Progressive failure of water-filled karst cave of stratified tunnel using coupled discontinuous smoothed particle hydrodynamics method

Abstract

Tunnel construction in karst terrain is influenced by water-filled karst caves and stratigraphic layers, which involves failure characteristics of water-resistant structures and complex fluid-solid interaction (FSI) processes. To cope with this challenge, this paper used coupled discontinuous smoothed particle hydrodynamics (CDSPH) method for investigating water inrush of tunnels considering stratigraphic layers and karst cave positions. Hydraulic fracturing test and sliding-induced impulsive wave test were carried out to verify the accuracy of the CDSPH method. Moreover, a comprehensive analysis of inrush events in the field-scale Qiyeshan (QYS) karst tunnel was conducted, considering different layer dip angles and cave positions on the evolution characteristics of inrush disasters, with quantitative parameters proposed for predicting water/mud inrush from local to overall disaster. The simulation results indicate that CDSPH karst model has been verified to faithfully capture the progressive failure of water-resistant structure during inrush in stratigraphic layers. Water/mud inrush in QYS tunnels can be divided into four stages based on vertical/horizontal stress characteristics, encompassing hydraulic fracturing of karst caves, local inrush, rock collapse, and overall inrush. The dip angle of the bedding planes affects the hydraulic failure characteristics of karst caves. When the cave is located at the top of the tunnel, the water-resistant structures with a dip angle (θ) of 45° poses the highest risk, while θ = 0° provides the most stability. Furthermore, the decrease in water pressure and the occurrence of the maximum flow velocity within the cave can serve as vital indexes to predict the transition from local inrush to overall inrush disaster. These findings emphasize the importance of the CDSPH tunnel model considering stratigraphic layers and karst cave positions when predicting water/mud inrush, and provide guidance for the prevention of inrush flow in karst tunnels.

Keywords

Coupled discontinuous smoothed particle hydrodynamics / Stratigraphic layers / Rock tunnel / Water inrush / Karst cave

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CRediT authorship contribution statement

Chengzhi Xia: Writing - review & editing, Software, Validation, Formal analysis, Writing - original draft, Data curation, Methodology, Visualization. Zhenming Shi: Project administration, Writing - review & editing, Supervision, Writing - original draft. Liu Liu: Writing - review & editing, Supervision, Writing - original draft, Resources, Investigation. Guangyin Lu: Writing - review & editing, Supervision, Funding acquisition, Project administration. Lin Zhou: Writing - review & editing, Formal analysis, Methodology. Chuanyi Tao: Writing - review & editing, Investigation, Software. Shaoqiang Meng: Software, Writing - review & editing, Data curation, Writing - original draft, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this study.

Acknowledgement

This research was supported by the National Natural Science Foundation for Doctoral Scholars (Grant No. 424B2055) and National Key Research and Development Program of China (Grant No. 2023YFC3008300), the National Natural Science Foundation of China (Grant Nos. 42172296 and 41974148), and the International Exchange Program for Graduate Students of Tongji University. We extend our gratitude to Professor Bo Li from Tongji University for his support with the flume experiments.

References

[1] An, H. M., Song, Y. S., & Liu, H. Y. (2021). FDEM modelling of rock fracture process during three-point bending test under quasistatic and dynamic loading conditions. Shock and Vibration, 2021 (1), 5566992.

[2] Bi, J., & Zhou, X. P. (2015). Numerical simulation of zonal disintegration of the surrounding rock masses around a deep circular tunnel under dynamic unloading. International Journal of Computational Methods, 12 (3), 150020.

[3] Bi, J., & Zhou, X. P. (2017). A novel numerical algorithm for simulation of initiation, propagation and coalescence of flaws subject to internal fluid pressure and vertical stress in the framework of general particle dynamics. Rock Mechanics and Rock Engineering, 50 (7), 1833-1849.

[4] Bui, H. H., Fukagawa, R., Sako, K., & Wells, J. C. (2009). Numerical simulation of granular materials based on smoothed particle hydrodynamics (SPH). AIP Conf. Proc., 1145 (1), 575-578.

[5] Bui, H. H., Sako, K., Fukagawa, R., & Wells, J. C. (2008). SPH-based numerical simulations for large deformation of geomaterial considering soil-structure interaction. In Proceedings of the 12th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) (pp. 570-578).

[6] Chakraborty, S., Islam, M. R. I., Shaw, A., Ramachandra, L. S., & Reid, S. R. (2017). A computational framework for modelling impact induced damage in ceramic and ceramic-metal composite structures. Composite Structures, 164, 263-276.

[7] Cui, W., Tang, Q. W., & Song, H. F. (2020). Washout resistance evaluation of fast-setting cement-based grouts considering time-varying viscosity using CFD simulation. Construction and Building Materials, 242, 117959.

[8] Douillet-Grellier, T., Pramanik, R., Pan, K., Albaiz, A., Jones, B., Pourpak, H., & Williams, J. (2016). Mesh-Free Numerical Simulation of Pressure-Driven Fractures in Brittle Rocks. Texas, USA: The Woodlands.

[9] Fang, L. F., Cao, C. M., Li, Q., Qin, K., Sun, X. D., & Ge, J. (2022). Fracture analysis of compacted clay soil beams with offset notches based on three-point bending test: Experimental characterization and numerical simulation. Advances in Civil Engineering, 2022 (1), 3699196.

[10] Gao, C. L., Li, L. P., Zhou, Z. Q., Li, Z. H., Cheng, S., Wang, L. G., & Zhang, D. S. (2021). Peridynamics simulation of water inrush channels evolution process due to rock mass progressive failure in karst tunnels. International Journal of Geomechanics, 21 (4), 04021028.

[11] Gao, J. Y., Peng, S. Y., Chen, G. Q., Mitani, Y., & Fan, H. Y. (2023). Coupled hydro-mechanical analysis for water inrush of fractured rock masses using the discontinuous deformation analysis. Computers and Geotechnics, 156, 105247.

[12] Gomez-Gesteira, M., Rogers, B. D., Crespo, A. J. C., Dalrymple, R. A., Narayanaswamy, M., & Dominguez, J. M. (2012). SPHysics - development of a free-surface fluid solver - Part 1: Theory and formulations. Computers & Geosciences, 48, 289-299.

[13] Gray, J. P., & Monaghan, J. J. (2004). Numerical modelling of stress fields and fracture around magma chambers. Journal of Volcanology and Geothermal Research, 135 (3), 259-283.

[14] Gray, J. P., Monaghan, J. J., & Swift, R. P. (2001). SPH elastic dynamics. Computer Methods in Applied Mechanics and Engineering, 190 (49), 6641-6662.

[15] Gui, Y., Bui, H. H., & Kodikara, J. (2015). An application of a cohesive fracture model combining compression, tension and shear in soft rocks. Computers and Geotechnics, 66, 142-157.

[16] Hoek, E., & Brown, E. T. (1997). Practical estimates of rock mass strength. International Journal of Rock Mechanics and Mining Sciences, 34 (8), 1165-1186.

[17] Jiang, H. M., Li, L., Rong, X. L., Wang, M. Y., Xia, Y. P., & Zhang, Z. C. (2017). Model test to investigate waterproof-resistant slab minimum safety thickness for water inrush geohazards. Tunnelling and Underground Space Technology, 62, 35-42.

[18] Jin, L., Zeng, Y., Cheng, T., & Li, J. (2021). Numerical simulation of mud inrush of tunnels with coupled LBM-DEM. Chinese Journal of Geotechnical Engineering, 43 (6), 1000-1009 (in Chinese).

[19] Lai, Y. B., Li, S., Guo, J. Q., Zhu, Z. G., & Huang, X. (2021). Analysis of seepage and displacement field evolutionary characteristics in water inrush disaster process of karst tunnel. Geofluids, 2021, 5560762.

[20] Li, H. Y., Xu, H. B., Li, Z. F., Li, H. W., Zhang, H. J., Zhang, Y. J., & Chang, T. (2018). Study on treatment of fault water gushing in deep roadway. Journal of Mining & Safety Engineering, 35 (3), 635-641 (in Chinese).

[21] Li, L. P., Sun, S. Q., Wang, J., Song, S. G., Fang, Z. D., & Zhang, M. G. (2020). Development of compound EPB shield model test system for studying the water inrushes in karst regions. Tunnelling and Underground Space Technology, 101, 103404.

[22] Li, S. C., Yuan, Y. C., Li, L. P., Ye, Z. H., & Lei, T. (2015). Water inrush mechanism and minimum safe thickness of rock wall of karst tunnel face under blast excavation. Chinese Journal of Geotechnical Engineering, 37 (2), 313-320 (in Chinese).

[23] Lian, Y. J., Bui, H. H., Nguyen, G. D., & Haque, A. (2023). An effective and stabilised ( u - p l ) SPH framework for large deformation and failure analysis of saturated porous media. Computer Methods in Applied Mechanics and Engineering, 408, 115967.

[24] Liang, D. X., Jiang, Z. Q., Zhu, S. Y., Sun, Q., & Qian, Z. W. (2016). Experimental research on water inrush in tunnel construction. Natural Hazards, 81 (1), 467-480.

[25] Lucy, L. B. (1977). A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 82, 1013-1024.

[26] Molteni, D., & Colagrossi, A. (2009). A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Computer Physics Communications, 180 (6), 861-872.

[27] Monaghan, J. J. (2000). SPH without a Tensile Instability. Journal of Computational Physics, 159 (2), 290-311.

[28] Monaghan, J. J. (2005). Smoothed particle hydrodynamics. Reports on Progress in Physics, 68 (8), 1703-1759.

[29] Mu, D. R., Wen, A. H., Zhu, D. Q., Tang, A. P., Nie, Z., & Wang, Z. Y. (2022). An improved smoothed particle hydrodynamics method for simulating crack propagation and coalescence in brittle fracture of rock materials. Theoretical and Applied Fracture Mechanics, 119, 103355.

[30] Peng, X. Y., Yu, P. C., Cheng, X., Chen, G. Q., Zhang, Y. B., Zhang, H., & Li, C. Z. (2022). Dynamic simulation of the water inrush process in tunnel construction using a three-dimensional coupled discontinuous deformation analysis and smoothed particle hydrodynamics method. Tunnelling and Underground Space Technology, 127, 104612.

[31] Qian, Q. H., & Lin, P. (2016). Safety risk management of underground engineering in China: Progress, challenges and strategies. Journal of Rock Mechanics and Geotechnical Engineering, 8 (4), 423-442.

[32] Shaw, A., Reid, S. R., Roy, D., & Chakraborty, S. (2015). Beyond classical dynamic structural plasticity using mesh-free modelling techniques. International Journal of Impact Engineering, 75, 268-278.

[33] Sheikh, B., Qiu, T., & Ahmadipur, A. (2021). Comparison of SPH boundary approaches in simulating frictional soil-structure interaction. Acta Geotechnica, 16 (8), 2389-2408.

[34] Shu, Q., Wang, X. B., Zhao, Y. F., & Bai, X. Y. (2020). Numerical simulation of failure processes of heterogeneous rock specimens under assumption of invariant spherical stress during stress drop. Rock and Soil Mechanics, 41 (10), 3465-3472 (in Chinese).

[35] Vacondio, R., Mignosa, P., & Pagani, S. (2013). 3D SPH numerical simulation of the wave generated by the Vajont rockslide. Advances in Water Resources, 59, 146-156.

[36] Wang, J., Zhang, Y., Qin, Z., Song, S. G., & Lin, P. (2020). Analysis method of water inrush for tunnels with damaged water-resisting rock mass based on finite element method-smooth particle hydrodynamics coupling. Computers and Geotechnics, 126, 103725.

[37] Wang, X. T., Li, S. C., Xu, Z. H., Hu, J., Pan, D. D., & Xue, Y. G. (2019). Risk assessment of water inrush in karst tunnels excavation based on normal cloud model. Bulletin of Engineering Geology and the Environment, 78 (5), 3783-3798.

[38] Williams, P. W. (2008). The role of the epikarst in karst and cave hydrogeology: A review. International Journal of Speleology, 37 (1), 1-10.

[39] Wu, J., Li, S. C., Xu, Z. H., & Zhao, J. (2019). Determination of required rock thickness to resist water and mud inrush from karst caves under earthquake action. Tunnelling and Underground Space Technology, 85, 43-55.

[40] Xia, C. Z., Shi, Z. M., & Li, B. (2024a). A modified SPH framework of for simulating progressive rock damage and water inrush disasters in tunnel constructions. Computers and Geotechnics, 167, 106042.

[41] Xia, C. Z., Shi, Z. M., & Li, B. (2024b). A revisit of disaster process of Vajont rockslide using a coupled discontinuous smooth particle hydrodynamics (CDSPH) method. Landslides, 21 (1), 197-216.

[42] Xia, C. Z., Shi, Z. M., Li, B., Zheng, H. C., & Liu, M. M. (2022). Verification and application of an improved smooth particle hydrodynamics method for a rock slope under seismic conditions. Earth Science, 47 (12), 4469-4483 (in Chinese).

[43] Xia, C. Z., Shi, Z. M., Liu, M. M., Li, B., Yu, S. B., & Xue, J. F. (2024c). Dynamic analysis of field-scale rockslides based on three-dimensional discontinuous smoothed particle hydrodynamics: A case study of Tangjiashan rockslide. Engineering Geology, 336, 107558.

[44] Xia, C. Z., Shi, Z. M., & Zheng, H. C. (2023). An improved smooth particle hydrodynamics method for modelling crack propagation in layered rock cells and slopes. Bulletin of Engineering Geology and the Environment, 82 (4), 129.

[45] Xie, Q., Cao, Z. L., Sun, W. C., Fumagalli, A., Fu, X., Wu, Z. H., & Wu, K. (2023). Numerical simulation of the fluid-solid coupling mechanism of water and mud inrush in a water-rich fault tunnel. Tunnelling and Underground Space Technology, 131, 104796.

[46] Xu, D. P., Feng, X. T., Chen, D. F., Zhang, C. Q., & Fan, Q. X. (2017). Constitutive representation and damage degree index for the layered rock mass excavation response in underground openings. Tunnelling and Underground Space Technology, 64, 133-145.

[47] Xu, W. J., Wang, Y. J., & Dong, X. Y. (2021a). Influence of reservoir water level variations on slope stability and evaluation of landslide tsunami. Bulletin of Engineering Geology and the Environment, 80 (6), 4891-4907.

[48] Xu, Z. H., Lin, P., Xing, H. L., Pan, D. D., & Huang, X. (2021b). Hydro-mechanical Coupling Response Behaviors in Tunnel Subjected to a Water-Filled Karst Cave. Rock Mechanics and Rock Engineering, 54 (8), 3737-3756.

[49] Yan, C. B., Xu, G. Y., & Zuo, Y. J. (2006). Destabilization analysis of overlapping underground chambers induced by blasting vibration with catastrophe theory. Transactions of Nonferrous Metals Society of China, 16 (3), 735-740.

[50] Yu, S. Y., Ren, X. H., Zhang, J. X., Wang, H. J., & Sun, Z. H. (2021a). An improved form of smoothed particle hydrodynamics method for crack propagation simulation applied in rock mechanics. International Journal of Mining Science and Technology, 31 (3), 421-428.

[51] Yu, S. Y., Ren, X. H., Zhang, J. X., Wang, H. J., & Sun, Z. H. (2021b). An improved smoothed particle hydrodynamics method and its application in rock hydraulic fracture modelling. Rock Mechanics and Rock Engineering, 54 (12), 6039-6055.

[52] Zhan, L., Peng, C., Zhang, B. Y., & Wu, W. (2020). A SPH framework for dynamic interaction between soil and rigid body system with hybrid contact method. International Journal for Numerical and Analytical Methods in Geomechanics, 44 (10), 1446-1471.

[53] Zhang, T., Gan, Q., Zhao, Y. X., Zhu, G. P., Nie, X. D., Yang, K., & Li, J. Z. (2019). Investigations into mining-induced stress-fracture-seepage field coupling effect considering the response of key stratum and composite aquifer. Rock Mechanics and Rock Engineering, 52 (10), 4017-4031.

[54] Zhou, X. P., Wang, Y. T., Shou, Y. D., & Kou, M. M. (2018). A novel conjugated bond linear elastic model in bond-based peridynamics for fracture problems under dynamic loads. Engineering Fracture Mechanics, 188, 151-183.

[55] Zhou, X. P., Zhao, Y., & Qian, Q. H. (2015a). Numerical simulation of rock failure process in uniaxial compression using smoothed particle hydrodynamics. Chinese Journal of Rock Mechanics and Engineering, 34, 2647-2658 (in Chinese).

[56] Zhou, X. P., Wang, Y. T., & Qian, Q. H. (2016). Numerical simulation of crack curving and branching in brittle materials under dynamic loads using the extended non-ordinary state-based peridynamics. European Journal of Mechanics - A/Solids, 60, 277-299.

[57] Zhou, X. P., Zhao, Y., & Qian, Q. H. (2015b). A novel meshless numerical method for modeling progressive failure processes of slopes. Engineering Geology, 192, 139-153.

[58] Zhou, Z. Q., Li, L. P., Shi, S. S., Liu, C., Gao, C. L., Tu, W. F., & Wang, M. X. (2020). Study on tunnel water inrush mechanism and simulation of seepage failure process. Rock and Soil Mechanics, 41 (11), 3621-3631 (in Chinese).

[59] Zhu, W. C., & Wei, C. H. (2011). Numerical simulation on mining-induced water inrushes related to geologic structures using a damage-based hydromechanical model. Environmental Earth Sciences, 62 (1), 43-54.