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Keywords = FLAC3D numerical simulation secondary development

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18 pages, 5589 KB  
Article
Research on Unsteady Burgers Creep Constitutive Model and Secondary Development Application
by Ruonan Zhu, Bo Wu, Shixiang Xu, Xi Liu and Heshan Li
Appl. Sci. 2026, 16(1), 424; https://doi.org/10.3390/app16010424 - 30 Dec 2025
Viewed by 322
Abstract
Considering the complexity and diversity of water-rich soft soil strata, indoor triaxial shear tests and creep tests were conducted on soft soil to explore its deformation law and creep characteristics. To address the nonlinear characteristics of soft soil creep, a nonlinear pot element [...] Read more.
Considering the complexity and diversity of water-rich soft soil strata, indoor triaxial shear tests and creep tests were conducted on soft soil to explore its deformation law and creep characteristics. To address the nonlinear characteristics of soft soil creep, a nonlinear pot element was proposed and substituted for the two linear pot elements in the Burgers model, thus establishing an unsteady parametric Burgers model. The one-dimensional creep equation of the unsteady Burgers model was derived, theoretically determining that the unsteady model can describe three stages of creep. Based on this, the creep equation of the unsteady Burgers model was extended to a three-dimensional stress state, and the triaxial compression creep test curves of Ningbo soft soil were fitted and parameters identified. The above model was derived from a three-dimensional finite difference scheme suitable for numerical solution in FLAC3D. A custom constitutive creep model was developed in FLAC3D, and the non-accelerated creep stage and accelerated creep stage of the improved model were analyzed to verify the accuracy and reliability of the constitutive model. The results show that the numerical simulation results and the indoor creep test results are in good agreement in terms of strain increment and the creep change curve, which confirms the effectiveness and applicability of the proposed unsteady Burgers creep constitutive model and its secondary development application. Full article
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22 pages, 7154 KB  
Article
Effects of Particle Segregation and Grain Pressure on Ventilation Airflow and Temperature–Humidity Distribution in Maize Pilot Silo
by Chaosai Liu, Boyi Zhao, Hao Zhang, Tong Shen and Jun Wang
Agriculture 2025, 15(21), 2205; https://doi.org/10.3390/agriculture15212205 - 23 Oct 2025
Cited by 2 | Viewed by 908
Abstract
The distribution of grain particles within a silo influences heat and moisture transfer during stored grain ventilation, leading to grain quality losses. A study on porosity distribution analysis and ventilation tests was conducted in a pilot silo with a height of 3 m, [...] Read more.
The distribution of grain particles within a silo influences heat and moisture transfer during stored grain ventilation, leading to grain quality losses. A study on porosity distribution analysis and ventilation tests was conducted in a pilot silo with a height of 3 m, a diameter of 1.5 m, and a conical dome height of 0.85 m. The E-B constitutive model was incorporated into the secondary development of FLAC3D 5.0 to analyze the vertical pressure distribution in the grain bulk. An anisotropic porosity distribution model for the maize bulk was developed, accounting for both vertical pressure and segregation mechanisms. The differences in airflow and heat transfer during ventilation between isotropic and anisotropic porosity distributions were quantified. A nonlinear model was innovatively proposed to predict the temperature front curve (TFC) during ventilation as affected by porosity variation. The results indicate that friction between the maize kernel and the silo wall led to vertical pressure at the center of the bottom that was 10.7% higher than that near the wall. The average surface porosity of the maize bulk was 2.8% higher than at the bottom. This led to a minimum porosity of 0.409 at the center of the silo bottom, due to the combined effect of impact during the loading process and vertical pressure. The numerical simulation demonstrated excellent consistency with the experimental data. At a supply vent air velocity of 0.126 m/s, an increase in the maize bulk height from 0.725 m to 2.9 m resulted in reductions in airflow rate and average relative humidity of 20.3% and 9.67%. The airflow velocity near the wall was 13.4% higher than that in the center, leading to a faster cooling rate in the peripheral region compared to the center of the maize bulk. The airflow velocity based on the isotropic porosity model was higher at the center than that predicted by the anisotropic model, whereas the opposite trend was observed near the wall. The temperature front during ventilation based on the anisotropic porosity model exhibited a concave curve. A nonlinear model was developed to predict this temperature front, showing strong agreement with computational data. Full article
(This article belongs to the Section Agricultural Product Quality and Safety)
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25 pages, 4115 KB  
Article
Rock Mass Failure Classification Based on FAHP–Entropy Weight TOPSIS Method and Roadway Zoning Repair Design
by Biao Huang, Qinghu Wei, Zhongguang Sun, Kang Guo and Ming Ji
Processes 2025, 13(10), 3154; https://doi.org/10.3390/pr13103154 - 2 Oct 2025
Viewed by 652
Abstract
After the original support system in the auxiliary transportation roadway of the northern wing of the Zhaoxian Mine failed, the extent of damage and deformation varied significantly across different sections of the drift. A single support method could not meet the engineering requirements. [...] Read more.
After the original support system in the auxiliary transportation roadway of the northern wing of the Zhaoxian Mine failed, the extent of damage and deformation varied significantly across different sections of the drift. A single support method could not meet the engineering requirements. Therefore, this paper conducted research on the classification of roadway damage and zoning repair. The overall damage characteristics of the roadway are described by three indicators: roadway deformation, development of rock mass fractures, and water seepage conditions. These are further refined into nine secondary indicators. In summary, a rock mass damage combination weighting evaluation model based on the FAHP–entropy weight TOPSIS method is proposed. According to this model, the degree of damage to the roadway is divided into five grades. After analyzing the damage conditions and support requirements at each grade, corresponding zoning repair plans are formulated by adjusting the parameters of bolts, cables, channel steel beams, and grouting materials. At the same time, the reliability of partition repair is verified using FLAC3D 6.0 numerical simulation software. Field monitoring results demonstrated that this approach not only met the support requirements for the roadway but also improved the utilization rate of support materials. This provides valuable guidance for the design of support systems for roadways with similar heterogeneous damage. Full article
(This article belongs to the Section Process Control and Monitoring)
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21 pages, 5966 KB  
Article
Study on Mechanism and Constitutive Modelling of Secondary Anisotropy of Surrounding Rock of Deep Tunnels
by Kang Yi, Peilin Gong, Zhiguo Lu, Chao Su and Kaijie Duan
Symmetry 2025, 17(8), 1234; https://doi.org/10.3390/sym17081234 - 4 Aug 2025
Cited by 1 | Viewed by 598
Abstract
Crack initiation, propagation, and slippage serve as the key mesoscopic mechanisms contributing to the deterioration of deep tunnel surrounding rocks. In this study, a secondary anisotropy of deep tunnels surrounding rocks was proposed: The axial-displacement constraint of deep tunnels forces cracks in the [...] Read more.
Crack initiation, propagation, and slippage serve as the key mesoscopic mechanisms contributing to the deterioration of deep tunnel surrounding rocks. In this study, a secondary anisotropy of deep tunnels surrounding rocks was proposed: The axial-displacement constraint of deep tunnels forces cracks in the surrounding rock to initiate, propagate, and slip in planes parallel to the tunnel axial direction. These cracks have no significant effect on the axial strength of the surrounding rock but significantly reduce the tangential strength, resulting in the secondary anisotropy. First, the secondary anisotropy was verified by a hybrid stress–strain controlled true triaxial test of sandstone specimens, a CT 3D (computed tomography three-dimensional) reconstruction of a fractured sandstone specimen, a numerical simulation of heterogeneous rock specimens, and field borehole TV (television) images. Subsequently, a novel SSA (strain-softening and secondary anisotropy) constitutive model was developed to characterise the secondary anisotropy of the surrounding rock and developed using C++ into a numerical form that can be called by FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions). Finally, effects of secondary anisotropy on a deep tunnel surrounding rock were analysed by comparing the results calculated by the SSA model and a uniform strain-softening model. The results show that considering the secondary anisotropy, the extent of strain-softening of the surrounding rock was mitigated, particularly the axial strain-softening. Moreover, it reduced the surface displacement, plastic zone, and dissipated plastic strain energy of the surrounding rock. The proposed SSA model can precisely characterise the objectively existent secondary anisotropy, enhancing the accuracy of numerical simulations for tunnels, particularly for deep tunnels. Full article
(This article belongs to the Section Engineering and Materials)
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21 pages, 3822 KB  
Article
Mechanisms of Tunnel Rockburst Development Under Complex Geostress Conditions in Plateau Regions
by Can Yang, Jinfeng Li, Yuan Qian, Wu Bo, Gen Zhang, Cheng Zhao and Kunming Zhao
Appl. Sci. 2025, 15(15), 8517; https://doi.org/10.3390/app15158517 - 31 Jul 2025
Cited by 2 | Viewed by 828
Abstract
The Qinghai–Xizang Plateau and its surrounding regions have experienced intense tectonic activity, resulting in complex geostress environments that cause frequent and distinctive rockburst disasters in plateau tunnel engineering. In this study, numerical simulations were conducted to investigate the distribution characteristics and patterns of [...] Read more.
The Qinghai–Xizang Plateau and its surrounding regions have experienced intense tectonic activity, resulting in complex geostress environments that cause frequent and distinctive rockburst disasters in plateau tunnel engineering. In this study, numerical simulations were conducted to investigate the distribution characteristics and patterns of tunnel rockbursts in high-altitude regions, using geostress orientation, lateral pressure coefficient, and tunnel depth as the primary independent variables. Secondary development of FLAC3D 7.00.126 was carried out using FISH language to enable the recording and visualization of tangential stress, the Russense rockburst criterion, and elastic strain energy. Based on this, the influence mechanisms of these key geostress parameters on the location, extent, and intensity of rockbursts within tunnel cross sections were analyzed. Results indicate that geostress orientation predominantly affects the location of rockbursts, with the surrounding rock in the direction of the minimum principal stress on the tunnel cross section being particularly prone to rockburst risks. The lateral pressure coefficient primarily influences the rockburst intensity and pit range within local stress concentration zones, with higher values leading to greater rockburst intensity. Notably, when structural stress is sufficiently large, rockbursts may occur even in tunnels with shallow burial depths. Tunnel depth determines the magnitude of geostress, mainly affecting the overall risk and potential extent of rockbursts within the cross section, with greater depths leading to higher rockburst intensities and a wider affected area. Full article
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19 pages, 7102 KB  
Article
Creep Model of Weakly Cemented Soft Rock Considering Damage and Secondary Development in FLAC3D
by Junhong Huang, Shanchao Hu, Xuelong Li, Shihao Guo, Chenxi Zhang, Zhihao Gao, Jinhao Dou, Dawang Yin and Yafei Cheng
Appl. Sci. 2025, 15(9), 4838; https://doi.org/10.3390/app15094838 - 27 Apr 2025
Viewed by 1272
Abstract
The time-dependent deformation control of weakly cemented soft rock in deep underground engineering is a critical scientific issue that directly affects the long-term stability of roadways. Traditional Nishihsara models encounter limitations in accurately capturing the weakening effects of material parameters during rock creep [...] Read more.
The time-dependent deformation control of weakly cemented soft rock in deep underground engineering is a critical scientific issue that directly affects the long-term stability of roadways. Traditional Nishihsara models encounter limitations in accurately capturing the weakening effects of material parameters during rock creep failure and in describing the accelerated creep stage, making them insufficient for analyzing the creep failure mechanisms of weakly cemented surrounding rock. To address these limitations, this study integrates SEM and X-ray scanning results to reveal the microscopic degradation process during creep: under external forces, clay minerals, primarily bonded face-to-face or through cementation, gradually fracture, leading to continuous microcrack propagation and progressive parameter degradation. Based on damage theory, an enhanced Nishihara creep model is proposed, incorporating a time-dependent damage factor to characterize the attenuation of the elastic modulus and a nonlinear winding element connected in series to represent the accelerated creep stage. The corresponding three-dimensional constitutive equations are derived. Using the Levenberg–Marquardt (L-M) algorithm for parameter inversion, the model achieves over 98% fitting accuracy across the full creep stages of weakly cemented soft rock, validating its applicability to other rock types such as salt rock and anthracite. The damage creep model is numerically implemented through secondary development in FLAC3D 6.0, with simulation results showing less than 5% deviation from experimental data and the failure mode is similar. These findings provide a solid theoretical foundation for further understanding the creep behavior of weakly cemented soft rocks. Full article
(This article belongs to the Special Issue Advances and Challenges in Rock Mechanics and Rock Engineering)
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14 pages, 35797 KB  
Article
Numerical Simulation of Surface Subsidence and Fracture Evolution Caused by Pulang Copper Mine Mining
by Zhengrong Li, Kepeng Hou, Tong Li, Jingtian Tang and Guangyin Lu
Appl. Sci. 2024, 14(6), 2416; https://doi.org/10.3390/app14062416 - 13 Mar 2024
Cited by 7 | Viewed by 2430
Abstract
Subsidence of the earth’s surface induced by mining activities has always been a critical concern in the relevant research fields. This subsidence disrupts the original geological structures and can lead to secondary geological hazards, environmental degradation, and threats to human lives and property. [...] Read more.
Subsidence of the earth’s surface induced by mining activities has always been a critical concern in the relevant research fields. This subsidence disrupts the original geological structures and can lead to secondary geological hazards, environmental degradation, and threats to human lives and property. An in-depth investigation of this issue led to us using the three-dimensional finite-difference numerical simulation software FLAC3D 6.0 in this study. The research focuses on the Prang Copper Mine subsidence area in Yunnan Province, China, with a particular emphasis on the comprehensive analysis of the formation mechanisms of a large-scale crack appearing on the south side of the subsidence area. The study also includes a predictive analysis of the future development trends of this crack. The simulation results indicate that the crack formation was a consequence of the combined effects of uneven surface subsidence induced by underground structural interfaces and underground mining activities. As mining activities continued, the non-uniform subsidence of the surface intensified. The northward (Y-axis) displacement difference of characteristic points A and B on both sides of the crack continuously increased, signifying the widening of the crack. Mining activities also influence the displacement in the X-axis direction, potentially posing risks to support structures on either side of existing drainage channels. Therefore, effective control measures are warranted. Furthermore, this study highlights the possibility that new mining activities may further exacerbate subsidence on the south side of the subsidence area. This research provides valuable insights into the complexity of surface subsidence and its associated risks, offering guidance for mining activity planning and safety measures. Full article
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19 pages, 15770 KB  
Article
Bedding Slope Destabilization under Rainfall: A Case Study of Zhuquedong Slope in Hunan Province, China
by Fan Xu, Huihua Hu, Hang Lin and Linglin Xie
Appl. Sci. 2024, 14(4), 1394; https://doi.org/10.3390/app14041394 - 8 Feb 2024
Cited by 13 | Viewed by 2113
Abstract
The soft interlayer and rock structure play a significant role in controlling the deformation of the bedding slope, and it is necessary to consider the phenomenon of the sudden change of local response in these key parts under rainfall conditions, and then to [...] Read more.
The soft interlayer and rock structure play a significant role in controlling the deformation of the bedding slope, and it is necessary to consider the phenomenon of the sudden change of local response in these key parts under rainfall conditions, and then to clarify the mechanism of rainfall infiltration and damage mechanism of such slopes. In this paper, a large red-layered flat-dipping bedding landslide was selected as the research object, and numerical calculations based on the Van Genuchten model for saturated–unsaturated flow were performed in order to investigate the hydrological response and distribution patterns of water within the slope during rainfall. Moreover, stability analysis was performed based on the seepage field results and secondary development of FLAC3D, and the landslide evolution process was simulated and reproduced using the constitutive model of double-variables and the strength reduction method (SRM). The results showed that the effects of heavy rainfall on the water distribution and stability of the highway slope are significant, while the effects on the natural slope are not significant. There are three phases of the slope destabilization: flexure and uplift state, deformation exacerbation state and shear failure state. The slope destabilization mechanism is a typical “sliding-bending-shearing” type. The results of the study can provide a theoretical basis for the study of the seepage, stability analysis and destabilization mechanism of bedding slopes. Full article
(This article belongs to the Section Civil Engineering)
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15 pages, 3349 KB  
Article
Research on Constitutive Model and Algorithm of High-Temperature-Load Coupling Damage Based on the Zienkiewicz–Pande Yield Criterion
by Tao Zhan, Tengfei Jiang, Shengbiao Shan, Fu Zheng, Annan Jiang and Xinping Guo
Appl. Sci. 2023, 13(17), 9786; https://doi.org/10.3390/app13179786 - 29 Aug 2023
Viewed by 2064
Abstract
The mechanical properties of rock can be weakened under the influence of high temperatures. To describe the mechanical behavior of rock under the action of high temperature more accurately, based on the Zienkiewicz–Pande yield criterion, the damage variable Dc which accounts for the [...] Read more.
The mechanical properties of rock can be weakened under the influence of high temperatures. To describe the mechanical behavior of rock under the action of high temperature more accurately, based on the Zienkiewicz–Pande yield criterion, the damage variable Dc which accounts for the coupling between high temperature and load is introduced. According to plastic potential theory and plastic flow law, the iterative incremental method for a high-temperature and load-coupled damage constitutive model in Flac3D is deduced in detail and compiled into the corresponding dynamic link library file (.dll file). By modifying the shape function to degenerate into the Mohr–Coulomb constitutive model, an elastic–plastic analysis of an ideal circular tunnel is performed, and a comparison is made between calculation results obtained from the built-in Mohr–Coulomb constitutive model in Flac3D, proving the correctness of the secondary development program. Finally, numerical simulations are conducted to study the effects of high-temperature damage using rock uniaxial compression tests, and the model’s validity is established by comparing it with previous experimental results. Full article
(This article belongs to the Section Civil Engineering)
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20 pages, 31789 KB  
Article
The Secondary Development and Application of the Improved Nishihara Creep Model in Soft Rock Tunnels
by Xianghui Deng, Junxin Shi, Xiaolin Li, Rui Wang, Jinzeng Zhang and Xin Yang
Buildings 2023, 13(8), 2082; https://doi.org/10.3390/buildings13082082 - 16 Aug 2023
Cited by 15 | Viewed by 2234
Abstract
Given the complexity and diversity of rock formations, existing constitutive models struggle to accurately portray their mechanical properties, leading to substantial discrepancies between numerical simulation outcomes and reality. This inadequacy fails to meet the demands of numerical analysis in practical engineering. This study [...] Read more.
Given the complexity and diversity of rock formations, existing constitutive models struggle to accurately portray their mechanical properties, leading to substantial discrepancies between numerical simulation outcomes and reality. This inadequacy fails to meet the demands of numerical analysis in practical engineering. This study first analyzes the physical and mechanical properties of thin-layered carbonaceous phyllite. Subsequently, an improved Nishihara rheological constitutive model is established based on these analyses. Utilizing the secondary development function offered by FLAC3D, the proposed model is further developed. The program’s correctness and reliability are confirmed through a numerical simulation using the triaxial creep test from existing research. Finally, the established constitutive model is applied in the numerical simulation of an actual soft rock tunnel engineering, obtaining results compared to real monitoring data. The results demonstrate that the improved Nishihara model is more effective at describing the creep deformation characteristics of soft rock. Moreover, the findings from this study can serve as a theoretical reference for predicting deformation in soft rock tunnel engineering. Full article
(This article belongs to the Special Issue Design, Construction and Maintenance of Underground Structures)
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17 pages, 1643 KB  
Article
Design of an Anthracite Creep Model Based on Fractional Order Theory: Experiments and Simulations
by Gang Li, Guochao Yan, Shaoqi Kong, Xuyang Bai, Chaofei Du, Jiajun Li and Jiawei Zhang
Appl. Sci. 2023, 13(11), 6522; https://doi.org/10.3390/app13116522 - 26 May 2023
Cited by 3 | Viewed by 1606
Abstract
Fractional order theory was used to characterize the accelerated creep phase of a nonlinear creep model. To accurately describe each stage of the anthracite creep model, the “gyroscope” unit was introduced by combining the Heaviside function and the creep damage definition. The effect [...] Read more.
Fractional order theory was used to characterize the accelerated creep phase of a nonlinear creep model. To accurately describe each stage of the anthracite creep model, the “gyroscope” unit was introduced by combining the Heaviside function and the creep damage definition. The effect of damage on anthracite creep was determined by designing and completing three-axis graded-separation loading creep tests on anthracite. The test curves were combined to classify anthracite into five stages: transient deformation, pseudo-acceleration, deceleration, isothermal, and acceleration creep. Each stage was combined with suitable components to form a combined fractional-order creep model. The one-dimensional equation of the state of the model was extended to three dimensions. The Levenberg–Marquardt optimization algorithm for fitting origin rheological curves was used to complete the fitting of the basic parameters. Finite differences were performed on the model equation of state, and a secondary development of a combined fractional-order creep model (NEG) was completed based on the built-in Burgers model in FLAC3D. A comparison of the numerical simulation results shows that the combined fractional-order creep model is important for accurately predicting the full creep stage of anthracite. Full article
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20 pages, 8298 KB  
Article
A Study of the Deformation Law of the Surrounding Rock of a Laminated Roadway Based on FLAC3D Secondary Development
by Tuo Wang, Jucai Chang and Hongda Wang
Appl. Sci. 2023, 13(10), 6077; https://doi.org/10.3390/app13106077 - 15 May 2023
Cited by 13 | Viewed by 2294
Abstract
To investigate and analyze the influence of different stress environments on the deformation and destabilization of the rocks surrounding laminated roadways under high stress, this study conducted numerical simulations of coal–rock combination under different circumferential pressures and of the surrounding rocks of highly [...] Read more.
To investigate and analyze the influence of different stress environments on the deformation and destabilization of the rocks surrounding laminated roadways under high stress, this study conducted numerical simulations of coal–rock combination under different circumferential pressures and of the surrounding rocks of highly stressed laminated roadways under different lateral pressure coefficients. In addition, a new custom constitutive structure model was constructed based on the Mohr–Coulomb criterion and realized in FLAC3D software by combining field working conditions. The model was then developed in FLAC3D software for a second time. The results show that the calculated results of the model in this study are in good agreement with the experimental results and the errors are small, while the calculated results of the Mohr–Coulomb model differ from the experimental values under two types of surrounding rock pressure. The deformation of the Mohr–Coulomb model is significantly smaller than that of the customized model, which verifies the reasonableness and superiority of the self-built model in combination with the field conditions. This provides theoretical and practical bases for the design and optimization of stratigraphic roadway support in underground coal mines. Full article
(This article belongs to the Special Issue Advanced Underground Coal Mining and Ground Control Technology)
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13 pages, 3989 KB  
Article
Numerical Study on Crack Propagation in Brittle Jointed Rock Mass Influenced by Fracture Water Pressure
by Yong Li, Hao Zhou, Weishen Zhu, Shucai Li and Jian Liu
Materials 2015, 8(6), 3364-3376; https://doi.org/10.3390/ma8063364 - 9 Jun 2015
Cited by 60 | Viewed by 7663
Abstract
The initiation, propagation, coalescence and failure mode of brittle jointed rock mass influenced by fissure water pressure have always been studied as a hot issue in the society of rock mechanics and engineering. In order to analyze the damage evolution process of jointed [...] Read more.
The initiation, propagation, coalescence and failure mode of brittle jointed rock mass influenced by fissure water pressure have always been studied as a hot issue in the society of rock mechanics and engineering. In order to analyze the damage evolution process of jointed rock mass under fracture water pressure, a novel numerical model on the basis of secondary development in fast Lagrangian analysis of continua (FLAC3D) is proposed to simulate the fracture development of jointed rock mass under fracture water pressure. To validate the feasibility of this numerical model, the failure process of a numerical specimen under uniaxial compression containing pre-existing fissures is simulated and compared with the results obtained from the lab experiments, and they are found to be in good agreement. Meanwhile, the propagation of cracks, variations of stress and strain, peak strength and crack initiation principles are further analyzed. It is concluded that the fissure water has a significant reducing effect on the strength and stability of the jointed rock mass. Full article
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