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A model for characterization of crack closure stage in stress–strain curves of Suizhou granite after exposure to various thermal shocks

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Abstract

Reservoir rocks have an obvious initial nonlinear crack-closure stage during geothermal energy exploration using enhanced geothermal systems (EGSs). Therefore, the purpose of this research is to establish a quantitative model considering the influence of initial nonlinear characteristics on geothermal reservoirs. According to effective medium theory (EMT), deformation of reservoir rocks after thermal shocks can be divided into rock frame and void sections, and the effect of microcracks is considered in the establishment of the proposed model. Compressive tests conducted on Suizhou granite specimens after cyclic water cooling were used to validate this model. Furthermore, the influence of microcracks on initial crack closure part of Suizhou granite specimens after thermal shocks was revealed by scanning electron microscope (SEM) observation. There is a negative exponential relationship between the axial stress–strain in void section of specimens after cyclic water cooling. The crack closure stage in the stress–strain relation of Suizhou granite after thermal shocks is more apparent with heating temperature and cyclic time. The proposed model well characterizes the crack closure part in the stress–strain curves of specimens after cyclic water cooling. The proposed model describes the initial nonlinear stage of surrounding geothermal reservoir granite and provides theoretical support for the evaluation of stability in EGS engineering design.

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Data Availability

Data will be made available on request.

Abbreviations

C ijkl :

Effective compliance tensor of rock after thermal shocks

C ijkl 0 :

Skeleton section compliance tensor

ΔC ijkl :

Extra void section compliance tensor

\({\delta }_{0}={h}_{0}^{v}/{h}_{0}\) :

Maximum strain of the crack closure stage

ε I (i = 1, 2 or 3):

Macroscopic principal strain of the representative column element (RCE)

ε sc :

Peak strain

\({\varepsilon }_{i}^{s}\) :

Microscopic strain of skeleton section

\({\varepsilon }_{i}^{v}\) :

Microscopic strain of void section

\({\varepsilon }_{i}^{vm}\) :

Transient strain of void section

ε ij :

Total strain of rock

\({\varepsilon }_{ij}^{0}\) :

Skeleton section

Δε ij :

Extra strain of void section

E T :

Elastic modulus of skeleton section

\({E}_{T}^{s}\) :

Elastic modulus of void section

\(\Delta {\sigma }_{i}^{m}\) (s = 1, 2, …, n):

m Multi-level stress increments

\({E}_{T}^{vm}\) :

Elastic modulus of void section being applied stress increment of Δσim.

h 0 :

Initial full height of RCE

Δh :

Macroscopic deformation of RCE

\({h}_{0}^{s}\) :

Heights of skeleton section

Δh s :

Macroscopic deformation induced by the skeleton section

h 0 v :

Heights of the void section

Δh v :

Macroscopic deformation induced by void section

Δh v m :

Microscopic deformation caused by s level stress increment Δσim

ρ f :

Microcrack density

R2 :

The correlation coefficient

σ cc :

Crack closure stress

σ ci :

Crack initiation stress

σ cd :

Crack damage stress

σ kl :

Applied stress

σ I (i = 1, 2 or 3):

Direction of principal stress

n :

Total number of multi-level stress increment

T :

Heating temperature

UCST :

Uniaxial compression stress

\({v}_{T}\) :

Poisson’s ratio of the skeleton section

\({v}_{T}^{v}\) :

Poisson’s ratio of void section

\({v}_{T}^{vm}\) :

Poisson’s ratio of void section being applied stress increment of Δσim

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Acknowledgements

This work is jointly supported by the National Natural Science Foundation of China (No. 42207178, 42077231), the China Postdoctoral Science Foundation Funded Project (No. 2022M713373), the Open Research Fund Program of Key Laboratory of Deep Geothermal Resources, Ministry of Natural Resources (No. KLDGR2022G03), the Open Research Fund of Engineering Research Center of Rock-Soil Drilling & Excavation and Protection, Ministry of Education (No. 202313) and Open Research Fund of Engineering Research Center of Geothermal Resources Development Technology and Equipment, Ministry of Education (No. 23004). We are grateful to the 3Gdeep group (Department of Civil Engineering, Monash University, Australia) for their help in providing valuable suggestions on English polishing.

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Zhennan Zhu & Shengqi Yang

  2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Zhennan Zhu & Shengqi Yang

  3. Engineering Research Center of Geothermal Resources Development Technology and Equipment, Ministry of Education, Jilin University, Changchun, 130026, China

    Zhennan Zhu & Yilong Yuan

  4. School of Resources and Geosciences, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Nuocheng Tian

  5. Department of Architecture and Engineering, Quzhou University, Quzhou, 324000, China

    Jingyu Xie

  6. Engineering Research Center of Rock-Soil Drilling & Excavation and Protection, Ministry of Education, China University of Geosciences, Wuhan, 430074, Hubei, China

    Zhennan Zhu, Hong Tian, Guosheng Jiang & Bin Dou

  7. Deep Earth Energy Laboratory, Department of Civil Engineering, Monash University, Melbourne, VIC, 3800, Australia

    Pathegama Gamage Ranjith

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  1. Zhennan Zhu
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Correspondence to Shengqi Yang.

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The authors declare that they have no conflicts of interest in this work. All data, models, or codes supporting the findings of this study are available from the corresponding author on request.

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Zhu, Z., Yang, S., Ranjith, P.G. et al. A model for characterization of crack closure stage in stress–strain curves of Suizhou granite after exposure to various thermal shocks. Bull Eng Geol Environ 83, 231 (2024). https://doi.org/10.1007/s10064-024-03685-y

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  • DOI: https://doi.org/10.1007/s10064-024-03685-y

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