Abstract
The investigation of localized deformation in rocks at the laboratory scale can yield valuable insights into the internal structures and mechanisms of shear zones and compaction bands that impact the permeability characterization and failure mechanisms of rocks. Combined with high-resolution X-ray computed tomography and in situ loading, the digital volume correlation (DVC) technique is an effective tool for mapping the deformation in rocks. This technique is mainly divided into two categories: subset-based local DVC (L-DVC), used for rocks because of its straightforward implementation and high efficiency, and finite-element-based global DVC (G-DVC), which usually offers better accuracy because of the continuity among element nodes. In this study, we compared the accuracy and precision of these two DVC approaches for five rocks and discussed two factors important for accuracy, namely element/subset size and microstructure. The results show that performance of the G-DVC is better than that of the L-DVC, albeit at the expense of computational efficiency, especially for smaller subset sizes. An indentation test on red sandstone was performed to further demonstrate the feasibility of the two methods. This study aims to supplement the lack of research on the two DVC approaches for rocks and provides a reference for subsequent related research.
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The raw/processed data required to reproduce these findings will be available upon request.
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Abbreviations
- a :
-
Displacement value
- f :
-
Grayscale value within the reference element
- g :
-
Grayscale value within the deformed element
- H :
-
Hessian matrix expressed
- p e :
-
Point in a single element
- S g :
-
Reference element in G-DVC
- S s :
-
Element/subset size
- η g :
-
Zero-mean normalized sum-of square difference criterion
- λ :
-
Penalty factor
- δ μ :
-
Mean value of the mean intensity gradient of all elements or subsets
- Φ:
-
FEM shape function
- Δf :
-
Standard deviations of grayscale of the reference element
- ▽f :
-
Gradient of the intensity within the reference subset
- Es:
-
Element size
- f m :
-
Mean intensity value of the reference element
- g m :
-
Mean intensity value of the deformed element
- I :
-
Identity matrix
- R 2 :
-
Power law coefficient of determination
- S l :
-
Reference subset in L-DVC
- u(p e):
-
Displacement shape function
- η l :
-
Residual integration
- ξ :
-
Local coordinates of a voxel point in the subset
- δ σ :
-
Standard deviation of the mean intensity gradient of all elements or subsets
- Ω :
-
Entire interested region
- Δg :
-
Standard deviations of grayscale of the deformed element
- CT:
-
Computed tomography
- FFT:
-
Fast Fourier transform
- DVC:
-
Digital volume correlation
- G-DVC:
-
Global digital volume correlation
- VOI:
-
Volume of interest
- FEM:
-
Finite-element method
- DIC:
-
Digital image correlation
- IC-GN:
-
Inverse compositional Gauss–Newton
- L-DVC:
-
Local digital volume correlation
- ZNSSD:
-
Zero-mean normalized sum-of square difference
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Acknowledgements
The coauthor, Dr. Fu-pen Chiang, wishes to thank Dr. Yapa Rajapakse, Director of ONR’s Solid Mechanics Program, for supporting the development of speckle techniques over the years.
Funding
This work was financially supported by the National Natural Science Foundation of China (51727807, 51374211, 51874309), the Fundamental Research Funds for the Central Universities (2021YJSMT05), the Innovation Teams of the Ten-thousand Talents Program sponsored by the Ministry of Science and Technology of China (Grant No. 2016RA4067), the Open-fund of State Key Laboratory of Earthquake Dynamics of China (LED2019B02), the US Office of Naval Research’s Solid Mechanics Program grant No: N0014-14-1-0419, and the Laboratory for Experimental Mechanic Research of the Department of Mechanical Engineering at Stony Brook University in USA.
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LM: conceptualization, methodology, investigation, and writing–original draft. HL: conceptualization, formal analysis, validation, software, and writing–original draft; YL: formal analysis and investigation; JW: investigation; YJ: methodology, resources, supervision, validation, and writing–review and editing; F-PC: writing–review and editing.
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Mao, L., Liu, H., Lei, Y. et al. Evaluation of Global and Local Digital Volume Correlation for Measuring 3D Deformation in Rocks. Rock Mech Rock Eng 54, 4949–4964 (2021). https://doi.org/10.1007/s00603-021-02517-9
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DOI: https://doi.org/10.1007/s00603-021-02517-9