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Size of representative elementary volume for heterogeneous rocks evaluated using distinct element method

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Abstract

The determination of the size of the representative elementary volume (REV) is important to measure or predict mechanical and physical effective properties of heterogeneous materials. This paper presents a numerical procedure to determine the REV size of intact rocks using a polygonal grain-based model. A large number of rock models with side lengths varying from 10 to 80 mm were generated in a square region based on the growing window technology. These models were then employed to carry out numerical compressive tests to determine the macroscopic mechanical properties of rocks for REV determination. Variations in the mineral volume fraction, compressive strength, elastic modulus, and Poisson’s ratio with the sample size were investigated. The coefficient of variation (\(\varepsilon\)) was introduced to denote the fluctuation of the properties. The REV sizes were determined by defining an acceptable value of \(\varepsilon\). As the sample size increased, the coefficients of variation of the properties decreased. The REV sizes varied for different investigated properties; among them, the REV size for compressive strength was largest. To achieve mechanical representation of the overall rocks, the REV size should be at least 20 times the largest mineral grain size in the specimen, which was verified in the simulations. Geometric heterogeneity and mineral volume fractions also influenced the REV size. The simulated results indicate that the REV size for compressive strength had a positive dependence on the heterogeneity index, while it slightly decreased with the increase in volume fraction of biotite from 10.4 to 60.4%.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\(\Delta \sigma_{n}^{{}}\) :

Effective contact stress increment (Pa)

\(\Delta U_{n}^{{}}\) :

Normal displacement increment (m)

\(\Delta U_{s}^{e}\) :

Elastic component of the shear displacement (m)

\(k_{{\text{n}}}\) :

Normal stiffness of the contact (GPa/m)

\(k_{{\text{s}}}\) :

Shear stiffness of the contact (GPa/m)

\(T_{m}\) :

Tensile strength for contact (MPa)

\(\tau_{{\text{s}}}\) :

Shear strength for contact (MPa)

\(c\) :

Cohesive strength (MPa)

\(\phi\) :

Friction coefficient

\(\sigma_{{\text{c}}}\) :

Compressive strength of rock (MPa)

\(\sigma_{{\text{t}}}\) :

Tensile strength of rock (MPa)

\(\varepsilon\) :

Coefficient of variation

\(H\) :

Heterogeneity index

\(\varphi\) :

Ratio of sample size to the maximum diameter of the grains (mm)

\(\varepsilon_{{\text{r}}}^{{}}\) :

Acceptable relative error for estimation

\(D_{Z}^{2} (V)\) :

Variance of its average value

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Funding

This work was supported by the Natural Science Foundation of Shaanxi Province in China (2022JQ-349, 2022JQ-333) and China Scholarship Council (202008615032).

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Authors and Affiliations

  1. School of Resources Engineering, XAUAT, Xi’an, 710055, Shaanxi, China

    Zhao Wang & Weiqin Wang

  2. Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering, School of Civil Engineering, XAUAT, Xi’an, 710055, Shaanxi, China

    Zhao Wang, Tiehang Wang & Weiqin Wang

  3. Oulu Mining School, University of Oulu, 90570, Oulu, Finland

    Zhao Wang & Zongxian Zhang

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  1. Zhao Wang
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Correspondence to Zhao Wang or Zongxian Zhang.

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Wang, Z., Wang, T., Wang, W. et al. Size of representative elementary volume for heterogeneous rocks evaluated using distinct element method. Acta Geotech. 18, 1883–1900 (2023). https://doi.org/10.1007/s11440-022-01663-w

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  • DOI: https://doi.org/10.1007/s11440-022-01663-w

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