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Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Civil Engineering".

Deadline for manuscript submissions: closed (31 March 2025) | Viewed by 10841

Special Issue Editors

Dr. Jiadong Qiu

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Guest Editor
School of Resources Environment and Safety Engineering, University of South China, Hengyang 421001, China
Interests: numerical simulation; constitutive model; metaheuristic algorithm; rock mechanics; seepage
Dr. Changtai Zhou

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Guest Editor
Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong SAR, China
Interests: DEM; modeling of fracture network; damage models; constitutive model of rock mass
Dr. Yichao Rui

E-Mail Website
Guest Editor
State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
Interests: numerical computation; disaster early warning; rock-soil interaction; rock mechanics
Special Issues, Collections and Topics in MDPI journals
Dr. Fan Feng

E-Mail Website
Guest Editor
College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao 266590, China
Interests: water-induced rockburst weakening mechanism; testing and experiment of rock mechanical properties; mining method and ground pressure control in deep mines; rockburst mechanism and control techniques; FEM/DEM approach
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With the excavation of geotechnical engineering in deep strata and complex geological environments, a large number of engineering problems, such as groundwater seepage, the dynamic failure of rock mass or soil, geothermal damage to rock mass, and microseismic effects, will strengthen the need for reliable numerical, mathematical, and engineering monitoring methods in engineering analysis, evaluation, and design processes.

This Special Issue focuses on the application and development of advanced numerical computation and mathematical methods in analyzing various geotechnical engineering problems. Original, review, and case study articles related to basic theories and advanced engineering applications will be welcomed.

The research topics covered include, but are not limited to, the following:

  1. Developing new numerical algorithms or constitutive models that can more accurately reflect the mechanical behavior of the object of concern, including new constitutive models of rock or soil, new metaheuristic algorithms, new numerical methods/means, etc.;
  2. Exploring advanced numerical or mathematical models for solving complex engineering problems, including dynamic and static models of rock or soil, and coupled computing models of multi-physical fields, etc.

Dr. Jiadong Qiu
Dr. Changtai Zhou
Dr. Yichao Rui
Dr. Fan Feng
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • advanced numerical method
  • constitutive model of rock or soil materials
  • FEM/DEM simulation
  • multi-physical field numerical simulation
  • advanced metaheuristic algorithms
  • applications of artifcial neural algorithms
  • seepage calculation model
  • rock mass dynamic and static calculation models
  • structural stability simulation
  • computation of rock–soil interaction

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Published Papers (11 papers)

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Research

14 pages, 4110 KiB  
Article
Numerical Modeling and Theoretical Analysis of Deformation Characteristics of Non-Equal-Width Retained Walls
by Kai Cui, Zheng Yang and Jing Li
Appl. Sci. 2025, 15(6), 3080; https://doi.org/10.3390/app15063080 - 12 Mar 2025
Viewed by 335
Abstract
The width of the pillar is an important factor in the stability of the underground space and the efficiency of resource recovery. This study aims to model the performance of retained walls in panel barrier pillar stopes. By simplifying the three-dimensional problem based [...] Read more.
The width of the pillar is an important factor in the stability of the underground space and the efficiency of resource recovery. This study aims to model the performance of retained walls in panel barrier pillar stopes. By simplifying the three-dimensional problem based on the mining operation, a two-dimensional mechanical model of non-equal-width retained walls was established, and the stress and deflection were solved analytically. The calculated deformation characteristics of equal-width and non-equal-width retained walls were analyzed and compared with numerical simulations. The results indicated that the deformation of retained walls is mainly influenced by the roof loads, the uniaxial compressive strength, and the internal friction angle of backfill materials. For equal-width retained wall design, corresponding to the areas of pillar stopes where the uniaxial compressive strength and internal friction angle of backfill materials are low, great lateral pressure will be created on the retained walls. This results in significant flexural wall deformations in this area, increasing the risk of wall collapses. In comparison, for non-equal-width retained walls, the width is defined based on the surrounding backfill materials, which could greatly reduce the risk of potential damage. For the mining operation at the actual mine, the non-equal-width design with 2.5 m and 4.0 m intervals was adopted for the panel barrier pillar stopes, and the final displacement of the roof of the stope after the completion of the mining is 34 mm, and the two sides of the mine wall remain in good integrity with no significant peeling or cracking identified. This design improves the recovery rate of mineral resources and the stability of mining. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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17 pages, 4593 KiB  
Article
Parameter Study and Engineering Verification of the Hardening Soil Model with Small-Strain Stiffness for Loess in the Xi’an Area
by Jiayuan Hu and Qinwen Du
Appl. Sci. 2025, 15(3), 1278; https://doi.org/10.3390/app15031278 - 26 Jan 2025
Viewed by 691
Abstract
With the advancement of the construction of urban underground spaces, it is inevitable that new tunnels will pass through existing pipelines. To ensure the safety and stability of these pipelines, it is essential to strictly control the impact of shield tunneling. The hardening [...] Read more.
With the advancement of the construction of urban underground spaces, it is inevitable that new tunnels will pass through existing pipelines. To ensure the safety and stability of these pipelines, it is essential to strictly control the impact of shield tunneling. The hardening soil model with small-strain stiffness (HSS) comprehensively accounts for the small-strain behavior of soil, and the calculated results are closer to the values measured in engineering compared to those of other models. Consequently, it has been widely adopted in the development and utilization of underground spaces. The selection of parameters for the HSS model is particularly critical when performing numerical simulations. This article establishes the proportional relationships between the small-strain moduli of the HSS model in the loess region of Xi’an through standard consolidation tests, triaxial consolidation drained shear tests, and triaxial consolidation drained loading−unloading shear tests. Additionally, an empirical formula for the static lateral pressure coefficient applicable to loess was derived and validated through engineering examples. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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20 pages, 5643 KiB  
Article
Open-Pit Bench Blasting Fragmentation Prediction Based on Stacking Integrated Strategy
by Yikun Sui, Zhiyong Zhou, Rui Zhao, Zheng Yang and Yang Zou
Appl. Sci. 2025, 15(3), 1254; https://doi.org/10.3390/app15031254 - 26 Jan 2025
Viewed by 651
Abstract
The size distribution of rock fragments significantly influences subsequent operations in geotechnical and mining engineering projects. Thus, accurate prediction of this distribution according to the relevant blasting design parameters is essential. This study employs artificial intelligence methods to predict the fragmentation of open-pit [...] Read more.
The size distribution of rock fragments significantly influences subsequent operations in geotechnical and mining engineering projects. Thus, accurate prediction of this distribution according to the relevant blasting design parameters is essential. This study employs artificial intelligence methods to predict the fragmentation of open-pit bench blasting. The study employed a dataset comprising 97 blast fragment samples. Random forest and XGBoost models were utilized as base learners. A prediction model was developed using the stacking integrated strategy to enhance predictive performance. The model’s performance was evaluated using the coefficient of determination (R2), the mean square error (MSE), the root mean square error (RMSE), and the mean absolute error (MAE). The results indicated that the model achieved the highest prediction accuracy, with an R2 of 0.943. In the training set, the model achieved MSE, RMSE, and MAE values of 0.00269, 0.05187, and 0.03320, while in the testing set, these values were 0.00197, 0.04435, and 0.03687, respectively. The model was validated using five sets of actual blasting block data from a northeastern mining area, which yielded more accurate prediction results. These findings demonstrate that the stacking strategy effectively enhances the prediction performance of a single model and offers innovative approaches to predicting blasting block size. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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23 pages, 3901 KiB  
Article
Hypoplastic Modeling of Soil–Structure Contact Surface Considering Initial Anisotropy and Roughness
by Jingtao Yu, Junwang Cao, Zixuan Chen, Jintao Zhu, Yulong Zhang and Pengqiang Yu
Appl. Sci. 2025, 15(1), 244; https://doi.org/10.3390/app15010244 - 30 Dec 2024
Viewed by 661
Abstract
The development of a constitutive model for soil–structure contact surfaces remains a pivotal area of research within the field of soil–structure interaction. Drawing from the Gudehus–Bauer sand hypoplasticity model, this paper employs a technique that reduces the stress tensor and strain rate tensor [...] Read more.
The development of a constitutive model for soil–structure contact surfaces remains a pivotal area of research within the field of soil–structure interaction. Drawing from the Gudehus–Bauer sand hypoplasticity model, this paper employs a technique that reduces the stress tensor and strain rate tensor components to formulate a hypoplastic model tailored for sand–structure interfaces. To capture the influence of initial anisotropy, a deposition direction peak stress coefficient is incorporated; meanwhile, a friction parameter is introduced to address the surface roughness of the contact. Consequently, a comprehensive hypoplastic constitutive model is developed that takes into account both initial anisotropy and roughness. Comparative analysis with experimental data from soils on contact surfaces with diverse boundary conditions and levels of roughness indicates that the proposed model accurately forecasts shear test outcomes across various contact surfaces. Utilizing the finite element software ABAQUS 2021, an FRIC subroutine was developed, which, through simulating direct shear tests on sand–structure contact surfaces, has proven its efficacy in predicting the shear behavior of these interfaces. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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26 pages, 13888 KiB  
Article
Effect of Design Parameters of Supporting Structure on the Energy Evolution Characteristic of Surrounding Rock
by Ying Chen, Qi Da, Lei Zhang, Danli Li and Bing Dai
Appl. Sci. 2024, 14(23), 11028; https://doi.org/10.3390/app142311028 - 27 Nov 2024
Viewed by 799
Abstract
A reasonable support parameter design scheme is the key to ensuring the stability of the roadway. This study established 217 models using FLAC3D to analyze the evolution characteristics of elastic strain energy and plastic dissipation energy of surrounding rock under different shotcrete and [...] Read more.
A reasonable support parameter design scheme is the key to ensuring the stability of the roadway. This study established 217 models using FLAC3D to analyze the evolution characteristics of elastic strain energy and plastic dissipation energy of surrounding rock under different shotcrete and rockbolt support structures. Additionally, five single models (BP, DT, ELM, RF, SVM) were introduced to explore the application of machine learning in predicting the stability of the roadway. The study found that in the parameters of the shotcrete layer support structure, the energy evolution of the surrounding rock is more sensitive to isotropic and thickness; in the parameters of the anchor rod support structure, the energy evolution of the surrounding rock is more sensitive to Young’s modulus, cross-sectional area young, and grout stiffness. Additionally, the parameters of the shotcrete layer support structure are not necessarily the larger the better. When isotropic is 100 GPa, both the dissipated energy and the elastic strain energy are higher than that at 25 GPa. The results of the single model test indicate that machine learning is relatively accurate in predicting different shotcrete and anchor support structures. The runtime difference between traditional methods and machine learning models highlights the potential advantages of machine learning. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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18 pages, 9755 KiB  
Article
Numerical Simulation Analysis of the Influence of Interlayer Quantity on the Long-Term Stable Operation of Gas Storage Facilities
by Lilong Li, Xin Jiang, Jiafeng Tan, Rong Liu, Xiaolinag Quan, Jinyang Fan, Cheng Qian and Jinjie Suo
Appl. Sci. 2024, 14(21), 9760; https://doi.org/10.3390/app14219760 - 25 Oct 2024
Cited by 1 | Viewed by 772
Abstract
Salt rock is considered as an ideal energy storage medium, and compressed air energy storage by a salt cavern can improve the utilisation efficiency of renewable energy. Salt rock in China mostly contains different interlayers, among which mudstone interlayers are the most common. [...] Read more.
Salt rock is considered as an ideal energy storage medium, and compressed air energy storage by a salt cavern can improve the utilisation efficiency of renewable energy. Salt rock in China mostly contains different interlayers, among which mudstone interlayers are the most common. At present, there are relatively few studies on the influence of mudstone interlayers on the long-term stable operation of gas storage. FLAC3D software was used to simulate the long-term operation of salt rock gas storage with different numbers of interlayers in the Yexian area of Pingdingshan. The results show that with the passage of time, the vertical displacement of the surrounding rock of the vertical single-cavity gas storage tank increases gradually. The maximum settlement value at the top of the surrounding rock is always greater than the maximum uplift value at the bottom. The horizontal displacement shows obvious symmetry with the vertical displacement at the top and bottom of the surrounding rock. The effect of the cyclic pressure interval on horizontal displacement is the same as that of vertical displacement. With the increase in the number of interlayers, the volume of the plastic zone gradually increases with the increase in the running time, and the increasing speed shows a growing trend. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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15 pages, 7768 KiB  
Article
Rock Slope Instability Mechanism Induced by Repeated Mining in Mountain Mining Areas
by Rong Luo, Guangyue Li, Lu Chen, Ling Zeng, Ke Pei and Xiangxi Yu
Appl. Sci. 2024, 14(21), 9634; https://doi.org/10.3390/app14219634 - 22 Oct 2024
Viewed by 905
Abstract
When mineral resources are extracted using underground mining methods in hilly regions, landslides or slope failures can be induced frequently. In this study, slope collapse disasters in mountain mining areas were analyzed. The model test and numerical simulation of the slope impacted by [...] Read more.
When mineral resources are extracted using underground mining methods in hilly regions, landslides or slope failures can be induced frequently. In this study, slope collapse disasters in mountain mining areas were analyzed. The model test and numerical simulation of the slope impacted by repeated mining were carried out. The crack evolution and failure process were analyzed to reveal the instability mechanism. The results show that the rock mass would topple to the inside of the slope first, when the subsidence of overlying rock was induced by the mining of the upper coal seam. When repeated mining was performed in the lower coal seam, the mining induced macro-cracks that could connect with natural fissures, inducing the outward displacement of the slope. Then, the rock mass at the foot of the slope has to bear the upper load, which is also squeezed out by the collapsed rock mass, forming the potential slip zone. Finally, the instability is caused by the shear slip of the slope toe rock mass. Therefore, the instability evolution of the slope under underground repeated mining disturbance can be divided into four stages as follows: roof caving and overlaying rock subsidence, joint rock toppling, fracture penetration, and slope toe shearing and slope slipping. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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23 pages, 18218 KiB  
Article
Analysis of Granite Deformation and Rupture Law and Evolution of Grain-Based Model Force Chain Network under Anchor Reinforcement
by Jiangfeng Guo, Doudou Fan, Liyuan Yu, Meixia Shi, Haijian Su, Tao Zhang and Bowen Hu
Appl. Sci. 2024, 14(18), 8548; https://doi.org/10.3390/app14188548 - 23 Sep 2024
Viewed by 899
Abstract
In actual underground rock engineering, to prevent the deformation and damage of the rock mass, rock bolt reinforcement technology is commonly employed to maintain the stability of the surrounding rock. Therefore, studying the anchoring and crack-stopping effect of rock bolts on fractured granite [...] Read more.
In actual underground rock engineering, to prevent the deformation and damage of the rock mass, rock bolt reinforcement technology is commonly employed to maintain the stability of the surrounding rock. Therefore, studying the anchoring and crack-stopping effect of rock bolts on fractured granite rock mass is essential. It can provide significant reference and support for the design of underground engineering, engineering safety assessment, the theory of rock mechanics, and resource development. In this study, indoor experiments are combined with numerical simulations to explore the impact of fracture dip angles on the mechanical behavior of unanchored and anchored granite samples from both macroscopic and microscopic perspectives. It also investigates the evolution of the anchoring and crack-stopping effect of rock bolts on granite containing fractures with different dip angles. The results show that the load-displacement trends, displacement fields, and debris fields from indoor experiments and numerical simulations are highly similar. Additionally, it was discovered that, in comparison to the unanchored samples, the anchored samples with fractures at various angles all exhibited a higher degree of tensile failure rather than shear failure that propagates diagonally across the samples from the regions around the fracture tips. This finding verifies the effectiveness of the numerical model parameter calibration. At the same time, it was observed that the internal force chain value level in the anchored samples is higher than in the unanchored samples, indicating that the anchored samples possess greater load-bearing capacity. Furthermore, as the angle αs increases, the reinforcing and crack-stopping effects of the rock bolts become increasingly less pronounced. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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33 pages, 6184 KiB  
Article
Numerical Simulation and Engineering Application of Synergistic Support Effect of Bolt–Mesh–Cable Support in Gob-Side Entry of Deep Soft Coal Seam
by Haifeng Ma, Shuo Zhang, Huaiyi Zhai, Zenghui Liu and Chuang Jie
Appl. Sci. 2024, 14(18), 8226; https://doi.org/10.3390/app14188226 - 12 Sep 2024
Cited by 1 | Viewed by 1060
Abstract
Aiming at solving the problem of support failure caused by a large deformation of roadway surrounding rock in a deep soft coal seam, and taking the surrounding rock control of the roadway in the 11-2 coal seam in Zhujidong Coal Mine as the [...] Read more.
Aiming at solving the problem of support failure caused by a large deformation of roadway surrounding rock in a deep soft coal seam, and taking the surrounding rock control of the roadway in the 11-2 coal seam in Zhujidong Coal Mine as the research background, numerical simulation and field industrial test and inspection methods were used to study the support effect of a supporting system of gob-side entry in deep soft coal seam. The deformation characteristics of various supporting systems of metal mesh, diamond mesh, metal mesh with anchor rod, steel ladder beam, M-shaped steel belt, 14#b channel steel, and 11# I-steel in the goaf supporting body of deep soft coal seam were studied under vertical load. The supporting effect of effective compressive stress zone generated by bolt and cable under different row spacings and lengths was analyzed, and the law of variation in the compressive stress field generated by supporting members with supporting parameters was explored. The length and interrow distance of bolt and cable were compared, respectively, and reasonable supporting parameters were selected. Based on the abovementioned research results and the geological conditions of the 1331 (1) track roadway, the support scheme of the 1331 (1) track roadway was designed, and the industrial test was carried out. The results show that the surrounding rock of the roadway is within the effective anchorage range of the supporting body, the active support function of the supporting components has been fully brought into play, and the overall control effect of the surrounding rock of the roadway is good, which can ensure the safety and stability of the goaf roadway. The maximum displacement of the roof and floor of the roadway is 86 mm, the maximum displacement of the solid coal side is 50 mm, the maximum displacement of the coal pillar side is 70 mm, and the maximum separation of layers is 22 mm. There is no failure phenomenon in relation to the anchor bolt and cable, and the overall deformation of the roadway surrounding the rock is good, which can provide some references for roadway-surrounding-rock control under similar conditions in deep coal seams. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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19 pages, 16746 KiB  
Article
Dynamic Response and Rock Damage of Different Shapes of Cavities under Blasting Loads
by Xuejiao Cui, Mingsheng Zhao and Qiyue Li
Appl. Sci. 2024, 14(17), 7743; https://doi.org/10.3390/app14177743 - 2 Sep 2024
Viewed by 1293
Abstract
In order to investigate the dynamic response and rock mass damage characteristics of cavities with different shapes under blasting loads, this paper, through a combination of model tests and numerical simulations, studies the stress distribution, strain, failure modes, and blasting fragment size distribution [...] Read more.
In order to investigate the dynamic response and rock mass damage characteristics of cavities with different shapes under blasting loads, this paper, through a combination of model tests and numerical simulations, studies the stress distribution, strain, failure modes, and blasting fragment size distribution of cavities with different shapes subjected to blasting loads. The results show that under the action of blasting loads, the presence of cavities with different shapes significantly affects the blasting effects and rock mass damage. Spherical cavities exhibit excellent blast resistance, whereas rectangular and triangular cavities are prone to stress concentration at their tips, which in turn promotes rock mass damage and failure. Subsequent analysis of the blasting fragment sizes reveals that rectangular and triangular cavities yield more favorable blasting results than spherical cavities. The research findings provide important theoretical foundations and practical guidance for the design and construction of underground engineering blasting, contributing to enhancing engineering safety and promoting the sustainable development of the underground engineering industry. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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20 pages, 5901 KiB  
Article
The Vibration Response to the High-Pressure Gas Expansion Method: A Case Study of a Hard Rock Tunnel in China
by Huaide Peng, Jia Sheng, Qi Da, Bing Dai, Lei Zhang and Lihai Tan
Appl. Sci. 2024, 14(15), 6645; https://doi.org/10.3390/app14156645 - 30 Jul 2024
Viewed by 1071
Abstract
The vibration of rock breaking in tunnel excavation may cause serious damage to nearby buildings if it is not controlled properly. With reference to a hard rock tunnel in China, the vibration response to the high-pressure gas expansion method (HPGEM), an emerging rock-breaking [...] Read more.
The vibration of rock breaking in tunnel excavation may cause serious damage to nearby buildings if it is not controlled properly. With reference to a hard rock tunnel in China, the vibration response to the high-pressure gas expansion method (HPGEM), an emerging rock-breaking approach, was investigated with field tests, theoretical derivations, and numerical simulations, then comparisons with the traditional dynamite blast were performed. Firstly, the vibration velocity prediction formulas of the two methods were fitted based on the field tests. Subsequently, the accuracy of the formula was verified by numerical simulation, and the vibration attenuation law of the HPGEM was explored. Comparisons were made between the blast and HPGEM, particularly the differences in peak particle velocity (PPV) for different agent qualities, distance from the blasting center, and engineering conditions. Furthermore, this study also analyzed the relationship between the agent qualities and the rock-breaking volume under different cases, finding that the HPGEM has slight vibration and good rock-breaking effect. The HPGEM is thus fully capable of replacing dynamite blasting to carry out rock-breaking operations in certain special areas. Full article
(This article belongs to the Special Issue Advances in Numerical Computation and Mathematical Modelling for Geotechnical Engineering)
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