Simulation of Land Subsidence Caused by Coal Mining at the Lupeni Mining Exploitation Using COMSOL Multiphysics
Abstract
1. Introduction
2. Materials and Methods
2.1. Barcelona Basic Model (BBM)
- -
- increment of volumetric plastic strain.
- -
- slope of the critical state line;
- -
- OCR—overconsolidation ratio;
- -
- initial void ratio.
2.2. Equations of the BBM
2.3. Equations of Associative Flow Rule
2.4. Closest Point Projection of the Constitutive Relation
3. Results and Discussion
3.1. Model Definition
3.2. Results of the Simulation and Discussion
4. Conclusions
- Subsidence Mechanisms—Underground coal extraction at Lupeni significantly alters the geomechanical equilibrium of the rock mass, leading to deformation, settlement, cracking, and in some cases heaving of the ground surface. The extent of these effects depends on the depth of mining, hydrogeological conditions, and geomechanical characteristics of the soil and overlying strata.
- Model Performance—The MCC model provides reasonable predictions for saturated soils but fails to capture suction effects that are essential in unsaturated conditions. In contrast, the BBM, which explicitly incorporates suction as a constitutive parameter, offers a more realistic representation of the mechanical behavior of unsaturated soils and better explains the collapse settlement observed when wetting occurs.
- Simulation Outcomes—The numerical results confirm that groundwater level variation plays a critical role in soil deformation. While the MCC model suggests reduced settlement or even heave under rising water levels, the BBM reveals an increased settlement due to suction loss, aligning more closely with field observations and the literature.
- Practical Implications—The study highlights the importance of using advanced constitutive models, such as BBM, for predicting the behavior of partially saturated soils in mining areas. These models are essential for assessing risks to infrastructure, land stability, and post-mining land use in the Jiu Valley region.
- Future Work—Further research should integrate long-term monitoring data with numerical simulations to refine model calibration, extend the analysis to deeper and more complex geological conditions, and evaluate mitigation strategies such as controlled flooding, backfilling, or reinforcement of surface infrastructure.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
- Mittelstädt, P.; Pollmann, N.; Karimzadeh, L.; Kories, H.; Klinger, C. Wastes in Underground Coal Mines and Their Behavior during Mine Water Level Rebound—A Review. Minerals 2023, 13, 1496. [Google Scholar] [CrossRef]
- Guo, W.; Guo, M.; Tan, Y.; Bai, E.; Zhao, G. Sustainable Development of Resources and the Environment: Mining-Induced Eco-Geological Environmental Damage and Mitigation Measures—A Case Study in the Henan Coal Mining Area, China. Sustainability 2019, 11, 4366. [Google Scholar] [CrossRef]
- Matei, O.-R.; Silaghi, L.D.; Dunca, E.-C.; Bungau, S.G.; Tit, D.M.; Mosteanu, D.-E.; Hodis, R. Study of Chemical Pollutants and Ecological Reconstruction Methods in the Tismana I Quarry, Rovinari Basin, Romania. Sustainability 2022, 14, 7160. [Google Scholar] [CrossRef]
- Radu, V.M.; Vîjdea, A.M.; Ivanov, A.A.; Alexe, V.E.; Dincă, G.; Cetean, V.M.; Filiuță, A.E. Research on the Closure and Remediation Processes of Mining Areas in Romania and Approaches to the Strategy for Heavy Metal Pollution Remediation. Sustainability 2023, 15, 15293. [Google Scholar] [CrossRef]
- Mojses, M.; Petrovič, F.; Bugár, G. Evaluation of Land-Use Changes as a Result of Underground Coal Mining—A Case Study on the Upper Nitra Basin, West Slovakia. Water 2022, 14, 989. [Google Scholar] [CrossRef]
- Ren, J.; Kang, X.; Tang, M.; Gao, L.; Hu, J.; Zhou, C. Coal Mining Surface Damage Characteristics and Restoration Technology. Sustainability 2022, 14, 9745. [Google Scholar] [CrossRef]
- Yu, X.Y.; Li, B.B.; Li, R.B. Analysis of mining damage in huge thick collapsible loess of western China. J. China Univ. Min. Technol. 2008, 37, 43. [Google Scholar]
- Jain, R.K.; Cui, Z.; Domen, J.K. Environmental Impact of Mining and Mineral Processing: Management, Monitoring, and Auditing Strategies; Butterworth-Heinemann: Oxford, UK, 2015; Available online: https://www.sciencedirect.com/book/9780128040409/environmental-impact-of-mining-and-mineral-processing?via=ihub= (accessed on 12 August 2025).
- Pena, J.C.d.C.; Goulart, F.; Fernandes, G.W.; Hoffmann, D.; Leite, F.S.F.; Santos, N.B.D.; Soares-Filho, B.; Sobral-Souza, T.; Vancine, M.H.; Rodrigues, M. Impacts of Mining Activities on the Potential Geographic Distribution of Eastern Brazil Mountaintop Endemic Species. Perspect. Ecol. Conserv. 2017, 15, 172–178. [Google Scholar] [CrossRef]
- Bakr, J.; Kompała-Bąba, A.; Bierza, W.; Chmura, D.; Hutniczak, A.; Kasztowski, J.; Jendrzejek, B.; Zarychta, A.; Woźniak, G. Borrow Pit Disposal of Coal Mining Byproducts Improves Soil Physicochemical Properties and Vegetation Succession. Agronomy 2024, 14, 1638. [Google Scholar] [CrossRef]
- Xu, Z.; Zhang, Y.; Yang, J.; Liu, F.; Bi, R.; Zhu, H.; Lv, C.; Yu, J. Effect of Underground Coal Mining on the Regional Soil Organic Carbon Pool in Farmland in a Mining Subsidence Area. Sustainability 2019, 11, 4961. [Google Scholar] [CrossRef]
- Mohsin, M.; Zhu, Q.; Naseem, S.; Sarfraz, M.; Ivascu, L. Mining Industry Impact on Environmental Sustainability, Economic Growth, Social Interaction, and Public Health: An Application of Semi-Quantitative Mathematical Approach. Processes 2021, 9, 972. [Google Scholar] [CrossRef]
- Galloway, D.L.; Erkens, G.; Kuniansky, E.L.; Rowland, J.C. Preface: Land subsidence processes. Hydrogeol. J. 2016, 24, 547–550. [Google Scholar] [CrossRef]
- Galloway, D.L.; Bawden, G.W.; Leake, S.A.; Honegger, D.G. Land Subsidence Hazards. In USGS Science for a Changing World; USGS: Reston, VA, USA, 2008. [Google Scholar]
- Aroca-Fernández, M.J.; Bravo-Fernández, J.A.; García-Viñas, J.I.; Serrada, R. Soil Compaction and Productivity Evolution in a Harvested and Grazed Mediterranean Scots Pine (Pinus sylvestris L.) Forest. Forests 2024, 15, 451. [Google Scholar] [CrossRef]
- Yang, P.; Dong, W.; Heinen, M.; Qin, W.; Oenema, O. Soil Compaction Prevention, Amelioration and Alleviation Measures Are Effective in Mechanized and Smallholder Agriculture: A Meta-Analysis. Land 2022, 11, 645. [Google Scholar] [CrossRef]
- Bussell, J.; Crotty, F.; Stoate, C. Comparison of Compaction Alleviation Methods on Soil Health and Greenhouse Gas Emissions. Land 2021, 10, 1397. [Google Scholar] [CrossRef]
- Guzy, A.; Malinowska, A.A. Assessment of the Impact of the Spatial Extent of Land Subsidence and Aquifer System Drainage Induced by Underground Mining. Sustainability 2020, 12, 7871. [Google Scholar] [CrossRef]
- Dacian-Paul, M.; Ilie, O. Land Surface Subsidence Under the Influence of the Underground Mining of the Ocnele Mari Rock Salt Deposit. In Annals of the University of Petrosani, Mining Engineering; Universitas Publishing House: Petroşani, Romania, 2021; pp. 41–52. [Google Scholar]
- Orellana, F.; Hormazábal, J.; Montalva, G.; Moreno, M. Measuring Coastal Subsidence after Recent Earthquakes in Chile Central Using SAR Interferometry and GNSS Data. Remote Sens. 2022, 14, 1611. [Google Scholar] [CrossRef]
- Sun, Z.; Zhao, L.; Hu, G.; Zhou, H.; Liu, S.; Qiao, Y.; Du, E.; Zou, D.; Xie, C. Effects of Ground Subsidence on Permafrost Simulation Related to Climate Warming. Atmosphere 2024, 15, 12. [Google Scholar] [CrossRef]
- Al-Hashim, M.H.; Al-Aidaros, A.; Zaidi, F.K. Geological and Hydrochemical Processes Driving Karst Development in Southeastern Riyadh, Central Saudi Arabia. Water 2024, 16, 1937. [Google Scholar] [CrossRef]
- Chen, C.N.; Tfwala, S.S. Impacts of Climate Change and Land Subsidence on Inundation Risk. Water 2018, 10, 157. [Google Scholar] [CrossRef]
- Xing, Y.F.; Tian, X.W.; Xing, Z.X. The Relationship between Land Subsidence and Groundwater in Cangzhou. Electron. J. Geotech. Eng. 2016, 21, 1803–1813. [Google Scholar]
- Li, H.; Zhu, L.; Guo, G.; Zhang, Y.; Dai, Z.; Li, X.; Chang, L.; Teatini, P. Land subsidence due to groundwater pumping: Hazard probability assessment through the combination of Bayesian model and fuzzy set theory. Nat. Hazards Earth Syst. Sci. 2021, 21, 823–835. [Google Scholar] [CrossRef]
- Chalá, D.C.; Quiñones-Bolaños, E.; Mehrvar, M. Land Subsidence Due to Groundwater Exploitation in Unconfined Aquifers: Experimental and Numerical Assessment with Computational Fluid Dynamics. Water 2024, 16, 467. [Google Scholar] [CrossRef]
- Collados-Lara, A.-J.; Pulido-Velazquez, D.; Mateos, R.M.; Ezquerro, P. Potential Impacts of Future Climate Change Scenarios on Ground Subsidence. Water 2020, 12, 219. [Google Scholar] [CrossRef]
- Yu, Y.; Chen, S.-E.; Deng, K.-Z.; Wang, P.; Fan, H.-D. Subsidence Mechanism and Stability Assessment Methods for Partial Extraction Mines for Sustainable Development of Mining Cities—A Review. Sustainability 2018, 10, 113. [Google Scholar] [CrossRef]
- Liu, J.; Wang, H.; Yan, X. Risk evaluation of land subsidence and its application to metro safety operation in Shanghai. Proc. Int. Assoc. Hydrol. Sci. 2015, 372, 543–553. [Google Scholar] [CrossRef]
- Blachowski, J.; Kopeć, A.; Milczarek, W.; Owczarz, K. Evolution of Secondary Deformations Captured by Satellite Radar Interferometry: Case Study of an Abandoned Coal Basin in SW Poland. Sustainability 2019, 11, 884. [Google Scholar] [CrossRef]
- Zhou, S.; Wang, H.; Shan, C.; Liu, H.; Li, Y.; Li, G.; Yang, F.; Kang, H.; Xie, G. Dynamic Monitoring and Analysis of Mining Land Subsidence in Multiple Coal Seams in the Ehuobulake Coal Mine Based on FLAC3D and SBAS-InSAR Technology. Appl. Sci. 2023, 13, 8804. [Google Scholar] [CrossRef]
- Zheng, L.; Zhu, L.; Wang, W.; Guo, L.; Chen, B. Land Subsidence Related to Coal Mining in China Revealed by L-Band InSAR Analysis. Int. J. Environ. Res. Public Health 2020, 17, 1170. [Google Scholar] [CrossRef]
- Liu, J.; Ma, F.; Li, G.; Guo, J.; Wan, Y.; Song, Y. Evolution Assessment of Mining Subsidence Characteristics Using SBAS and PS Interferometry in Sanshandao Gold Mine, China. Remote Sens. 2022, 14, 290. [Google Scholar] [CrossRef]
- Tatiya, R.R. Surface and Underground Excavations, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2013; ISBN 978-0-415-62119-9. Available online: https://minemountain.in/assets/uploads/attachment_36061686899462.pdf (accessed on 15 August 2025).
- Liu, H.; He, C.; Deng, K.; Bian, Z.; Fan, H.; Lei, S.; Zhang, A. An analysis of forming mechanism of collapsing ground fissure caused by mining. J. Min. Saf. Eng. 2013, 30, 380. [Google Scholar]
- Whittaker, B.N.; Reddish, D.J. Subsidence: Occurrence, Prediction, and Control; Elsevier: Amsterdam, The Netherlands, 1989; Available online: https://books.google.ro/books?hl=ro&lr=&id=J9B-iaMoUNwC&oi=fnd&pg=PP1&ots=ICZ5IqS8cQ&sig=nOOFbkrqKnHKF0-blC0vLrFPSfI&redir_esc=y#v=onepage&q&f=false (accessed on 12 August 2025).
- Gligor, V.; Nicula, E.-A.; Crețan, R. The Identification, Spatial Distribution, and Reconstruction Mode of Abandoned Mining Areas. Land 2024, 13, 1107. [Google Scholar] [CrossRef]
- Ma, K.; Zhang, Y.; Ruan, M.; Guo, J.; Chai, T. Land Subsidence in a Coal Mining Area Reduced Soil Fertility and Led to Soil Degradation in Arid and Semi-Arid Regions. Int. J. Environ. Res. Public Health 2019, 16, 3929. [Google Scholar] [CrossRef] [PubMed]
- Abdallah, M.; Verdel, T. Behavior of a masonry wall subjected to mining subsidence, as analyzed by experimental designs and response surfaces. Int. J. Rock Mech. Min. 2017, 100, 199–206. [Google Scholar] [CrossRef]
- Kapusta, A.; Szojda, L. The role of expansion joints for traditional buildings affected by the curvature of the mining area. Eng. Fail. Anal. 2021, 128, 105598. [Google Scholar] [CrossRef]
- Tajduś, K.; Sroka, A.; Misa, R.; Hager, S.; Rusek, J.; Dudek, M.; Wollnik, F. Analysis of Mining-Induced Delayed Surface Subsidence. Minerals 2021, 11, 1187. [Google Scholar] [CrossRef]
- Kratzsch, I.H. Mining subsidence engineering. Environ. Geol. 1986, 8, 133–136. [Google Scholar] [CrossRef]
- Wu, K.; Hu, Z.Q.; Chang, J.; Ge, J.X. Distribution law of ground crack induced by coal mining. J. China Univ. Min. Technol. 1997, 26, 56–59. [Google Scholar]
- Hu, Q.; Cui, X.; Yuan, D.; Deng, X. Development law of surface cracks caused by thick seam mining and its formation mechanism and hazard analysis. J. Min. Saf. Eng. 2012, 29, 864. [Google Scholar]
- Marian, D.P.; Onica, I. Analysis of the Geomechanical Phenomena that Led to the Appearance of Sinkholes at the Lupeni Mine, Romania, in the Conditions of Thick Coal Seams Mining with Longwall Top Coal Caving. Sustainability 2021, 13, 6449. [Google Scholar] [CrossRef]
- Cieślik, K.; Milczarek, W.; Warchala, E.; Kosydor, P.; Rożek, R. Identifying Factors Influencing Surface Deformations from Underground Mining Using SAR Data, Machine Learning, and the SHAP Method. Remote Sens. 2024, 16, 2428. [Google Scholar] [CrossRef]
- Huang, X.; Li, X.; Li, H.; Duan, S.; Yang, Y.; Du, H.; Xiao, W. Study on the Movement of Overlying Rock Strata and Surface Movement in Mine Goaf under Different Treatment Methods Based on PS-InSAR Technology. Appl. Sci. 2024, 14, 2651. [Google Scholar] [CrossRef]
- Guo, Y.; Luo, L.; Ma, R.; Li, S.; Zhang, W.; Wang, C. Study on Surface Deformation and Movement Caused by Deep Continuous Mining of Steeply Inclined Ore Bodies. Sustainability 2023, 15, 11815. [Google Scholar] [CrossRef]
- Guo, Y.; Luo, L.; Wang, C. Research on Fault Activation and Its Influencing Factors on the Barrier Effect of Rock Mass Movement Induced by Mining. Appl. Sci. 2023, 13, 651. [Google Scholar] [CrossRef]
- Fodor, D. Influenţa Industriei Miniere Asupra Mediului, Buletinul AGIR Nr. 3/2006 Iulie-Septembrie. 2006. Available online: https://www.agir.ro/buletine/199.pdf (accessed on 12 August 2025).
- Ilie, O. Contribuţii la Modelarea şi Analiza Stabilităţii Terenurilor Aflate Sub Influenţa Excavaţiilor Miniere Subterane şi Perfecţionarea Sistemelor de Exploatare a Zăcămintelor de Substante Minerale Utile, Teză de Abilitare. 2016. Available online: https://www.upet.ro/doctorat/abilitare/Onica%20Ilie/Teza%20abilitare%20Onica%20Ilie.pdf (accessed on 9 July 2025).
- Savulescu, M.C.; Tataru, A.C.; Stanci, A.; Tataru, D. Risk factors that may occur in the process of closing and greening the Lupeni Mining Exploitation. MATEC Web Conf. 2021, 342, 01017. [Google Scholar] [CrossRef]
- Marian, D.P.; Onica, I.; Marian, R.-R.; Floarea, D.-A. Finite Element Analysis of the State of Stresses on the Structures of Buildings Influenced by Underground Mining of Hard Coal Seams in the Jiu Valley Basin (Romania). Sustainability 2020, 12, 1598. [Google Scholar] [CrossRef]
- Popescu, F.D. Ways of controlling transport capacity variation of belt conveyors. In Proceedings of the 9th WSEAS International Conference Automation and Information (ICAI’08), Bucharest, Romania, 24–26 June 2008; pp. 120–123. [Google Scholar]
- Rezmerița, E.; Radu, S.M.; Călămar, A.-N.; Lorinț, C.; Florea, A.; Nicola, A. Urban Air Quality Monitoring in Decarbonization Context; Case Study—Traditional Coal Mining Area, Petroșani, Romania. Sustainability 2022, 14, 8165. [Google Scholar] [CrossRef]
- Smoliński, A.; Malashkevych, D.; Petlovanyi, M.; Rysbekov, K.; Lozynskyi, V.; Sai, K. Research into Impact of Leaving Waste Rocks in the Mined-Out Space on the Geomechanical State of the Rock Mass Surrounding the Longwall Face. Energies 2022, 15, 9522. [Google Scholar] [CrossRef]
- Țoc, S.; Alexandrescu, F.M. Post-Coal Fantasies: An Actor-Network Theory-Inspired Critique of Post-Coal Development Strategies in the Jiu Valley, Romania. Land 2022, 11, 1022. [Google Scholar] [CrossRef]
- Gâf-Deac, I.I.; Jaradat, M.; Bran, F.; Crețu, R.F.; Moise, D.; Gombos, S.P.; Breaz, T.O. Similarities and Proximity Symmetries for Decisions of Complex Valuation of Mining Resources in Anthropically Affected Areas. Sustainability 2022, 14, 10012. [Google Scholar] [CrossRef]
- Liliana, R. Cercetări Privind Impactul Închiderii Minelor din Valea Jiului Asupra Mediului Înconjurător. Ph.D. Thesis, Petrosani University, Petroșani, Romania, 2022. Available online: https://www.upet.ro/doctorat/resource/doc/sustineri/2022%2010%2024%20Roman/Rezumat%20tez%C4%83%20%20Roman%20Liliana%20RO.pdf (accessed on 12 August 2025).
- Costache, A. Vulnerabilitatea Așezărilor Umane și Riscurile Sociale din Depresiunea Petroșani; Editura Transversal: Târgoviște, Romania, 2020; ISBN 978-606-605-205-4. Available online: https://www.limnology.ro/Ro/Imag/Costache%20Andra%20Depresiunea%20Petrosani%20vulnerabilitatea%20asezarilor%20umane.pdf (accessed on 1 August 2025).
- Chwastek, J. Mine Surveying and Protection of Mining Areas; Politechnika Wroclawska: Wrocław, Poland, 1980; pp. 87–102, ISBN 83-7085-021-7. [Google Scholar]
- Chudek, M. Geomechanics with Elements of Mining Environment and Ground Surface Protection; Wydawnictwo Politechniki: Śląskiej, Gliwice, 2002. [Google Scholar]
- Blachowski, J.; Jiránková, E.; Lazecký, M.; Kadlečík, P.; Milczarek, W. Application of Satellite Radar Interferometry (PSInSAR) in Analysis of Secondary Surface Deformations in Mining Areas. Case Studies from Czech Republic and Poland. Acta Geodyn. Geomater. 2018, 15, 173–185. [Google Scholar] [CrossRef]
- Fenk, J. Analytical solution describing upward movement of the surface during liquidation of underground mines through flooding. Przegląd Górniczy (Min. Rev.) 2000, 11, 12–14. [Google Scholar]
- Mathey, M. Addressing the Challenges Involved with Abandoned Underground Coal Mines in South Africa. In Proceedings of the 13th ISM Congress, Aachen, Germany, 20 July 2013; pp. 113–123. [Google Scholar]
- Samsonov, S.; d’Oreye, N.; Smets, B. Ground deformation associated with post-mining activity at the French–German border revealed by novel InSAR time series method. Int. J. Appl. Earth Obs. Geoinf. 2013, 23, 142–154. [Google Scholar] [CrossRef]
- Vent, I.; Roest, H. Lagging Mining Damage in the Netherlands? Recent Signs of Soil Movement in the Zuid-Limburg Coal District. In Proceedings of the 13th ISM Congress, Aachen, Germany, 20 July 2013; pp. 27–41. [Google Scholar]
- Milczarek, W.; Blachowski, J.; Grzempowski, P. Application of PSInSAR for Assessment of Surface Deformations in Post-Mining Area—Case Study of the Former Walbrzych Hard Coal Basin (SW Poland). Acta Geodyn. Geomater. 2017, 14, 41–52. [Google Scholar]
- Roman, L. Considerations Regarding the Closure of the Mines in Valea Jiului. Min. Rev. 2021, 27, 57–71. [Google Scholar] [CrossRef]
- Belkin, H.E.; Tewalt, S.J.; Hower, J.C.; Stucker, J.D.; O’Keefe, J.M.K.; Tatu, C.A.; Buia, G. Petrography and geochemistry of Oligocene bituminous coal from the Jiu Valley, Petroşani basin (southern Carpathian Mountains), Romania. Int. J. Coal Geol. 2010, 82, 68–80. [Google Scholar] [CrossRef]
- Szabo, R.; Popescu, G.C.; Dumitraş, D.G.; Ghinescu, E. New Occurrences of Sulfate Minerals in Jiul de Vest Upper Basin, South Carpathians, Romania. Carpathian J. Earth Environ. Sci. 2020, 15, 347–358. [Google Scholar] [CrossRef]
- Archundia, D.; Prado-Pano, B.; González-Méndez, B.; Loredo-Portales, R.; Molina-Freaner, F. Water resources affected by potentially toxic elements in an area under current and historical mining in northwestern Mexico. Environ. Monit. Assess. 2021, 193, 236. [Google Scholar] [CrossRef]
- Kopeć, A.; Trybała, P.; Głąbicki, D.; Buczyńska, A.; Owczarz, K.; Bugajska, N.; Kozińska, P.; Chojwa, M.; Gattner, A. Application of Remote Sensing, GIS and Machine Learning with Geographically Weighted Regression in Assessing the Impact of Hard Coal Mining on the Natural Environment. Sustainability 2020, 12, 9338. [Google Scholar] [CrossRef]
- Bakhtavar, E.; Mahmoudi, H. Development of a scenario-based robust model for the optimal truck-shovel allocation in open-pit mining. Comput. Oper. Res. 2020, 115, 104539. [Google Scholar] [CrossRef]
- Lei, M.; Zhang, T.; Shi, J.; Yu, J. InSAR-CTPIM-Based 3D Deformation Prediction in Coal Mining Areas of the Baisha Reservoir, China. Appl. Sci. 2024, 14, 5199. [Google Scholar] [CrossRef]
- Ji, Z.; Yi, H.; Li, G.; Liu, B.; Wu, Z. Numerical Implementation of the Barcelona Basic Model Based on Return-Mapping Integration. Appl. Sci. 2022, 12, 11933. [Google Scholar] [CrossRef]
- Siemens, G.; Blatz, J.A. Evaluation of the influence of boundary confinement on the behaviour of unsaturated swelling clay soils. Can. Geotech. J. 2009, 46, 339–356. [Google Scholar] [CrossRef]
- Fattah, M.; Salim, N.; Irshayyid, E. Swelling behavior of unsaturated expansive soil. Transp. Infrastruct. Geotechnol. 2021, 8, 37–58. [Google Scholar] [CrossRef]
- Wang, W.; Kosakowski, G.; Kolditz, O. A parallel finite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media. Comput. Geosci. 2009, 35, 1631–1641. [Google Scholar] [CrossRef]
- Popescu, F.D.; Andras, A.; Radu, S.M.; Brinas, I.; Iladie, C.-M. Numerical Investigation of the Slope Stability in the Waste Dumps of Romanian Lignite Open-Pit Mines Using the Shear Strength Reduction Method. Appl. Sci. 2024, 14, 9875. [Google Scholar] [CrossRef]
- Popescu, F.D.; Radu, S.M.; Andras, A.; Brinas, I.; Marita, M.-O.; Radu, M.A.; Brinas, C.L. Stability Assessment of the Dam of a Tailings Pond Using Computer Modeling—Case Study: Coroiești, Romania. Appl. Sci. 2024, 14, 268. [Google Scholar] [CrossRef]
- Alonso, E.E.; Gens, A.; Josa, A. A constitutive model for partially saturated soils. Géotechnique 1990, 40, 405–430. [Google Scholar] [CrossRef]
- Available online: https://www.finesoftware.eu/help/geo5/en/modified-cam-clay-model-mcc-01/ (accessed on 12 August 2025).
- Wang, L.J.; Liu, S.H.; Fu, Z.Z.; Li, Z. Coupled hydro-mechanical analysis of slope under rainfall using modified elasto-plastic model for unsaturated soils. J. Cent. South Univ. 2015, 22, 1892–1900. [Google Scholar] [CrossRef]
- Gennaro, D.V.; Pereira, J.M. A viscoplastic constitutive model for unsaturated geomaterials. Comput. Geotech. 2013, 54, 143–151. [Google Scholar] [CrossRef]
- Wheeler, S.J.; Gallipoli, D.; Karstunen, M. Comments on use of the Barcelona Basic Model for unsaturated soils. Int. J. Numer. Anal. Methods Geomech. 2002, 26, 1561–1571. [Google Scholar] [CrossRef]
- Gens, A. Constitutive Laws. In Modern Issues in Non-Saturated Soils; Gens, A., Jouanna, P., Schrefler, B.A., Eds.; Springer: Vienna, Austria, 1995; pp. 129–158. Available online: https://link.springer.com/chapter/10.1007/978-3-7091-2692-9_2 (accessed on 15 August 2025).
- Li, G.; Zhou, J. COMSOL-Based Simulation of Microwave Heating of Al2O3/SiC Composites with Parameter Variations. Symmetry 2024, 16, 1254. [Google Scholar] [CrossRef]
Name | Expression | Value | Description |
---|---|---|---|
para | 0 | 0 | Parameter |
rhos | 1800 [kg/m3] | 1800 kg/m3 | Soil density |
rhow | 1000 [kg/ m3] | 1000 kg/m3 | Water density |
gammaw | rhow*g_const | 9806.7 N/m3 | Unit weight of water |
muw | 1 × 10−3 [Pa*s] | 0.001 Pa·s | Water dynamic viscosity |
Nu | 0.2 | 0.2 | Poisson’s ratio |
lambda | 0.21 | 0.21 | Compression index |
lambda_s | 0.125 | 0.125 | Compression index for changes in suction |
kappa | 0.006 | 0.006 | Swelling index |
kappa_s | 0.008 | 0.008 | Swelling index for changes in suction |
Mb | 1.26 | 1.26 | Slope of critical state line |
wb | 0.4 | 0.4 | Weight parameter |
mb | 55 [kPa] | 55,000 kPa | Soil stiffness parameter |
bb | 11 | 11 | Plastic potential parameter |
sy | 110 [kPa] | 110,000 Pa | Initial yield value for suction |
kb | 0.65 | 0.65 | Tension to suction ratio |
pref | 19 [kPa] | 19,000 Pa | Reference pressure |
pc0 | 85 [kPa] | 85,000 Pa | Initial consolidation pressure |
phi0 | 0.631 | 0.631 | Initial porosity |
e0 | phi0/(1−phi0) | 1.71 | Initial void ratio |
K_sat | 1 [m/day] | 1.1574 × 10−5 m/s | Saturated hydraulic conductivity |
alpha | 2 [1/m] | 21/m | Fitting parameter |
S_res | 0.24 | 0.24 | Residual degree of saturation |
S_sat | 1 | 1 | Degree of saturation at full saturation |
Name | Expression | Unit | Description |
---|---|---|---|
Suction | −p*(dl.Hp < 0) | Pa | Current suction |
PorePressure | p*(dl.Hp ≥ 0) | Pa | Pore Pressure |
k_rel | Se | Relative permeability | |
k | K_sat*muw/gammaw | m3 | Soil permeability |
Cm | phi0*(S_sat-S_res)*Se*alpha | 1/m | Specific moisture capacity |
Se | exp (alpha*dl.Hp)*(dl.Hp < 0) + 1*(dl.Hp ≥ 0) | Effective saturation |
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Tataru, A.C.; Tataru, D.; Popescu, F.D.; Andras, A.; Brinas, I. Simulation of Land Subsidence Caused by Coal Mining at the Lupeni Mining Exploitation Using COMSOL Multiphysics. Appl. Sci. 2025, 15, 10651. https://doi.org/10.3390/app151910651
Tataru AC, Tataru D, Popescu FD, Andras A, Brinas I. Simulation of Land Subsidence Caused by Coal Mining at the Lupeni Mining Exploitation Using COMSOL Multiphysics. Applied Sciences. 2025; 15(19):10651. https://doi.org/10.3390/app151910651
Chicago/Turabian StyleTataru, Andreea Cristina, Dorin Tataru, Florin Dumitru Popescu, Andrei Andras, and Ildiko Brinas. 2025. "Simulation of Land Subsidence Caused by Coal Mining at the Lupeni Mining Exploitation Using COMSOL Multiphysics" Applied Sciences 15, no. 19: 10651. https://doi.org/10.3390/app151910651
APA StyleTataru, A. C., Tataru, D., Popescu, F. D., Andras, A., & Brinas, I. (2025). Simulation of Land Subsidence Caused by Coal Mining at the Lupeni Mining Exploitation Using COMSOL Multiphysics. Applied Sciences, 15(19), 10651. https://doi.org/10.3390/app151910651