages of 2G‐NPR bolts, offering an effective reinforcement strategy for controlling large deformations in deep mining environments.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"104 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146095767","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}
Aoxi Zhang, Frédéric Collin, Antoine Wautier, Anne‐Catherine Dieudonné
Microbially induced carbonate precipitation (MICP) is an emerging technique for enhancing the mechanical properties of granular soils. Although several experimental studies have reported increased shear strength in MICP‐treated soils at both peak and residual states, other findings have shown reductions in residual strength compared to untreated soils. This study uses the discrete element method (DEM) to investigate the mechanisms governing the residual strength of bio‐cemented sands. The results indicate that residual strength may decrease when carbonate precipitates in the form of grain‐bridging patterns. In that case, the introduction of carbonates alters the contact network and may induce metastable configurations, particularly when the bonds are weak or non‐cohesive. These configurations are prone to strain localisation upon shearing, leading to the development of shear bands and a reduction in residual strength. Conversely, higher cohesive strength enhances microstructural stability, offsetting the weakening effects of localisation. The residual strength of bio‐cemented sands is therefore governed by two competing mechanisms, namely bond‐induced stabilisation and instability‐driven localisation.
{"title":"Insights Into the Mechanisms Controlling the Residual Strength of Bio‐cemented Sands","authors":"Aoxi Zhang, Frédéric Collin, Antoine Wautier, Anne‐Catherine Dieudonné","doi":"10.1002/nag.70239","DOIUrl":"https://doi.org/10.1002/nag.70239","url":null,"abstract":"Microbially induced carbonate precipitation (MICP) is an emerging technique for enhancing the mechanical properties of granular soils. Although several experimental studies have reported increased shear strength in MICP‐treated soils at both peak and residual states, other findings have shown reductions in residual strength compared to untreated soils. This study uses the discrete element method (DEM) to investigate the mechanisms governing the residual strength of bio‐cemented sands. The results indicate that residual strength may decrease when carbonate precipitates in the form of grain‐bridging patterns. In that case, the introduction of carbonates alters the contact network and may induce metastable configurations, particularly when the bonds are weak or non‐cohesive. These configurations are prone to strain localisation upon shearing, leading to the development of shear bands and a reduction in residual strength. Conversely, higher cohesive strength enhances microstructural stability, offsetting the weakening effects of localisation. The residual strength of bio‐cemented sands is therefore governed by two competing mechanisms, namely bond‐induced stabilisation and instability‐driven localisation.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"78 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071523","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}
A state‐based peridynamic model is proposed to simulate the failure mechanisms in porous rocks, using Bentheim sandstone as a specific example. Experimental observations reveal a transition from brittle to ductile failure under increasing triaxial compression. This behavior is attributed to pore compaction. The peridynamic model is enhanced to capture the strain hardening observed in hydrostatic compression experiments and calibrated to reproduce pore‐collapse behavior. Rock heterogeneity is incorporated through Weibull‐distributed strength parameters, reflecting the stochastic nature of material properties. Simulations of indentation tests for four specimen sizes demonstrate the predictive capability of the model. A qualitative validation is established through acoustic emission data, while a quantitative validation relies on the comparison of numerical force–penetration and indentation pressure–penetration relationships with experimental results. Beyond reproducing macroscopic force responses, the model captures the spatiotemporal evolution of the compaction zone, and an energy‐based analysis shows that grain comminution prior to failure contributes significantly to the total energy dissipation.
{"title":"A Peridynamic Framework for Modeling Progressive Failure in Porous Sandstone Indentation","authors":"Sahir N. Butt, Jörg Renner, Günther Meschke","doi":"10.1002/nag.70241","DOIUrl":"https://doi.org/10.1002/nag.70241","url":null,"abstract":"A state‐based peridynamic model is proposed to simulate the failure mechanisms in porous rocks, using Bentheim sandstone as a specific example. Experimental observations reveal a transition from brittle to ductile failure under increasing triaxial compression. This behavior is attributed to pore compaction. The peridynamic model is enhanced to capture the strain hardening observed in hydrostatic compression experiments and calibrated to reproduce pore‐collapse behavior. Rock heterogeneity is incorporated through Weibull‐distributed strength parameters, reflecting the stochastic nature of material properties. Simulations of indentation tests for four specimen sizes demonstrate the predictive capability of the model. A qualitative validation is established through acoustic emission data, while a quantitative validation relies on the comparison of numerical force–penetration and indentation pressure–penetration relationships with experimental results. Beyond reproducing macroscopic force responses, the model captures the spatiotemporal evolution of the compaction zone, and an energy‐based analysis shows that grain comminution prior to failure contributes significantly to the total energy dissipation.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"76 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071598","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}
Rock bolts are commonly used to stabilize surrounding rocks in deep underground excavations, such as mines, tunnels, and underground caves. In actual underground projects, it is common to form an oblique angle between the installed rock bolt and the surrounding rock surface, owing to the design parameters, construction quality, or rough excavation contour. Currently, studies on the mechanical characteristics of inclined rock bolts remain relatively limited. In this study, non‐fully anchored rock bolts are investigated, and an analytical model is presented for the surrounding rock supported by a bolt installed at any angle. In this model, the supporting effect produced by the rock bolt on the surrounding rock was considered to originate from the interfacial adhesion at the anchored part and uniform pressure at the bolt plate. Theoretical analytical solutions for the bolt stress and supporting stress within the surrounding rock were derived by applying elasticity theory to the model. The effectiveness of the proposed theoretical method was verified by comparing it with numerical simulations and experimental test results from previous studies. The effects of the bolt angle, pretension force, anchor length, deployment pattern, and rock parameters on the supporting stress distribution characteristics of the surrounding rock were analyzed. For the first time, this study determines the support effect of inclined rock bolts and provides a theoretical basis for the optimization of bolt deployment and the selection of support parameters in tunnels.
{"title":"Supporting Stress Analysis of Pre‐Tensioned Rock Bolts in Tunnels Considering the Effects of Installation Angles","authors":"Hongtao Wang, Mingzhu Zhao, Ping Liu, Xiaojing Li, Yunjuan Chen","doi":"10.1002/nag.70248","DOIUrl":"https://doi.org/10.1002/nag.70248","url":null,"abstract":"Rock bolts are commonly used to stabilize surrounding rocks in deep underground excavations, such as mines, tunnels, and underground caves. In actual underground projects, it is common to form an oblique angle between the installed rock bolt and the surrounding rock surface, owing to the design parameters, construction quality, or rough excavation contour. Currently, studies on the mechanical characteristics of inclined rock bolts remain relatively limited. In this study, non‐fully anchored rock bolts are investigated, and an analytical model is presented for the surrounding rock supported by a bolt installed at any angle. In this model, the supporting effect produced by the rock bolt on the surrounding rock was considered to originate from the interfacial adhesion at the anchored part and uniform pressure at the bolt plate. Theoretical analytical solutions for the bolt stress and supporting stress within the surrounding rock were derived by applying elasticity theory to the model. The effectiveness of the proposed theoretical method was verified by comparing it with numerical simulations and experimental test results from previous studies. The effects of the bolt angle, pretension force, anchor length, deployment pattern, and rock parameters on the supporting stress distribution characteristics of the surrounding rock were analyzed. For the first time, this study determines the support effect of inclined rock bolts and provides a theoretical basis for the optimization of bolt deployment and the selection of support parameters in tunnels.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"73 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071597","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}
Mingwei Gang, Atsushi Sainoki, Jun‐ichi Kodama, Lishuai Jiang, Hani Mitri, Adam K. Schwartzkopff
The frequency and magnitude of induced seismicity have been increasing in recent times. Induced seismicity can cause significant damage to underground workings and therefore has become a major global issue. Hence, it is necessary to assess and mitigate the associated risks of induced seismicity. Previously, various methods have been implemented to minimise the hazards of induced seismicity to underground workings. However, their effectiveness is limited due to the inherent heterogeneity of the stress state within natural geological structures. This can result in unexpectedly large seismic events in distant regions away from anthropogenic activities, such as ore extraction and fluid injection/production. Hence, the present study aims to develop a novel method to control the intensity of induced seismicity by increasing the stiffness of the fault damage zone surrounding the fault core. In the present study, the effect of increasing fracture stiffness in the damage zone on seismic source parameters is investigated. First, the validity of the proposed method is assessed through an analytical study by evaluating energy released from a seismic event whilst assuming linear slip‐weakening behaviour. Then, a mine‐wide numerical model is constructed that can reproduce a complex and heterogeneous stress state within the fault damage zone by computing and applying equivalent compliance tensors to each element in the model, based on a discrete fracture network composed of millions of fractures. A parametric study is subsequently carried out to quantitatively analyse the effect of fracture stiffnesses under distinct fault zone cases: (a) different near‐fault fracture densities, (b) different fracture dips, (c) different dip directions, (d) different depths, (e) different distances from fault core and (f) different initial stiffnesses. The results indicate that fracture stiffness significantly affects all the seismic source parameters in most cases. When the fracture stiffness is increased by a factor of five, the seismic source parameters are decreased to approximately 40%–50%. This result was found to closely align with that derived from the analytical study. However, its effectiveness becomes less significant with decreasing fracture densities, with seismic source parameters reduced only to 50%–75%, compared to approximately 40% under higher‐density conditions. Furthermore, the seismic source parameters remain almost unchanged with increasing distance from the fault core. These results suggest that increasing fracture stiffness within a severely fractured rock mass in the vicinity of the fault core can effectively mitigate seismic hazards. This work may provide a foundation for future implementation of increasing fracture stiffness as a means of reducing seismic risk.
{"title":"Numerical and Analytical Studies on Increasing Near‐Fault Fracture Stiffness to Control Induced Seismicity Based on an Equivalent Continuum Modelling Approach","authors":"Mingwei Gang, Atsushi Sainoki, Jun‐ichi Kodama, Lishuai Jiang, Hani Mitri, Adam K. Schwartzkopff","doi":"10.1002/nag.70218","DOIUrl":"https://doi.org/10.1002/nag.70218","url":null,"abstract":"The frequency and magnitude of induced seismicity have been increasing in recent times. Induced seismicity can cause significant damage to underground workings and therefore has become a major global issue. Hence, it is necessary to assess and mitigate the associated risks of induced seismicity. Previously, various methods have been implemented to minimise the hazards of induced seismicity to underground workings. However, their effectiveness is limited due to the inherent heterogeneity of the stress state within natural geological structures. This can result in unexpectedly large seismic events in distant regions away from anthropogenic activities, such as ore extraction and fluid injection/production. Hence, the present study aims to develop a novel method to control the intensity of induced seismicity by increasing the stiffness of the fault damage zone surrounding the fault core. In the present study, the effect of increasing fracture stiffness in the damage zone on seismic source parameters is investigated. First, the validity of the proposed method is assessed through an analytical study by evaluating energy released from a seismic event whilst assuming linear slip‐weakening behaviour. Then, a mine‐wide numerical model is constructed that can reproduce a complex and heterogeneous stress state within the fault damage zone by computing and applying equivalent compliance tensors to each element in the model, based on a discrete fracture network composed of millions of fractures. A parametric study is subsequently carried out to quantitatively analyse the effect of fracture stiffnesses under distinct fault zone cases: (a) different near‐fault fracture densities, (b) different fracture dips, (c) different dip directions, (d) different depths, (e) different distances from fault core and (f) different initial stiffnesses. The results indicate that fracture stiffness significantly affects all the seismic source parameters in most cases. When the fracture stiffness is increased by a factor of five, the seismic source parameters are decreased to approximately 40%–50%. This result was found to closely align with that derived from the analytical study. However, its effectiveness becomes less significant with decreasing fracture densities, with seismic source parameters reduced only to 50%–75%, compared to approximately 40% under higher‐density conditions. Furthermore, the seismic source parameters remain almost unchanged with increasing distance from the fault core. These results suggest that increasing fracture stiffness within a severely fractured rock mass in the vicinity of the fault core can effectively mitigate seismic hazards. This work may provide a foundation for future implementation of increasing fracture stiffness as a means of reducing seismic risk.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"86 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146070419","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}
Constitutive models with concise theoretical formulations and readily measurable parameters are vital for practical geotechnical engineering applications. This study presents a novel constitutive model for overconsolidated (OC) clays by integrating bounding surface plasticity theory into the modified Cam Clay (MCC) framework without introducing any additional model parameters. The proposed model enhances the MCC model in both strength and deformation predictions by (i) introducing the overconsolidation parameter into the dilatancy relation, enabling a more accurate representation of the shear dilatancy behavior of OC clays, and (ii) incorporating the Hvorslev envelope into the plastic modulus interpolation function to capture the strain‐softening behavior and peak strength. The model's performance is validated through element‐level simulations of compression and extension tests on clays, encompassing a broad range of overconsolidation ratios (OCRs) and stress paths. Additionally, the model is implemented in the ABAQUS finite element platform using an explicit integration scheme with automatic error control. Its practical applicability is demonstrated through the simulation of a centrifuge plate loading test on an OC clay foundation, with numerical results showing strong agreement with experimental data.
{"title":"A Simple Bounding Surface Plasticity Model for Overconsolidated Clays: Theory, Validation, and Numerical Implementation","authors":"Kehao Chen, Rui Pang, Bin Xu, Yang Zhou, Long Yu","doi":"10.1002/nag.70231","DOIUrl":"https://doi.org/10.1002/nag.70231","url":null,"abstract":"Constitutive models with concise theoretical formulations and readily measurable parameters are vital for practical geotechnical engineering applications. This study presents a novel constitutive model for overconsolidated (OC) clays by integrating bounding surface plasticity theory into the modified Cam Clay (MCC) framework without introducing any additional model parameters. The proposed model enhances the MCC model in both strength and deformation predictions by (i) introducing the overconsolidation parameter into the dilatancy relation, enabling a more accurate representation of the shear dilatancy behavior of OC clays, and (ii) incorporating the Hvorslev envelope into the plastic modulus interpolation function to capture the strain‐softening behavior and peak strength. The model's performance is validated through element‐level simulations of compression and extension tests on clays, encompassing a broad range of overconsolidation ratios (OCRs) and stress paths. Additionally, the model is implemented in the ABAQUS finite element platform using an explicit integration scheme with automatic error control. Its practical applicability is demonstrated through the simulation of a centrifuge plate loading test on an OC clay foundation, with numerical results showing strong agreement with experimental data.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"128 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146056197","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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