Constitutive Model of Uniaxial Compression for Rock (Coal) and Bursting Liability Index Based on the Structure Ensemble Dynamics Theory

• Published in: Rock mechanics and rock engineering 2024-12, Vol.57 (12), p.10831-10848
• Main Authors: Chen, Shuai, Tang, Jupeng, Pan, Yishan
• Format: Article
• Language: English
• Subjects: Bursting; Bursting strength; Civil Engineering; Coal; Coal mines; Compression; Compressive properties; Compressive strength; Constitutive models; Deformation; Deformation analysis; Deformation effects; Dimensional analysis; Dynamic mechanical properties; Dynamic structural analysis; Dynamics; Earth and Environmental Science; Earth Sciences; Geophysics/Geodesy; Instability; Liability; Mechanical properties; Original Paper; Parameter sensitivity; Parameters; Rock; Rock properties; Rockbursts; Rocks; Sensitivity analysis; Stability criteria; Strain; Strain analysis; Stress-strain relationships; Structural stability; Theories
• ISSN: 0723-2632; 1434-453X
• DOI: 10.1007/s00603-024-04112-0

The bursting liability is very important to evaluate the risk of rock burst in coal mine. Conducting uniaxial compression test is the main method to study the bursting liability of rock (coal). To establish an accurate uniaxial constitutive model, the structure ensemble dynamics theory is adopted. The model of rock (coal) specimen compression by testing machine is simplified. Through dimensional analysis, the stress–strain relationship of the specimen is a power model. The mechanical properties of rock (coal) vary with different levels of deformation and can be divided into four stages. The different states can be considered as different ensembles. By using the analysis method of structural ensembles dynamics, one formula completely represents the four stages accurately. The parameters in the formula are physically meaningful and can be uniquely determined based on experimental data. A criterion for instability criterion of the system of the specimen and the testing machine is derived, and a theoretical explanation of instability failure related to uniaxial compressive strength is given. Parameters sensitivity analysis and verification are conducted on the theoretical results. The theoretical results are highly accurate and can effectively reflect the stress–strain relationship of rock (coal) under uniaxial compression. A bursting liability index which contains the information of the peak and post-peak of the stress–strain relationship is proposed. The new index is positively correlated with the compressive strength and the bursting energy index and a classification of bursting liability levels for the new index was determined based on them. Highlights The structure ensemble dynamics theory is used to establish a constitutive model. One formula completely represents the stress-stain relationship accurately. The parameters are physically meaningful and can be uniquely determined. A theoretical explanation of instability failure related to strength is given. A new bursting liability index based on the new constitutive model is proposed.