Benchmark study of three statistical methods for six intact rock failure criteria constrained by different rock strength data

Abstract

To reduce the impact of potential strength outliers on parameter estimation, statistical methods based on the least median square and least absolute deviation have been proposed as alternatives to the traditional least square method. However, little research has been conducted to compare the performance of these different statistical methods. This study introduces a novel procedure for evaluating the three statistical approaches across six selected rock failure criteria, constrained by various rock strength datasets. The consistency of the best-fitting failure criterion and the robustness of the strength parameter estimations serve as the primary benchmarks for evaluation. Based on the benchmark analysis, the following conclusions are drawn. First, both the least square and least absolute deviation methods perform equivalently in identifying the best-fitting failure criterion for a given rock strength dataset, whereas the least median square method does not. Second, when estimating the strength parameters in a two-dimensional failure criterion with the conventional test data of low complexity, the least absolute deviation method is recommended for obtaining robust parameter estimations. Third, as the complexity of conventional test data increases or when true triaxial test data are used to estimate strength parameters for a three-dimensional failure criterion, it is essential to evaluate the outlier-proneness by analyzing the prediction error. If the kurtosis of the prediction error is less than 3, the least square method is preferred. Otherwise, the least absolute deviation method should be used to mitigate the influence of potential strength outliers. This benchmark study offers valuable insights for the future application of different statistical methods in rock mechanics.

Keywords

Rock strength / Failure criterion / Statistical method / Strength parameter / Robustness

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CRediT authorship contribution statement

Peng-fei He: Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization, Writing - original draft, Validation. Xin Li: Writing - review & editing, Validation, Investigation, Formal analysis, Data curation. Xu-long Yao: Writing - review & editing, Validation, Resources. Zhi-gang Tao: Writing - review & editing, Validation, Supervision, Resources, Project administration. Yan-ting Du: Writing - review & editing, Validation, Funding acquisition, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The research was supported by the National Natural Science Foundation of China (Grant No. 42002278), the Open Foundation of Collaborative Innovation Center of Green Development and Ecological Restoration of Mineral Resources (Grant No. HLCX-2024-03), and the Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. 202415012).

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