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Effects of length-to-diameter ratio on energy storage characteristics of rock materials under uniaxial compression

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Abstract

This study aims to investigate the influence of length-to-diameter (L/D) ratio on the strain energy storage and evolution characteristics of rock materials during progressive rock failure under compression. Uniaxial compression tests and single-cycle loading–unloading uniaxial compression tests were conducted on four rock materials with two specimen L/D ratios. The uniaxial compressive strength (UCS) and peak strain of the rock specimens with L/D = 1 were significantly greater than those of the specimens with L/D = 2, thus exhibiting a strong size effect. In the single-cycle loading-unloading uniaxial compression tests, the total energy density, elastic energy density and dissipated energy density of the specimens with different L/D ratios increased nonlinearly with the actual stress level. The specimen L/D ratio had a significant impact on the nonlinear energy evolutions over various actual stress levels. Interestingly, regardless of the L/D ratio, failure pattern and type of material in the tests, highly linear relationships exist between the elastic energy, dissipated energy and total energy. Although the UCS is sensitive to the specimen L/D ratio, the energy storage coefficient (ESC) and energy dissipation coefficient (EDC) almost show a size-independent behaviour. The ESC and EDC are not affected by the L/D ratio and failure mode and can be used as physical parameters in geotechnical engineering design.

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Abbreviations

CV:

Coefficient of variation

D :

Diameter of the rock specimens

EDC:

Energy dissipation coefficient

ESC:

Energy storage coefficient

i :

Actual stress level

ISRM:

International Society for Rock Mechanics

k :

Setting stress level

L :

Length of the rock specimens

LED:

Linear energy dissipation

LES:

Linear energy storage

LVDTs:

Linear variable differential transformers

SCLUC:

Single-cycle loading-unloading uniaxial compression

u :

Total energy density at peak strength of the rock specimens

UC:

Uniaxial compression

UCS:

Uniaxial compressive strength

UCS1 :

Uniaxial compressive strength of the specimens with L/D = 1

UCS2 :

Uniaxial compressive strength of the specimens with L/D = 2

UCSL :

Uniaxial compressive strength of the specimens with L/D ratio less than 2.0

UCSp :

Prediction of UCS2 value using Eq. (3)

\({u^d}\) :

Dissipated energy density at peak strength of the rock specimens

\(u^{di}\) :

Dissipated energy density at actual stress level i

u e :

Elastic energy density at peak strength of the rock specimens

\(u^{ei}\)  :

Elastic energy density at actual stress level i

\(u^{i}\) :

Total energy density at actual stress level i

v :

P-wave velocity of the rock specimens

ρ :

Density of the rock specimens

\({\sigma }_{\mathrm{c}}\) :

Strength of the specimens under conventional uniaxial compression

\({\sigma }_{\mathrm{c}}^{k}\) :

Strength of the specimens under single-cycle loading-unloading uniaxial compression at setting stress level k

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Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 42077244 and 41877272) and the Fundamental Research Funds for the Central Universities (Grant No. 2242022k30054).

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Authors and Affiliations

  1. School of Resources and Safety Engineering, Central South University, Changsha, 410083, China

    Jingyi Yan, Fengqiang Gong & Song Luo

  2. School of Civil Engineering, Southeast University, Nanjing, 211189, China

    Fengqiang Gong

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  1. Jingyi Yan
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Correspondence to Fengqiang Gong.

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Yan, J., Gong, F. & Luo, S. Effects of length-to-diameter ratio on energy storage characteristics of rock materials under uniaxial compression. Bull Eng Geol Environ 81, 508 (2022). https://doi.org/10.1007/s10064-022-03013-2

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