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Hydro-mechanical coupling algorithm of reinforced concrete lining in hydraulic pressure tunnel using cohesive elements

  • Li Zhou (State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University) ;
  • Kai Su (State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University) ;
  • Ding-wei Liu (China Three Gorges University) ;
  • Yin-quan Li (Three Gorges Geotechnical Consultants Co. Ltd. (Wuhan)) ;
  • Hong-ze Zhu (State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University)
  • Received : 2022.12.03
  • Accepted : 2023.03.12
  • Published : 2023.04.10

Abstract

The reinforced concrete lining in the hydraulic pressure tunnel tends to crack during the water-filling process. The lining will be detached from the surrounding rock due to the inner water exosmosis along concrete cracks. From the previous research achievements, the cohesive element is widely adopted to simulate the concrete crack but rarely adopted to simulate the lining-rock interface. In this study, the zero-thickness cohesive element with hydro-mechanical coupling property is not only employed to simulate the traditional concrete crack, but also innovatively introduced to simulate the lining-rock interface. Combined with the indirect-coupled method, the hydro-mechanical coupling algorithm of the reinforced concrete lining in hydraulic pressure tunnels is proposed and implemented in the finite element code ABAQUS. The calculated results reveal the cracking mechanism of the reinforced concrete lining, and match well with the observed engineering phenomenon.

Keywords

Acknowledgement

This research was financially supported by the National Natural Science Foundation of China (grant No. 51879207).

References

  1. ABAQUS (2011), User's Manual, Version 6.11, Dassault Systemes.
  2. Barani, O.R., Majidaie, S. and Mosallanejad, M. (2016), "Numerical modeling of water pressure in propagating concrete cracks", J. Eng. Mech., 142(4), 04016011. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001048.
  3. Barenblatt, G.I. (1959), "The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks", J. Appl. Math. Mech., 23(3), 622-636. https://doi.org/10.1016/0021-8928(59)90157-1
  4. Bian, K., Liu, J., Xiao, M. and Liu, Z. (2016), "Cause investigation and verification of lining cracking of bifurcation tunnel at Huizhou Pumped Storage Power Station", Tunnel. Undergr. Space Technol., 54, 123-134. https://doi.org/10.1016/j.tust.2015.10.030.
  5. Bian, K., Xiao, M. and Chen, J. (2009), "Study on coupled seepage and stress fields in the concrete lining of the underground pipe with high water pressure", Tunnel. Undergr. Space Technol., 24, 287-295. https://doi.org/10.1016/j.tust.2008.10.003.
  6. Camanho, P.P., Davila, C.G. and De Moura, M.F. (2003), "Numerical simulation of mixed-mode progressive delamination in composite materials", J. Compos. Mater., 37(16), 1415-1438. https://doi.org/10.1177/0021998303034505.
  7. Chang, X., Hu, C., Ma, G. and Zhou, W. (2011), "Continuous-discontinuous deformable discrete element method to simulate the whole failure process of rock masses and application", Chin. J. Rock Mech. Eng., 30(10), 2004-2011.
  8. Chauhan, A. (2021), "Crack propagation in reinforced concrete exposed to non-uniform corrosion under real climate", Eng. Fract. Mech., 248(1), 107719. https://doi.org/10.1016/j.engfracmech.2021.107719.
  9. Chen, G., Gao, H. and Hu, Y. (2019), "Hydraulic fracturing analysis of pressure tunnel lining based on random assignment of mechanical parameters of cohesive element", Adv. Eng. Sci., 51(5), 60-67.
  10. Chen, M., Li, M., Wu, Y. and Kang, B. (2020), "Simulation of hydraulic fracturing using different mesh types based on zero thickness cohesive element", Process., 8(2), 189. https://doi.org/10.3390/pr8020189.
  11. Chen, Z. (2012), "Finite element modelling of viscosity-dominated hydraulic fractures", J. Petrol. Sci. Eng., 88-89, 136-144. https://doi.org/10.1016/j.petrol.2011.12.021.
  12. Cunha, V.M.C.F., Barros, J. and Sena-Cruz, J.M. (2012), "A finite element model with discrete embedded elements for fibre reinforced composites", Comput. Struct., 94-95, 22-33. https://doi.org/10.1016/j.compstruc.2011.12.005.
  13. Dadashi, E., Noorzad, A., Shahriar, K. and Goshtasbi, K. (2017), "Hydro-mechanical interaction analysis of reinforced concrete lining in pressure tunnels", Tunnel. Undergr. Space Technol., 69, 125-132. https://doi.org/10.1016/j.tust.2017.06.006.
  14. Dugdale, D.S. (1960), "Yielding of steel sheets containing slits", J. Mech. Phys. Solid., 8(2), 100-104. https://doi.org/10.1016/0022-5096(60)90013-2.
  15. Durand, R. and da Silva, F.H.B.T. (2019), "A Coulomb-based model to simulate concrete cracking using cohesive elements", Int. J. Fract., 220(1), 17-43. https://doi.org/10.1007/s10704-019-00395-5.
  16. Elices, M., Guinea, G.V., Gomez, J. and Planas, J. (2002), "The cohesive zone model: Advantages, limitations and challenges", Eng. Fract. Mech., 69(2), 137-163. https://doi.org/10.1016/S0013-7944(01)00083-2.
  17. Fahimifar, A. and Zareifard, M.R. (2009), "A theoretical solution for analysis of tunnels below groundwater considering the hydraulic-mechanical coupling", Tunnel. Undergr. Space Technol., 24(6), 634-646. https://doi.org/10.1016/j.tust.2009.06.002.
  18. Fernhndez, G. (1994), "Behavior of pressure tunnels and guidelines for liner design", J. Geotech. Eng., 120(10), 1768-1791. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:10(1768).
  19. Galvez, J.C., Planas, J., Sancho, J.M., Reyes, E., Cendon, D.A. and Casati, M.J. (2013), "An embedded cohesive crack model for finite element analysis of quasi-brittle materials", Eng. Fract. Mech., 109, 369-386. https://doi.org/10.1016/j.engfracmech.2012.08.021.
  20. Hillerborg, A., Modeer, M. and Petersson, P.E. (1976), "Analysis of crack formulation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6, 773-784. https://doi.org/10.1016/0008-8846(76)90007-7.
  21. Hou, J. (2009), "Observed data analysis of water filling test of the high-pressure tunnel in Tianhuangping Pumped-Storage Power Station", Adv. Sci. Technol. Water Resour., 29(2), 27-31.
  22. Hou, S., Li, K., Wu, Z., Li, F. and Shi, C. (2022), "Quantitative evaluation on self-healing capacity of cracked concrete by water permeability test-A review", Cement Concrete Compos., 127, 104404. https://doi.org/10.1016/j.cemconcomp.2021.104404.
  23. Jiang, H. and Meng, D. (2018), "3D numerical modelling of rock fracture with a hybrid finite and cohesive element method", Eng. Fract. Mech., 199, 280-293. https://doi.org/10.1016/j.engfracmech.2018.05.037.
  24. Karami, M., Kabiri-Samani, A., Nazari-Sharabian, M. and Karakouzian, M. (2019), "Investigating the effects of transient flow in concrete-lined pressure tunnels, and developing a new analytical formula for pressure wave velocity", Tunnel. Undergr. Space Technol., 91, 102992. https://doi.org/10.1016/j.tust.2019.102992.
  25. Liu, C., Zhou, Z., Wang, X. and Zhang, B. (2012), "Analysis and determination for the parameters of "cohesive element" in the numerical model of single fiber composites: The elastic parameters", J. Reinf. Plast. Compos., 31(17), 1127-1135. https://doi.org/10.1177/0731684412453360.
  26. Lyu, D., Yu, C., Ma, S. and Wang, X. (2018), "Nonlinear seismic response of a hydraulic tunnel considering fluid-solid coupling", Math. Prob. Eng., 1-12. https://doi.org/10.1155/2018/9608542.
  27. Ma, G., Zhou, C., Chang, X. and Zhou, W. (2011), "Continuous-discontinuous coupling analysis for whole failure process of rock", Chin. J. Rock Mech. Eng., 30(12), 2444-2455.
  28. Mello, L., Le, J.L. and Ballarini, R. (2020), "Numerical modeling of delayed progressive collapse of reinforced concrete structures", J. Eng. Mech., 146(10), 04020113. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001843.
  29. Morales-Alonso, G., Rey-de-Pedraza, V., Galvez, F. and Cendon, D.A. (2018), "Numerical simulation of fracture of concrete at different loading rates by using the cohesive crack model", Theor. Appl. Fract. Mech., 96, 308-325. https://doi.org/10.1016/j.tafmec.2018.05.003.
  30. Picandet, V., Khelidj, A. and Bellegou, H. (2009), "Crack effects on gas and water permeability of concretes", Cement Concrete Res., 39(6), 537-547. https://doi.org/10.1016/j.cemconres.2009.03.009.
  31. Pulatsu, B., Erdogmus, E., Loureno, P.B., Lemos, J.V. and Tuncay, K. (2021), "Numerical modeling of the tension stiffening in reinforced concrete members via discontinuum models", Comput. Part. Mech., 8(3), 423-436. https://doi.org/10.1007/s40571-020-00342-5.
  32. Rabczuk, T., Zi, G., Bordas, S. and Nguyen-Xuan, H. (2008), "A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures", Eng. Fract. Mech., 75(16), 4740-4758. https://doi.org/10.1016/j.engfracmech.2008.06.019.
  33. Rosa, A.L., Yu, R.C., Ruiz, G., Saucedo, L. and Sousa, J.L.A.O. (2012), "A loading rate dependent cohesive model for concrete fracture", Eng. Fract. Mech., 82, 195-208. https://doi.org/10.1016/j.engfracmech.2011.12.013.
  34. Salehnia, F., Sillen, X., Li, X.L. and Charlier, R. (2017), "Numerical simulation of a discontinuous gallery lining's behavior, and its interaction with rock", Int. J. Numer. Anal. Meth. Geomech., 41, 1569-1589. https://doi.org/10.1002/nag.2689.
  35. Schleiss, A.J. (1986), "Design of pervious pressure tunnels", Int. Water Power Dam Constr., 5, 21-26.
  36. Schleiss, A.J. (1997), "Design of reinforced concrete linings of Pressure Tunnels and shafts", Int. J. Hydropow. Dam., 4(3), 88-94.
  37. Segura, J.M. and Carol, I. (2010), "Numerical modelling of pressurized fracture evolution in concrete using zero-thickness interface elements", Eng. Fract. Mech., 77(9), 1386-1399. https://doi.org/10.1016/j.engfracmech.2010.03.014.
  38. Shen, W. (2010), "Test research on the limiting crack design of hydraulic reinforced concrete tunnel lining", Water Resour. Power, 28(5), 78-81.
  39. Simanjuntak, T.D.Y.F., Marence, M., Mynett, A.E. and Schleiss, A.J. (2013), "Mechanical-hydraulic interaction in the lining cracking process of pressure tunnels", Int. J. Hydropow. Dam., 20(5), 98-105.
  40. Simanjuntak, T.D.Y.F., Marence, M., Schleiss, A.J. and Mynert, A.E. (2012), "Design of pressure tunnels using a finite element model", Int. J. Hydropow. Dam., 19(5), 98-105. 
  41. Sinaie, S., Ngo, T.D. and Nguyen, V.P. (2018), "A discrete element model of concrete for cyclic loading", Comput. Struct., 196, 173-185. https://doi.org/10.1016/j.compstruc.2017.11.014.
  42. Su, K., Yang, Z., Zhang, W., Wu, H., Zhang, Q. and Wu, H. (2017), "Bearing mechanism of composite structure with reinforced concrete and steel liner: An application in penstock", Eng. Struct., 141, 344-355. https://doi.org/10.1016/j.engstruct.2017.03.021.
  43. Suo, Y., Chen, Z., Yan, H., Wang, D. and Zhang, Y. (2019), "Using cohesive zone model to simulate the hydraulic fracture interaction with natural fracture in poro-viscoelastic formation", Energi., 12(7), 1254. https://doi.org/10.3390/en12071254.
  44. Wang, S., Zhong, Z. and Ren, Y. (2018), "Elastic-plastic solutions for a circular hydraulic pressure tunnel based on the D-P criterion considering the fluid field", Innov. Infrastr. Solut., 3(1), 1-13. https://doi.org/10.1007/s41062-018-0135-6.
  45. Wang, T., Hu, W., Wu, H., Zhou, W., Su, K. and Cheng, L. (2016), "Seepage analysis of a diversion tunnel with high pressure in different periods: A case study", Eur. J. Environ. Civil Eng., 22(4), 386-404. https://doi.org/10.1080/19648189.2016.1197159.
  46. Wu, H., Zhou, L., Su, K., Zhou, Y. and Wen, X. (2019), "Hydro-mechanical interaction of reinforced concrete lining in hydraulic pressure tunnel", Struct. Eng. Mech., 71(6), 699-712. https://doi.org/10.12989/sem.2019.71.6.699.
  47. Xiao, M. (2002), "Three-dimensional numerical analysis on lining seepage crack of underground concrete branch pipe with high pressure water", Chin. J. Rock Mech. Eng., 21(7), 1022-1026.
  48. Xue, W., Yao, Z., Jing, W., Tang, B., Kong, G. and Wu, H. (2019), "Experimental study on permeability evolution during deformation and failure of shaft lining concrete", Constr. Build. Mater., 195, 564-573. https://doi.org/10.1016/j.conbuildmat.2018.11.101.
  49. Yang, F., Zhou, H., Zhang, C., Lu, J., Lu, X. and Geng, Y. (2020), "An analysis method for evaluating the safety of pressure water conveyance tunnel in argillaceous sandstone under water-weakening conditions", Tunnel. Undergr. Space Technol., 97, 103264. https://doi.org/10.1016/j.tust.2019.103264.
  50. Yang, L., Chang, X., Zhou, W., Cheng, Y. and Ma, G. (2016), "Seismic cracking analysis of a gravity dam based on deformable distinct element method", J. Vib. Shock, 35(7), 49-55.
  51. Yoon, J., Han, J., Joo, E. and Shin, J. (2014), "Effects of tunnel shapes in structural and hydraulic interaction", KSCE J. Civil Eng., 18(3), 735-774. https://doi.org/10.1007/s12205-014-1325-1.
  52. Zareifard, M.R. (2018), "An analytical solution for design of pressure tunnels considering seepage loads", Appl. Math. Model., 62, 62-85. https://doi.org/10.1016/j.apm.2018.05.032
  53. Zhang, W., Dai, B., Liu, Z. and Zhou, C. (2018), "Numerical algorithm of reinforced concrete lining cracking process for pressure tunnels", Eng. Comput., 35(1), 91-107. https://doi.org/10.1108/EC-11-2016-0394.
  54. Zhang, W., Liu, M., Bian, K., Cong, P. and Yuan, W. (2021), "Modelling the hydro-mechanical behaviour of high-pressure tunnel with emphasis on the interaction between lining and rock mass", Comput. Geotech., 139, 104382. https://doi.org/10.1016/j.compgeo.2021.104382.
  55. Zhang, Y. (2001), "Experience and lessons of hydraulic tunnel construction (I)", Guizhou Water Power, 15(4), 76-84.
  56. Zhao, H., Liu, X., Bao, Y. and Yuan, Y. (2017), "Nonlinear simulation of tunnel linings with a simplified numerical modelling", Struct. Eng. Mech., 61(5), 593-603. https://doi.org/10.12989/sem.2017.61.5.593.
  57. Zhou, L., Su, K., Wang, Y., Zhang, Y., Zhu, H. and Wu, H. (2021), "Hydraulic fracturing analysis method of reinforced concrete lining in hydraulic tunnel", J. Hydraulic Eng., 52(1), 21-33.
  58. Zhou, L., Su, K., Wu, H. and Shi, C. (2018), "Numerical investigation of grouting of rock mass with fracture propagation using cohesive finite elements", Int. J. Geomech., 18(7), 04018075. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001184.
  59. Zhou, L., Su, K., Zhou, Y., Wen, X. and Wu, H. (2018), "Hydro-mechanical coupling analysis of pervious lining in high pressure hydraulic tunnel", J. Hydraulic Eng., 49(3), 313-322.
  60. Zhou, Y., Su, K. and Wu, H. (2015), "Hydro-mechanical interaction analysis of high pressure hydraulic tunnel", Tunnel. Undergr. Space Technol., 47, 28-34. https://doi.org/10.1016/j.tust.2014.12.004.
  61. Zhu, H.Y., Deng, J.G., Zhao, J., Zhao, H., Liu, H.L. and Wang, T. (2014), "Cementing failure of the casing-cement-rock interfaces during hydraulic fracturing", Comput. Concrete, 14(1), 91-107. https://doi.org/10.12989/csc.2014.14.1.091.
  62. Zou, Z., Reid, S.R., Li, S. and Soden, P.D. (2002), "Modelling interlaminar and intralaminar damage in filament-wound pipes under quasi-static indentation", J. Compos. Mater., 36(4), 477-499. https://doi.org/10.1177/0021998302036004539.