Full Text:   <794>

Summary:  <379>

CLC number: TU45

On-line Access: 2015-08-04

Received: 2015-02-10

Revision Accepted: 2015-07-01

Crosschecked: 2015-07-09

Cited: 3

Clicked: 1906

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Ting-chun Li

http://orcid.org/0000-0002-1275-0517

Lian-xun Lyu

http://orcid.org/0000-0002-6066-5149

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2015 Vol.16 No.8 P.644-655

10.1631/jzus.A1500034


Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements


Author(s):  Ting-chun Li, Lian-xun Lyu, Shi-lin Zhang, Jie-cheng Sun

Affiliation(s):  Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao 266590, China

Corresponding email(s):   tchli_sd@163.com

Key Words:  Rock materials, Damaged elements, Statistical theory, Load-bearing capacity, Constitutive model


Ting-chun Li, Lian-xun Lyu, Shi-lin Zhang, Jie-cheng Sun. Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements[J]. Journal of Zhejiang University Science A, 2015, 16(6): 644-655.

@article{title="Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements",
author="Ting-chun Li, Lian-xun Lyu, Shi-lin Zhang, Jie-cheng Sun",
journal="Journal of Zhejiang University Science A",
volume="16",
number="8",
pages="644-655",
year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1500034"
}

%0 Journal Article
%T Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements
%A Ting-chun Li
%A Lian-xun Lyu
%A Shi-lin Zhang
%A Jie-cheng Sun
%J Journal of Zhejiang University SCIENCE A
%V 16
%N 8
%P 644-655
%@ 1673-565X
%D 2015
%I Zhejiang University Press & Springer

TY - JOUR
T1 - Development and application of a statistical constitutive model of damaged rock affected by the load-bearing capacity of damaged elements
A1 - Ting-chun Li
A1 - Lian-xun Lyu
A1 - Shi-lin Zhang
A1 - Jie-cheng Sun
J0 - Journal of Zhejiang University Science A
VL - 16
IS - 8
SP - 644
EP - 655
%@ 1673-565X
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -


Abstract: 
It is difficult to establish a constitutive model of damage for rock materials due to the complex meso-mechanism of the rock deterioration process. In this paper, by analysis of the damage mechanism, the reason for the existence of a rock damage threshold is explained and we conclude that damaged rock elements of micro scale can still bear stress. The correlation between damaged and undamaged elements is examined in relation to stress distribution. Rocks under different initial conditions can be defined as undamaged materials with different properties, to avoid the issue of the solution of the undamaged condition and to simplify the damage model. On the basis of the Mohr-Coulomb criterion and theories of continuum damage and statistical mechanics, a constitutive model of rock materials affected by the load-bearing capacity of damaged elements under triaxial compression is established. Compared with previous experimental data and theoretical results, we show that this model can reflect the stress-strain relationship of the whole process of rock failure. In particular, the description of the strain softening stage after peak strength is proved to be more reasonable. Programming of the constitutive model applied to stability analysis of the Qingdao subway station is achieved by secondary development of FLAC3D. The computing results compare very well with field monitoring data, indicating that the constitutive model of damaged rock can reflect the deterioration effect of weathered rock at the site. This constitutive model of rock damage may provide a useful reference for practical application.

The manuscript brought minor but useful modifications to the common statiscal damage model mainly aiming at improving the post-peak mechanical behaviors of geomaterials. It is a very interesting and relevant topic.

考虑受损基元承载影响的岩石统计损伤本构模型及工程应用

目的:建立三轴压缩作用下考虑受损基元承载影响的岩石材料损伤本构关系,并将其应用于工程实际。
创新点:1. 进行岩石损伤机理分析,探讨损伤阈值存在的原因,提出损伤修正系数,确定受损基元与无损基元的应力分配关系;2. 建立能够反映岩石破裂全过程的损伤本构模型,验证模型的合理性并实现其程序化。
方法:1. 通过数值计算探讨岩石在初始缺陷下的损伤劣化机理,将不同初始状态的岩石定义为不同岩性的无损材料,建立合理的损伤模型;2. 基于Mohr-Coulomb准则,结合连续损伤和统计理论,推导基于受损基元承载影响的岩石材料本构方程;3. 与前人试验数据及理论成果进行对比,验证本构模型的合理性,最后利用C++语言编译的动态链接库(DLL)实现有限差分软件FLAC3D的二次开发,实现模型的工程应用。
结论:1. 岩体损伤劣化是无损基元发生物理性状改变导致材料刚度变小的结果,受损基元与无损基元的应力分配关系与岩体的瞬时损伤状态和应力状态有关;2. 建立的岩石损伤本构模型与试验数据的拟合精度较高,能够准确地描述岩石的应力-应变关系;3. 数值模拟结果与现场监测数据的吻合程度较高,表明该模型能够合理反映软弱岩体的损伤劣化效应。

关键词:岩石材料;损伤基元;统计理论;承载能力;本构模型

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Andrä, H., Combaret, N., Dvorkin, J., et al., 2013. Digital rock physics benchmarks-part I: imaging and segmentation. Computers & Geosciences, 50:25-32.

[2]Cao, W.G., Li, X., Zhao, H., 2007. Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination. Journal of Central South University of Technology, 14(5):719-724.

[3]Cao, W.G., Zhao, H., Zhang, L., et al., 2008. Damage statistical softening constitutive model for rock considering effect of damage threshold and its parameters determination method. Chinese Journal of Rock Mechanics and Engineering, 27(6):1148-1154 (in Chinese).

[4]Chandler, N.A., 2013. Quantifying long-term strength and rock damage properties from plots of shear strain versus volume strain. International Journal of Rock Mechanics and Mining Sciences, 59:105-110.

[5]Chen, W.Q., 2014. The renaissance of continuum mechanics. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 15(4):231-240.

[6]Deng, J., Gu, D., 2011. On a statistical damage constitutive model for rock materials. Computers & Geosciences, 37(2):122-128.

[7]Fu, Q., Xie, Y.J., Long, G.C., et al., 2013. Study on statistical damage model of triaxial creep of concrete. Engineering Mechanics, 30(10):205-210 (in Chinese).

[8]Jiang, W., Deng, J., Li, Y., 2010. Study on constitutive model of rock damage based on lognormal distribution. Chinese Journal of Underground Space and Engineering, 6(6):1190-1194 (in Chinese).

[9]Kaiser, P.K., Morgenstern, N.R., 1981. Phenomenological model for rock with time-dependent strength. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 18(2):153-165.

[10]Kawamoto, T., Ichikawa, Y., Kyoya, T., 1988. Deformation and fracturing behaviour of discontinuous rock mass and damage mechanics theory. International Journal for Numerical and Analytical Methods in Geomechanics, 12(1):1-30.

[11]Krajcinovic, D., Silva, M.A.G., 1982. Statistical aspects of the continuous damage theory. International Journal of Solids and Structures, 18(7):551-562.

[12]Ladani, L.J., Dasgupta, A., 2009. A meso-scale damage evolution model for cyclic fatigue of viscoplastic materials. International Journal of Fatigue, 31(4):703-711.

[13]Lee, H.K., Simunovic, S., 2001. A damage constitutive model of progressive debonding in aligned discontinuous fiber composites. International Journal of Solids and Structures, 38(5):875-895.

[14]Lemaitre, J., 1984. How to use damage mechanics. Nuclear Engineering and Design, 80(2):233-245.

[15]Levasseur, S., Collin, F., Charlier, R., et al., 2013. A micro–macro approach of permeability evolution in rocks excavation damaged zones. Computers and Geotechnics, 49:245-252.

[16]Li, S.C., Xu, J., Li, K.G., et al., 2007. Study on damages constitutive model of rocks based on Weibull distributing. Journal of Hunan University of Science & Technology, 22(4):65-68 (in Chinese).

[17]Li, X., Cao, W.G., Su, Y.H., 2012. A statistical damage constitutive model for softening behavior of rocks. Engineering Geology, 143-144:1-17.

[18]Mazars, J., Cabot, G.P., 1989. Continuum damage theory-application to concrete. Journal of Engineering Mechanics, 115(2):345-365.

[19]Molladavoodi, H., Mortazavi, A., 2011. A damage-based numerical analysis of brittle rocks failure mechanism. Finite Elements in Analysis and Design, 47(9):991-1003.

[20]Mortazavi, A., Molladavoodi, H., 2012. A numerical investigation of brittle rock damage model in deep underground openings. Engineering Fracture Mechanics, 90:101-120.

[21]Rinaldi, A., Lai, Y.C., 2007. Statistical damage theory of 2D lattices: energetics and physical foundations of damage parameter. International Journal of Plasticity, 23(10-11):1796-1825.

[22]Shan, Z.G., Di, S.J., 2013. Loading-unloading test analysis of anisotropic columnar jointed basalts. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 14(8):603-614.

[23]Shi, C., Jiang, X.X., Zhu, Z.D., et al., 2011. Study of rock damage constitutive model and discussion of its parameters based on Hoek-Brown criterion. Chinese Journal of Rock Mechanics and Engineering, 30(S1):2647-2652 (in Chinese).

[24]Wang, T.T., Wang, C., Zhang, J.B., et al., 2013. The study of rock body damage constitutive model on refracturing. Advances in Petroleum Exploration and Development, 6(2):38-40.

[25]Wang, Z.L., Li, Y.C., Wang, J.G., 2007. A damage-softening statistical constitutive model considering rock residual strength. Computers & Geosciences, 33(1):1-9.

[26]Xu, Q., Chen, J.Y., Li, J., et al., 2013. Coupled elasto-plasticity damage constitutive models for concrete. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 14(4):256-267.

[27]Yu, S.W., Feng, X.Q., 1997. Damage Mechanics. Tsinghua University Press, Beijing, China, p.5-25 (in Chinese).

[28]Zhang, M., Wang, F., Yang, Q., 2013. Statistical damage constitutive model for rocks based on triaxial compression tests. Chinese Journal of Geotechnical Engineering, 35(11):1965-1971 (in Chinese).

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE