Abstract
Size effect is a project that cannot be ignored in rock mechanics. To investigate the size effect on the energy distribution and evolution laws, several groups of uniaxial compression tests and single-cycle loading–unloading uniaxial compression tests were performed on red sandstone specimens of different sizes (diameters of 25, 37, 50, 75, and 100 mm; a constant length-to-diameter ratio of 2.0) using the INSTRON 1346 test system. Experimental results show that mechanical properties are influenced by specimen size while failure mode has no significant variation for different diameter specimens. Strain energy parameters (input strain energy, elastic strain energy, and dissipated strain energy) under each unloading stress level were calculated by integration based on the stress–strain curves. The input strain energy, elastic strain energy, and dissipated strain energy nonlinearly increase with actual unloading stress levels, expressed as unified quadratic function relationships. Furthermore, the elastic strain energy and dissipated strain energy have linear relationships with the input strain energy. Through analyzing coefficients of variation of common parameters, it was found that the energy storage capacity of rock was not sensitive to the specimen size, and therefore, the energy storage coefficient could be considered an essential property of rock materials.
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Abbreviations
- \(E_{{\mathrm{i}}}\) :
-
Input strain energy
- \(E_{{\mathrm{d}}}\) :
-
Dissipated strain energy
- \(E_{{\mathrm{e}}}\) :
-
Elastic strain energy
- \(\sigma_{{\mathrm{c}}}\) :
-
Peak strength
- \(\sigma_{{{\mathrm{cn}}}}\) :
-
Normalized strength of specimens
- \(\sigma_{{\mathrm{c}}}^{D}\) :
-
Peak strength of “D” diameter specimens
- \(k\) :
-
Preset unloading stress level
- \(i\) :
-
Actual unloading stress level
- \(\sigma_{{\mathrm{c}}}^{k}\) :
-
Peak strength of specimens with preset unloading stress level k
- \(k\sigma_{{\mathrm{c}}}\) :
-
Preset unloading stress
- \(E_{{\mathrm{i}}}^{i}\) :
-
Input strain energy at actual unloading stress level i
- \(E_{{\mathrm{e}}}^{i}\) :
-
Elastic strain energy at actual unloading stress level i
- \(E_{{\mathrm{d}}}^{i}\) :
-
Dissipated strain energy at actual unloading stress level i
- \(E_{{\mathrm{i}}}^{D}\) :
-
Input strain energy of “D” diameter specimens
- \(E_{{\mathrm{e}}}^{D}\) :
-
Elastic strain energy of “D” diameter specimens
- \(E_{{\mathrm{d}}}^{D}\) :
-
Dissipated strain energy of “D” diameter specimens
- \(\varepsilon_{0}\) :
-
Permanent strain after unloading
- \(\varepsilon_{{\mathrm{u}}}\) :
-
Strain at unloading point
- \(\varepsilon_{{\mathrm{p}}}\) :
-
Peak strain
- D :
-
Specimen diameter
- L/D :
-
Ratio of specimen length to the specimen diameter
- CoV:
-
Coefficient of variation
- \(\beta\) :
-
Standard deviation
- \(\mu\) :
-
Average value
- ISE:
-
Input strain energy
- ESE:
-
Elastic strain energy
- DSE:
-
Dissipated strain energy
- LES:
-
Linear energy storage
- LED:
-
Linear energy dissipation
- UC:
-
Uniaxial compression
- SCLUC:
-
Single-cycle loading–unloading uniaxial compression
- ESC :
-
Compression energy storage coefficient
- EDC:
-
Compression energy dissipation coefficient
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Funding
This work was supported by the National Natural Science Foundation of China (Grant No. 42077244, 41877272) and the Fundamental Research Funds for the Central Universities (Grant No. 2242022k30054).
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Gong, F., Ni, Y. & Jia, H. Effects of specimen size on linear energy storage and dissipation laws of red sandstone under uniaxial compression. Bull Eng Geol Environ 81, 386 (2022). https://doi.org/10.1007/s10064-022-02881-y
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DOI: https://doi.org/10.1007/s10064-022-02881-y