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Variable Parameter Creep Model Based on the Separation of Viscoelastic and Viscoplastic Deformations

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Abstract

The MTS815.02 rock test system is used for performing triaxial compression creep experiments on sandstone to reveal the rheological properties of the rock in deep roadways. Instantaneous elastic, viscoelastic, and viscoplastic strains are separated, and the relationship between the model parameters and the stress and time is established by combining the characteristics of the creep curve. According to non-linear rheological theory, the constitutive equation of a creep model of the rock under a three-dimensional stress state is deduced, and the validity of the model is verified by the experimental data. Results show that the improved creep model comprehensively considers instantaneous elastic, non-linear viscoelastic, and viscoplastic strains, making the theoretical curve of the model highly consistent with the experimental curve. The model can describe the non-linear creep during the loading of sandstone. It can also reflect the creep parameters during the deformation. The correlation coefficients of the experimental curve and the theoretical curve under the same stress are both greater than 0.90. The comparison results verify the validity and feasibility of the creep model.

Highlights

  • According to the characteristics of creep curve, the instantaneous strain, viscoelastic strain and viscoplastic strain are separated.

  • The creep model based on viscoelastic-plastic strain separation can well describe the accelerated creep characteristics of rock creep process.

  • The variation of creep parameters also reflects the evolution process of damage accumulation and deterioration of material properties.

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Data availability

The datasets used in this study are available upon reasonable request from the corresponding author.

Abbreviations

σ 1 :

Axial stress

ε e :

Instantaneous strain

K e :

Bulk modulus at the instantaneous strain stage

σ m :

Spherical tensor of stress

a i :

Fitting parameter

c i :

Fitting parameter

σ A :

Critical damage stress

η ve :

Viscosity coefficient of the viscoelastic body

G vei :

Shear modulus at any time

A i :

Value of parameter A at any time

S 11 :

Stress tensor

ε vp :

Strain of the Newton’s dashpot

ε nl :

Strain of the non-linear dashpot

t * :

Time to enter the accelerated creep

σ 3 :

Radial stress

G e :

Shear modulus at the instantaneous strain stage

ε m :

Spherical tensor of strain

ε V :

Volumetric strain

b i :

Fitting parameter

ε :

Total creep strain

ε ve :

Viscoelastic strain

G ve :

Shear modulus of the viscoelastic body

η vei :

Viscosity coefficient at any time

η nl :

Viscosity coefficient of the non-linear dashpot

g(·):

A function

η vp :

Viscosity coefficient of the Newton’s dashpot

t i :

Different time point

σ S :

Long-term strength

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos. 4206070032 and 41941018), the Science and Technology Service Network Initiative of the Chinese Academy of Sciences (Grant no. KFJSTS-QYZD-174), and the Guangxi Natural Science Foundation (Grant no. 2020GXNSFAA159125).

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, Hubei, China

    Wenbo Liu, Hui Zhou & Chengwei Zhao

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Wenbo Liu, Hui Zhou & Chengwei Zhao

  3. Guangxi Key Laboratory of Geomechanics and Geotechnical Engineering, Guilin, 541004, China

    Shuguang Zhang

  4. School of Civil Engineering, Guilin University of Technology, Guilin, 541004, China

    Shuguang Zhang

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  1. Wenbo Liu
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  2. Hui Zhou
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  3. Shuguang Zhang
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  4. Chengwei Zhao
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Contributions

WL: conceptualization, data curation, writing—original draft, investigation, and methodology. HZ: conceptualization, writing—original draft, writing—review and editing, software, supervision, and methodology. SZ: conceptualization, data curation, methodology, and investigation. CZ: English grammar correction and language polishing, supervision and writing—review and editing.

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Correspondence to Hui Zhou or Shuguang Zhang.

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Liu, W., Zhou, H., Zhang, S. et al. Variable Parameter Creep Model Based on the Separation of Viscoelastic and Viscoplastic Deformations. Rock Mech Rock Eng 56, 4629–4645 (2023). https://doi.org/10.1007/s00603-023-03266-7

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  • DOI: https://doi.org/10.1007/s00603-023-03266-7

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