Bulletin of Engineering Geology and the Environment

, Volume 78, Issue 7, pp 5387–5408 | Cite as

A new transversely isotropic nonlinear creep model for layered phyllite and its application

  • Guowen Xu
  • Chuan He
  • Jian YanEmail author
  • Gaoyu Ma
Original Paper


Phyllite, which is a low-grade metamorphic rock with well-developed foliation planes, is encountered frequently during tunnel construction in western China. Its creep behavior is affected significantly by the foliation planes and has a crucial influence on the long-term safety of tunnel structures. Uniaxial compressive creep testing was conducted to analyze the time-dependent features of phyllite obtained from the Zhegu mountain tunnel on the Wenma expressway, China. A new creep model that connects a Maxwell body, a Kelvin body, and a nonlinear visco-plastic body was proposed to describe both the full creep process (including the transient, steady, and accelerated creep stages) and the transversely isotropic characteristics of phyllite. The creep model was also applied to investigate the long-term safety of a cracked tunnel lining in phyllite bedrock. The results showed that the creep strength and corresponding axial strain of phyllite exhibited maximum and minimum values at θ (the angle between the loading direction and the weak planes) = 90° and 30°, respectively. Good agreement was found between the calculated and experimental creep curves, indicating that the creep model replicates the physical creep process of phyllite well. The safety of the cracked lining was affected mainly by the damage degree of cracks and the creep behavior of the surrounding rock. Uncracked sections, because of their greater stiffness, were more sensitive to creep load than cracked ones. The inclination angle of foliation planes influenced the location of unsafe sections (those with a safety factor less than one), and this effect was weakened as the number of pre-existing cracks increased.


Nonlinear creep model Transverse isotropy Tunnel Secondary lining Long-term safety 



This research was supported by the National key research and development program of China (Grant No. 2016YFC0802201).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.


  1. Andargol MBE, Shahriar K, Ramezanzadeh A, Goshtasbi K (2018) The analysis of dates obtained from long-term creep tests to determine creep coefficients of rock salt. Bull Eng Geol Environ 1:1–13Google Scholar
  2. Aydan O, Ito T, Ozbay U et al (2014) ISRM suggested methods for determining the creep characteristics of rock. Rock Mech Rock Eng 47:275–290CrossRefGoogle Scholar
  3. Barla G, Debernardi D, Sterpi D (2012) Time-dependent modeling of tunnels in squeezing conditions. Int J Geomec 12:697–710CrossRefGoogle Scholar
  4. Brantut N, Heap MJ, Baud P, Meredith PG (2014) Mechanisms of time-dependent deformation in porous limestone. J Geophys Res 119:5444–5463CrossRefGoogle Scholar
  5. Chen L, Wang CP, Liu JF, Li Y, Liu J, Wang J (2017) Effects of temperature and stress on the time-dependent behavior of Beishan granite. Int J Rock Mech Min Sci 93:316–323CrossRefGoogle Scholar
  6. Chin HP, Rogers JD (1987) Creep parameters of rocks on an engineering scale. Rock Mech Rock Eng 20:137–146CrossRefGoogle Scholar
  7. Dubey RK, Gairola VK (2008) Influence of structural anisotropy on creep of rocksalt from Simla Himalaya, India: an experimental approach. J Struct Geol 30:710–718CrossRefGoogle Scholar
  8. Fu ZL, Gao YF, Ning W, Xu JP (2007) Creep of anisotropic soil shale. J Min Saf Eng 24:353–356Google Scholar
  9. Guan ZC, Jiang YJ, Tanabashi Y, Huang H (2008) A new rheological model and its application in mountain tunnelling. Tunn Undergr Space Technol 23:292–299CrossRefGoogle Scholar
  10. Guan ZC, Jiang YJ, Tanabashi Y (2009) Rheological parameter estimation for the prediction of long-term deformations in conventional tunneling. Tunn Undergr Space Technol 24:250–259CrossRefGoogle Scholar
  11. Itasca Consulting Group, Inc. (2009) Fast lagrangian analysis of continua, version 4.0. User’s manual. Consulting Group, Inc.,MinneapolisGoogle Scholar
  12. Li XC, Yang CL, Ren T, Nie BS, Zhao CH (2017) Creep behaviour and constitutive model of coal filled with gas. Int J Min Sci Technol 27:847–851CrossRefGoogle Scholar
  13. Liao MK, Lai YM, Liu EL, Wan XS (2017) A fractional order creep constitutive model of warm frozen silt. Acta Geotech 12:377–389CrossRefGoogle Scholar
  14. Lisjak A, Garitte B, Grasselli G, Müller HR, Vietor T (2015) The excavation of a circular tunnel in a bedded argillaceous rock (Opalinus clay): short-term rock mass response and FDEM numerical analysis. Tunn Undergr Space Technol 45:227–248CrossRefGoogle Scholar
  15. Liu ZB, Xie SY, Shao JF, Conil N (2015) Effects of deviatoric stress and structural anisotropy on compressive creep behavior of a clayey rock. Appl Clay Sci 114:491–496CrossRefGoogle Scholar
  16. Lockner D (1993) Room temperature creep in saturated granite. J Geophys Res 10:475–487CrossRefGoogle Scholar
  17. Lu PL, Wu KT, Jiao YB, Li JH, Liu XH (1992) The experimental study of acoustic emission during creep of rocks. Acta Seismol Sin 5:169–176CrossRefGoogle Scholar
  18. Manh HT, Sulem J, Subrin D, Billaux D (2015) Anisotropic time-dependent modeling of tunnel excavation in squeezing ground. Rock Mech Rock Eng 48:2301–2317CrossRefGoogle Scholar
  19. Meng LB, Li TB, Jiang Y, Wang R, Li YR (2013) Characteristics and mechanisms of large deformation in the Zhegu mountain tunnel on the Sichuan–Tibet highway. Tunn Undergr Space Technol 37:157–164CrossRefGoogle Scholar
  20. Ministry of Transport of PRC (2004) Gode for design of road tunnel. China Communication Publisher Ltd., BeijingGoogle Scholar
  21. Mishra B, Verma P (2015) Uniaxial and triaxial single and multistage creep tests on coal-measure shale rocks. Int J Coal Geol 137:55–65CrossRefGoogle Scholar
  22. Paraskevopoulou C, Perras M, Diederichs M, Loew S, Lam T, Jensen M (2018) Time-dependent behaviour of brittle rocks based on static load laboratory testing. Geotech Geol Eng 36:337–376CrossRefGoogle Scholar
  23. Sterpi D, Gioda G (2009) Visco-plastic behaviour around advancing tunnels in squeezing rock. Rock Mech Rock Eng 42:319–339CrossRefGoogle Scholar
  24. Sun J (1999) Rheological behavior of geomaterials and its engineering applications. China Architecture and Building Press, BeijingGoogle Scholar
  25. Tang MM, Wang ZY (2008) Experimental study on rheological deformation and stress properties of limestone. J Cent S Univ Technol 15:475–478CrossRefGoogle Scholar
  26. Tang H, Wang DP, Huang RQ, Pei XJ, Chen WL (2018) A new rock creep model based on variable-order fractional derivatives and continuum damage mechanics. Bull Eng Geol Environ 77:375–383CrossRefGoogle Scholar
  27. Tonon F (2016) Sequential excavation, NATM and ADECO: what they have in common and how they differ. Tunn Undergr Space Technol 25:245–265CrossRefGoogle Scholar
  28. Torres CC, Diederichs M (2009) Mechanical analysis of circular liners with particular reference to composite supports. For example, liners consisting of shotcrete and steel sets. Tunn Undergr Space Technol 24:506–532Google Scholar
  29. Wang GJ, Zhang L, Zhang YW, Ding GS (2014) Experimental investigations of the creep–damage–rupture behavior of rock salt. Int J Rock Mech Min Sci 66:181–187CrossRefGoogle Scholar
  30. Wang JH, Zhang WJ, Guo X, Koizumi A, Tanaka H (2015) Mechanism for buckling of shield tunnel linings under hydrostatic pressure. Tunn Undergr Space Technol 49:144–155CrossRefGoogle Scholar
  31. Wu CZ, Shi ZM, Fu YK, Yang LD, Li QS (2014) Experimental investigations on structural anisotropy on creep of greenschist. Chin J Rock Mech Eng 33:493–499 (in Chinese)Google Scholar
  32. Xu GW, He C, Chen ZQ, Wu D (2018) Effects of the micro-structure and micro-parameters on the mechanical behaviour of transversely isotropic rock in Brazilian tests. Acta Geotech 13:887–910CrossRefGoogle Scholar
  33. Yang SQ, Cheng L (2011) Non-stationary and nonlinear visco-elastic shear creep model for shale. Int J Rock Mech Min Sci 48:1011–1020CrossRefGoogle Scholar
  34. Yang CH, Daemen JJK, Yin JH (1999) Experimental investigation of creep behavior of salt rock. Int J Rock Mech Min Sci 36:233–242CrossRefGoogle Scholar
  35. Yang DS, Chen LF, Yang SQ, Chen WZ, Wu GJ (2014) Experimental investigation of the creep and damage behavior of Linyi red sandstone. Int J Rock Mech Min Sci 72:164–172CrossRefGoogle Scholar
  36. Ye GL, Nishimura T, Zhang F (2015) Experimental study on shear and creep behavior of green tuff at high temperature. Int J Rock Mech Min Sci 79:19–28CrossRefGoogle Scholar
  37. Zhang SL (2012) Study on health diagnosis and technical condition assessment for tunnel lining structure. Dissertation, Beijing Jiaotong University, China (in Chinese)Google Scholar
  38. Zhao BY, Liu DY, Dong Q (2011) Experimental research on creep behaviors of sandstone under uniaxial compressive and tensile stresses. J Rock Mech Geotech Eng 3:438–444CrossRefGoogle Scholar
  39. Zhao XJ, Chen BR, Zhao HB, Jie BH, Ning ZF (2012) Laboratory creep tests for time-dependent properties of a marble in Jinping II hydropower station. J Rock Mech Geotech Eng 4:168–176CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Transportation Tunnel Engineering, Ministry of EducationSouthwest Jiaotong UniversityChengduChina

Personalised recommendations