Sensitivity analyses of random cave groups on karst tunnel stability based on water-rock interaction using a novel contact dynamic method

Abstract

This paper concentrates on the sensitivity and dynamic simulation of randomly distributed karst cave groups on tunnel stability and connectivity extended ratio based on water-rock interaction using a novel contact dynamic method (CDM). The concept of karst cave group connectivity extended ratio during tunneling and water inrush is proposed. The effects of cave shape and spatial distribution on Qiyueshan tunnel are investigated. Tunnel deformation and damage index, and connectivity extended ratio with uniform random karst cave groups are evaluated. The results demonstrate that the connectivity extended ratio is verified as a crucial judgment in predicting the safe distance and assessing the stability of the tunnel with the karst cave group. CDM model captures the fracture propagation and contact behavior of rock mass, surface flow, as well as the bidirectional water-rock interaction during the water inrush of Qiyueshan tunnel with multiple caves. A larger cave radius and smaller minimum distance between the cave and tunnel increase the deformation and damage index of the surrounding rock. When the cave radius and cave area ratio increase, the failure pattern shifts from overall to local failure. These findings potentially have broad applications in various surface and subsurface scenarios involving water-rock interactions.

Keywords

Karst tunnel stability / Contact dynamic method / Connectivity extended ratio / Karst cave groups / Qiyueshan tunnel / Water-rock interaction

CRediT authorship contribution statement

Chengzhi Xia: Conceptualization, Resources, Software, Writing - original draft, Writing - review & editing, Methodology. Zhenming Shi: Funding acquisition, Supervision, Project administration. Huanjia Kou: Data curation, Validation, Writing - review & editing. Shaoqiang Meng: Data curation, Investigation, Validation. Maomao Liu: Data curation, Investigation, Resources, Supervision, Writing - review & editing, Project administration.

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 paper.

Acknowledgment

The authors appreciate the financial support provided by the National Key Research and Development Program of China (Grant Nos. 2019YFC1509702 and 2023YFC3008300), and the National Natural Science Foundation of China (Grant No. 42172296).

References

[1] Abdelrazek, A. M., Kimura, I., & Shimizu, Y. (2016). Simulation of the erosion and seepage failure around sheet pile using two-phase WCSPH method. Journal of Japan Society of Civil Engineers Ser A2, 72 (2), I_495-I_504.

[2] Biot, M. (1941). General theory of three-dimensional consolidation. Journal of Applied Physics, 12(2), 155-164.

[3] Bui, H. H., & Fukagawa, R. (2013). An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore-water pressure. International Journal for Numerical and Analytical Methods in Geomechanics, 37(1), 31-50.

[4] Bui, H. H., Sako, K., & Fukagawa, R. (2005). Numerical simulation of soil-water interaction using smoothed particle hydrodynamics (SPH) method. In proceedings of:15th International Conference of the International Society for Terrain Vehicle Systems 2005, ISTVS 2005. pp 126-140.

[5] Cavarretta, I., O’Sullivan, C., & Coop, M. R. (2017). The relevance of roundness to the crushing strength of granular materials. Géotechnique, 67(4), 301-312.

[6] Chakraborty, S., & Shaw, A. (2013). A pseudo-spring based fracture model for SPH simulation of impact dynamics. International Journal of Impact Engineering, 58, 84-95.

[7] Ding, Z., Zhang, W., Yang, Z., Wang, Z., Du, X., & Li, L. (2022). An analytical solution for self-weight consolidation based on onedimensional small-strain consolidation wave theory. Géotechnique, 72 (7), 583-595.

[8] Gao, C., Li, L., Zhou, Z., Li, Z., Cheng, S., Wang, L., & Zhang, D. (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.

[9] 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.

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

[11] Huang, F., Zhao, L., Ling, T., & Yang, X. (2017). Rock mass collapse mechanism of concealed karst cave beneath deep tunnel. International Journal of Rock Mechanics and Mining Sciences, 91, 133-138.

[12] Huang, M., Fei, W., Wei, L., & Tan, Z. (2009). Numerical study on the process of water inrush in Karst caves with hydraulic pressure caused by tunnel excavation. Engineering Sciences, 11(12), 93-96 (in Chinese).

[13] Huang, Q., Huang, H., Ye, B., Zhang, D., & Zhang, F. (2018). Evaluation of train-induced settlement for metro tunnel in saturated clay based on an elastoplastic constitutive model. Underground Space, 3(2), 109-124.

[14] Kallianiotis, A., Papakonstantinou, D., Tolias, I. C., & Benardos, A. (2022). Evaluation of fire smoke control in underground space. Underground Space, 7(3), 295-310.

[15] Lai, Y., Li, S., Guo, J., Zhu, Z., & Huang, X. (2021). Analysis of seepage and displacement field evolutionary characteristics in water inrush disaster process of karst tunnel. Geofluids, 2021(4), 1-20.

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

[17] Li, S.-c., Pan, D.-d., Xu, Z.-h., Li, L.-p., Lin, P., Yuan, Y.-c., Gao, C.-l., & Lu, W. (2018b). A model test on catastrophic evolution process of water inrush of a concealed karst cave filled with confined water. Rock and Soil Mechanics, 39(9), 3164-3173 (in Chinese).

[18] Li, S., Yuan, Y., Li, L., Ye, Z., Zhang, Q., & 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).

[19] Li, S. C., Wu, J., Xu, Z. H., & Li, L. P. (2017). Unascertained measure model of water and mud inrush risk evaluation in karst tunnels and its engineering application. KSCE Journal of Civil Engineering, 21(4), 1170-1182.

[20] Libersky, L. D., Petschek, A. G., Carney, T. C., Hipp, J. R., & Allahdadi, F. A. (1993). High strain lagrangian hydrodynamics: a threedimensional SPH code for dynamic material response. Journal of Computational Physics, 109(1), 67-75.

[21] Lin, C., Zhang, M., Zhou, Z., Li, L., Shi, S., Chen, Y., & Dai, W. (2020). A new quantitative method for risk assessment of water inrush in karst tunnels based on variable weight function and improved cloud model. Tunnelling and Underground Space Technology, 95, 103136.

[22] Ma, J. J., Guan, J. W., Duan, J. F., Huang, L. C., & Liang, Y. (2021). Stability analysis on tunnels with karst caves using the distinct lattice spring model. Underground Space, 6(4), 469-481.

[23] Mahmoudi, M., & Rajabi, A. M. (2023). A numerical simulation using FLAC3D to analyze the impact of concealed karstic caves on the behavior of adjacent tunnels. Natural Hazards, 117(1), 555-577.

[24] Mardalizad, A., Saksala, T., Manes, A., & Giglio, M. (2020). Numerical modeling of the tool-rock penetration process using FEM coupled with SPH technique. Journal of Petroleum Science and Engineering, 189, 107008.

[25] Monaghan, J. J. (1994). Simulating Free Surface Flows with SPH. Journal of Computational Physics, 110(2), 399-406.

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

[27] Nader, J. J. (2009). Darcy’s law and the differential equation of motion. Géotechnique, 59(6), 551-552.

[28] Peng, X., Chen, G., Fu, H., Yu, P., Zhang, Y., Tang, Z., & Wang, W. (2021). Development of coupled DDA-SPH method for dynamic modelling of interaction problems between rock structure and soil. International Journal of Rock Mechanics and Mining Sciences, 146, 104890.

[29] Rattez, H., Shi, Y., Sac-Morane, A., Klaeyle, T., Mielniczuk, B., & Veveakis, M. (2022). Effect of grain size distribution on the shear band thickness evolution in sand. Géotechnique, 72(4), 350-363.

[30] Rodriguez-Paz, M. X., & Bonet, J. (2002). SPH numerical simulation of debris flows and avalanches. Paper presented at the Numerical Models in Geomechanics - 8th Proceedings of the International Symposium on Numerical Models in Geomechanics, NUMOG 2002.

[31] Shabdirova, A., Hop Minh, N., & Zhao, Y. (2022). Role of plastic zone porosity and permeability in sand production in weak sandstone reservoirs. Underground Space, 7(6), 1003-1020.

[32] Singh, R., Vishal, V., Singh, T. N., & Ranjith, P. G. (2013). A comparative study of generalized regression neural network approach and adaptive neuro-fuzzy inference systems for prediction of unconfined compressive strength of rocks. Neural Computing and Applications, 23(2), 499-506.

[33] Vu-Hoang, T., Vo-Minh, T., & Nguyen-Xuan, H. (2018). Bubbleenhanced quadrilateral finite element formulation for nonlinear analysis of geotechnical problems. Underground Space, 3(3), 229-242.

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

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

[36] Xia, C., Shi, Z., Li, B., & Liu, M. (2024c). A discontinuous smooth particle hydrodynamics method for modeling deformation and failure processes of fractured rocks. Journal of Rock Mechanics and Geotechnical Engineering, in press. doi:10.1016/j.jrmge.2023.11.011.

[37] Xia, C., Shi, Z., Zheng, H., & Wu, X. (2023). Kernel broken smooth particle hydrodynamics method for crack propagation simulation applied in layered rock cells and tunnels. Underground Space, 10, 55-75.

[38] Xu, W.-J., Zhou, Q., & Dong, X.-Y. (2022). SPH-DEM coupling method based on GPU and its application to the landslide tsunami. Part II: Reproduction of the Vajont landslide tsunami. Acta Geotechnica, 17(6), 2121-2137.

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

[40] Yu, S., Ren, X., Zhang, J., Wang, H., & Sun, Z. (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(63), 421-428.

[41] 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.

[42] Zhu, J.-Q., & Li, T.-Z. (2020). Catastrophe theory-based risk evaluation model for water and mud inrush and its application in karst tunnels. Journal of Central South University, 27(5), 1587-1598.

[43] Zhuang, L., Kim, K. Y., Jung, S. G., Diaz, M., & Min, K.-B. (2019). Effect of water infiltration, injection rate and anisotropy on hydraulic fracturing behavior of granite. Rock Mechanics and Rock Engineering, 52(2), 575-589.