Technical Papers
Sep 22, 2023

Numerical Study on Dynamic Fracture and Energy Transformation Characteristics of Rock Unloading Failure under Identical Energy Stored Levels

Publication: International Journal of Geomechanics
Volume 23, Issue 12

Abstract

Rock bursts are aggressive dynamic failure processes that involve the rapid release of strain energy stored in a rock under unloading conditions. The dynamic fracture and strain energy transformation characteristics of rock unloading failure must be investigated to predict and control rock bursts. This study adopts the discretized virtual internal bond (DVIB) method to investigate this problem. The element partition method is performed in the DVIB method to investigate the effect of cracks on rock unloading failure. Three indicators, i.e., fracture area, the fractal dimension of the failure pattern, and energy release ratio (kinetic energy over strain energy), are adopted to evaluate the failure intensity. Simulation results show that a critical strain energy density (SED) for rock unloading failure exists. The unloading failure occurs only when the SED exceeds the critical value. Subsequently, under the same SED conditions, the effect of the lateral pressure coefficient (LPC), heterogeneity, and size on rock unloading failure is investigated. As the LPC increases, the failure intensity increases slowly and then decreases significantly. The critical LPC is approximately 0.5, indicating that the unloading failure is the most severe. The simulation results suggest that the crack can reduce the energy release capacity of the rock and then restrain rock unloading failure. When the precrack angle is 0° or 90°, the precrack barely affects the rock unloading failure, and the failure intensity is similar to that of the intact rock. When the precrack length or the density of random precracks is larger, the rock unloading failure is weaker.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, and algorithms for programming this method that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

This study was funded by the National Natural Science Foundation of China (No. 12202334), China Postdoctoral Science Foundation (No. 2022MD713786), and the Natural Science Basic Research Program of Shaanxi (No. 2022JQ-427).

References

Ai, C., J. Zhang, Y.-w. Li, J. Zeng, X.-l. Yang, and J.-g. Wang. 2016. “Estimation criteria for rock brittleness based on energy analysis during the rupturing process.” Rock Mech. Rock Eng. 49 (12): 4681–4698. https://doi.org/10.1007/s00603-016-1078-x.
Akdag, S., M. Karakus, G. D. Nguyen, A. Taheri, and T. Bruning. 2021. “Evaluation of the propensity of strain burst in brittle granite based on post-peak energy analysis.” Underground Space 6 (1): 1–11. https://doi.org/10.1016/j.undsp.2019.08.002.
Chen, G., M. He, and F. Fan. 2018. “Rock burst analysis using DDA numerical simulation.” Int. J. Geomech. 18 (3): 04018001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001055.
Deng, J., S. Li, Q. Jiang, and B. Chen. 2021. “Probabilistic analysis of shear strength of intact rock in triaxial compression: A case study of Jinping II project.” Tunnelling Underground Space Technol. 111: 103833. https://doi.org/10.1016/j.tust.2021.103833.
Du, K., X.-b. Li, D.-y. Li, and L. Weng. 2015. “Failure properties of rocks in true triaxial unloading compressive test.” Trans. Nonferrous Met. Soc. China 25 (2): 571–581. https://doi.org/10.1016/S1003-6326(15)63639-1.
Gale, W. J. 2018. “A review of energy associated with coal bursts.” Int. J. Min. Sci. Technol. 28 (5): 755–761. https://doi.org/10.1016/j.ijmst.2018.08.004.
Gao, L., F. Gao, Z. Zhang, and Y. Xing. 2020. “Research on the energy evolution characteristics and the failure intensity of rocks.” Int. J. Min. Sci. Technol. 30 (5): 705–713. https://doi.org/10.1016/j.ijmst.2020.06.006.
Gong, F., J. Yan, X. Li, and S. Luo. 2019. “A peak-strength strain energy storage index for rock burst proneness of rock materials.” Int. J. Rock Mech. Min. Sci. 117: 76–89. https://doi.org/10.1016/j.ijrmms.2019.03.020.
Gonzato, G. 1998. “A practical implementation of the box counting algorithm.” Comput. Geosci. 24 (1): 95–100. https://doi.org/10.1016/S0098-3004(97)00137-4.
He, M. C., J. L. Miao, and J. L. Feng. 2010. “Rock burst process of limestone and its acoustic emission characteristics under true-triaxial unloading conditions.” Int. J. Rock Mech. Min. Sci. 47 (2): 286–298. https://doi.org/10.1016/j.ijrmms.2009.09.003.
Jiang, Q., X.-T. Feng, T.-B. Xiang, and G.-S. Su. 2010. “Rockburst characteristics and numerical simulation based on a new energy index: A case study of a tunnel at 2,500 m depth.” Bull. Eng. Geol. Environ. 69 (3): 381–388. https://doi.org/10.1007/s10064-010-0275-1.
Kazerani, T. 2013. “Effect of micromechanical parameters of microstructure on compressive and tensile failure process of rock.” Int. J. Rock Mech. Min. Sci. 64: 44–55. https://doi.org/10.1016/j.ijrmms.2013.08.016.
Khademian, Z., and O. Ugur. 2018. “Computational framework for simulating rock burst in shear and compression.” Int. J. Rock Mech. Min. Sci. 110: 279–290. https://doi.org/10.1016/j.ijrmms.2018.06.022.
Liu, Z., J. Shao, W. Xu, and Y. Meng. 2013. “Prediction of rock burst classification using the technique of cloud models with attribution weight.” Nat. Hazard. 68 (2): 549–568. https://doi.org/10.1007/s11069-013-0635-9.
Manouchehrian, A., and M. Cai. 2016. “Simulation of unstable rock failure under unloading conditions.” Can. Geotech. J. 53 (1): 22–34. https://doi.org/10.1139/cgj-2015-0126.
Mitri, H. S., B. Tang, and R. Simon. 1999. “FE modelling of mining-induced energy release and storage rates.” J. South Afr. Inst. Min. Metall. 99 (2): 103–110.
Pan, P.-Z., S. Miao, Z. Wu, X.-T. Feng, and C. Shao. 2020. “Laboratory observation of spalling process induced by tangential stress concentration in hard rock tunnel.” Int. J. Geomech. 20 (3): 04020011. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001620.
Qi, C., M. Wang, J. Bai, X. Wei, and H. Wang. 2016. “Investigation into size and strain rate effects on the strength of rock-like materials.” Int. J. Rock Mech. Min. Sci. 86: 132–140. https://doi.org/10.1016/j.ijrmms.2016.04.008.
Salamon, M. 1984. “Energy considerations in rock mechanics: Fundamental results.” J. South Afr. Inst. Min. Metall. 84 (8): 233–246.
Sharan, S. K. 2007. “A finite element perturbation method for the prediction of rockburst.” Comput. Struct. 85 (17–18): 1304–1309. https://doi.org/10.1016/j.compstruc.2006.08.084.
Singh, S. P. 1987. “The influence of rock properties on the occurrence and control of rockbursts.” Min. Sci. Technol. 5 (1): 11–18. https://doi.org/10.1016/S0167-9031(87)90854-1.
Singh, S. P. 1989. “Classification of mine workings according to their rockburst proneness.” Min. Sci. Technol. 8 (3): 253–262. https://doi.org/10.1016/S0167-9031(89)90404-0.
Su, G., J. Jiang, S. Zhai, and G. Zhang. 2017. “Influence of tunnel axis stress on strainburst: An experimental study.” Rock Mech. Rock Eng. 50 (6): 1551–1567. https://doi.org/10.1007/s00603-017-1181-7.
Tang, C. A., H. Liu, P. K. K. Lee, Y. Tsui, and L. G. Tham. 2000. “Numerical studies of the influence of microstructure on rock failure in uniaxial compression—Part I: Effect of heterogeneity.” Int. J. Rock Mech. Min. Sci. 37 (4): 555–569. https://doi.org/10.1016/S1365-1609(99)00121-5.
Tarasov, B. G., and M. F. Randolph. 2011. “Superbrittleness of rocks and earthquake activity.” Int. J. Rock Mech. Min. Sci. 48 (6): 888–898. https://doi.org/10.1016/j.ijrmms.2011.06.013.
Wang, J.-A., and H. D. Park. 2001. “Comprehensive prediction of rockburst based on analysis of strain energy in rocks.” Tunnelling Underground Space Technol. 16 (1): 49–57. https://doi.org/10.1016/S0886-7798(01)00030-X.
Wang, P., L. Jiang, J. Jiang, P. Zheng, and W. Li. 2018. “Strata behaviors and rock burst–inducing mechanism under the coupling effect of a hard, thick stratum and a normal fault.” Int. J. Geomech. 18 (2): 04017135. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001044.
Wang, Q. Z., S. Zhang, and H. P. Xie. 2010. “Rock dynamic fracture toughness tested with holed-cracked flattened Brazilian discs diametrically impacted by SHPB and its size effect.” Exp. Mech. 50 (7): 877–885. https://doi.org/10.1007/s11340-009-9265-2.
Wang, Y., and Z. Zhang. 2020. “Fully hydromechanical coupled hydraulic fracture simulation considering state transition of natural fracture.” J. Pet. Sci. Eng. 190: 107072. https://doi.org/10.1016/j.petrol.2020.107072.
Wang, Y., X. Zhou, and X. Xu. 2016. “Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics.” Eng. Fract. Mech. 163: 248–273. https://doi.org/10.1016/j.engfracmech.2016.06.013.
Wen, T., H. Tang, and Y. Wang. 2020. “Brittleness evaluation based on the energy evolution throughout the failure process of rocks.” J. Pet. Sci. Eng. 194: 107361. https://doi.org/10.1016/j.petrol.2020.107361.
Weng, L., L. Huang, A. Taheri, and X. Li. 2017. “Rockburst characteristics and numerical simulation based on a strain energy density index: A case study of a roadway in Linglong gold mine, China.” Tunnelling Underground Space Technol. 69: 223–232. https://doi.org/10.1016/j.tust.2017.05.011.
Wu, K., Z. Shao, Y. Jiang, N. Zhao, S. Qin, and Z. Chu. 2023. “Determination of stiffness of circumferential yielding lining considering the shotcrete hardening property.” Rock Mech. Rock Eng. 56: 3023–3036. https://doi.org/10.1007/s00603-022-03122-0.
Wu, K., Z. Shao, M. Sharifzadeh, S. Hong, and S. Qin. 2022. “Analytical computation of support characteristic curve for circumferential yielding lining in tunnel design.” J. Rock Mech. Geotech. Eng. 14 (1): 144–152. https://doi.org/10.1016/j.jrmge.2021.06.016.
Xia, Y., H. Zhou, C. Zhang, S. He, Y. Gao, and P. Wang. 2022. “The evaluation of rock brittleness and its application: A review study.” Eur. J. Environ. Civ. Eng. 26 (1): 239–279. https://doi.org/10.1080/19648189.2019.1655485.
Yang, J. H., C. Yao, Q. H. Jiang, W. B. Lu, and S. H. Jiang. 2017. “2D numerical analysis of rock damage induced by dynamic in-situ stress redistribution and blast loading in underground blasting excavation.” Tunnelling Underground Space Technol. 70: 221–232. https://doi.org/10.1016/j.tust.2017.08.007.
Yang, Y., and Z. Zhang. 2020. “Dynamic fracturing process of fissured rock under abrupt unloading condition: A numerical study.” Eng. Fract. Mech. 231: 107025. https://doi.org/10.1016/j.engfracmech.2020.107025.
Yang, Y., and Z. Zhang. 2022. “Micro-fracture simulation of rock under unloading condition by grain-based discretized virtual internal bond method.” Int. J. Appl. Mech. 14 (01): 2250001. https://doi.org/10.1142/S1758825122500016.
Yin, Y.-c., Y.-l. Tan, Y.-w. Lu, and Y.-b. Zhang. 2019. “Numerical research on energy evolution and burst behavior of unloading coal–rock composite structures.” Geotech. Geol. Eng. 37 (1): 295–303. https://doi.org/10.1007/s10706-018-0609-5.
Zhang, Z. 2013. “Discretized virtual internal bond model for nonlinear elasticity.” Int. J. Solids Struct. 50 (22–23): 3618–3625. https://doi.org/10.1016/j.ijsolstr.2013.07.003.
Zhang, Z., and Y. Chen. 2009. “Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds.” Int. J. Rock Mech. Min. Sci. 46 (6): 1010–1022. https://doi.org/10.1016/j.ijrmms.2009.01.003.
Zhang, Z., H. Zheng, and X. Ge. 2013. “Triangular element partition method with consideration of crack tip.” Sci. China Technol. Sci. 56: 2081–2088. https://doi.org/10.1007/s11431-013-5267-5.
Zhao, F., and M. C. He. 2017. “Size effects on granite behavior under unloading rockburst test.” Bull. Eng. Geol. Environ. 76 (3): 1183–1197. https://doi.org/10.1007/s10064-016-0903-5.
Zhou, J., X. Li, and H. S. Mitri. 2018. “Evaluation method of rockburst: State-of-the-art literature review.” Tunnelling Underground Space Technol. 81: 632–659. https://doi.org/10.1016/j.tust.2018.08.029.
Zhou, J., X. Li, and X. Shi. 2012. “Long-term prediction model of rockburst in underground openings using heuristic algorithms and support vector machines.” Saf. Sci. 50 (4): 629–644. https://doi.org/10.1016/j.ssci.2011.08.065.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 23Issue 12December 2023

History

Received: Nov 7, 2022
Accepted: Jun 3, 2023
Published online: Sep 22, 2023
Published in print: Dec 1, 2023
Discussion open until: Feb 22, 2024

Permissions

Request permissions for this article.

Authors

Affiliations

Lecturer, School of Science, Xi’an Univ. of Architecture and Technology, Xi’an 710055, China. ORCID: https://orcid.org/0000-0003-3560-4501. Email: [email protected]
Assistant Research Fellow, CAEP Software Center for High Performance Numerical Simulation, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China. ORCID: https://orcid.org/0000-0002-1576-501X. Email: [email protected]
Lecturer, School of Science, Xi’an Univ. of Architecture and Technology, Xi’an 710055, China (corresponding author). Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share