Skip to main content
SpringerLink
Log in

Anisotropic time-dependent deformation and damage constitutive model of rock under true triaxial compression

  • Research
  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

Time-dependent characteristics are key factors for the instability and safety in underground engineering projects. Due to geological structure and manual excavation, any rock mass is subjected to true triaxial stress. Therefore, true triaxial tests under the monotonous loading were conducted on sandstones first under different intermediate principal stresses along with a constant pore pressure to simulate rock in situ, and subsequently, the creep experiments were performed at different stress proportions under corresponding conditions. The experimental results show that anisotropic deformation and rates vary with stress levels and the intermediate principal stress. Combined with literature data, the lateral deformation ratio of the intermediate principal strain (\(\varepsilon _{2}\)) to the minimum principal strain (\(\varepsilon _{3}\)), is closely related to the reciprocal of the side stress ratio for instant and creep increments in the penultimate stage. The intermediate principal stresses (\(\sigma _{2}\)) have a significant effect on the creep behavior of sandstone. Based on the experimental results, a new anisotropic creep-damage model is subsequently developed, and anisotropic damage is defined based on statistical damage theory. The parameter values can be obtained using the method of Universal Global Optimization (UGO). The theoretical predictions show good consistency with laboratory data and field data, respectively. The model is reliably used to simulate creep behavior and gives a good account of the effect of intermediate principal stresses. Therefore, it could provide a better understanding of the long-term stability of engineering projects.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  • Cai, T., Feng, Z., Zhao, D., Jiang, Y.: A creep model for lean coal based on hardening-damage mechanism. Rock Soil Mech. 39(S1), 61–68 (2018)

    Google Scholar 

  • Cao, W., Chen, K., Tan, X., Chen, H.: A novel damage-based creep model considering the complete creep process and multiple stress levels. Comput. Geotech. 124, 103599 (2020)

    Article  Google Scholar 

  • Chen, Y., Lin, H., Wang, Y., Xie, S., Zhao, Y., Yong, W.: Statistical damage constitutive model based on the Hoek–Brown criterion. Arch. Civ. Mech. Eng. 21, 117 (2021)

    Article  Google Scholar 

  • Cheng, X., Tang, C., Zhuang, D.: A finite-strain viscoelastic-damage numerical model for time-dependent failure and instability of rocks. Comput. Geotech. 143, 104596 (2022)

    Article  Google Scholar 

  • Chu, Z., Wu, Z., Liu, Q., Weng, L., Wang, Z., Zhou, Y.: Evaluating the microstructure evolution behaviors of saturated sandstone using NMR testing under uniaxial short-term and creep compression. Rock Mech. Rock Eng. 54, 4905–4927 (2021)

    Article  Google Scholar 

  • Ding, X., Xiao, X., Cui, J., Wu, D., Pan, Y.: Damage evolution, fractal dimension and a new crushing energy formula for coal with bursting liability. Process Saf. Environ. Prot. 169, 619–628 (2023)

    Article  Google Scholar 

  • Du, K., Yang, C., Su, R., Tao, M., Wang, S.: Failure properties of cubic granite, marble, and sandstone specimens under true triaxial stress. Int. J. Rock Mech. Min. Sci. 130, 104309 (2020)

    Article  Google Scholar 

  • Duan, M., Jiang, C., Yin, W., Yang, K., Li, J., Liu, Q.: Experimental study on mechanical and damage characteristics of coal under true triaxial cyclic disturbance. Eng. Geol. 295, 106445 (2021)

    Article  Google Scholar 

  • Feng, X., Pei, S., Jiang, Q., Zhou, Y., Li, S., Yao, Z.: Deep fracturing of the hard rock surrounding a large underground cavern subjected to high geostress: in situ observation and mechanism analysis. Rock Mech. Rock Eng. 50(8), 2155–2175 (2017a)

    Article  Google Scholar 

  • Feng, X., Zhang, X., Yang, C., et al.: Evaluation and reduction of the end friction effect in true triaxial tests on hard rocks. Int. J. Rock Mech. Min. Sci. 97, 144–148 (2017b)

    Article  Google Scholar 

  • Feng, X., Xu, H., Yang, C., Zhang, X., Gao, Y.: Influence of loading and unloading stress paths on the deformation and failure features of jinping marble under true triaxial compression. Rock Mech. Rock Eng. 34(1), 53 (2020)

    Google Scholar 

  • Huang, X., Li, S., Xu, D., Pan, P.: Time-dependent behavior of jinping deep marble taking into account the coupling between excavation damage and high pore pressure. Rock Mech. Rock Eng. 55, 4893–4912 (2022)

    Article  Google Scholar 

  • Innocente, J.C., Paraskevopoulou, C., Diederichs, M.S.: Estimating the long-term strength and time-to-failure of brittle rocks from laboratory testing. Int. J. Rock Mech. Min. Sci. 147, 104900 (2021)

    Article  Google Scholar 

  • Kabwe, E., Karakus, M., Chanda, E.K.: Creep constitutive model considering the overstress theory with an associative viscoplastic flow rule. Comput. Geotech. 124, 103629 (2020)

    Article  Google Scholar 

  • Li, W., Zhou, H., Zhong, Z., Zhang, Y., Hao, Q.: Development of rock mass true-triaxial site creep testing system and its application. Chin. J. Rock Mech. Eng. 31(8), 1636–1641 (2012)

    Google Scholar 

  • Liang, M., Miao, S., Cai, M., Huang, Z., Yang, P.: A damage constitutive model of rock with consideration of dilatation and post-peak shape of the stress-strain curve. Chin. J. Rock Mech. Eng. 40(12), 2392–2401 (2021)

    Google Scholar 

  • Li, H., Liao, H., Xiong, G., Han, B., Zhao, G.: A three-dimensional statistical damage constitutive model for geomaterials. J. Mech. Sci. Technol. 29(1), 71–77 (2015)

    Article  Google Scholar 

  • Li, C., Wang, J., Xie, H.: Anisotropic creep characteristics and mechanism of shale under elevated deviatoric stress. J. Pet. Sci. Eng. 185, 106670 (2020)

    Article  Google Scholar 

  • Liu, L., Xu, W., Wang, H., Wang, W., Wang, R.: Permeability evolution of granite gneiss during triaxial creep tests. Rock Mech. Rock Eng. 49(9), 3455–3462 (2016)

    Article  Google Scholar 

  • Liu, X., Yu, J., Zhu, Y., Yao, W., Lai, Y.: Creep damage evolution of marble from acoustic emission and the damage threshold. Front. Earth Sci. 8, 58 (2020b)

    Article  Google Scholar 

  • Liu, W., Zhang, S., Chen, L., Sun, B., Lu, P.: Accelerated creep model for rock based on statistical damage principle. Chin. J. Geotech. Eng. 42(9), 1696–1704 (2020a)

    Google Scholar 

  • Liu, W., Zhou, H., Zhang, S., Jiang, S.: Constitutive model of concrete creep damage considering the deterioration of creep parameters. Constr. Build. Mater. 308, 125047 (2021)

    Article  Google Scholar 

  • Liu, W., Zhou, H., Zhang, S., Jiang, S., Liu, Y.: A nonlinear creep model for surrounding rocks of tunnels based on kinetic energy theorem. J. Rock Mech. Geotech. Eng. (2022)

  • Lyu, C., Liu, J., Ren, Y., Liang, C., Liao, Y.: Study on very long-term creep tests and nonlinear creep-damage constitutive model of salt rock. Int. J. Rock Mech. Min. Sci. 146, 104873 (2021)

    Article  Google Scholar 

  • Ren, C., Yu, J., Cai, Y., Yao, W., Lai, Y., Li, B.: A novel constitutive model with plastic internal and damage variables for brittle rocks. Eng. Fract. Mech. 248, 107731 (2021)

    Article  Google Scholar 

  • Ren, C., Yu, J., Liu, S., Yao, W., Zhu, Y., Liu, X.: A plastic strain-induced damage model of porous rock suitable for different stress paths. Rock Mech. Rock Eng. 55(4), 1887–1906 (2022a)

    Article  Google Scholar 

  • Ren, C., Yu, J., Liu, X., Zhang, Z., Cai, Y.: Cyclic constitutive equations of rock with coupled damage induced by compaction and cracking. Int. J. Min. Sci. Technol. 32(5), 1153–1165 (2022b)

    Article  Google Scholar 

  • Tang, C.A., Liu, H., Lee, P.K.K., Tsui, Y., Tham, L.G.: Numerical studies of the influence of microstructure on rock failure in uniaxial compression - part I: effect of heterogeneity. Int. J. Rock Mech. Min. Sci. 37(4), 555–569 (2000)

    Article  Google Scholar 

  • Wu, F., Gao, R., Zou, Q., Chen, J., Liu, W., Peng, K.: Long-term strength determination and nonlinear creep damage constitutive model of salt rock based on multistage creep test: implications for underground natural gas storage in salt cavern. Energy Sci. Eng. 8(5), 1592–1603 (2020)

    Article  Google Scholar 

  • Xia, K., Li, X., Qi, C., Yao, W., Xiao, X., Zhang, J., Nasseri, M.H.B.: Anisotropic seismic wave velocity of fractured tight sandstone under in-situ stress conditions and its correlation to permeability. J. China Coal Soc. 47(1), 246–258 (2022)

    Google Scholar 

  • Xu, T., Zhou, G.L., Heap, M.J., Zhu, W.C., Chen, C.F., Baud, P.: The influence of temperature on time-dependent deformation and failure in granite: a mesoscale modeling approach. Rock Mech. Rock Eng. 50(9), 2345–2364 (2022)

    Article  Google Scholar 

  • Yang, S., Hu, B.: Creep and long-term permeability of a red sandstone subjected to cyclic loading after thermal treatments. Rock Mech. Rock Eng. 51(10), 2981–3004 (2018)

    Article  Google Scholar 

  • Yang, S., Hu, B.: Creep and permeability evolution behavior of red sandstone containing a single fissure under a confining pressure of 30 MPa. Sci. Rep. 10(1), 1900 (2020)

    Article  Google Scholar 

  • Yang, W., Gamage, R., Huang, C., Luo, G., Guo, J., Wang, S.: Loading history effect on creep deformation of rock. Energies 11(6), 1462 (2018)

    Article  Google Scholar 

  • Yu, M., Liu, B., Sun, J., Feng, W., Wang, Q.: Study on improved nonlinear viscoelastic-plastic creep model based on the Nishihara model. Geotech. Geolog. Eng. 41, 439 (2020b)

    Google Scholar 

  • Yu, J., Yao, W., Duan, K., Liu, X., Zhu, Y.: Experimental study and discrete element method modeling of compression and permeability behaviors of weakly anisotropic sandstones. Int. J. Rock Mech. Min. Sci. 134, 104437 (2020a)

    Article  Google Scholar 

  • Yu, Q., Zhu, Q., Chen, L., Shao, J.: Experimental investigation and semi-analytical simulation of instantaneous and time-dependent damage behaviors of beishan granite. Rock Mech. Rock Eng. 55, 2341–2352 (2022)

    Article  Google Scholar 

  • Zha, E., Zhang, Z., Zhang, R., Wu, S., Li, C., Ren, L., Gao, M., Zhou, J.: Long-term mechanical and acoustic emission characteristics of creep in deeply buried jinping marble considering excavation disturbance. Int. J. Rock Mech. Min. Sci. 139, 104603 (2021)

    Article  Google Scholar 

  • Zhang, L., Li, X., Ren, T.: A theoretical and experimental study of stress–strain, creep and failure mechanisms of intact coal. Rock Mech. Rock Eng. 53, 5641–5658 (2020)

    Article  Google Scholar 

  • Zhao, H., Shi, C., Zhao, M., Li, X.: Statistical damage constitutive model for rocks considering residual strength. Int. J. Geomech. 17(1), 04016033 (2017)

    Article  Google Scholar 

  • Zhao, J., Feng, X., Zhang, X., Yang, C., Zhou, Y.: Time-dependent behaviour and modeling of Jinping marble under true triaxial compression. Int. J. Rock Mech. Min. Sci. 110, 218–230 (2018)

    Article  Google Scholar 

  • Zhao, J., Feng, X., Zhang, X., Yang, C.: Brittle and ductile creep behavior of Jinping marble under true triaxial stress. Eng. Geol. 258, 105157 (2019)

    Article  Google Scholar 

  • Zhao, J., Feng, X., Yang, C., Zhang, X., Jiang, M.: Differential time-dependent fracturing and deformation characteristics of Jinping marble under true triaxial stress. Int. J. Rock Mech. Min. Sci. 138, 104651 (2021a)

    Article  Google Scholar 

  • Zhao, J., Feng, X., Yang, C., Zhou, Y., Zhang, Y.: Study on time-dependent fracturing behaviour for three different hard rock under high true triaxial stress. Rock Mech. Rock Eng. 54(3), 1239–1255 (2021b)

    Article  Google Scholar 

  • Zheng, Z., Cai, Z., Su, G., Huang, S., Wang, W., Zhang, Q., Wang, Y.: A new fractional-order model for time-dependent damage of rock under true triaxial stresses. Int. J. Damage Mech. 32(1), 50–72 (2023)

    Article  Google Scholar 

  • Zhou, H., Wang, L., Rong, T., Zhang, L., Ren, W., Su, T.: Creep-based permeability evolution in deep coal under unloading confining pressure. J. Nat. Gas Sci. Eng. 65, 185–196 (2019)

    Article  Google Scholar 

  • Zhou, X., Pan, X., Berto, F.: A state-of-the-art review on creep damage mechanics of rocks. Fatigue Fract. Eng. Mater. Struct. 45(3), 627–652 (2022)

    Article  Google Scholar 

  • Zhu, Y., Yu, J., Xu, H., Ma, L., Liu, X., Yao, W., Ren, C.: Experimental study on mechanical properties of marble under alternation between short-time creep and low-cycle fatigue. Chin. J. Geotech. Eng. 44(11), 2115–2124 (2022)

    Google Scholar 

Download references

Funding

This study was supported by the National Natural Science Foundation of China (Nos. 51978292, 42077254, 52109124).

Author information

Authors and Affiliations

  1. Fujian Research Center for Tunneling and Urban Underground Space Engineering, Huaqiao University, Xiamen, 361021, People’s Republic of China

    Xueying Liu, Jin Yu & Yanyan Cai

  2. Zijin School of Geology and Mining, Fuzhou University, Fuzhou, 350108, China

    Jianzhi Zhang

  3. School of Civil Engineering & Architecture, Xiamen University of Technology, Xiamen, 361024, China

    Wei Yao & Xianqi Zhou

Authors
  1. Xueying Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jin Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jianzhi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yanyan Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xianqi Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Liu X. wrote the main manuscript text. Yao W. and Zhou X. provided the use of experimental system. Yu J., Cai Y., and Zhang J. provided the fund for the research. All authors reviewed the munuscript.

Corresponding author

Correspondence to Jin Yu.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Yu, J., Zhang, J. et al. Anisotropic time-dependent deformation and damage constitutive model of rock under true triaxial compression. Mech Time-Depend Mater (2023). https://doi.org/10.1007/s11043-023-09617-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11043-023-09617-9

Keywords

Search

Navigation