Tewodros Y. Yosef, Chen Fang, Seunghee Kim, Ronald K. Faller, Quasi A. Almari, Mojtaba Atash Bahar, Gnyarienn S. Kumar
This study presents large deformation computational methods to simulate lateral vehicular impacts on steel piles in granular soil. Soil‐mounted longitudinal barrier systems rely on energy dissipation in both the piles and the surrounding soil to safely redirect errant vehicles, so dynamic pile‐soil interaction is important for design. Conventional Updated Lagrangian finite element methods suffer from mesh distortion at large strains, which limits their use for simulating these impact events. To address this, Smoothed Particle Hydrodynamics (SPH) and Element‐Free Galerkin (EFG) formulations are coupled with finite elements to form hybrid SPH+FEM and EFG+FEM models that represent large soil deformations. The models are applied to full‐scale bogie impact tests on laterally loaded steel piles and are validated against measured energy, impulse‐time histories, and resistive force‐displacement responses. Both hybrid models reproduce the main pile behaviors, including rotation, bending, and yielding, and they capture the change in soil response from stiff resistance at small displacements to more fluid flow at large displacements. Displacement‐averaged forces and total energy are predicted within 5% to 15% of test results. The SPH+FEM model provides a more detailed description of local soil failure, whereas the EFG+FEM model was more efficient for predicting the overall system response. Because full‐scale crash tests are expensive and difficult to repeat, these validated hybrid models offer a practical tool for the design and optimization of piles in soil‐embedded barrier systems and support more reliable roadside safety design based on numerical analysis.
{"title":"Large Deformation Pile‐soil Interaction Under Lateral Vehicle Impact Using Hybrid SPH+FEM and EFG+FEM Models","authors":"Tewodros Y. Yosef, Chen Fang, Seunghee Kim, Ronald K. Faller, Quasi A. Almari, Mojtaba Atash Bahar, Gnyarienn S. Kumar","doi":"10.1002/nag.70244","DOIUrl":"https://doi.org/10.1002/nag.70244","url":null,"abstract":"This study presents large deformation computational methods to simulate lateral vehicular impacts on steel piles in granular soil. Soil‐mounted longitudinal barrier systems rely on energy dissipation in both the piles and the surrounding soil to safely redirect errant vehicles, so dynamic pile‐soil interaction is important for design. Conventional Updated Lagrangian finite element methods suffer from mesh distortion at large strains, which limits their use for simulating these impact events. To address this, Smoothed Particle Hydrodynamics (SPH) and Element‐Free Galerkin (EFG) formulations are coupled with finite elements to form hybrid SPH+FEM and EFG+FEM models that represent large soil deformations. The models are applied to full‐scale bogie impact tests on laterally loaded steel piles and are validated against measured energy, impulse‐time histories, and resistive force‐displacement responses. Both hybrid models reproduce the main pile behaviors, including rotation, bending, and yielding, and they capture the change in soil response from stiff resistance at small displacements to more fluid flow at large displacements. Displacement‐averaged forces and total energy are predicted within 5% to 15% of test results. The SPH+FEM model provides a more detailed description of local soil failure, whereas the EFG+FEM model was more efficient for predicting the overall system response. Because full‐scale crash tests are expensive and difficult to repeat, these validated hybrid models offer a practical tool for the design and optimization of piles in soil‐embedded barrier systems and support more reliable roadside safety design based on numerical analysis.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"7 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146042950","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}
Emil Rinatovich Gallyamov, Guillaume Anciaux, Nicolas Richart, Jean‐François Molinari, Brice Lecampion
We present a fully implicit formulation of coupled fluid flow and geomechanics for fluid injection/withdrawal in fractured reservoirs in the context of storage. Utilizing a Galerkin finite‐element approach, both flow and poroelasticity equations are discretized on a shared three‐dimensional mesh. The fluid flow is assumed to be single‐phase. The hydraulic behaviour of fractures is represented through a double‐nodes flow element, which allows to efficiently model longitudinal and transversal fracture permeabilities. In addressing the mechanical sub‐problem, fractures are explicitly modelled using cohesive elements to account for contact, friction and opening phenomena. The non‐linear set of equations is solved implicitly through an iterative partitioned conjugate gradient procedure, extending its traditional application to continuous problems to those involving explicit discontinuities such as faults and fractures. The model's accuracy is verified against analytical solutions for different geomechanical problems, notably for the growth of a frictional slip rupture along a fault due to fluid injection. Such a particularly challenging benchmark for a critically stressed fault is here reproduced for the first time by a finite element–based scheme. The capabilities of the developed parallel solver are then illustrated through a scenario involving injection into a faulted aquifer. The original solver code, tutorials and data visualization routines are publicly accessible.
{"title":"A Parallelized 3D Geomechanical Solver for Fluid‐Induced Fault Slip in Poroelastic Media","authors":"Emil Rinatovich Gallyamov, Guillaume Anciaux, Nicolas Richart, Jean‐François Molinari, Brice Lecampion","doi":"10.1002/nag.70240","DOIUrl":"https://doi.org/10.1002/nag.70240","url":null,"abstract":"We present a fully implicit formulation of coupled fluid flow and geomechanics for fluid injection/withdrawal in fractured reservoirs in the context of storage. Utilizing a Galerkin finite‐element approach, both flow and poroelasticity equations are discretized on a shared three‐dimensional mesh. The fluid flow is assumed to be single‐phase. The hydraulic behaviour of fractures is represented through a double‐nodes flow element, which allows to efficiently model longitudinal and transversal fracture permeabilities. In addressing the mechanical sub‐problem, fractures are explicitly modelled using cohesive elements to account for contact, friction and opening phenomena. The non‐linear set of equations is solved implicitly through an iterative partitioned conjugate gradient procedure, extending its traditional application to continuous problems to those involving explicit discontinuities such as faults and fractures. The model's accuracy is verified against analytical solutions for different geomechanical problems, notably for the growth of a frictional slip rupture along a fault due to fluid injection. Such a particularly challenging benchmark for a critically stressed fault is here reproduced for the first time by a finite element–based scheme. The capabilities of the developed parallel solver are then illustrated through a scenario involving injection into a faulted aquifer. The original solver code, tutorials and data visualization routines are publicly accessible.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"238 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014352","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}
Shirui Zhang, Quan Jiang, Shili Qiu, Shishu Zhang, Yong Xia, Zebin Song
To investigate the mechanical properties of fractured rock masses, a novel numerical model is proposed to characterize jointed rock masses via breakable Voronoi blocks and discrete fracture networks (DFNs). Based on the block scale factor and the strength factor, a meso‐parameter calibration method is established to correlate the parameters of intact rock blocks and jointed rock masses. The proposed model can effectively simulate the strength and fracture mechanisms of intact to moderately jointed rock masses. The joint dip angle, density, and length significantly influence the fracture mechanisms and strength of rock masses. The excavation damage zones of tunnels are controlled by joint dip angle, with long fractures dominating macroscopic instability. The acoustic emission (AE) characteristics can quantify the damage degree of the surrounding rock and are closely related to joint density, as well as the stress coupling between joints and excavation boundaries. This study provides an efficient analytical method and theoretical basis for the mechanical analysis of jointed rock masses and engineering stability assessment.
{"title":"A Hybrid Numerical Modeling for Cross‐Scale Mechanical Properties of Rock Materials","authors":"Shirui Zhang, Quan Jiang, Shili Qiu, Shishu Zhang, Yong Xia, Zebin Song","doi":"10.1002/nag.70247","DOIUrl":"https://doi.org/10.1002/nag.70247","url":null,"abstract":"To investigate the mechanical properties of fractured rock masses, a novel numerical model is proposed to characterize jointed rock masses via breakable Voronoi blocks and discrete fracture networks (DFNs). Based on the block scale factor and the strength factor, a meso‐parameter calibration method is established to correlate the parameters of intact rock blocks and jointed rock masses. The proposed model can effectively simulate the strength and fracture mechanisms of intact to moderately jointed rock masses. The joint dip angle, density, and length significantly influence the fracture mechanisms and strength of rock masses. The excavation damage zones of tunnels are controlled by joint dip angle, with long fractures dominating macroscopic instability. The acoustic emission (AE) characteristics can quantify the damage degree of the surrounding rock and are closely related to joint density, as well as the stress coupling between joints and excavation boundaries. This study provides an efficient analytical method and theoretical basis for the mechanical analysis of jointed rock masses and engineering stability assessment.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"12 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014351","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}
Rational determination of surrounding rock grades is critically important for accurately predicting tunnel instability mechanisms and designing support structures scientifically. However, the traditional Q‐system classification method exhibits considerable subjectivity in determining key parameters, especially those pertaining to rock mass integrity, which remains a persistent challenge in engineering geology practice. This study proposes a quantitative modification to the Q‐system by integrating the response relationship between joint geometric parameters and block stability. High‐definition tunnel face images were processed to extract joint spacing and the number of joint sets. Based on numerical simulations of 115 working conditions, a quantitative relationship was established between these joint parameters and block response. Using the entropy weight method, multiple instability indicators—including displacement, number of unstable blocks, volume, and stress—were comprehensively integrated to derive a modified, continuous parameter that simultaneously captures joint set frequency and spacing. Additionally, the two‐dimensional rock block index (RBI 2D ) was introduced to refine the rock quality designation (RQD), enabling a more accurate characterization of rock mass integrity. Engineering applications demonstrated that the modified Q ′ value provides a more reliable assessment of rock mass quality, particularly in joint‐intensive zones or near faulted sections. The proposed approach effectively reduces the subjectivity inherent in conventional assessments and offers a technically robust basis for balancing safety and economy in tunnel construction.
{"title":"Refined Modification of the Fractured Rock Mass Classification Method Considering Geometric Parameters of Joints and Block Stability","authors":"Chengcheng Zheng, Peng He, Gang Wang, Yujing Jiang, Feng Jiang, Zhiyong Xiao","doi":"10.1002/nag.70245","DOIUrl":"https://doi.org/10.1002/nag.70245","url":null,"abstract":"Rational determination of surrounding rock grades is critically important for accurately predicting tunnel instability mechanisms and designing support structures scientifically. However, the traditional Q‐system classification method exhibits considerable subjectivity in determining key parameters, especially those pertaining to rock mass integrity, which remains a persistent challenge in engineering geology practice. This study proposes a quantitative modification to the Q‐system by integrating the response relationship between joint geometric parameters and block stability. High‐definition tunnel face images were processed to extract joint spacing and the number of joint sets. Based on numerical simulations of 115 working conditions, a quantitative relationship was established between these joint parameters and block response. Using the entropy weight method, multiple instability indicators—including displacement, number of unstable blocks, volume, and stress—were comprehensively integrated to derive a modified, continuous parameter that simultaneously captures joint set frequency and spacing. Additionally, the two‐dimensional rock block index (RBI <jats:sub>2D</jats:sub> ) was introduced to refine the rock quality designation (RQD), enabling a more accurate characterization of rock mass integrity. Engineering applications demonstrated that the modified <jats:italic>Q</jats:italic> ′ value provides a more reliable assessment of rock mass quality, particularly in joint‐intensive zones or near faulted sections. The proposed approach effectively reduces the subjectivity inherent in conventional assessments and offers a technically robust basis for balancing safety and economy in tunnel construction.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"9 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014408","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 finite element elastoplastic analysis method was applied to examine the failure mode and stress deflection characteristics of narrow cohesionless soils behind foundation pit support structures under the drum deformation mode. The mobilized friction angle in the non‐limit state was derived from the quantitative relationship between structural displacement and depth. By introducing soil arching theory and incorporating the stress‐deflected arcuate trajectories of the major and minor principal stresses, earth pressure coefficients for different zones were established. An analytical solution for non‐limit active earth pressure in narrow soils under the drum deformation mode was proposed by improving the horizontal differential element method. The analytical solution showed favorable agreement with finite element simulations, validating the method. Parametric analysis further indicated that the slip surface can be simplified as linear, the support structure requires a horizontal displacement of approximately 0.3% of its height to reach the limit state, and earth pressure varies nonlinearly with depth under the influence of soil arching effect. With increasing displacement, earth pressure transitions from the at‐rest state to the narrow soils state. Furthermore, decreasing the soil width‐to‐depth ratio and increasing either the soil internal friction angle or the interface friction angle were shown to effectively reduce earth pressure on the support structure. These findings contribute to the refinement of the earth pressure theory in narrow soils and provide practical guidance for optimizing the design of support structures.
{"title":"Non‐Limit Earth Pressure Behind Foundation Pit Support Structures Under the Drum Deformation Mode","authors":"Xiao‐Chen Li, Fu‐Quan Chen, Chang Chen, Gang Cai","doi":"10.1002/nag.70211","DOIUrl":"https://doi.org/10.1002/nag.70211","url":null,"abstract":"The finite element elastoplastic analysis method was applied to examine the failure mode and stress deflection characteristics of narrow cohesionless soils behind foundation pit support structures under the drum deformation mode. The mobilized friction angle in the non‐limit state was derived from the quantitative relationship between structural displacement and depth. By introducing soil arching theory and incorporating the stress‐deflected arcuate trajectories of the major and minor principal stresses, earth pressure coefficients for different zones were established. An analytical solution for non‐limit active earth pressure in narrow soils under the drum deformation mode was proposed by improving the horizontal differential element method. The analytical solution showed favorable agreement with finite element simulations, validating the method. Parametric analysis further indicated that the slip surface can be simplified as linear, the support structure requires a horizontal displacement of approximately 0.3% of its height to reach the limit state, and earth pressure varies nonlinearly with depth under the influence of soil arching effect. With increasing displacement, earth pressure transitions from the at‐rest state to the narrow soils state. Furthermore, decreasing the soil width‐to‐depth ratio and increasing either the soil internal friction angle or the interface friction angle were shown to effectively reduce earth pressure on the support structure. These findings contribute to the refinement of the earth pressure theory in narrow soils and provide practical guidance for optimizing the design of support structures.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"213 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014349","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 investigates the effects of liquefied saturated sand infilling joints within complex strata on the transmission of obliquely incident seismic P‐wave. Using the boundary transformation method, analytical solutions were derived for the propagation of obliquely incident seismic P‐wave through joints filled with liquefied saturated sand. The relationship between transmission coefficients and the incident angle was analyzed. The influences of normalized joint thickness, elastic modulus of the joint filling material, and the wave impedance ratio (WIR) of the rock media on the transmission coefficients accounting for the liquefaction of saturated sand were examined. The results were compared with those obtained without considering liquefaction. The findings indicate that the liquefaction of saturated sand in filled joints significantly affects the transmission of obliquely incident seismic P‐wave, while it has a negligible impact on normally incident P‐wave propagation. Moreover, an increase in normalized joint thickness reduces the transmission coefficients for both P‐wave and SV‐wave under liquefaction conditions. Increasing the elastic modulus of the joint filling material leads to higher transmission coefficients when liquefaction is considered, which is different from the transmission behavior of SV‐wave without liquefaction. The results also show that as WIR increases, the transmission coefficients for both P‐wave and SV‐wave eventually decrease to zero.
{"title":"Effects of Liquefied Saturated Sand Filling Joints in Complex Strata on Seismic P‐Wave Transmission for Oblique Incident","authors":"Meng Wang, Feng Jiang, Lifeng Fan, Xiuli Du","doi":"10.1002/nag.70246","DOIUrl":"https://doi.org/10.1002/nag.70246","url":null,"abstract":"This study investigates the effects of liquefied saturated sand infilling joints within complex strata on the transmission of obliquely incident seismic P‐wave. Using the boundary transformation method, analytical solutions were derived for the propagation of obliquely incident seismic P‐wave through joints filled with liquefied saturated sand. The relationship between transmission coefficients and the incident angle was analyzed. The influences of normalized joint thickness, elastic modulus of the joint filling material, and the wave impedance ratio (WIR) of the rock media on the transmission coefficients accounting for the liquefaction of saturated sand were examined. The results were compared with those obtained without considering liquefaction. The findings indicate that the liquefaction of saturated sand in filled joints significantly affects the transmission of obliquely incident seismic P‐wave, while it has a negligible impact on normally incident P‐wave propagation. Moreover, an increase in normalized joint thickness reduces the transmission coefficients for both P‐wave and SV‐wave under liquefaction conditions. Increasing the elastic modulus of the joint filling material leads to higher transmission coefficients when liquefaction is considered, which is different from the transmission behavior of SV‐wave without liquefaction. The results also show that as WIR increases, the transmission coefficients for both P‐wave and SV‐wave eventually decrease to zero.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"22 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014350","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 construction of deep excavation inevitably impacts the surrounding strata, posing risk to the safety of adjacent buildings. Therefore, accurately evaluating strata settlement during the construction is essential. This study considers Shenzhen Metro Chegongmiao Station as a case study, offering a comprehensive analysis of the mechanical behavior throughout the entire deep excavation process. A predictive method is proposed, incorporating the Mindlin solution and the Source‐Sink Imaging method. This method includes simplified representations of the unloading effects from diaphragm wall construction and soil excavation. Additionally, nonlinear fitting is employed to derive the dewatering curve, addressing the challenge of predicting the groundwater level outside the excavation zone. The influence of the dewatering is thus quantified through calculating the seepage volumetric forces. The results demonstrate that in water‐rich strata, the unloading effect due to diaphragm wall construction‐ a factor frequently underestimated in conventional analysis‐ exerts a profound influence on the surrounding strata. Quantitative evidence from the case study reveals that this phase alone contributed 12 mm to the surface settlement, accounting for a significant 44% of the cumulative displacement (27 mm). The settlement curves exhibit variations across different construction stages. Notably, the location of the maximum surface settlement during the diaphragm wall trenching occurs at the point farthest from the excavation. Furthermore, an analysis of the factors influencing settlement shows that slurry density has the most substantial effect. With the same relative change, slurry density exerts an influence on settlement that is up to 30 times larger than the effects of other variables. These findings provide a scientific foundation for the design, construction, and safety assessment of deep excavations in water‐rich strata.
{"title":"Ground Settlement and Mechanical Response of a Deep Excavation in Soft Soils: A Field and Semi‐Analytical‐Based Case Study in Shenzhen, China","authors":"Xuefeng Ou, Xiaolong Tang, Xiangcou Zheng, Yongjie Zhang, Xuemin Zhang","doi":"10.1002/nag.70242","DOIUrl":"https://doi.org/10.1002/nag.70242","url":null,"abstract":"The construction of deep excavation inevitably impacts the surrounding strata, posing risk to the safety of adjacent buildings. Therefore, accurately evaluating strata settlement during the construction is essential. This study considers Shenzhen Metro Chegongmiao Station as a case study, offering a comprehensive analysis of the mechanical behavior throughout the entire deep excavation process. A predictive method is proposed, incorporating the Mindlin solution and the Source‐Sink Imaging method. This method includes simplified representations of the unloading effects from diaphragm wall construction and soil excavation. Additionally, nonlinear fitting is employed to derive the dewatering curve, addressing the challenge of predicting the groundwater level outside the excavation zone. The influence of the dewatering is thus quantified through calculating the seepage volumetric forces. The results demonstrate that in water‐rich strata, the unloading effect due to diaphragm wall construction‐ a factor frequently underestimated in conventional analysis‐ exerts a profound influence on the surrounding strata. Quantitative evidence from the case study reveals that this phase alone contributed 12 mm to the surface settlement, accounting for a significant 44% of the cumulative displacement (27 mm). The settlement curves exhibit variations across different construction stages. Notably, the location of the maximum surface settlement during the diaphragm wall trenching occurs at the point farthest from the excavation. Furthermore, an analysis of the factors influencing settlement shows that slurry density has the most substantial effect. With the same relative change, slurry density exerts an influence on settlement that is up to 30 times larger than the effects of other variables. These findings provide a scientific foundation for the design, construction, and safety assessment of deep excavations in water‐rich strata.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"29 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145993111","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 influence of primary waves on the seismic stability of underground structures is often overlooked, assuming that these structures remain stable under increased vertical body forces. Only a limited number of studies have examined the combined action of shear and primary waves on tunnel response, while clear guidance on whether the inclusion of primary wave effects is necessary remains unavailable. Moreover, seismic design standards typically specify only the vertical acceleration coefficient, providing little insight into the conditions under which its inclusion is essential or negligible. The present study addresses this gap by evaluating the variation of dynamic support pressure in circular tunnels embedded in granular and cohesive‐frictional soils over various frequencies and time instances. The results highlight conditions were considering primary waves is crucial for designing safe and efficient systems. The influence of primary waves on support pressure is found to be more significant in soils with higher shear strength (higher friction angle for granular soils and increased cohesion and/or friction angle for cohesive‐frictional soils) and an increasing tunnel cover depth. For the parameters analyzed, neglecting vertical acceleration effects can lead to an underestimation of the maximum dynamic support pressure by up to 94%. Finally, design charts incorporating shear and primary wave effects are proposed to facilitate reliable and efficient tunnel design under seismic loading.
{"title":"Significance of Primary Waves on the Seismic Stability of Underground Tunnels: A Numerical Perspective","authors":"G Gowtham, Jagdish Prasad Sahoo","doi":"10.1002/nag.70235","DOIUrl":"https://doi.org/10.1002/nag.70235","url":null,"abstract":"The influence of primary waves on the seismic stability of underground structures is often overlooked, assuming that these structures remain stable under increased vertical body forces. Only a limited number of studies have examined the combined action of shear and primary waves on tunnel response, while clear guidance on whether the inclusion of primary wave effects is necessary remains unavailable. Moreover, seismic design standards typically specify only the vertical acceleration coefficient, providing little insight into the conditions under which its inclusion is essential or negligible. The present study addresses this gap by evaluating the variation of dynamic support pressure in circular tunnels embedded in granular and cohesive‐frictional soils over various frequencies and time instances. The results highlight conditions were considering primary waves is crucial for designing safe and efficient systems. The influence of primary waves on support pressure is found to be more significant in soils with higher shear strength (higher friction angle for granular soils and increased cohesion and/or friction angle for cohesive‐frictional soils) and an increasing tunnel cover depth. For the parameters analyzed, neglecting vertical acceleration effects can lead to an underestimation of the maximum dynamic support pressure by up to 94%. Finally, design charts incorporating shear and primary wave effects are proposed to facilitate reliable and efficient tunnel design under seismic loading.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"33 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145993112","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 theoretically analyzes the gradient geostress field effects on the propagation of stress waves in the deep rock mass. First, a segmented equivalent medium model of deep rock mass is established, in which the rock mass subjected to gradient geostress is divided into multiple segments and the geostress applied to each segment is considered to be uniform. Then, the governing equations of each segmented equivalent medium model were derived, and the nonlinear–discontinuous characteristics method was introduced. Finally, the proposed method was utilized to systematically explore the relationship between the gradient k g of the geostress field and the transmission coefficient T σ . The effects of frequency f0 and depth x on the transmission coefficient T σ in a gradient geostress field were analyzed. The findings demonstrate that the gradient k g of the geostress field significantly affects stress wave transmission properties. The transmission coefficient T σ increases as the gradient k g of the geostress field increases, and even reaches a value greater than 1.0, indicating amplitude amplification of the transmitted wave. In addition, the transmission coefficient T σ decreases from a value greater than 1.0 to eventually approaching zero as the frequency f0 increases. Notably, the transmission coefficient T σ increases with increasing depth x when considering the gradient k g of the geostress field, whereas it decreases when not considering the gradient k g of the geostress field. This research offers theoretical insights into the behavior of stress wave propagation during blasting and mineral extraction in deep rock masses.
{"title":"Theoretical Study on Stress Wave Transmission Through Deep Rock Masses Under a Gradient Geostress Field","authors":"Meng Wang, Jiantong Zhang, Lifeng Fan, Wei Wang, Wei Yuan","doi":"10.1002/nag.70222","DOIUrl":"https://doi.org/10.1002/nag.70222","url":null,"abstract":"This study theoretically analyzes the gradient geostress field effects on the propagation of stress waves in the deep rock mass. First, a segmented equivalent medium model of deep rock mass is established, in which the rock mass subjected to gradient geostress is divided into multiple segments and the geostress applied to each segment is considered to be uniform. Then, the governing equations of each segmented equivalent medium model were derived, and the nonlinear–discontinuous characteristics method was introduced. Finally, the proposed method was utilized to systematically explore the relationship between the gradient <jats:italic> k <jats:sub>g</jats:sub> </jats:italic> of the geostress field and the transmission coefficient <jats:italic> T <jats:sub>σ</jats:sub> </jats:italic> . The effects of frequency <jats:italic>f</jats:italic> <jats:sub>0</jats:sub> and depth <jats:italic>x</jats:italic> on the transmission coefficient <jats:italic> T <jats:sub>σ</jats:sub> </jats:italic> in a gradient geostress field were analyzed. The findings demonstrate that the gradient <jats:italic> k <jats:sub>g</jats:sub> </jats:italic> of the geostress field significantly affects stress wave transmission properties. The transmission coefficient <jats:italic> T <jats:sub>σ</jats:sub> </jats:italic> increases as the gradient <jats:italic> k <jats:sub>g</jats:sub> </jats:italic> of the geostress field increases, and even reaches a value greater than 1.0, indicating amplitude amplification of the transmitted wave. In addition, the transmission coefficient <jats:italic> T <jats:sub>σ</jats:sub> </jats:italic> decreases from a value greater than 1.0 to eventually approaching zero as the frequency <jats:italic>f</jats:italic> <jats:sub>0</jats:sub> increases. Notably, the transmission coefficient <jats:italic> T <jats:sub>σ</jats:sub> </jats:italic> increases with increasing depth <jats:italic>x</jats:italic> when considering the gradient <jats:italic> k <jats:sub>g</jats:sub> </jats:italic> of the geostress field, whereas it decreases when not considering the gradient <jats:italic> k <jats:sub>g</jats:sub> </jats:italic> of the geostress field. This research offers theoretical insights into the behavior of stress wave propagation during blasting and mineral extraction in deep rock masses.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"38 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145993113","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}
Zhennan Zhu, Francois Nicot, Antoine Wautier, Klaus Regenauer‐lieb, Manman Hu
Localized deformation in dense granular materials, often culminating in the formation of shear bands, is a key failure mechanism in geotechnical and material systems. However, predicting the onset of such localization remains a fundamental challenge due to the system's inherent inelasticity and microstructural complexity. In this study, we propose that the evolution of internal configuration—characterized by changes in contact topology and stored potential energy—governs the collective mechanical response and encodes precursors to material failure. To quantify this evolving internal state, we introduce the notion of configurational energy, defined as the change in contact‐scale elastic potential energy resulting from a controlled loading—unloading probe. This metric is first formulated at the contact level and subsequently analyzed at the specimen scale using Discrete Element Method (DEM) simulations of biaxial compression. Our results demonstrate that configurational energy captures the system's sensitivity to perturbations and reflects local instability: both positive and negative values emerge at the contact level, with large magnitudes concentrated near regions of active rearrangement. Despite this local variability, the specimen‐scale configurational response remains strictly negative, and its magnitude increases systematically as the material approaches failure. Notably, spatial localization of configurational energy precedes the formation of macroscopic shear bands with an evolving internal length scale, offering a mesoscale energetic signature of incipient failure. These findings establish configurational energy as a physically grounded descriptor of microstructural evolution and a promising tool for anticipating failure in frictional granular systems.
{"title":"Configurational Energy as a Microstructural Descriptor of Failure Precursors in 2D Frictional Granular Materials","authors":"Zhennan Zhu, Francois Nicot, Antoine Wautier, Klaus Regenauer‐lieb, Manman Hu","doi":"10.1002/nag.70209","DOIUrl":"https://doi.org/10.1002/nag.70209","url":null,"abstract":"Localized deformation in dense granular materials, often culminating in the formation of shear bands, is a key failure mechanism in geotechnical and material systems. However, predicting the onset of such localization remains a fundamental challenge due to the system's inherent inelasticity and microstructural complexity. In this study, we propose that the evolution of internal configuration—characterized by changes in contact topology and stored potential energy—governs the collective mechanical response and encodes precursors to material failure. To quantify this evolving internal state, we introduce the notion of configurational energy, defined as the change in contact‐scale elastic potential energy resulting from a controlled loading—unloading probe. This metric is first formulated at the contact level and subsequently analyzed at the specimen scale using Discrete Element Method (DEM) simulations of biaxial compression. Our results demonstrate that configurational energy captures the system's sensitivity to perturbations and reflects local instability: both positive and negative values emerge at the contact level, with large magnitudes concentrated near regions of active rearrangement. Despite this local variability, the specimen‐scale configurational response remains strictly negative, and its magnitude increases systematically as the material approaches failure. Notably, spatial localization of configurational energy precedes the formation of macroscopic shear bands with an evolving internal length scale, offering a mesoscale energetic signature of incipient failure. These findings establish configurational energy as a physically grounded descriptor of microstructural evolution and a promising tool for anticipating failure in frictional granular systems.","PeriodicalId":13786,"journal":{"name":"International Journal for Numerical and Analytical Methods in Geomechanics","volume":"4 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145993190","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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