基于改进后光滑GZZ准则的弹塑性本构模型在ABAQUS中的数值实现

doi:10.3724/1000-6915.jrme.2024.0575

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Abstract The Smoothed Zhang-Zhu(GZZ) criterion is a three-dimensional strength criterion for rocks proposed in recent years，which can reasonably and reliably describe the nonlinear strength characteristics of rock materials. However，only a few finite element software are equipped with this criterion，and most of the existing constitutive model programs based on the GZZ criterion are carried out in the principal stress space，making it difficult to apply in ABAQUS. In addition，the current numerical simulations based on the Smoothed GZZ criterion often use the associated ideal elastoplastic model，ignoring the plastic deformation characteristics and strength nonlinearity of rocks. In this paper，the plastic potential function of the Smoothed GZZ criterion is improved，and a numerical implementation method of the constitutive model based on the Smoothed GZZ criterion in the general stress space is proposed to avoid the problem of principal stress transformation. Meanwhile，a calculation method considering the dilation characteristics and strength variation of rocks is given. Finally，the calculation of this constitutive model is implemented by writing a UMAT subroutine in ABAQUS. Verified by three calculation examples，this model can directly conduct calculations in the general stress space，can reflect the dilation characteristics and strength nonlinearity of rocks，and the numerical solutions are in good agreement with the analytical solutions and the results of model tests，showing a relatively high calculation accuracy.

Key words： rock mechanics the GZZ criterion constitutive model return mapping algorithm numerical simulation

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	Articles by authors
	WU Wenjie1
	WU Wei1
	2
	ZOU Yulin3
	GU Hao4
	ZHU Hehua1
	2

Cite this article:

WU Wenjie1,WU Wei1,2, et al. Numerical implementation of the elastoplastic constitutive model based on the improved smoothed GZZ criterion into ABAQUS[J]. , 2025, 44(4): 1001-1012.

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https://rockmech.whrsm.ac.cn/EN/10.3724/1000-6915.jrme.2024.0575 OR https://rockmech.whrsm.ac.cn/EN/Y2025/V44/I4/1001

[1]	HOEK E，BROWN E T. Underground excavations in rock[M]. [S. l.]：CRC Press，1980：131-178.
[2]	何满潮，谢和平，彭苏萍，等. 深部开采岩体力学研究[J]. 岩石力学与工程学报，2005，24(16)：2 803-2 813.(HE Manchao，XIE Heping，PENG Suping，et al. Study on rock mechanics in deep mining engineering[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(16)：2 803-2 813.(in Chinese))
[3]	ZHU H H，YAN J X，LIANG W H. Challenges and development prospects of ultra-long and ultra-deep mountain tunnels[J]. Engineering，2019，5(3)：384-392.
[4]	QIAN Q H，ZHOU X P. Failure behaviors and rock deformation during excavation of underground cavern group for Jinping I hydropower station[J]. Rock Mechanics and Rock Engineering，2018，51(8)： 2 639-2 651.
[5]	CHENG T，HE M C，LI H R，et al. Experimental investigation on the influence of a single structural plane on rockburst[J]. Tunnel and Underground Space Technology，2023，132(1)：104914.
[6]	HOEK E，BROWN E T. Practical estimates of rock mass strength[J]. International Journal of Rock Mechanics and Mining Sciences，1997，34(8)：1 165-1 186.
[7]	蔡武强. 岩体三维精细本构理论与深埋隧道应力控制设计分析方法[博士学位论文][D]. 上海：同济大学，2022.(CAI Wuqiang. Three-dimensional refined constitutive theory of rock mass and its integration in stress control-based design and analysis of deep tunnel[Ph. D. Thesis][D]. Shanghai：Tongji University，2022.(in Chinese))
[8]	PAN X D，HUDSON J A. A simplified three dimensional Hoek-Brown yield criterion[C]// Paper Presented at the ISRM International Symposium. Madrid，Spain：[s. n.]，1988：95-103.
[9]	ZHANG L Y，ZHU H H. Three-dimensional Hoek-Brown strength criterion for rocks[J]. Journal of Geotechnical and Geoenvironmental Engineering，2007，133(9)：1 128-1 135.
[10]	ZHANG Q，ZHU H H，ZHANG L Y. Modification of a generalized three-dimensional Hoek-Brown strength criterion[J]. International Journal of Rock Mechanics and Mining Sciences，2013，59(1)：80-96.
[11]	WILLAM K J. Constitutive model for the triaxial behaviour of concrete[J]. International Association of Bridge Structural Engineers，1975，19(1)：1-30.
[12]	俞茂宏. 强度理论新体系[M]. 西安：西安交通大学出版社，1992：115-140.(YU Maohong. New system of strength theory[M]. Xi'an：Xi'an Jiaotong University Press，1992：115-140.(in Chinese))
[13]	CAI W Q，ZHU H H，LIANG W H，et al. A new version of the generalized Zhang-Zhu strength criterion and a discussion on its smoothness and convexity[J]. Rock Mechanics and Rock Engineering，2021，54(8)：4 265-4 281.
[14]	XIAO Y M，XIAO Y F，GUO Y F. Elastic-plastic response of tunnel in GZZ-based constitutive model[C]// Geoshanghai 2024 International Conference. London：IOP Publishing Ltd.，2024：012011.
[15]	CAI W Q，ZHU H H，LIANG W H. Three-dimensional stress rotation and control mechanism of deep tunneling incorporating generalized Zhang-Zhu strength-based forward analysis[J]. Engineering Geology，2022，308(1)：106806.
[16]	ZHU H H，ZHANG Q，HUANG B Q，et al. A constitutive model based on the modified generalized three-dimensional Hoek-Brown strength criterion[J]. International Journal of Rock Mechanics and Mining Sciences，2017，98(1)：78-87.
[17]	CHEN H H，ZHU H H，ZHANG L Y. A unified constitutive model for rock based on newly modified GZZ criterion[J]. Rock Mechanics and Rock Engineering，2021，54(2)：921-935.
[18]	XIAO Y M，HE M C，QIAO Y F，et al. A novel implementation method of GZZ-based constitutive model into FLAC3D[J]. Tunnelling and Underground Space Technology，2024，145(1)：105601.
[19]	CLAUSEN J，DAMKILDE L. An exact implementation of the Hoek-Brown criterion for elasto-plastic finite element calculations[J]. International Journal of Rock Mechanics and Mining Sciences，2008，45(6)：831-847.
[20]	SU C C，LU D C，ZHOU X，et al. An implicit stress update algorithm for the plastic nonlocal damage model of concrete[J]. Computer methods in applied mechanics and engineering，2023，414(1)：116189.
[21]	ZHOU X，LU D C，ZHANG Y N，et al. An open-source unconstrained stress updating algorithm for the modified Cam-clay model[J]. Computer methods in applied mechanics and engineering，2022，390(1)：114356.
[22]	ZHOU X，SHI A Y，LU D C，et al. A return mapping algorithm based on the hyper dual step derivative approximation for elastoplastic models[J]. Computer Methods in Applied Mechanics and Engineering，2023，417(1)：116418.
[23]	SORENSEN E，CLAUSEN J，DAMKILDE L. Finite element implementation of the Hoek-Brown material model with general strain softening behavior[J]. International Journal of Rock Mechanics and Mining Sciences，2015，78(1)：163-174.
[24]	SCHERZINGER W M. A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method[J]. Computer Methods in Applied Mechanics and Engineering，2017，317(1)：526-553.
[25]	HOEK E，BROWN E T. The Hoek-Brown failure criterion and GSI-2018 edition[J]. Journal of Rock Mechanics and Geotechnical Engineering，2019，11(3)：445-463.
[26]	MOGI K. Effect of the intermediate principal stress on rock failure[J]. Journal of Geophysical Research，1967，72(20)：5 117-5 131.
[27]	ZHANG L Y. A generalized three-dimensional Hoek-Brown strength criterion[J]. Rock Mechanics and Rock Engineering，2008，41(6)：893-915.
[28]	CAI M，KAISER P K，TASAKA Y，et al. Determination of residual strength parameters of jointed rock masses using the GSI system[J]. International Journal of Rock Mechanics and Mining Sciences，2007，44(2)：247-265.
[29]	SU C L，CAI W Q，ZHU H H. Elastoplastic semi-analytical investigation on a deep circular tunnel incorporating generalized Zhang-Zhu rock mass strength[J]. Computer and Geotechnics，2020，150(1)：104926.
[30]	VU B T. Investigation on progressive failure of deep weak rock tunnels by physical model tests and numerical analyses[Ph. D. Thesis][D]. Shanghai：Tongji University，2014.