Numerical Investigation of Hard Rock Strength and Fracturing under Polyaxial Compression Based on Mogi-Coulomb Failure Criterion

Significance 

Rocks are normally subjected to three-dimensional stress state in their natural state. As such, studying their strength and underlying failure modes especially under polyaxially compression conditions is of great importance. Presently, laboratory testing is widely used in the investigation of the underlying rock mechanics as well as the true-triaxial loading and unloading conditions. Unfortunately, it is difficult to characterize the influence of the intermediate principal stress using conventional compression triaxial tests. The challenge was, however, addressed by Mogi in the late twentieth century by assuming a homogenous stress distribution, taking into account the role of the intermediate principal stress in the strength and failure modes of rocks subjected to true-trial axial conditions. This paved the way for extensive research on the rock strength and fracturing under polyaxial compression.

Despite several laboratory tests attempts based on true-triaxial apparatuses, numerical simulation of the process and rock behavior is not fully explored. Taking the advantage of the advanced computing technology, numerical simulation is considered the game-changer in reducing the cost of studying the rock behavior as well as enhancing the efficiency and accuracy as it can permit investigations of various stress combinations. However, the main challenge associated with the numerical simulations is the inability of the existing constitutive models to reflect the actual rock behavior and failure characteristics under true-triaxial stress conditions. In an attempt to address the aforementioned drawback, researchers have been looking for alternative solutions and have proposed Mogi-Coulomb failure criterion as a promising solution.

To this note, Shandong University of Science and Technology and Central South University-based researchers: Dr. Fan Feng, Professor Xibing Li, Dingxiao Peng, Diyuan Li, and Professor Kun Du together with professor Jamal Rostami at Colorado School of Mines modeled hard rock strength and fracturing under polyaxial compression based on the Mogi-Coulomb failure criterion. They used a commercially available finite-difference program to simulate the relevant parameters obtained from triaxial tests to determine the effects of intermediate principal stress on fracture characteristics taking into consideration the material strain-softening properties. A dynamically linked library was used to compile the results obtained from the user-defined model interface. To validate the effectiveness and accuracy of the developed approach, the numerical results were compared to the previous experimental data. The work is published in International Journal of Geomechanics.

The authors observed brittle rock failure under high intermediate stress owing to a decreasing trend in the fracture angle. This was equally confirmed through both visual and microcosmic observations of the failure modes on the samples. Additionally, it was established that the Mohr-Coulomb model does not take into account the effects of the intermediate stress and thus cannot offer a better representation of strength characteristics of failure modes under polyaxial compression conditions. This gave credits to the effectiveness of Mogi-Coulomb based model in simulating hard rock failure characteristics under polyaxial compression conditions, and especially those involving high intermediate stress. Their study indeed provides vital information that will pave way for better understanding of the stain-hardening and strain-softening behavior based on the current and newly developed constitutive models.

Numerical Investigation of Hard Rock Strength and Fracturing under Polyaxial Compression Based on Mogi-Coulomb Failure Criterion - Advances in Engineering
Strain yy at residual strength on plane cutting through central section of the rock specimen under different intermediate principal stresses σ2: (a) σ2=10MPa; (b) σ2=30MPa; and (c) σ2=100MPa.

Strain yy at residual strength on plane cutting through central section of the rock specimen under different intermediate principal stresses σ2: (a) σ2=10MPa; (b) σ2=30MPa; and (c) σ2=100MPa.  - Advances in Engineering
Displacement vector field at peak strength on plane cutting through midheight of the rock specimen under different intermediate principal stresses σ2: (a) σ2=10MPa; (b) σ2=30 MPa; and (c) σ2=100 MPa.

About the author

Fan Feng is currently a lecturer in College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao, China. He obtained his PhD from Central South University, Changsha, China in 2018. Dr. Feng has been a joint PhD student (visiting scholar) to study in Mining Engineering Department, Colorado School of Mines, CO, USA from 2017 to 2018.

His research interests involve deep rock mechanics, mine disaster prevention and control and mining theory and technologies of underground metal mines. He has published more than 20 journal papers and 4 registered patents. He is the member of China Society of Rock Mechanics (CSRM) and International Society of Rock Mechanics (ISRM).

Profile: Lecturer, College of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao, China

Email: [email protected]

About the author

Xibing Li obtained his PhD from Central South University, Changsha, China in 1992. Dr. Li is a Professor of Rock Dynamics and Mining Engineering at the Central South University, China. As the principal investigator, he has been in charge of over ten national research projects, such as the National Science Foundation for Distinguished Young Scholars, Cheung Kong Scholars Program, State Key Program of the National Natural Science Foundation, and State Key Development Program for Basic Research (973).

He proposed an innovative approach based on SHPB system with half sine wave loading. Considering the mechanical state of deep mining, he proposed a coupled static-dynamic loading theory and developed associated system. To date, he has published about 200 scientific papers on rock failure mechanisms and mining engineering, and he is the author of ten books of rock mechanics and mining engineering.

Profile : Professor, School of Resources and Safety Engineering, Central South University, Changsha, China

Email : [email protected]

About the author

Jamal Rostami is currently an associate professor in Department of Mining Engineering, Colorado School of mines (CSM). He is also the director of Excavation Engineering and Earth Mechanics Institute (EMI). He has over 30 years of combined design, management, research, and teaching in the field of mining, tunneling, civil infrastructure, and underground construction. Prof. Rostami Member of SME, ASCE, ARMA, ISRM, ISEE. 2013 chair of PE exam committee and member Structure and Governance Strategic Committee of SME 2011-2014, and currently in Education committee. He is the Editor-in-Chief of Tunneling and Underground Space Technology (Elsevier) and Associate Editor of Mining Engineering (SME) journal.

Profile: Associate professor, Department of Mining Engineering, Colorado School of mines, CO, USA

Email: [email protected]

Reference

Feng, F., Li, X., Rostami, J., Peng, D., Li, D., & Du, K. (2019). Numerical Investigation of Hard Rock Strength and Fracturing under Polyaxial Compression Based on Mogi-Coulomb Failure CriterionInternational Journal of Geomechanics19(4), 04019005.

Go To International Journal of Geomechanics

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