{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T08:42:46Z","timestamp":1789634566606,"version":"build-2803163510"},"reference-count":116,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T00:00:00Z","timestamp":1756857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005632","name":"Polish National Center for Research and Development","doi-asserted-by":"publisher","award":["TANGO-IV-A\/0058\/2019"],"award-info":[{"award-number":["TANGO-IV-A\/0058\/2019"]}],"id":[{"id":"10.13039\/501100005632","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100016775","name":"Lublin University of Technology","doi-asserted-by":"crossref","award":["No. FD-20\/IM-5\/052"],"award-info":[{"award-number":["No. FD-20\/IM-5\/052"]}],"id":[{"id":"10.13039\/100016775","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This paper presents an analysis of the influence of the termination geometry of an undercutting anchor drive bolt and the shape of the bottom of the anchor hole on the initiation and progression of failure processes in a rock medium. The study employed the finite element method (FEM) to model various bolt termination configurations, including cylindrical terminations with a 2 \u00d7 2 mm chamfer, a rounded termination with radius R, and a conical termination. The interaction of these bolt geometries with both cylindrical and conical hole bottoms was analyzed. The numerical simulations enabled the identification of stress concentration zones and crack propagation paths, which are critical to understanding the efficiency and mechanism of rock failure. The results indicate that the geometry of the bolt termination significantly influences stress distribution within the contact zone, as well as the extent and morphology of the resulting failure zone. Specifically, employing a cylindrical termination with a 2 \u00d7 2 mm chamfer in combination with a conical hole bottom promotes the development of deep fractures, which may lead to the detachment of larger rock fragments. This mechanism may be useful in the development of non-explosive rock fragmentation technologies. The findings provide a foundation for further optimization of anchor designs and the development of targeted excavation methods in mining and geotechnical engineering.<\/jats:p>","DOI":"10.3390\/ma18174136","type":"journal-article","created":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T15:15:57Z","timestamp":1756912557000},"page":"4136","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Parametric Study of the Effect of Anchor Drive Bolt Geometry on Stress Distribution and Direction of Crack Formation in the Rock Medium"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4658-4569","authenticated-orcid":false,"given":"J\u00f3zef","family":"Jonak","sequence":"first","affiliation":[{"name":"Department of Machine Design and Mechatronics, Faculty of Mechanical Engineering, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4063-8503","authenticated-orcid":false,"given":"Robert","family":"Karpi\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Machine Design and Mechatronics, Faculty of Mechanical Engineering, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6329-5764","authenticated-orcid":false,"given":"Andrzej","family":"W\u00f3jcik","sequence":"additional","affiliation":[{"name":"Department of Machine Design and Mechatronics, Faculty of Mechanical Engineering, Lublin University of Technology, ul. 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Ind."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.engstruct.2014.10.008","article-title":"Prediction of the Nonlinear Pull-out Response of FRPG round Anchors Using an Analytical Transfer Matrix Method","volume":"81","author":"Zheng","year":"2014","journal-title":"Eng. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Jonak, J., Karpi\u0144ski, R., Siegmund, M., W\u00f3jcik, A., and Jonak, K. (2020). Analysis of the Rock Failure Cone Size Relative to the Group Effect from a Triangular Anchorage System. Materials, 13.","DOI":"10.3390\/ma13204657"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Jonak, K., Karpi\u0144ski, R., W\u00f3jcik, A., and Jonak, J. (2025). Simulation of Rock Failure Cone Development Using a Modified Load-Transferring Anchor Design. Appl. Sci., 15.","DOI":"10.3390\/app15147653"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/j.conbuildmat.2013.05.032","article-title":"Tensile Behavior of Post-Installed Chemical Anchors Embedded to Low Strength Concrete","volume":"47","author":"Yilmaz","year":"2013","journal-title":"Constr. Build. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"196","DOI":"10.3221\/IGF-ESIS.29.17","article-title":"Predictionofthe Pull-out Strength of Chemical Anchors in Natural Stone","volume":"8","author":"Contrafatto","year":"2014","journal-title":"Fract. Struct. Integr."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s10064-005-0011-4","article-title":"Ground Anchors in an Aggressive Hydro-Environment","volume":"65","author":"Shaqour","year":"2006","journal-title":"Bull. Eng. Geol. Environ."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Mottl, M., Reiterman, P., and Pazderka, J. (2023). The Influence of Aggressive Environmental Conditions on the Adhesion of Applied Crystalline Materials. J. Compos. Sci., 8.","DOI":"10.3390\/jcs8010005"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.engfailanal.2019.02.054","article-title":"An Overview of Austenitic Stainless-Steel Rock Anchors Damage in an Environment Rich with Chlorides","volume":"100","author":"Gruttadauria","year":"2019","journal-title":"Eng. Fail. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lamplmair-Irsigler, S., Zeman, O., Stierschneider, E., and Voit, K. (2024). Fastening in Rock Mass\u2014Structural Design of Shallow Embedded Anchors in Inhomogeneous Substrate. Materials, 17.","DOI":"10.3390\/ma17246044"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s00603-011-0138-5","article-title":"Rock Mass Characterization and Rock Property Variability Considerations for Tunneland Cavern Design","volume":"44","author":"Cai","year":"2011","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4547","DOI":"10.1007\/s00603-019-01887-5","article-title":"Effect of Fracture Heterogeneity on Rock Mass Stability in a Highly Heterogeneous Underground Roadway","volume":"52","author":"Kong","year":"2019","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bokor, B., T\u00f3th, M., and Sharma, A. (2018). Fasteners in Steel Fiber Reinforced Concrete Subjected to Increased Loading Rates. Fibers, 6.","DOI":"10.3390\/fib6040093"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"254","DOI":"10.37544\/0005-6650-2021-07-08-52","article-title":"Befestigungen Im Stahlfaserverst\u00e4rkten Beton Bei Betonbruch\u2014Stand Der Technik Und Bemessungsansatz\/Anchorages in Steel Fiber Reinforced Concrete in the Case of Concrete Break out Failure\u2014State of the Art and Design Concept","volume":"96","author":"Bokor","year":"2021","journal-title":"Bauingenieur"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.engstruct.2018.12.007","article-title":"Anchorage in Steel Fiber Reinforced Concrete\u2013Concept, Experimental Evidence and Design Recommendations for Concrete Cone and Concrete Edge Break out Failure Modes","volume":"181","author":"Bokor","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.engstruct.2019.03.019","article-title":"Experimental Investigations on Concrete Cone Failure of Rectangular and Non-Rectangular Anchor Groups","volume":"188","author":"Bokor","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7249","DOI":"10.1002\/suco.202300255","article-title":"An Assessment Method to Ensure Applicability of Concrete Capacity Method for Design of Anchorages: Linear Force Distribution Approach","volume":"24","author":"Bokor","year":"2023","journal-title":"Struct. Concr."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4314","DOI":"10.1016\/j.jrmge.2024.09.056","article-title":"Shear Behavior of Rock Joints Reinforced with Fully-Grouted and Energy-Absorbing Bolts Subjected to Shear Cycles","volume":"17","author":"Zheng","year":"2024","journal-title":"J. Rock Mech. Geotech. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"112273","DOI":"10.1016\/j.engstruct.2021.112273","article-title":"Seismic Upgrading of Existing Reinforced Concrete Buildings: A State-of-the-Art Review","volume":"240","author":"Gkournelos","year":"2021","journal-title":"Eng. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1177\/87552930211057581","article-title":"Self-Centering Seismic-Resistant Structures: Historical Overview and State-of-the-Art","volume":"38","author":"Zhong","year":"2022","journal-title":"Earthq. Spectra"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104904","DOI":"10.1016\/j.jobe.2022.104904","article-title":"Seismic Retrofitting of Existing Frame Buildings through Externally Attached Sub-Structures: State of the Art Review and Future Perspectives","volume":"57","author":"Cao","year":"2022","journal-title":"J. Build. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.tust.2014.05.006","article-title":"An Experimental Study on Anchorage Strength and Deformation Behavior of Large-Scale Jointed Rock Mass","volume":"43","author":"Jing","year":"2014","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1007\/s12583-022-1785-z","article-title":"Mechanical Behaviors of Anchorage Interfaces in Layered Rocks with Fractures under Axial Loads","volume":"34","author":"Wang","year":"2023","journal-title":"J. Earth Sci."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"W\u00f3jcik, A., Jonak, K., Karpi\u0144ski, R., Jonak, J., Kalita, M., and Prosta\u0144ski, D. (2024). Mechanism of Rock Mass Detachment Using Undercutting Anchors: A Numerical Finite Element Method (FEM) Analysis. Materials, 17.","DOI":"10.3390\/ma17184468"},{"key":"ref_27","unstructured":"Caldwell, T. (2005, January 17\u201320). A Comparison of Non-Explosive Rock Breaking Techniques. Proceedings of the 12th Australian Tunnelling Conference, Brisbane, Australia."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/S0886-7798(98)00062-5","article-title":"Non-Explosive Applications of the PCF Concept for Underground Excavation","volume":"13","author":"Singh","year":"1998","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xu, K. (2023). Rock Fragmentation. The ECPH Encyclopedia of Mining and Metallurgy, Springer Nature Singapore.","DOI":"10.1007\/978-981-19-0740-1"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhu, C., Huang, M., Cai, Q., Zuo, Y., Tang, S., and Yin, Q. (2025). Complex Rock Mechanics Problems and Risk Prevention Solutions. Appl. Sci., 15.","DOI":"10.3390\/app15020755"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2076","DOI":"10.1007\/s11629-023-7999-4","article-title":"Optimization of Anchorage Support Parameters for Soft Rock Tunnel Based on Displacement Control Theory","volume":"20","author":"Li","year":"2023","journal-title":"J. Mt. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Li, M., Ye, L., Feng, J., Fang, Y., Wen, H., and Wu, X. (2024). Failure Mechanism and Control Technology of Soft-Rock Roadways Subjected to High Structural Stress. Front. Earth Sci., 12.","DOI":"10.3389\/feart.2024.1473108"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wang, D., He, F., Chen, D., Bascompta, M., Wang, X., Xu, C., Liu, B., and Tian, W. (2025). Mechanism of Enhanced Control and Technological Application of Surrounding Rock Anchoring in Fully Mechanized Caving Face of Extra-Thick Coal Seams. Processes, 13.","DOI":"10.3390\/pr13041216"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"105910","DOI":"10.1016\/j.ijrmms.2024.105910","article-title":"Insights into Velocity-Dependent Shear Characteristics of Bolted Rock Joints: A Comparative Study of Fully-Grouted and Energy-Absorbing Bolts","volume":"183","author":"Zheng","year":"2024","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wang, Z., Liao, L., Guo, S., Zheng, H., and Wu, X. (2024). Numerical Investigation of Bolted Rock Joints under Varying Normal Stressand Joint Roughness Coefficient Conditions. Front. Earth Sci., 12.","DOI":"10.3389\/feart.2024.1402708"},{"key":"ref_36","unstructured":"Deutsches Institut f\u00fcr Bautechnik (2018). European Technical Assessment ETA-18\/0629 of 4 September 2018, Deutsches Institut f\u00fcr Bautechnik."},{"key":"ref_37","unstructured":"American Certification Institute (2020). Building Code Requirements for Structural Concrete (ACI 318\u201319) Commentary on Building Code Requirements for Structural Concrete: ACI 318M ERTA\u20142020, HISMarkit."},{"key":"ref_38","unstructured":"Hilti (2017). Technical Datasheet Update: Dec-17, HDA Undercut Anchor, Hilti."},{"key":"ref_39","unstructured":"Hilti (2025). Hilti Mechanical Anchors Catalog, Hilti."},{"key":"ref_40","unstructured":"MIYANAGA Co., Ltd. (2020). ANZEX Undercut Anchor System Installation Manual (ANZEX-D), MIYANAGA Co., Ltd."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"012012","DOI":"10.1088\/1742-6596\/2130\/1\/012012","article-title":"Numerical Analysis of the Effect of Embedment Depth on the Geometry of the Cone Failure","volume":"2130","author":"Jonak","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"012011","DOI":"10.1088\/1742-6596\/2130\/1\/012011","article-title":"Numerical Analysis of Under cut Anchor Effect on Rock","volume":"2130","author":"Jonak","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Zhang, B., and Chen, Z. (2025). Numerical Simulation and Parametric Study of Pull out Behavior of Anchor Studs in Normal-strength and High-strength Concrete. Struct. Concr., suco.70278.","DOI":"10.1002\/suco.70278"},{"key":"ref_44","first-page":"73","article-title":"Concrete Capacity Design (CCD) Approach for Fastening to Concrete","volume":"92","author":"Fuchs","year":"1995","journal-title":"Struct. J."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Di Nunzio, G. (2019, January 23\u201326). A Literature Review about the Head-Size Effect on the Capacity of Cast-in Anchors. Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures, Bayonne, France.","DOI":"10.21012\/FC10.239783"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1016\/j.proeng.2017.01.391","article-title":"Experimental Analysis of Anchor Bolt in Concrete under the Pull-Out Loading","volume":"171","author":"Hariyadi","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"05021005","DOI":"10.1061\/(ASCE)SC.1943-5576.0000615","article-title":"Effect of Adhesive through Pilot Pull-Out Tests on Handcrafted Headed Studs Postinstalled in Steel Fiber Concrete","volume":"26","year":"2021","journal-title":"Pract. Period. Struct. Des. Constr."},{"key":"ref_48","unstructured":"Elgehausen, R., and Sawade, G. (1989). A Fracture Mechanics Based Description of the Pull-out Behavior of Headed Studs Embedded in Concrete. Communities Collect."},{"key":"ref_49","unstructured":"Eligehausen, R., Mall\u00e9e, R., and Silva, J.F. (2006). Anchorage in Concrete Construction, Wiley Library."},{"key":"ref_50","first-page":"2","article-title":"Tensile Resistance of Steel-Reinforced Anchorages: Experimental Evaluation","volume":"110","author":"Henriques","year":"2013","journal-title":"ACI Struct. J."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/s40069-021-00464-x","article-title":"Research on Whole-Process Tensile Behavior of Headed Studs inSteel\u2013Concrete Composite Structures","volume":"15","author":"Zhuang","year":"2021","journal-title":"Int. J. Concr. Struct. Mater."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"131","DOI":"10.3221\/IGF-ESIS.73.09","article-title":"Parametric Study on the Effect of Anchor\u2019s Geometry on the Stress Distribution and Crack Initiation Direction in a Concrete Body","volume":"19","author":"Malikova","year":"2025","journal-title":"Fract. Struct. Integr."},{"key":"ref_53","unstructured":"Mahrenholtz, P. (2013). Experimental Performance and Recommendations for Qualification of Post-Installed Anchors for Seismic Applications, Inst. f\u00fcr Werkstoffe im Bauwesen."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2339","DOI":"10.1007\/s00603-023-03689-2","article-title":"Behavior of a Rock Mass in Uplift Field Tests of Rock Anchors","volume":"57","author":"Grindheim","year":"2024","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Lamplmair, S., Zeman, O., and Voit, K. (2021). Factors Influencing the Load-Bearing Capacity of Rock as Base Material forPost-Installed Anchors. Materials, 14.","DOI":"10.3390\/ma14185130"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"106563","DOI":"10.1016\/j.compgeo.2024.106563","article-title":"Large Deformation Numerical Assessment of Rock Anchor Response under Axial Loading for Offshore Renewable Energy Applications","volume":"173","author":"Genco","year":"2024","journal-title":"Comput. Geotech."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Ferrari, A., Rosone, M., Ziccarelli, M., and Gottardi, G. (2023). Geotechnical Engineering in the Digital and Technological Innovation Era, Springer.","DOI":"10.1007\/978-3-031-34761-0"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"230","DOI":"10.12913\/22998624\/132279","article-title":"Experimental Verification of Standard Recommendations for Estimating the Load-Carrying Capacity of Undercut Anchorsin Rock Material","volume":"15","author":"Jonak","year":"2021","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Jonak, J., W\u00f3jcik, A., Karpi\u0144ski, R., and Jonak, K. (2025). Effect of Under cut Bolt Anchor Depth on Failure Cone Geometry: A Numerical FEM Analysis and Experimental Verification. Materials, 18.","DOI":"10.3390\/ma18030686"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Krzysztof, K., and Piotr, M. (2019). Methods of Mechanical Mining of Compact-Rock\u2014A Comparison of Efficiency and Energy Consumption. Energies, 12.","DOI":"10.3390\/en12183562"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.tust.2019.03.001","article-title":"The Use of Kernel Density Estimates for Classification of Ripping Tool Wear","volume":"88","author":"Gajewski","year":"2019","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.tust.2005.07.003","article-title":"Utilisation of Neural Networks to Identify the Status of the Cutting Tool Point","volume":"21","author":"Gajewski","year":"2006","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.tust.2018.11.042","article-title":"Optimal Selection of Signal Features in the Diagnostics of Mining Head Tools Condition","volume":"84","author":"Gajewski","year":"2019","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Liang, F., Pei, C., Luo, W., You, M., and Tan, F. (2024). Numerical Simulation Analysis of Different Excavation Parameters for TBM3DDisc Cutters Based on the Discrete Element Method. Appl. Sci., 15.","DOI":"10.3390\/app15010038"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"108076","DOI":"10.1016\/j.measurement.2020.108076","article-title":"Degradation Process and Failure Estimation of Drilling System Based on RealDataand Diffusion Process Supported by State Space Models","volume":"164","author":"Vintr","year":"2020","journal-title":"Measurement"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1007\/s11440-018-0709-7","article-title":"Three-Dimensional Numerical Study on the Failure Characteristics of Intermittent Fissures under Compressive-Shear Loads","volume":"14","author":"Wang","year":"2019","journal-title":"Acta Geotech."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.euromechsol.2016.08.009","article-title":"Numerical Simulation of Crack Curving and Branching in Brittle Materials under Dynamic Loads Using the Extended Non-Ordinary State-Based Peridynamics","volume":"60","author":"Zhou","year":"2016","journal-title":"Eur. J. Mech. A Solids"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.ijrmms.2015.09.006","article-title":"Numerical Simulations of Propagation, Bifurcation and Coalescence of Cracks in Rocks","volume":"80","author":"Zhou","year":"2015","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1007\/s00603-023-03636-1","article-title":"Introducing a New Model for Prediction of Mean Cutting Forces Acting on Conical Pick Cutters","volume":"57","author":"Morshedlou","year":"2024","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1007\/s00603-022-03147-5","article-title":"Experimental and Numerical Investigations on Rock Breaking of TBM Disc Cutter Based on a Novel Platform with Rotational Cutting","volume":"56","author":"Deng","year":"2023","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"108448","DOI":"10.1016\/j.ymssp.2021.108448","article-title":"Drilling Head Knives Degradation Modelling Based on Stochastic Diffusion Processes Backed upby State Space Models","volume":"166","author":"Gajewski","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Cao, Y., Zhang, Q., Zhang, S., Tian, Y., Dong, X., Song, X., and Wang, D. (2025). Optimization of Rock-Cutting Tools: Improvements in Structural Design and Process Efficiency. Computation, 13.","DOI":"10.3390\/computation13070152"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Jonak, J., Karpi\u0144ski, R., and W\u00f3jcik, A. (2021). Influence of the Undercut Anchor Head Angle on the Propagation of the Failure Zone of the Rock Medium\u2014Part II. 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Materials, 14.","DOI":"10.3390\/ma14092371"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"012014","DOI":"10.1088\/1757-899X\/679\/1\/012014","article-title":"Analysis of the Process of Loosening the Rocks with Different Strength Properties Using the Undercutting Bolts","volume":"Volume 679","author":"Siegmund","year":"2019","journal-title":"IOP Conference Series: Materials Science and Engineering"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"012046","DOI":"10.1088\/1757-899X\/710\/1\/012046","article-title":"FEM 3D Analysis of Rock Cone Failure Range during Pull-out of Undercut Anchors","volume":"Volume 710","author":"Jonak","year":"2019","journal-title":"IOP Conference Series: Materials Science and Engineering"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"290","DOI":"10.12913\/22998624\/170301","article-title":"Influence of Anchor Depth and Friction Coefficient Between Anchor and Rock on the Trajectory of Rock Masses Detachment","volume":"17","author":"Jonak","year":"2023","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Jonak, J., Karpi\u0144ski, R., W\u00f3jcik, A., Siegmund, M., and Kalita, M. (2022). Determining the Effect of Rock Strength Parameters on the Breakout Area Utilizing the New Design of the Undercut\/Breakout Anchor. Materials, 15.","DOI":"10.3390\/ma15030851"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"101","DOI":"10.12913\/22998624\/190133","article-title":"A Numerical Study of the Influence of Cone Angle of the Breakout Anchor Head on the Crack Trajectory of the Medium","volume":"18","author":"Jonak","year":"2024","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"7443","DOI":"10.1007\/s00603-024-03905-7","article-title":"Digital Microscopic Multiphase Heterogeneity Representation and Its Effects on Micromechanics and Cracking Behaviors of Geomaterials","volume":"57","author":"Zhao","year":"2024","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.ijrmms.2010.11.006","article-title":"Anchor Application in Karatepe Andesite Rock Slope, Izmir\u2014T\u00fcrkiye","volume":"48","author":"Koca","year":"2011","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_82","first-page":"1","article-title":"A Comprehensive Review of Various AI-Based Segmentation Algorithms for Multiscale Rocks: Principles, Evaluations, Simple Applications and Future Directions","volume":"2025","author":"Zhao","year":"2025","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"104304","DOI":"10.1016\/j.ijrmms.2020.104304","article-title":"Cracking Behaviors and Hydraulic Properties Evaluation Based on Fractural Microstructure Models in Geomaterials","volume":"130","author":"Zhou","year":"2020","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"e2021GL095001","DOI":"10.1029\/2021GL095001","article-title":"Microscopic Characterizations of Heterogeneous Pores, ITZs, Multiple-Solids, and Their Impacts on Damage Property of Sandstone by Low-High Resolution 3D Reconstruction","volume":"48","author":"Zhao","year":"2021","journal-title":"Geophys. Res. Lett."},{"key":"ref_85","unstructured":"Cook, R.A. (1989). Behavior and Design of Ductile Multiple-Anchor Steel-to-Concrete Connections, The University of Texas at Austin."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"08001","DOI":"10.1051\/matecconf\/201925208001","article-title":"Numerical Analysis of Crack Propagation in a Pull-out Test","volume":"Volume 252","author":"Gontarz","year":"2019","journal-title":"MATEC Web of Conferences"},{"key":"ref_87","unstructured":"(ABAQUS, 2019). ABAQUS, Version 2019."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Jnak, J., Siegmund, M., Karpi\u0144ski, R., and W\u00f3jcik, A. (2020). Three-Dimensional Finite Element Analysis of the Undercut Anchor Group Effect in Rock Cone Failure. Materials, 13.","DOI":"10.3390\/ma13061332"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1061\/(ASCE)0733-9445(1985)111:3(505)","article-title":"Friction Coefficient of Steel on Concrete or Grout","volume":"111","author":"Rabbat","year":"1985","journal-title":"J. Struct. Eng."},{"key":"ref_90","first-page":"311","article-title":"Comparison Between Numerical Analysis and Actual Results for a Pull-Out Test","volume":"67","author":"Gotarz","year":"2019","journal-title":"Eng. Trans."},{"key":"ref_91","first-page":"341","article-title":"Contact Analysis for the Modelling of Anchors in Concrete Structures","volume":"14","author":"Walter","year":"1997","journal-title":"WIT Trans. Eng. Sci."},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Jonak, J., Karpi\u0144ski, R., W\u00f3jcik, A., and Siegmund, M. (2021). The Influence of the Physical-Mechanical Parameters of Rock on the Extent of the Initial Failure Zone under the Action of an Undercut Anchor. Materials, 14.","DOI":"10.3390\/ma14081841"},{"key":"ref_93","doi-asserted-by":"crossref","unstructured":"Wysmulski, P. (2024). Analysis of the Effect of an Open Hole on the Buckling of a Compressed Composite Plate. Materials, 17.","DOI":"10.3390\/ma17051081"},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Wysmulski, P. (2023). Failure Mechanism of Tensile CFRP Composite Plates with Variable Hole Diameter. Materials, 16.","DOI":"10.3390\/ma16134714"},{"key":"ref_95","first-page":"2","article-title":"Prediction of Crack Path in Concrete-like Composite using Extended Finite Element Method","volume":"19","author":"Gontarz","year":"2025","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_96","doi-asserted-by":"crossref","unstructured":"Falkowicz, K. (2022). Numerical Investigations of Perforated CFRPZ-Cross-Section Profiles, under Axial Compression. Materials, 15.","DOI":"10.3390\/ma15196874"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"309","DOI":"10.12913\/22998624\/167451","article-title":"Validation of Extension-Bending and Extension-Twisting Coupled Laminates in Elastic Element","volume":"17","author":"Falkowicz","year":"2023","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/S1365-1609(03)00013-3","article-title":"A Review of Techniques, Advances and Outstanding Issues in Numerical Modelling for Rock Mechanics and Rock Engineering","volume":"40","author":"Jing","year":"2003","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/S1365-1609(02)00065-5","article-title":"Numerical Methods in Rock Mechanics","volume":"39","author":"Jing","year":"2002","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.enganabound.2013.01.001","article-title":"3D Non-Linear Time Domain FEM\u2013BEM Approachto Soil\u2013Structure Interaction Problems","volume":"37","author":"Romero","year":"2013","journal-title":"Eng. Anal. Bound. Elem."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.enganabound.2020.04.008","article-title":"An Accurate Treatment of Non-Homogeneous Boundary Conditions for Development of the BEM","volume":"116","author":"Romero","year":"2020","journal-title":"Eng. Anal. Bound. Elem."},{"key":"ref_102","first-page":"108","article-title":"Experimental and Numerical Anisotropic Rock Mechanics","volume":"1","author":"Min","year":"2017","journal-title":"Rock Mech. Eng."},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/s004660050504","article-title":"Periodic BEM and FEM-BEM Coupling","volume":"25","author":"Clouteau","year":"2000","journal-title":"Comput. Mech."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1016\/j.apm.2021.04.002","article-title":"A Fast Boundary-Finite Element Approach for Estimating Anchor Losses in Micro-Electro-Mechanical System Resonators","volume":"97","author":"Aimi","year":"2021","journal-title":"Appl. Math. Model."},{"key":"ref_105","first-page":"235","article-title":"Boundary Element Analysis of the Pullout Behaviour of an Anchor Bolt Embedded in Concrete","volume":"1","author":"Saleh","year":"1996","journal-title":"Mech. Cohesive-Frict. Mater. Int. J. Exp. Model. Comput. Mater. Struct."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/S0013-7952(97)00051-3","article-title":"A New Approach to Numerical Method of Modelling Geological Processes and Rock Engineering Problems\u2014Continuum to Discontinuum and Linearity to Nonlinearity","volume":"49","author":"Tang","year":"1998","journal-title":"Eng. Geol."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.enggeo.2005.06.033","article-title":"Developments in the Characterization of Complex Rock Slope Deformation and Failure Using Numerical Modelling Techniques","volume":"83","author":"Stead","year":"2006","journal-title":"Eng. Geol."},{"key":"ref_108","unstructured":"Wei, X., Li, Z., and Zhao, G. (2024). A Review of Multiscale Numerical Modeling of Rock Mechanics and Rock Engineering. Deep Undergr. Sci. Eng., dug2.12127."},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"4957","DOI":"10.1007\/s00603-016-1030-0","article-title":"Numerical Simulation of Heterogeneous Rock Using Discrete Element Model Based on Digital Image Processing","volume":"49","author":"Tan","year":"2016","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"5137","DOI":"10.1007\/s00603-019-01851-3","article-title":"Investigating Hydraulic Fracturing Complexity in Naturally Fractured Rock Masses Using Fully Coupled Multiscale Numerical Modeling","volume":"52","author":"Zhang","year":"2019","journal-title":"Rock Mech. Rock Eng."},{"key":"ref_111","doi-asserted-by":"crossref","unstructured":"Szabelski, J., Karpi\u0144ski, R., and Machrowska, A. (2022). Application of an Artificial Neural Network in the Modelling of Heat Curing Effects on the Strength of Adhesive Joints at Elevated Temperature with Imprecise Adhesive Mix Ratios. Materials, 15.","DOI":"10.3390\/ma15030721"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"276","DOI":"10.2478\/sgem-2019-0052","article-title":"Testing the Rocks Loosening Process by Undercutting Anchors","volume":"42","author":"Siegmund","year":"2020","journal-title":"Stud. Geotech. Mech."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"261","DOI":"10.12913\/22998624\/154894","article-title":"The Effect of Undercut Anchor Diameter on the Rock Failure Cone Area in Pullout Tests","volume":"16","author":"Jonak","year":"2022","journal-title":"Adv. Sci. Technol. Res. J."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"130011","DOI":"10.1063\/1.5019141","article-title":"Comparison of Crack Propagation Analyses in a Pull-out Test","volume":"Volume 1922","author":"Gontarz","year":"2018","journal-title":"AIP Conference Proceedings"},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1007\/s40544-021-0535-z","article-title":"Tuning of Frictional Properties in Torsional Contact by Means of Disk Grading","volume":"10","author":"Costagliola","year":"2022","journal-title":"Friction"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.jmbbm.2016.04.034","article-title":"Research on Torsional Friction Behavior and Fluid Load Support of PVA\/HA Composite Hydrogel","volume":"62","author":"Chen","year":"2016","journal-title":"J. Mech. Behav. Biomed. Mater."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/18\/17\/4136\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T06:17:43Z","timestamp":1760509063000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/18\/17\/4136"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,3]]},"references-count":116,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["ma18174136"],"URL":"https:\/\/doi.org\/10.3390\/ma18174136","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,3]]}}}