New Statistical Quantification Method for the Size Effect Behavior of Rock Mass Using Compressive Strength as an Example
Publication: International Journal of Geomechanics
Volume 22, Issue 11
Abstract
The statistical law on mechanical parameters of rock mass with size is the key to the study of the size effect. Since the existing statistical methods of the size effect only consider the continuity of the size but not the difference between the samples of each size, a new statistical method that considers single size and multisize is proposed. Based on the proposed method, the true representative elementary volume (TREV) value is used to determine the size effect stability threshold. Combined with the analysis of the three major size effect theories, the unified size effect law model and variation index k are proposed. The results are validated by statistical test data on the uniaxial compressive strength (UCS) obtained in realistic failure process analysis (RFPA) numerical test and from other works, which proves that the proposed method can reflect the variation law of UCS value with size and provide a basis for theoretical research on the size effect in mechanical behavior.
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Acknowledgments
The study was funded by the National Natural Science Foundation of China (Grant No. 41427802) and the Natural Science Foundation of Zhejiang Province (Grant No. LY18D020003). This support is gratefully acknowledged.
Notation
The following symbols are used in this paper:
- CVi
- coefficient of variation;
- D0
- reference size;
- fc0
- uniaxial compressive strength;
- average variation coefficient;
- variation coefficient based on a single sample;
- k
- variation index;
- L
- total length of rock mass;
- li
- sampling size;
- l1
- reference size in the size effect law model;
- M
- parameter;
- corresponding mean parameter in the size effect law model;
- mean corresponding to li;
- parameters of each size ;
- maximum parameter corresponding to li;
- minimum parameter corresponding to li;
- Muj
- average of Mij when size is greater than or equal to ;
- m
- sampling times;
- mw
- Weibull coefficient;
- n
- sampling capacity;
- nd
- dimensionality of the structure;
- u
- sampling serial number;
- η
- empirical constant;
- μ
- mean;
- σ
- standard deviation;
- σNu
- nominal strength;
- mean nominal strength;
- σ0
- reference parameter;
- mean reference parameter;
- σ1
- maximum principal stress;
- σ2
- minimum principal stress; and
- φ
- internal friction angle.
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Published In
International Journal of Geomechanics
Volume 22 • Issue 11 • November 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Aug 26, 2021
Accepted: Jun 12, 2022
Published online: Aug 23, 2022
Published in print: Nov 1, 2022
Discussion open until: Jan 23, 2023
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