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 FLAC^3D. 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.

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

[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).