Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-20T03:26:36.619Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of Shape Characteristics of Plastic Zone Around Circular Tunnel Under Different Strength Criteria

Published online by Cambridge University Press:  23 October 2020

H. Y. Shi Open the ORCID record for H. Y. Shi [Opens in a new window] ,
Z. K. Ma ,
Q. J. Zhu ,
J. J. Shi  and
Z. Q. Zhao
H. Y. Shi
Affiliation:
North China Institute of Science and Technology, Beijing101601, China
Z. K. Ma*
Affiliation:
School of Mining, Liaoning Technical University, Fuxin123000, China
Q. J. Zhu
Affiliation:
North China Institute of Science and Technology, Beijing101601, China
J. J. Shi
Affiliation:
North China Institute of Science and Technology, Beijing101601, China
Z. Q. Zhao
Affiliation:
College of Resources and Safety Engineering, China University of Mining and Technology (Beijing), Beijing100083, China.
*
*Corresponding author ([email protected])
Get access

Abstract

The butterfly plastic zone theory based on Mohr Coulomb criterion has been widely used in coal mine production. In order to verify the universality of the theory, it is necessary to compare the distribution of plastic zone under different strength criteria. Based on the elastic-plastic mechanics, the principal stress distribution function around the circular tunnel is deduced in the paper, and the boundary and radius of the plastic zone under different strength criteria are calculated. The results show that the change laws of the plastic zone around the circular tunnel under different strength criteria has the following commonness: firstly, with the increase of the lateral pressure coefficient, the shape of the plastic zone presents the change laws of “circle ellipse butterfly”; Secondly, with the increase of the lateral pressure coefficient, the radius of the plastic zone is exponential distribution, while the characteristic value is different when the radius of the plastic zone is infinite. At same time, it shows that the butterfly plastic zone has a low sensitivity dependence on the strength criterion, no matter which strength criterion is adopted, and the butterfly plastic zone will inevitably appear in the surrounding rock mass of circular tunnel in the high deviator stress environment; The plastic zone with butterfly shape is highly sensitive to the stress change, and the small stress change may promote the expansion of the plastic zone. This result is significant for us to understand and prevent rock engineering disasters and accidents.

Keywords

Shape of plastic zoneCircular tunnelStrength CriterionSusceptibility
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 6 , December 2020 , pp. 849 - 856
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Zhao, Z Q, Ma, N J, Jia, H S, et al. Partitioning characteristics of gas channel of coal rockmass in mining space and gas orientation method. International Journal of Mining Science and Technology, 23, pp. 96-100 (2013).CrossRefGoogle Scholar
Wang, W J, Guo, G Y, Zhu, Y J, et al. Malignant development process of plastic zone and control technology of high stress and soft rock tunnel. Journal of China Coal Society, 40, pp.2747-2754 (2015).Google Scholar
Jing, P H, Khraishi, T. Analytical solutions for crack tip plastic zone shape using the von mises and tresca yield criteria: effects of crack mode and stress condition. Journal of Mechanics, 20: pp.199-210 (2004).CrossRefGoogle Scholar
Khan, Shafique M.A., Khraisheh, Marwan K.. Analysis of mixed mode crack initiation angles under various loading conditions. Engineering Fracture Mechanics, 67, pp. 397-4192000.CrossRefGoogle Scholar
Ma, N J, Li, J, Zhao, Z Q. Distribution of the deviatoric stress field and plastic zone in circular tunnel surrounding rock．Journal of China University of Mining & Technology, 44, pp. 206-213 (2015).Google Scholar
Zhao, Z Q, Ma, N J, Guo, X F, et al. Butterfly failure roof falling principle and support design of large deformation mining tunnels. Journal of China Coal Society, 41, pp. 2932-2939 (2016).Google Scholar
Guo, X F, Ma, N J, Zhao, X D, et al. General shapes and criterion for surrounding rock mass plastic zone of round tunnel. Journal of China Coal Society, 41： pp. 1871-1877 (2016).Google Scholar
Zhao, Z Q, Jin, J X, Shen, J C. Transition characteristics and induced outburst mechanism of coal damage zone in rockcross-cut coal uncovering. Chinese Journal of Rock Mechanics and Engineering, 38, pp. 343-352 (2019).Google Scholar
Jia, H S, Ma, N J, Zhu, Q K. Mechanism and control method of roof fall resulting from butterfly plastic zone penetration. Journalof China Coal Society, 41, pp. 1384-1392 (2016).Google Scholar
Ma, N J, Guo, X F, Zhao, Z Q, et al. Occurrence mechanisms and judging criterion on circular tunnel butterfly rock burst in homogeneous medium. Journal of China Coal Society, 41, pp. 2679-2688 (2016).Google Scholar
Ma, N J, Zhao, X D, Zhao, Z Q, et al. Conjecture about mechanism of butterfly-shape coal and gas outburst in excavation tunnel. Journal of Mining Science and Technology, 40, pp. 137-149 (2017).Google Scholar
Shi, H Y, Ma, N J, Xu, H T. Discussion on mechanism of coal and gas outburst based on energy theory. Journal of Safety Science and Technology, 15, pp.88-92 (2019).Google Scholar
Shi, H Y, Ma, N J, Ma, J. Numerical simulation for the formation process of the Longmenshan fault zone and its crustal stress state. Chinese Journal of Geophysics, 61, pp.1817-1823 (2018).Google Scholar
Ma, J, Zhao, Z Q, Shi, H Y, et al. Research on sources of seismic energy based on butterfly failure theory. Journal of China Coal Society, 44, pp. 1654-1665 (2019).Google Scholar
Qiao, J Y, Ma, N J, Ma, J, et al. Conjugate fault-seismic composite model based on structural stability of dynamic system. Journal of China Coal Society, 44, pp. 1637-1646 (2019).Google Scholar
Shi, H Y, Ma, N J, Shi, J J, et al. Simulation on energy release of fault rockmass triggered by stress increment and discussion on seismogenesis: Taking Longmenshan fault zone as an example. Acta Seismologica Sinica, 41, pp. 502-511 (2019).Google Scholar
Shi, H Y, Huang, F Q, Ma, Z K, et al. Mechanical mechanism of fault dislocation based on in-situ stress state. Frontiers in Earth Science. 8. Article 52.Google Scholar
Zhao, Z Q, Ma, N J. Stability analysis of tunnel surrounding rock and discussion on the connotation of butterfly failure theory: responses to “discussionon ‘a butterfly failure theory of rock mass around tunnel and its application prospect’”. Journal of China University of Mining& Technology, 48, pp. 685-692 (2019).Google Scholar
Wang, W J, Dong, E Y, Yuan, C. Boundary equation of plastic zone of circular tunnel in non-axisymmetric stress and its application. Journal of China Coal Society, 44, pp. 105-114 (2019).Google Scholar
Shen, M R, Shi, Z M, Zhang, L. Deformation properties of samples under different loading paths. Chinese Journal of Rock Mechanics and Engineering, 22, pp.1234-1238 (2003).Google Scholar
Cheng, Y M. Modified Kastner Formula for Cylindrical Cavity Contraction in Mohr-Coulomb Medium for Circular Tunnel in Isotropic Medium. Journal of Mechanics, 28, pp. 163-169 (2012).CrossRefGoogle Scholar
Li, C, Yang, G T, Huang, Z Z. On constitutive equations of isotropic non-linear elastic medium. Engineering Mechanics, 27, pp. 1-5 (2010).Google Scholar
Coulomb, C. A. Essai sur une application des regles des maximis et minimis a quelques problemes de statique relatifs a 1’architecture. Memoires de Mathematique and de Physique, presentes a I’ Academie. Royale des Sciences par divers Savans, and Ius dans ses Assemblees, 7, pp. 343-382 (1773).Google Scholar
Liu, Y J, Sun, Q. A dynamic ductile fracture model on the effects of pressure, Lode angle and strain rate. Materials Science & Engineering A, 589, pp. 262-270 (2013).CrossRefGoogle Scholar
Fei, J B, Jie, Y X, Zhang, B Y, et al. Application of a three - dimensional yield criterion to granular flow modeling. Rock and Soil Mechanics, 37, pp. 1809-1817 (2016).Google Scholar
Von Mises, R. Mechanik der festen Körper im plastisch-deformablen Zustand. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 582 (1913)Google Scholar
Tresca, H. Sur l’ecoulement des corps solides soumis a defortes pression. Comptes Rendus de l’Académie des Sciences. Série I. Mathématique. Académie des Sciences, Paris, 59, pp. 754 (1864).Google Scholar
Drucker, D.C. and Prager, W. Soil mechanics and plastic analysis for limit design. Quarterly of Applied Mathematics, 10, pp.157-165 (1952).CrossRefGoogle Scholar
Prager, W. The theory of plasticity a survey of recent achievenments. ARCHIVE: Proceedings of the Institution of Mechanical Engineers, 1-196, pp. 3-19 (1955).Google Scholar
Lade, P.V. and Duncan, J.M. Elastoplastic stress strain theory for cohesionless soil. Journal of Ggeotechnical and Geoenvironmental Engineering, 101, pp. 1037-1053 (1975).Google Scholar
Matsuoka, H. and Nakai, T. Stress deformation and strength characteristics of soil under three different principal stresses. Proceedings of the Japan Society of Civil Engineers, 232, pp. 59 (1974,).CrossRefGoogle Scholar
Saroglou, H, Tsiambaos, G. A modified Hoek–Brown failure criterion for anisotropic intact rock. International Journal of Rock Mechanics and Mining Sciences, 45, pp. 223–234 (2008).CrossRefGoogle Scholar
Li, Q S, Xu, Z H, Zhang, Y, et al. Study on deformation and failure characteristics of overlying strata with thick loose layers and thin bedrock based on Hoek-Brown criterion. Journal of Mining Science and Technology, 4, pp. 417-424 (2019).Google Scholar
Wu, T H, Zhou, Y, Wang, L, et al. Mesoscopic study of interaction mechanism between circular hole and fissures in rock under uniaxial compression. Rock and Soil Mechanics, 39, pp. 463-472 (2018).Google Scholar
Huang, M L, Feng, X T, Wang, S L. Numerical simulation of propagation and coalescence processes of multi-crack in different rock media. Rock and Soil Mechanics, 23, pp. 142-146 (2002).Google Scholar